We explore the perspective of considering the squeezed thermal reservoir as an equilibrium reservoir in a generalized Gibbs ensemble with two noncommuting conserved quantities. We outline the main properties of such a reservoir in terms of the exchange of energy, both heat and work, and entropy, giving some key examples to clarify its physical interpretation. This allows for a correct and insightful interpretation of all thermodynamical features of the squeezed thermal reservoir, as well as other similar nonthermal reservoirs, including the characterization of reversibility and the first and second laws of thermodynamics.

We describe a microcanonical approach for polymer models that combines atmospheric methods with urn theory. We show that large deviation properties of urn models can provide quite deep mathematical insight by analyzing the random walk range problem in ${\mathbb{Z}}^d$. We also provide a new mean-field theory for the range problem that is exactly solvable by analogy with the Bagchi-Pal urn model.

Recently there have been several considerations by different authors of viscosity and the Green-Kubo stress correlation function from the microscopic perspective. In most of these and earlier works the atomic level stress is the minimal element of stress. It is also possible to consider, for pairwise interaction potentials, as the minimal elements of stress, the stress tensors associated with the pairs of interacting particles. From this perspective, the atomic level stress is not the minimal stress element, but a sum of all pair stress elements in which involved a selected particle. In this paper, we consider the Green-Kubo stress correlation function from a microscopic perspective using the stress tensors of interacting pairs as the basic stress elements. The obtained results show the presence of a long-range bond-orientational order in the studied model liquid and naturally elucidate the connection of the bond-orientational order with viscosity. It turns out that the long-range bond-orientational order is more clearly expressed in the pairs' stress correlation function than in the atomic-stress correlation function. On the other hand, previously observed stress waves are much better expressed in the atomic-stress correlation functions. We also address the close connection of our approach with the previous bond-orientational order considerations. Finally, we consider the probability distributions for the bond-stress and atomic-stress correlation products at selected distances. The character of the obtained probability distributions raises questions about the meaning of the average correlation functions at large distances.

Sound can hold partially ionized sulfur at the center of a spherical bulb. We use the sulfur plasma itself to drive a 180 dB re 20 $\mu \mathrm{Pa}$ sound wave by periodically heating it with microwave pulses at a frequency that matches the lowest order, spherically symmetric, acoustic resonance of the bulb. To clarify the trapping mechanism, we generalize acoustic radiation pressure theory to include gaseous inhomogeneities and find an interaction of high-amplitude sound with density gradients in the gas through which it propagates. This is the pycnoclinic acoustic force (PAF). Though generated by rapidly oscillating sound waves, it has a finite time average and manipulates the plasma through density gradients at its boundary. The PAF is essential for the description of the trap holding a plasma against its own buoyancy as well as understanding convection in the region outside the plasma. It has implications for pulse tubes, thermoacoustic engines, thermal vibrational convection in microgravity, combustion in the presence of sound, and the modeling of Cepheid variable stars.

We investigate analytically the transport characteristics of the triangular bead-spring microswimmer and its dependence on the sizes of the beads as well as on the relative bead configurations. The microswimmer is composed of three beads connected by linear springs in an isosceles triangular arrangement. The bead at the apex of the isosceles triangle is taken to be of arbitrary size, while the other two beads are of equal and fixed size. This arrangement of the beads and springs undergoes autonomous propulsion thanks to the time-dependent active forces which act along the connecting springs. For small active force amplitudes we obtain an explicit expression for the average velocity of the microswimmer as a function of the shape of the isosceles triangle and the size of the central bead. This enables us to identify the conditions on the shape configuration and the relative bead sizes that yield the fastest motion. We find that the magnitude as well as the direction of motion critically depend on these parameters. In the limit where the central bead is large enough, the swimming direction becomes insensitive to the shape of the microswimmer. This limit is appropriate for modeling Chlamydomonas reinhardtii, an alga which moves with the help of its two flagella. Finally, we estimate the efficiency of the microswimmer and identify the model parameters that produce efficient swimming. These findings will help us understand the nature of biological swimming mechanisms and aid in the designing and tuning of rapid and efficient microswimmers capable of moving along arbitrary paths.

