Disks of two sizes and weights in alternating sequence are confined to a long and narrow channel. The axis of the channel is horizontal and its plane vertical. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations subject to moderate pressure, gravity, and random agitations. Disk sizes and channel width are such that under jamming no disk remains loose and all disks touch one wall. We present exact results for the characterization of jammed macrostates including volume and entropy. The rigorous analysis divides the disk sequences of jammed microstates into overlapping tiles from which we construct a small number of species of statistically interacting particles. Jammed macrostates depend on dimensionless control parameters inferred from ratios between measures of expansion work against the pistons, gravitational potential energy, and intensity of random agitations. These control parameters enter the configurational statistics via the activation energies prior to jamming of the particles. The range of disk weights naturally divides into regimes where qualitatively different features come into play. We sketch a path toward generalizations that include random sequences under a modified jamming protocol.

An improved curved-boundary scheme with second-order velocity slip condition for multiple-relaxation-time–lattice Boltzmann (MRT-LB) simulation of microgas flow is proposed. The proposed interpolation bounce-back (IBB)–explicit counter-extrapolation (ECE) scheme adopts the IBB method to describe the curved boundary, while the ECE method is employed to predict the slip velocity on gas-solid interface. To incorporate the effect of second-order velocity slip term and the influence of boundary curvature, a slip velocity model is also derived, from which the gas slip velocity is captured by the ECE discretization method. The influence of fictitious slip velocity can be eliminated by adopting the present ECE method, and the influence of actual offset between the lattice node and the physical boundary can be well considered by the IBB method. The proposed IBB-ECE boundary scheme is then implemented with the MRT-LB model and tested by simulations of force-driven gas flow in horizontal (inclined) microchannel, gas flow around a micro-cylinder, and Couette flow between two micro-cylinders. Numerical results show that the proposed IBB-ECE scheme improves the computational accuracy of gas slip flow $(0.001<\mathrm{Kn}\le 0.1)$ when compared with other boundary schemes reported in the literature, and provides a precise and easy implementing scheme for curved boundary with second-order slip condition.

Applications of Bose-Einstein condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii equation (GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equation to a low-dimensional Hamiltonian ordinary differential equation system. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as the chopped random basis to derive a finite-dimensional nonlinear programing problem, which we solve with a differential evolution algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.

In a recent paper, Tanogami [Phys. Rev. E 103, 023106 (2021)] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the intervortex distance is dominated by a quantum stress cascade, in opposition to Kelvin-wave cascade predictions. The purpose of the present Comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.

We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [Phys. Rev. E 105, 027101 (2022)] on our paper [Phys. Rev. E 103, 023106 (2021)]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.

We derive an analytical expression for maximum efficiency at fixed power of heat pumps operating along a finite-time reverse Carnot cycle under the low-dissipation assumption. The result is cumbersome, but it implies simple formulas for tight upper and lower bounds on the maximum efficiency and various analytically tractable approximations. In general, our results qualitatively agree with those obtained earlier for endoreversible heat pumps. In fact, we identify a special parameter regime when the performance of the low-dissipation and endoreversible devices is the same. At maximum power, heat pumps operate as work to heat converters with efficiency 1. Expressions for maximum efficiency at given power can be helpful in the identification of more practical operation regimes.

Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay, and a fourth mode $\mathit{\Delta }$ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the $\mathit{\Delta }$ mode of director deformation. Because of geometric frustration, the $\mathit{\Delta }$ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.

The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the case in which the foundation is made of a structured material such as a polymer network, which has characteristic scales of length and time. We use the two-fluid model of viscoelastic structured materials to treat a film of finite thickness, supported on a rigid solid and subjected to a concentrated normal force at its free surface. We obtain the foundation modulus (Winkler constant) as a function of the film's thickness, intrinsic correlation length, and viscoelastic moduli, for three choices of boundary conditions. The results can be used to readily extend earlier applications of the Winkler model to more complex, microstructured substrates. They also provide a way to extract the intrinsic properties of such complex materials from mechanical surface measurements.

