diff --git "a/4NFKT4oBgHgl3EQfRi0P/content/tmp_files/load_file.txt" "b/4NFKT4oBgHgl3EQfRi0P/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/4NFKT4oBgHgl3EQfRi0P/content/tmp_files/load_file.txt" @@ -0,0 +1,871 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf,len=870 +page_content='Phase separation of passive particles in active liquids Pragya Kushwaha1, Vivek Semwal2, Sayan Maity1, Shradha Mishra2, Vijayakumar Chikkadi1 1 Indian Institute of Science Education and Research Pune, India 411008 2 Indian Institute of Technology (BHU) Varanasi, India 221005 (Dated: January 30, 2023) The transport properties of colloidal particles in active liquids have been studied extensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It has led to a deeper understanding of the interactions between passive and active particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, the phase behavior of colloidal particles in active media has received little attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Our study reveals dynamic clustering of colloids in active media due to an interplay of active noise and an attractive effective potential between the colloids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The size-ratio of colloidal particles to the bacteria sets the strength of the interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' As the relative size of the colloids increases, the effective potential becomes stronger and the average size of the clusters grows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The simulations reveal a macroscopic phase separation of passive colloids at sufficiently large size-ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We will present the role of density fluctuations and hydrodynamic interactions in the emergence of effective interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The Brownian colloids self-assemble to display a wide variety of phases depending on their shapes and inter- actions [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Their equilibrium phase behavior is gov- erned by the principles of equilibrium statistical mechan- ics [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, our understanding of the collective behavior of colloids far from equilibrium remains a chal- lenge [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In recent years, active matter has emerged as a new paradigm for understanding nonequilibrium sys- tems [8–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' They are known to display many interest- ing phenomena such as flocking [12, 13], motility induced phase separation [14–16], active turbulence [17], superflu- idity [18], that are absent in equilibrium systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' There- fore, active matter offers novel approaches to colloidal assembly in systems far from equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In this let- ter, we have investigated the phase behavior of colloidal particles dispersed in active liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Wu and Libchaber [19] did seminal experiments on the active transport of colloidal particles in suspensions of bacteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' They discovered anomalous diffusion and a large effective diffusion constant, when compared to dif- fusion at equilibrium, which inspired a slew of theoreti- cal investigations and detailed experiments [20–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The subsequent efforts have elucidated how enhanced diffu- sion arises due to an interplay of entrainment of colloids by bacteria, far-field hydrodynamic interactions, direct collisions, and the relative size of bacteria and colloid [23–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Further, the effective interaction between a pair of passive particles in active media has been the focus of several investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It has been predicted to be at- tractive, repulsive, and long-ranged, depending on the ge- ometry of passive particles, the activity of active species, and their density [28–36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This understanding has opened new routes to colloidal assembly mediated by active flu- ids [7, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The phase behavior of active-passive mixtures is a topic of recent interest [11, 37–43, 45, 47], where ex- perimental investigations are scarce [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' On the one hand, theory and simulations at high Peclet numbers have shown that homogeneous mixtures of active and passive particles are unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The underlying physics is similar to motility induced phase separation (MIPS) [40, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' On the other hand, in the diffusive limit, theory and simulations of nonequilibrium binary mixtures with different diffusivities and temperatures reveal phase sep- aration [41, 45, 46] due to spinodal-like instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Sur- prisingly, there is little known about mixtures at moder- ate Peclet numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This is the range where most of the active matter experiments involving living matter or syn- thetic systems, such as diffusio-phoretic colloids, fall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' A recent study of colloids in active suspensions of bacteria reports dynamical clustering and absence of phase sepa- ration at moderate Peclet numbers [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The conclusions were based on the phase diagram obtained from varia- tions of Peclet number and rotation rate of active par- ticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In contrast, earlier numerical studies have shown a macroscopic phase separation [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Therefore, it is not clear whether active-passive mixtures show macroscopic phase separation at moderate Peclet numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This letter presents a combined experimental and nu- merical study of the phase behavior of colloidal parti- cles in active liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The experiments were performed using colloids in bacteria suspensions, and simulations of active-passive mixtures were realized using Brownian dynamics [48–50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Earlier simulations of active-passive mixtures, by one of the authors of this letter, had shown a significant influence of the size-ratio of passive to ac- tive particles on their phase diagram [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Motivated by this study, our experiments were performed over a range of densities and sizes of passive colloidal particles in active suspensions of bacteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The colloids display dynamic clustering due to an interplay of activity and an attractive effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, the average size of the clusters increases with the size of colloidal par- ticles, suggesting an enhanced interaction between the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Using simulations, we confirm an attractive effective potential between passive particles in an active medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The strength of the interaction is shown to grow with an increasing size-ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' When the size-ratio is sufficiently large, the interactions are strong enough to arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='11771v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='soft] 27 Jan 2023 