The Richtmyer-Meshkov (RM) instability of a planar interface (${\mathrm{N}}_2-{\mathrm{SF}}_6$) subjected to a sinusoidal rippled shock, as the variant of a sinusoidal interface impinged by a planar shock, is investigated through high-order compressible multicomponent hydrodynamic simulations. The rippled shock is generated by a planar shock penetrating through a single-mode interface ($\mathrm{He}-{\mathrm{N}}_2$), and its propagation characteristic agrees reasonably with Bates' analytical solution. Evolution of the flat contact surface impacted by the rippled shock is found to be heavily dependent on the rippled shock phase, and it can be well explained by the impulsive perturbation and continuous perturbation regimes. Various rippled shocks with different Mach numbers ranging from 1.15 to 1.80 are considered. It is found that the influence of the shock strength on the instability growth behaves differently for rippled shocks at different phases. In the case that the shock-interface collision happens when the rippled shock amplitude vanishes for the first time, as the shock strength increases, the impulsive perturbation (i.e., amplitude growth caused by the impulsive shock impact) plays an increasingly more important role in the instability growth than the continuous perturbation (i.e., amplitude growth induced by the disturbed postshock pressure field). In contrast, in the case that the impingement occurs when the rippled shock amplitude becomes zero for the second time, the instability development contributed by the impulsive perturbation is a certain percentage of the total instability growth regardless of the shock strength. The role of the impulsive perturbation in the present nonstandard RM instability within the single-mode framework can be reasonably predicted by an empirical formula combined with the model of Ishizaki et al. [Phys. Rev. E 53, R5592 (1996)].

The response of amorphous materials to an applied strain can be continuous or instead discontinuous if the initial configuration is very stable. We study theoretically how such a stress drop emerges as the system's initial stability is increased. We show that this emergence is well reproduced by elastoplastic models and is predicted by a mean field approximation, where it corresponds to a continuous transition. In the mean field, failure can be forecasted from the avalanche statistics. We show that this is not the case for very stable materials in finite dimensions due to rare weak regions where a shear band nucleates. To understand the nucleation, we build an analogy with fracture mechanics predicting that the critical nucleation radius of a shear band follows $a_c\sim {(\mathrm{\Sigma }-{\mathrm{\Sigma }}_b)}^{-2}$, where $\mathrm{\Sigma }$ is the stress and ${\mathrm{\Sigma }}_b$ is the stress that a shear band can carry.

Cell-fate induction is a very important concept in developmental biology, which involves an intrinsic irreversibility in the developmental process. In order to explore how cell-fate induction will be influenced by environmental noise, the effects of the time-correlated noises on the saddle-node landscape of cell-fate induction are investigated in this study. The main results show clearly that if the correlation time is not zero, then the time-correlated noises may not only lead to the change (or disappearance) of saddle-node bifurcation of cell-fate induction but also lead to the occurrence of the reentrance phenomena. All of these results provide a theoretical possibility that the time-correlated noise could lead to the abnormality of a saddle-node landscape of cell-fate induction.

Vesicles are sacs made of a phospholipid bilayer, and they mimic the cytoplasmic membrane of real cells, for which red blood cells constitute a canonical example. Vesicles deform under flow, such as a shear flow. Under a linear shear flow, they are known to exhibit several motions that combine orientation and shape deformation (such as tank treading, vacillating breathing, and so on). It is shown here that the equations of motion of a vesicle under shear flow in the weak deformation regime can be mapped onto those of a loaded (or heavy bottom) rigid sphere in five dimensions in fictitious gravitational and shear fields. Based on our previous exact analytical solutions for vesicles (which we extend here to out-of-shear-plane motions), we provide hitherto unrevealed exact explicit solution for the rigid sphere problem. We explain how deformation of a vesicle in real space can be extracted from a rigid body dynamics in five dimensions upon appropriate projection onto a lower dimension. This study offers a framework where rigid spheres and deformable vesicles are recast into the same universality class in which both systems are described by the same formal equations differing only by the space dimension.

Suspensions of elongated micelles under shear display complex nonlinear behavior including shear banding, spatiotemporal oscillatory patterns, and chaotic response. Based on a suitable rheological model [S. M. Fielding and P. D. Olmsted, Phys. Rev. Lett. 92, 084502 (2004)], we here explore possibilities to manipulate the dynamical behavior via closed-loop (feedback) control involving a time delay $\tau$. The model considered relates the viscoelastic stress of the system to a structural variable, that is, the length of the micelles, yielding two time- and space-dependent dynamical variables ${\xi }_1,{\xi }_2$. As a starting point we perform a systematic linear stability analysis of the uncontrolled system for (i) an externally imposed average shear rate and (ii) an imposed total stress, and compare the results to those from extensive numerical simulations. We then apply the so-called Pyragas feedback scheme where the equations of motion are supplemented by a control term of the form $K\left[a\left(t\right)-a(t-\tau )\right]$ with $a$ being a measurable quantity depending on the rheological protocol. For the choice of an imposed shear rate, the Pyragas scheme for the total stress reduces to a nondiagonal scheme concentrating on the viscoelastic stress. Focusing on parameters close to a Hopf bifurcation, where the uncontrolled system displays oscillatory states as well as hysteresis in the shear rate controlled protocol, we demonstrate that (local) Pyragas control leads to a full stabilization to the steady-state solution of the total stress, while a global control scheme does not work. In contrast, for the case of imposed total stress, global Pyragas control fully stabilizes the system. In both cases, the control does not change the space of solutions, rather it selects the steady-state solutions out of the existing solutions. This underlines the noninvasive character of the Pyragas scheme.

