diff --git "a/HdE1T4oBgHgl3EQfFgNH/content/tmp_files/load_file.txt" "b/HdE1T4oBgHgl3EQfFgNH/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/HdE1T4oBgHgl3EQfFgNH/content/tmp_files/load_file.txt" @@ -0,0 +1,708 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf,len=707 +page_content='Inertial effects on rectification and diffusion of active Brownian particles in an asymmetric channel Narender Khatri1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' ∗ and Raymond Kapral1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' † 1Chemical Physics Theory Group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Department of Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' University of Toronto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Toronto,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Ontario M5S 3H6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Canada (Dated: January 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2023) Micro- and nano-swimmers moving in a fluid solvent confined by structures that produce entropic barriers are often described by overdamped active Brownian particle dynamics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' where viscous effects are large and inertia plays no role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' However, inertial effects should be considered for confined swimmers moving in media where viscous effects are no longer dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Here, we study how inertia affects the rectification and diffusion of self-propelled particles in a two-dimensional asymmetric channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We show that most of the particles accumulate at the channel walls as the masses of the particles increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Furthermore, the average particle velocity has a maximum as a function of the mass, indicating that particles with an optimal mass M ∗ op can be sorted from a mixture with particles of other masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In particular, we find that the effective diffusion coefficient exhibits an enhanced diffusion peak as a function of the mass, which is a signature of the accumulation of most of the particles at the channel walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The dependence of M ∗ op on the rotational diffusion rate, self- propulsion force, aspect ratio of the channel, and active torque is also determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The results of this study could stimulate the development of strategies for controlling the diffusion of self-propelled particles in entropic ratchet systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' INTRODUCTION Many biological microorganisms, as well as artificial active particles, take free energy from their environments and convert it under nonequilibrium conditions into per- sistent motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The mechanisms that underlie such ac- tive motion and the dynamical properties of these sys- tems are diverse and have been studied extensively [1– 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For the most part, the biological and synthetic ac- tive agents mentioned above have micrometer or sub- micrometer dimensions and move in viscous environ- ments under conditions where inertia does not play an important role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In such circumstances, the active dy- namics is often described by the overdamped Langevin or continuum models that neglect inertia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Inertia cannot al- ways be neglected, and an increasing body of research [16] considers the effects of inertia on active particle motion and describes the new phenomena that arise as a result of its inclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' While the systems where inertial effects are important are diverse, some examples include sys- tems that support a temperature gradient across coexist- ing phases [17], vibrobots [18–20], active particle motion in low-density media, such as gases [21], plasmas [22– 24], superfluids [25], and active aerosols [26], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Such inertia-dominated active particles are termed micro- and nano-flyers rather than swimmers [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The rectification of artificial active particles in con- fined environments in the absence of external forces has attracted interest [27–32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Geometrical confinement con- trols the volume of phase space that is accessible to the ∗ Corresponding author: narender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='khatri@utoronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='ca † Corresponding author: r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='kapral@utoronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='ca active particles, resulting in entropic barriers that signif- icantly influence their transport properties [33–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As well, confined environments possessing spatial ratchet asymmetry give rise to an entropic ratchet potential that can induce active directed transport in the system [27, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We investigate the underdamped dynamics of self- propelled particles confined by a two-dimensional asym- metric channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We use a minimal underdamped Langevin model for the dynamics of the self-propelled particles that accounts for inertia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The collisional dy- namics of particles with the channel walls are modeled by sliding-reflecting boundary conditions [27, 31, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We fo- cus on how inertial effects influence the rectification and diffusion of active particles in the asymmetric channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The article is organized as follows: in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' II, we in- troduce the underdamped Langevin model used to de- scribe the dynamics of the active particles in the two- dimensional asymmetric channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Section III discusses the effects of inertia on the spatial distribution of par- ticles, while Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' IV presents results on the rectification and effective diffusion in the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The main conclu- sions of the article are given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' MODEL The system is confined to a two-dimensional asym- metric channel with periodicity L (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 1), and, as in other studies [16], a minimal underdamped Langevin model is used to describe the active dynamics under con- ditions where inertia is important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The