A two-dimensional Monte Carlo simulation of dead-end diafiltration of bidispersed particle suspensions was performed. The diafiltration process involves separation of components based on their size by using a permeable membrane. The continuous model was applied to study separation of mixture of disks with diameter $d$ and $D$ $(D>d)$. It was assumed that the membrane at the bottom was permeable to the particles of the smaller diameter $d$, and impermeable to the particles of the larger diameter $D$. The process of vertical filtration was accompanied by the simultaneous Brownian motion of the particles and downward movement of the piston. The mixtures with different numerical concentrations of particles, diameter ratio, and initial size of the systems in the vertical direction $L_y$ have been studied. The time dependencies of the rejection coefficient $k$ and relative height of suspension $h/L_y$ revealed the presence of complete and incomplete separation regimes. The presence of filtration and diffusion-driven stratification of the disks in the vertical direction was observed. The phenomenon of incomplete separation was explained by the formation of an impenetrable barrier from larger particles at the bottom of the deposit.

Thin elastic two-dimensional systems under compressive stresses may relieve part of their stretching energy by developing out-of-plane undulations. We investigate experimentally and theoretically the indentation of an elastic disk supported by a circular ring and show that compressive stresses are relieved via two different routes: either developing buckles which are spread over the system or developing a d-cone where deformation is concentrated in a subregion of the system. We characterize the indentation threshold for wrinkles or d-cone existence as a function of aspect ratio.

The aim of this work is to elucidate the type of transitions that take place when the periodic axisymmetric flows, which can set up at the onset of thermal convection in rotating fluid spheres, lose stability and to study the behavior of the new stable velocity fields until the flows become temporally chaotic. The computations for Prandtl numbers $\mathrm{Pr}=0.715$, 0.1, and 0.01 show that when it decreases, the range of stability of these flows becomes narrower because the kinetic energy of the axisymmetric periodic solutions increases very fast, favoring their instability. From the stability analysis and direct three-dimensional simulations it is found that the transition to stable quasiperiodic flows through Neimark-Sacker bifurcations is supercritical when $\mathrm{Pr}\ge 0.01$. For $\mathrm{Pr}=0.1$ two branches of stable periodic flows emerging from the conduction state have been found due to the proximity to a double Hopf bifurcation. However, only the branches bifurcating from the azimuthal rotating waves are stable at large Rayleigh numbers. Far from this bifurcation the stable flows keep the influence of the axisymmetric dynamics up to large Rayleigh numbers. For small Pr they behave as repeated transients of mixed dynamics, controlled by the azimuthal wave numbers $m=0, m=1$, and $m=2$.

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with $ln(1+S_i·S_j)$ interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical formula of the efficiency at maximum power with explicit expressions of dissipation coefficients under the optimized protocols. When the relative temperature difference between the two baths in the cycle is insignificant, this expression satisfies the universal law of efficiency at maximum power up to the quadratic term of the Carnot efficiency. For large relative temperature differences, the efficiency at maximum power tends to be $1/2$. Furthermore, we analyze the issue of power at any given efficiency for general low-dissipation engines and then obtain the supremum of the power in three limiting cases, respectively. These expressions of maximum power at given efficiency provide the optimal relations between power and efficiency which are tighter than the results in previous references.

A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting. In the absence of any resets, the location of intersection of the two walkers follows a Cauchy distribution. In the presence of resetting, the distribution of the location of annihilation is composed of two parts: one in which the trajectories cross without being reset (center) and the other where trajectories are reset at least once before they cross each other (tails). We find that the tail part decays exponentially for both the resetting protocols. The central part of the distribution, on the other hand, depends on the nature of the restart protocol, with Cauchy for Poisson resetting and Gaussian for sharp resetting. We find good agreement of the analytical results with numerical calculations.

We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method, which has a close relationship with the slow driving perturbation. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections. We analyze two types of excess entropy production and confirm that the leading adiabatic contribution reproduces known results, and then obtain nonadiabatic corrections written in terms of thermodynamic metrics defined in protocol parameter spaces. We also numerically study the resulting excess entropy production in a two-state system.

Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resulting disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling. The functional form is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form, to quantify the distance between the subnetwork's degree distribution and either of the reference distributions. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including uniform random removal and preferred or protective (i.e., biased random) removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.

The configurations taken by polymers embedded in out-of-equilibrium baths may have broad implications in a variety of biological systems. As such, they have attracted considerable interest, particularly in simulation studies. Here we analyze the distribution of configurations taken by a passive flexible chain in a bath of hard, self-propelled, vibrated disks and systematically compare it to that of the same flexible chain in a bath of hard, thermal-like, vibrated disks. We demonstrate experimentally that the mean length and mean radius of gyration of both chains agree with Flory's law. However, the Kuhn length associated with the number of correlated monomers is smaller in the case of the active bath, corresponding to a higher effective temperature. Importantly, the active bath does not just simply map on a hot equilibrium bath. Close examination of the chains' configurations indicates a marked bias, with the chain in the active bath more likely assuming configurations with a single prominent bend.

Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular processes. One crucial question is how vesicles respond to external osmotic stresses, imposed by differences in solute concentrations between the vesicle interior and exterior. Previous analyses of the membrane bending energy have predicted that micron-sized giant unilamellar vesicles (GUVs) should become globally deformed already for nanomolar concentration differences, in contrast to experimental findings that find deformations at much higher osmotic stresses. In this article, we analyze the mechanical stability of a spherical vesicle exposed to an external osmotic pressure in a statistical-mechanical model, including the effect of thermally excited membrane bending modes. We find that the inclusion of thermal fluctuations of the vesicle shape changes renders the vesicle deformation continuous, in contrast to the abrupt transition in the athermal picture. Crucially, however, the predicted critical pressure associated with global vesicle deformation remains the same as when thermal fluctuations are neglected, approximately six orders of magnitude smaller than the typical collapse pressure recently observed experimentally for GUVs. We conclude by discussing possible sources of this persisting dissonance between theory and experiments.

We study the dynamics of a tracer in a dense mixture of particles connected to different thermostats. Starting from the overdamped Langevin equations that describe the evolution of the system, we derive the expression of the self-diffusion coefficient of a tagged particle in the suspension, in the limit of soft interactions between the particles. Our derivation, which relies on the linearization of the Dean-Kawasaki equations obeyed by the density fields and on a path-integral representation of the dynamics of the tracer, extends previous derivations that held for tracers in contact with a single bath. Our analytical result is confronted to results from Brownian dynamics simulations. The agreement with numerical simulations is very good even for high densities. We show how the diffusivity of tracers can be affected by the activity of a dense environment of soft particles that may represent polymer coils—a result that could be of relevance in the interpretation of measurements of diffusivity in biological media. Finally, our analytical result is general and can be applied to the diffusion of tracers coupled to different types of fluctuating environments, provided that their evolution equations are linear and that the coupling between the tracer and the bath is weak.

Shoaling surface gravity waves induce rogue wave formation. Though commonly reduced to water waves passing over a step, nonequilibrium physics allows finite slopes to be considered in this problem. Using nonhomogeneous spectral analysis of a spatially varying energy density ratio, we describe the dependence of the amplification as a function of the slope steepness. Increasing the slope increases the amplification of rogue wave probability until this amplification saturates at steep slopes. In contrast, the increase of the down slope of a subsequent de-shoal zone leads to a monotonic decrease in the rogue wave probability, thus featuring a strong asymmetry between shoaling and de-shoaling zones. Due to the saturation of the rogue wave amplification at steep slopes, our model is applicable beyond its range of validity up to a step, thus elucidating why previous models based on a step could describe the physics of steep finite slopes. We also explain why the rogue wave probability increases over a shoal while it is lower in shallower water.