We study universal relationships in linear responses to instances when mechanical and thermal perturbations are applied to a nonequilibrium steady state. For perturbations in nonequilibrium Langevin systems, we consider a time-dependent external force exerted on a particle along with a time-dependent temperature for the heat bath. In this system, by calculating heat currents and particle velocity, we obtain the kinetic coefficients (Onsager's coefficients) and the time correlation functions using the Fokker–Planck equations. With these quantities, we derive the reciprocal relation associated with the violation of the fluctuation response relation. We obtain the relation by integrating the extent of the violation with respect to the frequency. We also find the reciprocity in the first moment of the frequency integration. These frequency sum rules hold for both overdamped and underdamped regimes for any type of potential and any strength of the external force.

We investigate work extraction from noninteracting fermions under arbitrary unitary operations and the more restricted class of Gaussian unitary operations that can be feasibly implemented. We characterize general quantum states in fermionic systems according to their ability to yield work (or not) under such transformations and study the limit for which multiple copies of passive states in fermionic systems can be activated for work extraction. We find that a sufficient number of copies of nonthermal passive states can achieve this, yielding an upper bound on the number of copies needed.

A four-stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions, such as different speeds of the work strokes, different temperatures of the heat bath, and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is analyzed. A comparison with a two-temperature Otto engine is provided in the particular case of adiabatic work and ideal thermalization strokes.

The dynamics of an ensemble of particles driven out of a potential well, with replacement, by the Poissonian arrival of amplitude-distributed shot noise is examined. A general formula for the high-frequency limit of the escape-rate susceptibility is derived. For certain choices of potential well and amplitude distribution the decay of the high-frequency susceptibility exhibits a nonuniversal exponent. This is a qualitatively different response to that predicted by the diffusion approximation. To provide an example the general framework is applied to a problem of current interest in the biophysics of neuronal voltage dynamics. It is shown that the firing-rate response of neurons to rapidly varying stimuli can be significantly enhanced depending on the ratio between the scale of excitatory postsynaptic potentials and the voltage range over which an action potential initiates. The result is robust to various choices of threshold definition and also to synaptic filtering at physiologically reasonable time scales.

In this work, we study the constitutive behavior of interacting colloidal suspensions for moderate and high concentrations. Specifically, using a lattice Boltzmann solver, we numerically examine suspensions flowing through narrow channels, and explore the significance of the interaction potential strength on the system's macroscopic response. When only a short-range interaction potential is considered, a Newtonian behavior is always recovered and the system's effective viscosity mostly depends on the suspension concentration. However, when using a Lennard-Jones potential we identify two rheological responses depending on the interaction strength, the volume fraction, and the pressure drop. Exploiting a model proposed in the literature we rationalize the simulation data and propose scaling relations to identify the relevant energy scales involved in these transport processes. Moreover, we find that the spatial distribution of colloids in layers parallel to the flow direction does not correlate with changes in the system macroscopic response; but, interestingly, the rheology changes do correlate with the spatial distribution of colloids within individual layers. Namely, suspensions characterized by a Newtonian response display a cubiclike structure of the colloids within individual layers, whereas for suspensions with non-Newtonian response colloids organize in a hexagonal structure.

The development of localized fluidization is experimentally studied in the central plane of an immersed cohesionless granular bed using planar laser induced fluorescence and refractive index matching. The upward growth of the fluidized zone is characterized from the initial localized particle movement within a cavity to the fully fluidized state. The primary outcome of the present study is the identification of two very distinct regimes for the expansion of the fluidized cavity depending on the flow rate at the injection point: a regular regime that has been observed as in previous works, and a newly observed ultraslow regime that requires much longer time to achieve full fluidization. The ultraslow regime was formerly identified only in its nonstationary state as a cavity regime. Experimental results show that at a particular flow rate, the diameter of the injection port is a significant parameter in the evolution of the fluidization in the area close to the injection, while having almost no effect in the final phase of the expansion, provided that the granular bed is high enough. Consequently, the duration of the expansion from cavity to fluidized chimney depends strongly on the injection port size in the ultraslow regime, but only depends weakly in the regular regime. In addition, a parametric study of particle size, injection port diameter, and bed height is performed for the regular regime, based on an apparent divergence of the expansion time as the flow rate approaches a critical flow rate. For this regime, an empirical expression is developed that allows the collapse of the expansion time for all the different variables studied.