2 drive the phase separation of passive colloids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The ori- gin of the effective potential in simulations appears to be related to long-ranged density fluctuations of active par- ticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In contrast, the correlations of density fluctuations of bacteria decay rapidly in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These results indicate a hydrodynamic origin of effective interactions between the colloids in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Thus, shedding new light on the phase behavior of passive particles in active media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The active suspensions were prepared using E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='coli cells (U5/41 type strain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The cells were cultured using well established protocols in the literature [18, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' They are suspended in a motility media to get desired concentra- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Details of the method are given in the supplemen- tary section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The density of bacteria in our experiments was well below the density threshold for the onset of col- lective motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The average speed and average size of bacteria cells were estimated to be v = 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='84±9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='98 µm/s [supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S1(a)] and l = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='86 µm [sup- plementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S1(b)], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Their rotational dif- fusion time scale was estimated to be τr = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='67 s [supple- mentary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S1(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The Peclet number, which is defined as Pe = τrv/l, turns out to be Pe ∼ 21 for our system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The phase behavior of colloidal particles in suspensions of bacteria was investigated by varying the size and den- sity of the beads at a constant density of bacteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The diameters of the particles used in the experiments were σ = 7µm, 10µm and 15µm, and their density is varied from φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4, where φ = N ∗ πσ2/(4A) is the area fraction, N is the number of colloidal particles in the field of view of area A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The size-ratio S = σ/l is defined as the ratio of the diameter of colloids to the length of the bacteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The simulations were performed using a binary mix- ture of active Brownian particles (ABP) with Na small active particles of radius aa and Np big passive particles of radius ap (ap > aa) moving on a two dimensional fric- tional substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The active particles are associated with a self propulsion speed v and an orientation unit vector ˆvi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The equations of motion and other simulation details are given in the supplementary section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We simulate the system in a square box of size lbox × lbox, with periodic boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The system is defined by the area fractions φa = Naπa2 a/l2 box and φp = Npπa2 p/l2 box of the active and passive particles respectively, the activity v of active particles and the size-ratio (S = ap/aa) defined as the ratio of the radius of a passive particle to the radius of an active particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We start with a random homoge- neous distribution of active and passive particles in the box and with random directions for the velocity of active particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (S1-S3) are updated for all particles and one simulation step is counted after a single update for all the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The simulations does not include the hydrodynamic interactions that are present in exper- iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The effect of hydrodynamic interaction can be included using coarse-grained studies similar to [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The colloids used in our experiments are bigger than 5 µm, so they are non-Brownian particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, they FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The structure of passive particles in active suspen- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Main panel : The pair correlation function g(r) for φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10 and S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The g(r) curves are shifted along the y − axis for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Insets: The bright field images of particles at φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10 and size ratios S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (left) and S ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (right), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The scale bar in the images is 50µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' diffuse in suspensions of bacteria due to active fluctua- tions with a characteristic super-diffusive motion on short time scales and a diffusive motion on long time scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' To investigate their collective behavior in active suspen- sions, we first analyze their pair correlation function g(r), which is shown in the main panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 1 at an area fraction of φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 and size ratios S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The normalized g(r) for different size-ratios is shifted along the y-axis for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' What is prominent is the pres- ence of a sharp peak at r = σ, and additional peaks develop at r = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7σ and r = 2σ with increasing size ra- tio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The peak at 2σ indicates a second shell of neighbors, and the one at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7σ is a signature of hexagonal order- ing in the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These observations are evident in the bright field images presented in the insets of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The larger size ratios lead to larger clusters with enhanced order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These images are reminiscent of clustering in sys- tems of purely active particles [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, the clusters of passive particles in our experiments break and form much more rapidly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' A real-time video of dynamic clus- ter formation is presented in the supplementary section Video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' SV1 for φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10 and S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Recent simulations have reported similar dynamic clustering and traveling interfaces of active-passive particles that are not observed in our current study [40, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' One