coupled Langevin equations for an active particle with position r = (x, y), orientation ˆn = (cos θ, sin θ), mass M, and moment of arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='02902v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='soft] 7 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Schematic illustration of an active (self-propelled) Brownian particle of mass M and moment of inertia I con- fined in a two-dimensional triangular channel with periodicity L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The active force F0 = F0ˆn, angle θ, active torque T0, local width of the channel 2 w(x), and local length of a cell of the channel ∆(y) are indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The shape of the channel struc- ture is prescribed by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The particle cannot penetrate through the channel walls, which are considered rigid;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' how- ever, the particle is free to rotate and slide along the walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' inertia I read M ¨r(t) = −γt ˙r(t) + F0ˆn(t) + γt � 2Dt ξ(t), I ¨θ(t) = −γr ˙θ(t) + T0 + γr � 2Dr ζ(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' (1) Here γt and γr are the translational and rotational fric- tion coefficients, Dt and Dr are the translational and rotational diffusion constants, and F0 and T0 are the ac- tive force and torque, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The random variables ξ(t) and ζ(t) are the Gaussian white noise terms with zero mean and unit variances given by ⟨ξ(t)⊗ξ(t′)⟩ = δ(t−t′)1 and ⟨ζ(t)ζ(t′)⟩ = δ(t − t′), respectively, where 1 is the unit matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Such a set of coupled Langevin equa- tions can serve as models for a variety of active sys- tems, including systems subject to athermal noise [39– 42], if {γt, γr, Dt, Dr} are regarded as independent pa- rameters, and Dt and Dr control the strength of noise terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For systems with thermal noises that satisfy the fluctuation-dissipation relation, the Einstein relations ap- ply, Dt = kBT/γt and Dr = kBT/γr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The set of coupled Langevin equations (1) is a simplified version of a more general set of coupled Langevin equations that applies to asymmetric particles and accounts for translation- rotation coupling [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The set of general underdamped coupled Langevin equations for chemically-active colloids has been derived using fluctuating chemohydrodynam- ics [44] and molecular theory [45], where expressions for the active force and torque are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The two-dimensional asymmetric and spatially peri- odic channel shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 1 is specified as follows: for the upper wall, we have wu(x) = � wmin, x = 0 wmax − (wmax − wmin) x L, 0 < x ≤ L, (2) where L is the periodicity of the channel, and wmin and wmax refer to the minimum and maximum half-widths of the channel, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The dimensionless aspect ratio of the channel is ϵ = wmin/wmax, where we set wmax = 1 throughout the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The local length of a cell of the channel is given by ∆(y) = (wmax −|y|)L/(wmax −wmin), where y is bounded between the lower and upper walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Due to the symmetry about the principal axis of the channel, the lower wall is described by wl(x) = −wu(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Consequently, 2 w(x) = wu(x)−wl(x) corresponds to the local width of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' When a particle encounters a channel wall, it is elas- tically reflected [31, 38, 46, 47], and its orientation θ is unchanged during the collision (sliding-reflecting bound- ary conditions [27, 38, 48]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' So, the particle slides along the channel walls until a fluctuation in the orientation vector ˆn causes it to change so that it may move away from the wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For translational motion described by Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' (1), inertial effects dominate frictional effects for times t ≪ M/γt ≡ τv, while for orientational motion, they are important for times t ≪ I/γr ≡ τω, where τv and τω are the characteristic times for linear and angular velocity relax- ation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For active particles in a bulk medium, these times may be compared to the reorientation time τr = 1/Dr that determines the time scale on which orien- tation vector ˆn decays, and the time τa = 2a/v0 it takes a particle with speed v0 to move a distance equal to the particle diameter 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For the present study, where the dynamics takes place in a periodic channel, we are interested in the effects of inertia on time scales that reflect the motion on the length scale L of the periodic channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We define the characteristic diffusion time τ = L2/Dt, which gauges the time the particle takes to diffuse one period of the channel length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' This characteristic diffusion time is related to τv by τv/τ = � τv/τth �2, where τth = L/vth with vth = � kBT/M the thermal speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Given these considerations, we use a dimensionless de- scription where lengths are scaled by the periodicity of the channel L, r′ = r/L, and time by τ, t′ = t/τ, analo- gous to that in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [37, 49], so that Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' (1) read, M ∗¨r(t) = − ˙r(t) + f0ˆn(t) + √ 2 ξ(t), I∗¨θ(t) = − ˙θ(t) + t0 + √ 2α ζ(t), (3) and we dispensed with the primes in writing this coupled set of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The dimensionless mass and moment of inertia are given by M ∗ = τv/τ = MDt/(γtL2) and I∗ = τω/τ = IDt/(γrL2), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In these vari- ables, the dimensionless mass M ∗ depends on physical mass M as well as Dt, γt, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Similarly, I∗ depends on the moment of inertia I as well as Dt, γr, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The di- mensionless active force and torque are f0 = F0L/(Dtγt) and t0 = T0L2/(Dtγr), respectively, and the parameter α = Drτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In the following sections, we present results for the average velocity, effective diffusion coefficient, and other properties obtained from simulations of the coupled Langevin equations (3) in the channel [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' At t = 0, the particles are