By employing the exact enumeration technique on the lattice model of a polymer, we study the migration of the polymer chain across an entropic trap in a quasiequilibrium condition and explore the effect of solvent gradient present in the entropic trap which acts both parallel and perpendicular to the direction of migration. The Fokker-Planck formalism utilizes the free energy landscape of a polymer chain across the channel in the presence of the entropic trap to calculate the migration time. It is revealed that the migration is fast when the solvent gradient acts along the migration axis (i.e., $x$ axis) inside the channel in comparison to the channel having the entropic trap. We report here for the first time that the entropic trap makes the migration faster at a certain value of solvent gradient. We also study the effect of transverse solvent gradient (along the $y$ axis) inside the trap and investigate the structural changes of the polymer during migration through the channel. We observe the nonmonotonic dependence of migration time on the solvent gradient.

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

We propose a one-dimensional diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalizing the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short-time regime, which is estimated to be $t<{10}^{-2}\mathrm{s}$ for the $a\sim {10}^{-3}\mathrm{m}$ system and $t<1\mathrm{s}$ for the $a\sim {10}^{-2}\mathrm{m}$ system composed of two kinds of familiar metals such as titanium, zirconium, and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high-energy edge states also contribute to very rapid heat conduction in a very short-time regime.

The principle of maximum entropy (PME), as expounded by Jaynes, is based on the maximization of the Boltzmann-Gibbs-Shannon (BGS) entropy subject to linear constraints. The resulting probability distributions are of canonical (exponential) form. However, the rationale for linear constraints is nebulous, and probability distributions are not always canonical. Here we show that the correct noncanonical distribution for a system in equilibrium with a finite heat bath is implied by the unconstrained maximization of the total BGS entropy of the system and bath together. This procedure is shown to be equivalent to maximizing the BGS entropy of the system alone subject to a contrived nonlinear constraint which reduces to (a) the usual linear constraint for an infinite heat bath, and (b) a previously enigmatic logarithmic constraint which implies a power-law distribution for a large but finite heat bath. This procedure eliminates the uncertainty as to the proper constraints, and easily generalizes to arbitrary composite systems, for which it provides a simpler alternative to the Jaynes PME.

We show experimentally and theoretically that the heliconical fluctuations that develop in a cholesteric phase (Ch) close to a transition to a chiral twist-bend nematic phase $\left({\mathrm{N}}_{\mathrm{TB}}\right)$ may lead to the appearance of a compensation point. At this point, the equilibrium twist of the cholesteric phase vanishes and changes sign. Mixtures of the flexible dimer CB7CB and the rodlike molecules 8CB or 5CB, doped with a small amount of the chiral molecules R811, S2011, CC, or CB15, are used in experiments to determine the conditions for the appearance of a compensation point.

We describe classical stochastic processes by using dynamical Lee-Yang zeros. The system is in contact with external leads and the time evolution is described by the two-state classical master equation. The cumulant generating function is written in a factorized form and the current distribution is characterized by the dynamical Lee-Yang zeros. We show that a continuous distribution of zeros is obtained by discretizing the time variable. When the transition probability is a periodically oscillating function of time, the distribution of zeros splits into many parts. We study the geometric property of the current by comparing the result with that of the adiabatic approximation. We also use the Floquet-Magnus expansion in the continuous-time case to study dynamical effects on the current at the fast-driving regime.

We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints are modeled by a perceptron constraint satisfaction problem. We show that depending on the density of constraints, one can have different situations. If the number of constraints is small, one typically has a phase where the ground state of the cost function is unique and sits on the boundary of the island of configurations allowed by the constraints. In this case, there is a hypostatic number of marginally satisfied constraints. If the number of constraints is increased one enters a glassy phase where the cost function has many local minima sitting again on the boundary of the regions of allowed configurations. At the phase transition point, the total number of marginally satisfied constraints becomes equal to the number of degrees of freedom in the problem and therefore we say that these minima are isostatic. We conjecture that by increasing further the constraints the system stays isostatic up to the point where the volume of available phase space shrinks to zero. We derive our results using the replica method and we also analyze a dynamical algorithm, the Karush-Kuhn-Tucker algorithm, through dynamical mean-field theory and we show how to recover the results of the replica approach in the replica symmetric phase.