of the main difference between our experiments and these simulations are the large Peclet numbers used in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Further, as re- ported by earlier investigations, self-propulsion of parti- cles is a manifestation of an attractive effective potential between the passive particles due to active fluctuations [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We next turn our attention to cluster size distribution (CSD), p(n), which is a count of clusters of n particles [43, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The clusters in our experiments were determined by setting a distance criterion of rc ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1σ to identify pairs of particles as neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This was set based on the 60 S=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 S=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 8 50 88 ☆-S=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 % 8 8 40 8 888 88 30 b 20 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 3 0 Y3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Cluster statistics of passive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (a) Cluster size distribution in the main panel is shown for different size-ratios S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 at a density of φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The symbols distinguish different size ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The inset shows the CSD plot for same size ratios at φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (b) The average cluster size < n > for varying S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The curves with different symbols correspond to different particle densities, ranging from φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' position of the first peak of g(r) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1, and to account for small polydispersity (< 5%) in the size distribution of colloidal particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The results of our analysis are pre- sented in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 2a & 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The main panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='2a shows CSD for varying size ratios of S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5, and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 at a density of φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For small size ratios S < 5, p(n) has an exponential form exp(−n/n0) as observed in the equilibrium case [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The clustering is weak at these size ratios, however, for S > 5 the p(n) displays a power-law decay with an exponential cut-off at large n, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=', it is best described by p(n)/p(1) ∼ 1/nα exp(−n/n0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The fits of this form to our data are shown in the figure using dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These results indicate that the characteristic size of clusters grows with increasing size ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The growth of clusters is dramatic at larger area fractions, the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='2a shows cluster distribution at φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We further elucidate the clustering of colloids by com- puting the average cluster size using the expression < n >= � n p(n), which is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 2b where the curves with different symbols correspond to different area fractions ranging from φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These mea- surements were made in the steady state where the mean cluster sizes fluctuates around a mean value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This data is provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S2(a-c) for various size ratios and area fractions for over 5000 frames or 500 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' What is clear from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 2b is that increasing the size-ratio or the rel- ative size of colloids leads to larger cluster sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' This suggests that the effective potential between the colloids becomes stronger with an increasing size ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' One can intuitively understand the underlying physics by consid- ering the interaction between an isolated colloidal parti- cle and a swimmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' When the size of a particle is small, a bacterium entrains the particle to larger distances be- fore changing its direction of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, when the particle is large, the entrainment distance is small, and the scattering angle of the swimmer is large [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It in- dicates that the bacteria can suppress cluster formation when the colloidal particles are smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' What is not clear from our experiments is whether larger size-ratios lead to a macroscopic phase separation in our system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' To understand this aspect, we turn to numerical simulations that allow a detailed exploration of parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The first quantity we have calculated in the simulations is the effective potential between two passive particles in the medium of ABPs with torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In order to calculate the effective potential between two passive particles, we choose Np = 2 at positions r1 and r2, respectively, in a system of ABPs with Na = 1800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We keep r1 fixed and slowly vary r2 in small steps of ∆x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5aa starting from the zero surface to surface distance between two passive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The cartoon of the system simulated for the force calculation for a fixed r is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S3 (SM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In the figure, ABPs are shown in red and passive particles in blue for S = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For resolution, only a part of the sys- tem near the two passive particles is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The active particles’ positions and orientations are updated accord- ing to the Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (S1 and S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For each configuration at a given distance between two passive particles, the system is allowed to reach the steady state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Further, we use the steady state configuration to calculate the force FS(r) between two-passive particles at a surface to surface sep- aration r, such that FS(r) = F12(r)+�Na i=1 F1i(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Here F12(r) is the force due to passive particle 2nd on 1st, and �Na i=1 F1i(r) represents the sum of all the forces due to active particles on 1st passive particle for a given con- figuration of two passive particles at separation r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The potential is then calculated by integrating the force over the distance U(r) = � r −∞ FS(r)dr [53–55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Here we set the lower limit as one-fourth of the