uniformly distributed with random orientations in a periodic cell of the channel located between x = 0 and x = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The results are obtained from 3 averages over 104 stochastic trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' SPATIAL DISTRIBUTION −1 0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 1 100 y Pst(y) M ∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 M ∗ = 1 M ∗ = 1000 M ∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 M ∗ = 1 M ∗ = 1000 f0 = 5, I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 t0 = 0 α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, ǫ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 (a) (b) (c) (d) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The steady state distribution of particles, mapped into a single cell of the channel, is depicted in (a)-(c) for different values of M ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The corresponding normalized prob- ability densities Pst(y) along the y direction are depicted in (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The parameters are: I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, f0 = 5, t0 = 0, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In order to analyze the effects of inertia on the rec- tification and diffusion of self-propelled particles in an asymmetric channel, we first consider the spatial dis- tribution of particles mapped onto a single cell of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Figure 2 shows the steady state distribution of particles and the corresponding normalized probability density Pst(y) along the y direction for different values of M ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For M ∗ → 0 in the overdamped limit, the dis- tribution of particles is inhomogeneous, and most of the particles tend to accumulate near the left corners of the cell (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2(a) and the Pst(y) plots in (d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The in- homogeneous distribution of particles can be ascribed to the active motion due to broken detailed balance and the presence of the spatial asymmetry imposed by the shape of the channel [27, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' It is interesting to see that on increasing M ∗ further, most of the particles quickly accumulate at the channel walls;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' while the rest of the particles adopt the shape of a funnel about the principal axis of the channel at the middle region due to narrow bottleneck openings (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Most of the parti- cles accumulate at the left corners of the cell, and the distribution of particles is symmetric about the principal axis of the channel (see the Pst(y) plots, especially the curve for M ∗ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Such an observation provides evi- dence that the rectification of particles in an asymmetric channel can be enhanced by increasing M ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For strongly underdamped situations where M ∗ → ∞, the qualitative behavior of the distribution of particles and the corre- sponding Pst(y) are very similar;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' however, the rectifi- cation and diffusion of particles approach zero because inertia dominates the self-propulsion mechanism [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' −1 0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 1 100 y P(y) t = 0 t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 Steady State t = 0 t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 t = 1 (a) (b) (c) (d) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The time evolution of the distribution of parti- cles with M ∗ = 1 is shown in (a)-(c) at increasing times, t = 0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5, 1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The normalized probability den- sity P(y) versus y is plotted in (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The parameters are: I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, f0 = 5, t0 = 0, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The probability density evolution to its steady state distribution is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 3 for a system with M ∗ = 1 and parameters as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' At t = 0, particles are distributed uniformly inside the periodic cell consistent with thermodynamic equilibrium [33–35, 46, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As time increases to t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5, the distribution becomes inhomoge- neous: particles near the channel walls quickly begin ac- cumulating there, and the funnel-shaped distribution of particles in the middle region of the cell starts to develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' At a yet later time t = 1, the funnel-shaped distribution sharpens, and particles have continued to accumulate at the walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The distribution at this time closely resembles the steady state distribution shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Note that the probability of accumulation at the left corners of the cell is much higher than in other regions, which is reflected in the structure of the probability density P(y) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 3(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' RECTIFICATION AND EFFECTIVE DIFFUSION Figure 4 shows the dependence of the average velocity v and effective diffusion coefficient Deff on M ∗ for differ- ent values of the self-propulsion force f0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We observe that the particles exhibit rectification (v ̸= 0) in the positive x direction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' v is positive due to the chosen shape of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' If the shape of the channel were inverted with respect to the y axis, then the magnitude of rectification would remain the same, but v would lie in the negative x direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In the small M ∗ limit, the channel asym- metry affects the particle dynamics more strongly since most of the particles accumulate at the channel walls (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 2 and 3), resulting in an increase in v with M ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In the strongly underdamped limit, when M ∗ → ∞, inertia dominates self-propulsion resulting in a rapid decay of v and Deff with M ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Therefore, as one might expect, v has a peak at an optimal mass M ∗ op;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' thus, in a mixture, recti- 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 10 100 1000 25 50 M ∗ Deff 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 