We provide a perturbative scheme that is suitable to study oscillating states in driven Langevin systems in the large viscous regime. We explicitly determine the oscillating state distribution of an underdamped Brownian particle driven by a time-dependent periodic potential. Apart from the harmonic and anharmonic parameters of the potential, the noise strength and the viscous parameter (or equivalently their ratio referred to as the thermal parameter), which appear in the dynamics of the Brownian particle, are also driven periodically. We specify various nonequilibrium observables, relevant to characterize the oscillating states, and evaluate them to linear order in anharmonic perturbation. We find that the effect of viscous drives on oscillating states is measurable even at leading order and show that the thermodynamic properties of the system in these states are significantly distinct from those in equilibrium or even from those exhibited by oscillating states of overdamped driven systems.

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not hold in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in $N$-component coupled nonlinear Schrödinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameter regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

Wiener's path integral plays a central role in the study of Brownian motion. Here we derive exact path-integral representations for the more general fractional Brownian motion (FBM) and for its time derivative process, fractional Gaussian noise (FGN). These paradigmatic non-Markovian stochastic processes, introduced by Kolmogorov, Mandelbrot, and van Ness, found numerous applications across the disciplines, ranging from anomalous diffusion in cellular environments to mathematical finance. Their exact path-integral representations were previously unknown. Our formalism exploits the Gaussianity of the FBM and FGN, relies on the theory of singular integral equations, and overcomes some technical difficulties by representing the action functional for the FBM in terms of the FGN for the subdiffusive FBM and in terms of the derivative of the FGN for the super-diffusive FBM. We also extend the formalism to include external forcing. The exact and explicit path-integral representations make inroads in the study of the FBM and FGN.

We study the tunneling tail of eigenfunctions of the quantum map using arbitrary precision arithmetic and find that nonmonotonic decaying tails accompanied by step structures appear even when the corresponding classical system is extremely close to the integrable limit. Using the integrable basis constructed with the Baker-Campbell-Hausdorff (BCH) formula, we clarify that the observed structure emerges due to the coupling with excited states via the quantum resonance mechanism. Further calculations reveal that the step structure gives stretched exponential decay as a function of the inverse Planck constant, which is not expected to appear in normal tunneling processes.

Dynamics of density fluctuations in quantum supercooled liquids is analyzed using molecular dynamics simulations. In contrast to the classical case, the uncertainty in the particle position (delocalization of quantum particle in space) leads to significant differences in the dynamics of quantum liquids, both in the short- and long-time limits. The effect of uncertainty is found to be significant for length scales smaller than the uncertainty itself, and diminishes as the length scale grows. The dynamic heterogeneity of the system at short times is enhanced due to uncertainty. In the intermediate ($\beta$-relaxation) time regime, the heterogeneity tends to get suppressed due to quantum uncertainty. The probability distribution of particle displacements shows highly nonclassical behavior with double-peak structure at short timescales.

A well-known class of nonstationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. Due to noise and trends superimposed on data and even sample size and irregularity impacts, the well-known computational algorithm to compute the Hurst exponent ($H$) has encountered superior results. Motivated by this discrepancy, we examine the homology groups of high-dimensional point cloud data (PCD), a subset of the unit $D$-dimensional cube, constructed from synthetic fBm data as a pipeline to compute the $H$ exponent. We compute topological measures for embedded PCD as a function of the associated Hurst exponent for different embedding dimensions, time delays, and amount of irregularity existing in the dataset in various scales. Our results show that for a regular synthetic fBm, the higher value of the embedding dimension leads to increasing the $H$ dependency of topological measures based on zeroth and first homology groups. To achieve a reliable classification of fBm, we should consider the small value of time delay irrespective of the irregularity presented in the data. More interestingly, the value of the scale for which the PCD to be path connected and the postloopless regime scale are more robust concerning irregularity for distinguishing the fBm signal. Such robustness becomes less for the higher value of the embedding dimension. Finally, the associated Hurst exponents for our topological feature vector for the S&P500 were computed, and the results are consistent with the detrended fluctuation analysis method.