box-length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The re- sults are averaged over 30 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We calculated the effective potentials U(r) for Pe = 25 (which is comparable to the experimental system) and four size-ratios S = 3, 5, 8 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The comparable size-ratio in experimental system is S ∼ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We first plot the effective potential U(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In the main panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3(a) we show the plot of U(r) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' r for the system for S = 3, 5, 8 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The distance is nor- malised by the radius of active particles, which is kept fixed to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The negative side of the potential shows attraction and the positive nature is repulsion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For all the parameters the potential approaches zero at large distances, and it is negative at intermediate distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The depth of the potential becomes deeper with increas- ing S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The inset shows the effective potential with the distance r scaled by the size of passive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Sur- prisingly, the minima of the potentials for the size ratios S = 5, 8 and 10 fall at r/ap = 1, which implies that the length scale characterizing the range of the interaction potential is set by size passive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We investigate further the origin of long-range interactions by consider- ing a single passive particle in the center of our system, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It is evident that the passive par- ticle disturbs the density field of active particles, lead- ing to clustering around the passive particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The main panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3(b) shows the normalised density correla- tion C(r) = (⟨ρ(0)ρ(r)⟩ − ⟨ρ(r)⟩2)/( � ρ(r)2� − ⟨ρ(r)⟩2) of (a) 10 100 P(n)/P(1) 米 10-5 米 10-2 100 104 /(u) n P 10 V S=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 米 S=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 S=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 10-6 ★ 100 102 m(b) 20 1Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10 fΦ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='20 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='30 15 IΦ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='40 V V 10 5 2 3 4 5 6 S4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Top left figure: The effective potential between a pair ,of colloidal particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The main panel shows the plot of the effective potential U(r) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' distance r for Pe = 25 and size-ratios S = 3, 5, 8, and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The inset shows the effec- tive potential with the scaled distance r/ap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Top right figure: The main panel shows normalized correlations of density fluc- tuations C(r) due to a passive particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The inset show the length scale extracted from C(r) as function of the size-ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The length scale is expressed in terms of active particle size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Bottom panel: Snapshots of the system obtained from the microscopic simulation: two types of particles for different size ratio S = 3, 5 and 8 (left, central and right columns) at Pe = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Red particles are ABPs and blue particles are pas- sive particles, for fixed packing fraction φ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='60 in a system of size lbox = 140aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' active particles calculated from the surface of the big pas- sive particle for four different size ratios S = 3, 5, 8 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3(b) shows the typical size of clus- ters L(S) around a single passive particle in the center of the box for different size ratios S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The L(S) is measured in terms of size of ABP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Clearly, L(S) increases with in- creasing S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The number fluctuations of active particles around an isolated passive particle yield similar conclu- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S5 (SM) shows number fluctuations for three different sizes of the passive particle or for three different size ratios S = 3, 5 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The details of the cal- culations are give in the supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For all the cases the graph is a power law with ∆N ≃ N α, where α ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7 for moderate N for all S and starts to deviate for large N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The deviation appears at relatively larger N on increasing size ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Hence increasing the size of pas- sive particle increases the stretch of density fluctuation of ABP’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These results establishes that the density fluctu- ations play a central role in the emergence of long-range effective attractive interactions between passive particles in our simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We elucidate the effect of such effective potential, full microscopic simulations of mixtures of active and passive were performed using the Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (S1-S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We simulated the system for Pe = 25 and size ratio S = 3, 5 and 8, which are close to experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3 the steady state snapshots of passive (blue, big- ger) and active (red, smaller) are shown for different size ratios S = 3, 5 and 8 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Clusters with moder- ate to strong ordering is found on increasing S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For small S = 3 clusters are present but without strong local hexag- onal ordering, whereas as we increase S the ordering and clustering is enhanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We also calculated the percent of passive particles participating in the largest cluster for different size ratios and it increases from 35% to 67% as we increase size from 3 to 8 (data not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Hence for large size ratio passive particles show the macroscopic phase separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' A similar examination of correlations of density fluc- tuations of bacteria in experiments reveals that they are suppressed, which is evident from C(r) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The clustering of colloidal particles appears to arise from their hydrodynamic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' An earlier numerical study of active-passive matter with pusher-type swimmers at dilute concentrations had shown hydrodynamic interac- tions to stabilize colloidal clusters [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In addition, a re- cent theoretical model of active gels shows a long-ranged attractive