We study a system of purely repulsive spherical self-propelled particles in the minimal setup inducing motility-induced phase separation (MIPS). We show that, even if explicit alignment interactions ...are absent, a growing order in the velocities of the clustered particles accompanies MIPS. Particles arrange into aligned or vortexlike domains whose size increases as the persistence of the self-propulsion grows, an effect that is quantified studying the spatial correlation function of the velocities. We explain the velocity alignment by unveiling a hidden alignment interaction of the Vicsek-like form, induced by the interplay between steric interactions and self-propulsion.
General aspects of the Fluctuation–Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we ...illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein’s work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo’s linear response theory.
The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed.
Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nanosystems and biological systems.
We propose a new experiment to measure the running of the electromagnetic coupling constant in the space-like region by scattering high-energy muons on atomic electrons of a low-
Z
target through the ...elastic process
μ
e
→
μ
e
. The differential cross section of this process, measured as a function of the squared momentum transfer
t
=
q
2
<
0
, provides direct sensitivity to the leading-order hadronic contribution to the muon anomaly
a
μ
HLO
. By using a muon beam of 150 GeV, with an average rate of
∼
1.3
×
10
7
muon/s, currently available at the CERN North Area, a statistical uncertainty of
∼
0.3% can be achieved on
a
μ
HLO
after two years of data taking. The direct measurement of
a
μ
HLO
via
μ
e
scattering will provide an independent determination, competitive with the time-like dispersive approach, and consolidate the theoretical prediction for the muon
g
-2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon
g
-2 experiments at Fermilab and J-PARC.
We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike ...phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.
We propose a mechanism to control the formation of stable obstructions in two-dimensional microchannels of variable sections taking advantage of the peculiar clustering property of active systems. ...Under the activation of the self-propulsion by external stimuli, the system behaves as a switch according to the following principle: by turning-on the self-propulsion the particles become active and even at very low densities stick to the walls and form growing layers eventually blocking the channel bottleneck, while the obstruction dissolves when the self-propulsion is turned off. We construct the phase diagram distinguishing clogged and open states in terms of density and bottleneck width. The study of the average clogging time, as a function of density and bottleneck width, reveals the marked efficiency of the active clogging that swiftly responds to the self-propulsion turning on. The resulting picture shows a profound difference with respect to the clogging obtained through the slow diffusive dynamics of attractive passive Brownian disks. This numerical work suggests a novel method to use particles with externally tunable self-propulsion to create or destroy plugs in microchannels.
Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at ...static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity c. With respect to both the cases of passive colloids with c>0 and AP with c=0, the AP with finite c show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to cτ/ξ, where τ is the AP's reorientation time and ξ the width characterizing the surface's smoothness (ξ→0 for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.
We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the ...particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.
We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a ...short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.
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