It is well established that the packing density (volume fraction) of the random close packed (RCP) state of congruent three-dimensional spheres, i.e., ${\phi }_c\sim 0.64$, can be improved by introducing particle size polydispersity. In addition, the RCP density ${\phi }_c$ can also be increased by perturbing the particle shape from a perfect sphere to nonspherical shapes (e.g., superballs or ellipsoids). In this paper, we numerically investigate the coupling effects of particle size and shape on improving the density of disordered polydisperse particle packings in a quantitative manner. A previously introduced concept of “equivalent diameter” ($D_e$), which encodes information of both the particle volume and shape, is reexamined and utilized to quantify the effective size of a nonspherical particle in the disordered packing. In a highly disordered packing of mixed shapes (i.e., polydispersity in particle shapes) with particles of identical $D_e$, i.e., no size dispersity effects, we find that the overall specific volume $e$ (reciprocal of ${\phi }_c$) can be expressed as a linear combination of the specific volume $e_k$ for each component $k$ (particles with identical shape), weighted by its corresponding volume fraction $X_k$ in the mixture, i.e., $e={\sum }_k{X}_k{e}_k$. In this case, the mixed-shape packing can be considered as a superposition of RCP packings of each component (shape) as implied by a set Voronoi tessellation and contact number analysis. When size polydispersity is added, i.e., $D_e$ of particles varies, the overall packing density can be decomposed as ${\phi }_c={\phi }_L+f_{\mathrm{inc}}$, where ${\phi }_L$ is the linear part determined by the superposition law, i.e., ${\phi }_L=1/{\sum }_k{X}_k{e}_k$, and $f_{\mathrm{inc}}$ is the incremental part owing to the size polydispersity. We empirically estimate $f_{\mathrm{inc}}$ using two distribution parameters, and apply a shape-dependent modification to improve the accuracy from $\sim 0.01$ to $\sim 0.005$. Especially for nearly spherical particles, $f_{\mathrm{inc}}$ is only weakly coupled with the particle shape. Generalized polydisperse packings even with a moderate size ratio ($\sim 4$) can achieve a relatively high density ${\phi }_c\sim 0.8$ compared with polydisperse sphere packings. Our results also have implications for the rational design of granular materials and model glass formers.

We analyze the fluctuation of the number of individuals when two species competing for the same limited resources, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying capacity, the number of each species is subject to giant fluctuations (variance $\sim {\mathrm{mean}}^2$) if the two species have similar growth rates. We show that the deterministic logistic equation can be used only when the growth rates are significantly different, otherwise such growth has to be investigated by stochastic processes tools. These results generalize to a wide class of growth law for two species competing for the same resources.

Motivated by biological transport phenomena and vehicular traffic flow we investigate the dynamics of interacting molecular motors or interacting vehicles that move along linear filaments (tracks) and can reversibly associate or dissociate from them. To analyze these processes, we introduced a model assimilating the interactions in a totally asymmetric simple exclusion process coupled with nonconserving Langmuir kinetics. The model is analyzed first using the continuum version of the simple mean-field approach that neglects the correlations between the particles. It is shown that even for weak interactions theoretical predictions deviate significantly from computer simulation results. To alleviate the problems, we developed a theoretical method that takes into account some correlations in the system. The effect of interactions on stationary phase diagrams, particle currents, and densities are explicitly evaluated. The analysis of two-point correlation function on the lattice indicates that the correlations are stronger at the locations of localized shocks. Our theoretical calculations are in excellent agreement with Monte Carlo computer simulations.

Preferential attachment is a popular candidate mechanism for generating power-law networks. However, incoming nodes require global information about existing nodes' connectivities before connecting, whereas such information access within real-world networks may be only anisotropic and localized. Here we investigate how anisotropic and localized information access affect the resulting network topology. We find that anisotropy impacts the power-law exponent significantly but has only a weak influence on the clustering coefficient. By contrast, we find that locality influences the clustering coefficient significantly but has only weak influence on the power-law exponent. We show that this generalized network-generation mechanism is capable of generating networks with a broad range of power-law exponents and clustering coefficients. Our findings contribute to the debate about why so many real-world networks have degree distributions that crudely resemble power laws, even if this resemblance doesn't survive strict statistical testing procedures.