effective potential between colloids due to hy- drodynamic effects [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Considering these studies, hy- drodynamics is likely to promote the formation of col- loidal clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Our investigations conclude that the interplay of ef- fective potential and active noise determines the phase behavior of colloidal particles in active liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The strength of the effective potential is set by the size ra- tio of passive particles to active ones;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' larger size ra- tios lead to stronger interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The simulations re- veal a long-ranged effective potential extending to sev- eral active particle diameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It appears to emerge from the long-ranged density fluctuations of active particles in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' When the size-ratio is small, the passive particles display dynamic clusters that form and break rapidly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' However, the effective potential is strong enough to lead to phase separation of passive particles at suffi- ciently large size-ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' These are the novel features of active-passive mixtures absent in the equilibrium ana- log of colloid-polymer mixtures where the range of effec- tive potential is short-ranged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The density fluctuations of Bacteria are suppresses in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Further investi- gation is needed to understand the role of hydrodynamic interactions on the effective potential of colloids in our experiments with active suspensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We thank Chaitanya Athale, Apratim Chatterji, Thomas Pucadyil, Sunish Radhakrishnan, Rajesh Singh, and Ganesh Subramanian for helpful discussions and sup- port.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We thank Madan Rao for drawing our attention to [58], and Kumar Gourav for assistance in the initial stages of experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' acknowledges financial sup- port from IISER Pune and DST/SERB under the project grant CRG/2021/007824.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' is supported by CSIR- UGC fellowship 1353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' thank I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (BHU) Varanasi computational facility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' thanks DST IN- SPIRE (INDIA) for the research fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' thanks DST, SERB (INDIA), Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' ECR/2017/000659 for partial financial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S=3 S=5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 S=8 S=10 0 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 100 (6), 062602 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' [59] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Krafnick and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Garcia, Impact of hydrodynam- ics on effective interactions in suspensions of active and passive matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' E 91, 022308 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Supplementary information Phase separation of passive particles in active liquids Pragya Kushwaha1, Vivek Semwal2, Sayan Maity1, Shradha Mishra2, Vijayakumar Chikkadi11 11 Indian Institute of Science Education and Research Pune, India 411008 2 Indian Institute of Technology (BHU) Varanasi, India 221005 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' METHODS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Experiments The active suspensions were prepared using E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='coli cells (U5/41 type strain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The bacteria were grown overnight at 37◦C in LB agar plate containing 1% tryptone, 1% NaCl, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5% yeast extract and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5% agar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' A single colony of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' coli was added to 10 ml of LB broth and kept at 37◦C until OD600 (optical density at 600 nm wavelength) reached a value of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Bacterial cells were then harvested and washed three times with motility media (10 mM potassium phosphate (pH 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='0), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 mM EDTA , 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='002% Tween-20 and 50 mM L-Serine) by centrifugation at 3000 rpm for 5 minutes at room temperature to remove the traces of LB broth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The pellet was later resuspended in motility media to get desired concentrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The observation chamber was created using a circular cavity of size 1 cm and 100 µm deep, which was glued to a PEG coated coverslip using double-sided tape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The bacteria density of the sample with OD600 = 1 was estimated to contain 6 × 109 cells/ml (b0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The density of bacteria in our experiments was fixed at 10b0, which was well below the density threshold for the onset of collective motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Simulations The simulations were performed using a binary mixture with Na small active particles of radius aa and Np big passive particles of radius ap (ap > aa) moving on a two dimensional frictional substrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The active particles are associated with a self propulsion speed v and an orientation unit vector ˆvi = (cosθi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' sinθi), where θi is the angle between the velocity vector and a reference direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The motion of active Brownian particles (ABP) is governed by the following Langevin equations: dri dt = vˆvi − µ1 � j̸=i Fij + � 2DT ηT i (S1) dθi dt = Γ � i sin(θi − θij) + � 2Drηri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (S2) Here µ1 is the mobility and Fij is the force acting on particle i due to particle j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The noise term is defined as < ηr,T i(t)ηr,T j(t′) >= 2Dr,T δijδ(t − t′), DT and Dr are the translational and rotational diffusion constants of active particles and Γ is the magnitude of alignment and θij = arg (ri − rj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The persistence length lp = v/Dr of active particles is constant in our simulations, it is set at lp = 20aa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The other constants in our simulations are DT = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='005 and Γ = 1 The equation of motion for passive particles is dri dt = µ2 � j̸=i Fij, (S3) where µ2 is the mobility of passive particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' There is no translational noise in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' 3, so the dynamics of passive particles is only due to interaction force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' We choose the mobility of both species to be the same i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=', µ1 = µ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Particles