We numerically investigate the rectification of the probability flux and dynamical relaxation of particles moving in a system with and without noise. The system, driven by two external forces, consists of two substrate potentials that have identical shapes and different potential barriers with different friction coefficients. The deterministic model exhibits the perfect rectification of the probability flux, ratchet effect, and the dependence of the unpredictability of the dynamics on basin of attraction. In contrast, the stochastic model displays that the rectification is sensitive to the temperature and an external bias. They can induce kinetic phase transitions between no transport and a finite net transport. These transitions lead to an unexpected phenomenon, called negative rectification. The results are analyzed through the corresponding time-dependent diffusion coefficient, information entropy (IE), etc. At a low temperature, anomalous diffusions occur in system. For the occurrence of the flux in certain parameter regimes, the larger the diffusion is, the smaller the corresponding IE is, and vice versa. We also present the selected parameter regimes for the emergence of the rectification and negative rectification. Additionally, we study the rectification of the interacting particles in the system and find that the flux may depend on the coupling strength and the number of the interacting particles, and that collective motions occur for the forward flux. Our work provides not only a way of the rectification for the transport of various particles (e.g., ions, electrons, photons, phonons, molecules, DNA chains, nanoswimmers, dust particles, etc.) in physics, chemistry, biology, and material science, but also a design of various circuits.

A growing body of evidence suggests that cerebrospinal fluid circulates through the brain to sweep away high-molecular-weight solutes. Multiple studies demonstrate that flow through this pathway, often referred to as the glymphatic system, is most active during sleep. We numerically model the clearance of amyloid-$\beta$ (a high-molecular-weight protein connected to Alzheimer's disease) from the brain interstitium by combined diffusion and glymphatic advection. We first compare the clearance for a range of different flow conditions and quantify the relation between the clearance rates and Péclet number Pe. We then simulate protein buildup using a reaction-advection-diffusion equation based on the Smoluchowski aggregation scheme and quantify the buildup for different Pe. We find that for flows with $\text{Pe}\gtrsim 1$, the rate of accumulation of heavy aggregates decreases exponentially with Pe. We finally explore the effect of the sleep-wake cycle by incorporating a variation in the flow speed motivated by experimental measurements. We find that periods of sleep lead to better clearance of intermediate protein aggregates and deter the buildup of large aggregates in the brain. In a conservative estimate, for $\text{Pe}\approx 1$, we find a $32\%$ reduction in the buildup rate of heavier protein aggregates compared to purely diffusive clearance.

We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.

Enhanced diffusion is an emergent property of many experimental microswimmer systems that usually arises from a combination of ballistic motion with random reorientations. A subset of these systems, autophoretic droplet swimmers that move as a result of Marangoni stresses, have additionally been shown to respond to local, self-produced chemical gradients that can mediate self-avoidance or self-attraction. Via this mechanism, we present a mathematical model constructed to encode experimentally observed self-avoidant memory and numerically study the effect of this particular memory on the enhanced diffusion of such swimming droplets. To disentangle the enhanced diffusion due to the random reorientations from the enhanced diffusion due to the self-avoidant memory, we compare to the widely used active Brownian model. Paradoxically, we find that the enhanced diffusion is substantially suppressed by the self-avoidant memory relative to that predicted by only an equivalent reorientation persistence timescale in the active Brownian model. We attribute this to transient self-caging that we propose is novel for self-avoidant systems. Additionally, we further explore the model parameter space by computing emergent parameters that capture the velocity and reorientation persistence, thus finding a finite parameter domain in which enhanced diffusion is observable.

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.