1 v f0 = 1 f0 = 5 f0 = 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 1 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 t0 = 0, ǫ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 (a) (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Average velocity v as a function of M ∗ is shown in (a) for different values of the self-propulsion force f0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The corresponding effective diffusion coefficient Deff is shown in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The inset plots Deff versus M ∗ for f0 = 1 on an expanded scale to show its structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Here and below, the solid lines are guides to the eye, and the statistical errors for v and Deff are smaller than the symbol sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The other parameters are: I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, t0 = 0, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 10 100 1000 5 10 15 M ∗ Deff 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='6 v α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 α = 1 α = 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 1 1000 1 2 f0 = 5, I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 t0 = 0, ǫ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 (a) (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Average velocity v and effective diffusion coefficient Deff as a function of M ∗ are plotted in (a) and (b), respec- tively, for different values of the scaled rotational diffusion rate α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The inset in (b) shows Deff versus M ∗ for α = 1 and α = 10 on an expanded scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The other parameters are: I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, t0 = 0, f0 = 5, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' fied particles with M ∗ op will have a higher speed compared to particles with other M ∗ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The peak is more pro- nounced as f0 increases, and the value of the optimal mass can be controlled by changing f0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For the effective diffusion coefficient, we see that Deff initially decreases with increasing M ∗, but on increasing M ∗ further, Deff exhibits an enhanced diffusion peak, which is a signature of the accumulation of most of the particles at the chan- nel walls [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As expected, Deff increases monotonically with f0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As f0 → 0, the motion of self-propelled parti- cles approaches that of passive Brownian motion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' thus, v will tend to zero, and the enhanced diffusion peak will no longer be present (see the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 4(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The variation of v and Deff with M ∗ for different val- ues of the rotational diffusion rate α is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The qualitative trends for different α are the same as those described above for different f0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' however, the peak is more pronounced as α decreases, and now M ∗ op can be changed by tuning α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As expected, Deff decreases mono- tonically with increasing α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In particular, as α → ∞ where reorientation is rapid, the self-propelled motion tends to passive Brownian motion, v tends to zero, and the enhanced diffusion peak vanishes (see the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 5(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 10 100 1000 0 5 10 15 M ∗ Deff 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='6 v t0 = 0 t0 = 1 t0 = 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 1 1000 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 f0 = 5, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, ǫ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 (a) (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Average velocity v and effective diffusion coefficient Deff as a function of M ∗ are plotted in (a) and (b), respec- tively, for different values of the active torque t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The inset in (b) shows Deff versus M ∗ for t0 = 1 and t0 = 10 on an ex- panded scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The parameters are: I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, f0 = 5, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Figure 6 shows v and Deff versus M ∗ for different val- ues of the active torque t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Again one observes that the qualitative trends are the same as those discussed above, and the values of M ∗ op can also be changed by changes in the active torque t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Finally, we point out that the qualitative behavior of v and Deff versus M ∗ remains the same for different val- ues of the moment of inertia I∗ and aspect ratio of the 5 channel ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In addition, M ∗ op is found to be independent of I∗, and it is only weakly dependent on ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 α M ∗ op 2 5 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 1 f0 M ∗ op 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='8 ǫ M ∗ op 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 1 t0 M ∗ op (a) (b) (c) (d) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Dependence of M ∗ op on the rotational diffusion rate α (a), self-propulsion force f0 (b), aspect ratio of the channel ϵ (c), and active torque t0 (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The moment of inertia I∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The dependence of M ∗ op on the rotational diffusion rate α, self-propulsion force f0, aspect ratio of the channel ϵ, and active torque t0 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For fixed values of f0, ϵ, and t0, M ∗ op decreases monotonically with α (panel (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' From panel (b), for fixed values of α, ϵ, and t0, M ∗ op varies nonmonotonically with f0 with the appearance of a peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Note that M ∗ op is weakly dependent on ϵ (panel (c), observe change in the ordinate scale);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' for fixed values of α, f0, and t0, M ∗ op has a minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Lastly, from panel (d), M ∗ op monotonically decreases with t0 for fixed values of α, f0, and ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' REMARKS AND CONCLUSION This study of the rectification and diffusion of self- propelled particles in a two-dimensional asymmetric channel showed that the inclusion of