interact through short ranged soft repulsive forces Fij = Fijˆrij, where Fij = k(ai + aj − rij) when rij ≤ (ai + aj) and Fij = 0 otherwise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' rij = |ri − rj| and k is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The elastic time scale in our system is defined by (µk)−1 = (150)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='11771v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='soft] 27 Jan 2023 2 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' SUPPLEMENTARY FIGURES A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Peclet number estimation FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (a) Histogram of bacteria velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The average velocity is < v >= 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='84 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='98 µm/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (b) Histogram of the size of the bacteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The size of the bacteria is its length along the longer axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The average length of the cells is < l >= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='68±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='86 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' (c) The rotational diffusion time of the bacteria was estimated from their normalised velocity auto-correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The dashed line is an exponential fit to the data, which gives a rotational diffusion time of τr ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='67 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' SUPPLEMENTARY FIGURES A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Steady state in experiments FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The average cluster size in our system as a function of frame number for a range of area fractions from φ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4 and at S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (a), S ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (b) and S ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The steady state of the system is evident from these figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The total duration of the measurement was 500 s 350 (a) 300 250 200 Count 150 100 50 0 20 40 60 um/sec 225 (b) 20 15 Count 10 5 0 2 3 1 4 5 um(c) 100 é(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='é(0) 10-1 0 1 2 3 4 t(s)5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 (a) Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='10 5 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='20 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='30 cluster size 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='39 4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 2 ha 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 1 1000 2000 3000 4000 5000 Frames(b) —Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='11 7 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='22 --Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='30 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='40 6 5 4 3 2 1 1000 2000 3000 4000 5000 Frames(c) 一Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='11 30 Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='21 ---Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='30 size Φ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='40 25 cluster s 20 Average 15 10 5 1000 2000 3000 4000 5000 Frames3 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Calculation of effective potential FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Snapshot of the part of the system to calculate the potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The two bigger particles are passive particles with the left one marked as particle 1 and the right one marked 2 with positions r1 and r2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The red circles are ABPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The line shows the surface to surface distance r between two passive particles C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Density of active particles in the vicinity of an isolated passive particle in simulations FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Density fluctuations of active particles due to a single passive particle in the center of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Instantaneous snapshots of the system for four size ratios S = 3, 5, 8 and 10, from left to right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Many such configurations are used to calculate the density correlations C(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Red particles are ABP’s and blue particle at the center is the bigger passive particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Number fluctuations of active particles in the vicinity of an isolated passive particle in simulations FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Number fluctuation ∆N vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' N for different size ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The slopes of dotted line is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 and dashed line is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7 For calculating number fluctuation, we start with an annular disc with an inner radius the radius of the passive particle and outer radius is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The mean and variance of number of ABP’s are calculated for different outer S=3 S=5 S=8 slope=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 slope=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7 10 10 100 1000 N4 radius of the disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The same is repeated for three different sizes of the passive particle or for three different size ratios S = 3, 5 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' In the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S6 we show the plot of ∆N vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' N for three sizes S = 3, 5 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' For all the cases the graph is power law with ∆N ≃ N α, where α ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='7 for moderate N for all S and starts to deviate for large N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The deviation appears at relatively larger N on increasing size ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Hence increasing the size of passive particle increases the stretch of density fluctuation of ABP’s and it might be one of the factor to introduce a long ranged attraction among passive particles for larger size ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' Correlations of density fluctuations of bacteria in the vicinity of an isolated colloidal particle in experiments FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The correlations of density fluctuations C(r), as defined in the main text, is shown for two different size ratios S ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' The x-axis is scaled by the size of the bacteria l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' It is clear from these results that the density fluctuations are suppressed in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content=' ε-S = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 e-S = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4 r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'} +page_content='4 5 10 15 0 20 r/l' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4NFKT4oBgHgl3EQfRi0P/content/2301.11771v1.pdf'}