inertia leads to sev- eral distinctive features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In particular, most of the parti- cles accumulate at the channel walls with increasing par- ticle mass, while the remaining particles are distributed in a funnel-shaped region about the principal axis of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' This effect leads to enhanced rectification of heavier particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The presence of a maximum in the ef- fective diffusion coefficient as a function of the mass is also a consequence of the accumulation of most of the particles at the channel walls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Furthermore, for vari- ous parameter values, the average particle velocity has a maximum as a function of the mass, indicating that par- ticles with an optimal mass M ∗ op drift faster than other particles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' hence, they can be sorted from a mixture with particles of different masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' While the Langevin model (1) can describe a wide va- riety of physical systems whose active agents are powered by various mechanisms and are subject to either thermal or athermal noise [16], it is instructive to discuss possible experimental realizations of the rectification effects de- scribed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The asymmetric channels we considered can be constructed by microprinting on a substrate, and the effects of inertia can be determined from measure- ments of the average velocity and effective diffusion co- efficient [53–55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' From the results presented in the text, one can see that the effects of inertia described above will manifest themselves only for certain values of the system parameters, in particular, the particle mass, friction coef- ficients, diffusion constants, self-propulsion force, solvent viscosity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The ability to control all of these parame- ters within desirable ranges places limits on the physical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' A class of systems that may be of interest in this con- text are aerosols [26], where diffusiophoresis has been used to separate micrometer-scale particles [56, 57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' As an example, consider identically-sized active particles with radii a ∼ 200 nm, mass M ∼ 10−15 kg, mo- ment of inertia I ∼ 10−31 kg m2 in air at room tem- perature and pressure p = 104 − 105 Pa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The vis- cosity is given by η ∼ 10−5 kg/(m s), independent of pressure, with translational and rotational friction coeffi- cients, γt ∼ 10−11 kg/s and γr ∼ 10−24 kg m2/s, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The active force lies in the range F0 ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1−1 pN, and the active torque is taken to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The transla- tional and rotational noise strengths are then determined by the values of Dt and Dr, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' The ratchet channel parameters are L = 10 µm, wmax = 10 µm, and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For thermal noise, the Einstein relations hold, and Dt = kBT/γt ∼ 10−9 m2/s and Dr = kBT/γr ∼ 103 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' In the dimensionless units introduced earlier, we have τ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1 s, M ∗ ∼ 10−3, I∗ ∼ 10−6, f0 ∼ 102 − 103, and α ∼ 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' From these parameter values, we can see that the regime where inertial effects play a role cannot be accessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' For athermal noise, take Dt ∼ 10−8 − 10−6 m2/s and Dr ∼ 103 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' We then have τ ∼ 10−2 − 10−4 s, M ∗ ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='01 − 1, I∗ ∼ 10−5 − 10−3, f0 ∼ 100 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1, and α ∼ 10 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Under these conditions, the interesting regime where inertial effects lead to an optimal mass can be reached, provided the system is driven by external noise sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' These results could stimulate the development of strategies for controlling the diffusion of active particles in entropic ratchet systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Moreover, since the rectifi- cation of particles strongly depends on their mass, the model could be used to design lab-on-a-chip devices and artificial channels for the mass-based separation of par- ticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' ACKNOWLEDGMENT This work was supported in part by the Nat- ural Sciences and Engineering Research Coun- cil (NSERC) of Canada and Compute Canada (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='computecanada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content='ca).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 6 [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Lauga and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Powers, Rep.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 48, 1938 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Elgeti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Winkler, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 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Solon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Nar- dini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Peruani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' L¨owen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Golestanian, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Kaupp, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 123, 228001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Scholz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' D’Silva, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Morfill and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Ivlev, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' 81, 1353 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [23] 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Trukhachev, Molecules 26, 561 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [24] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Reichhardt, C.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Greybush, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Fontana, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Express 30, 42276 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' [27] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} +page_content=' Ghosh, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE1T4oBgHgl3EQfFgNH/content/2301.02902v1.pdf'} 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