We study the linear response in systems driven away from thermal equilibrium into a nonequilibrium steady state with nonvanishing entropy production rate. A simple derivation of a general response formula is presented under the condition that the generating function describes a transformation that (to lowest order) preserves normalization and thus describes a physical stochastic process. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration $\tau$, length $l$, and velocity $v$. We solve our model with independent $l$ and $v$. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter $\alpha$. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of $\alpha$, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent $l$ and $\tau$. Universality of tracer diffusion in the porous medium is considered.

A concept of bypass rewiring is introduced, and random bypass rewiring is analytically and numerically investigated with simulations. Our results show that bypass rewiring makes networks robust against removal of nodes including random failures and attacks. In particular, random bypass rewiring connects all nodes except the removed nodes on an even degree infinite network and makes the percolation threshold 0 for arbitrary occupation probabilities. In our example, the even degree network is more robust than the original network with random bypass rewiring, while the original network is more robust than the even degree networks without random bypass. We propose a greedy bypass rewiring algorithm which guarantees the maximum size of the largest component at each step, assuming which node will be removed next is unknown. The simulation result shows that the greedy bypass rewiring algorithm improves the robustness of the autonomous system of the Internet under attacks more than random bypass rewiring.

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson-type autocorrelations in the index. These non-Pearson-type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such autocorrelations. Their characteristic time scale proves to be smaller (less than 25 trading days) than what was previously believed. It is also found that this characteristic time scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown [A. S. Mikhailov and R. Kapral, Proc. Natl. Acad. Sci. USA 112, E3639 (2015)] that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

The flow-induced aggregation of dilute colloidal polystyrene nanoparticles suspended in Newtonian and viscoelastic solutions is reported. A rheo-optical method has been used to detect real-time aggregation processes via measuring optical absorption or scattering in a quartz Couette cell. The observed absorbance decreases over time are attributed to the flow-induced coagulation. Numerical simulations show that the aggregation processes still follow the Smoluchowski coagulation equation in a revised version. Suspensions in a series of media are studied to evaluate the effect of the media rheological properties on the particle aggregation. The data shows that elasticity reduces the aggregation while the solution viscosity enhances the aggregation processes.

The effects of friction mobilization on the stress profile within a two-dimensional silo are investigated via simulations of discrete elements. Friction mobilization is driven by cyclic vertical displacement of the sidewalls. Two regimes have been observed for small filling height, with stress profiles identified as saturated (Janssen's profile) and exponentially growing. The transition between these regimes is denoted by an almost linear stress profile, similar to that of a hydrostatic system, with a significantly greater characteristic height compared to the height of the column of grains. For tall columns, the process of friction inversion is more complex. A partial inversion of friction mobilization is observed when the motion is reversed from upward to downward, which results in two coexisting zones of opposite mobilization. These zones are separated by a wide compaction front with a gradual upward progression sustained by the displacement of the walls. Conversely, if the motion is reversed, the two opposing friction mobilization zones retract, the transition zone becomes smooth, and the system rapidly transforms from two coexisting mobilization states to a Janssen-like regime. In both regimes, the general characteristics from the resulting stress profiles are depicted by generalizing Janssen's equation to include partial mobilization through the varying effective friction coefficient along the silo walls.

This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of capillary waves in the underdamped regime is proposed, including predictions for the wave number of critical damping based on a harmonic-oscillator model. The scaling resulting from this parametrization leads to a self-similar solution of the frequency dispersion of capillary waves that covers the entire underdamped regime, which allows an accurate evaluation of the frequency at a given wave number, irrespective of the fluid properties. This similarity also reveals characteristic features of capillary waves, for instance that critical damping occurs when the characteristic time scales of dispersive and dissipative mechanisms are balanced. In addition, the presented results suggest that the widely adopted hydrodynamic theory for damped capillary waves does not accurately predict the dispersion when viscous damping is significant, and an alternative definition of the damping rate, which provides consistent accuracy in the underdamped regime, is presented.

To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

Hydrodynamic interactions between air bubbles and particles have wide applications in multiphase separation and reaction processes. In the present work, we explore the fundamental mechanism of such complex processes by studying the collision of a single bubble with a fixed solid particle inside a Hele-Shaw cell. Physical experiments show that an air bubble either splits or slides around the particle depending on the initial transverse distance between the bubble and particle centroids. An air bubble splits into two daughter bubbles at small transverse distances, and slides around the particle at large distances. In order to predict the critical transverse distance that separates these two behaviors, we also develop a theoretical model by estimating the rate of the bubble volume transfer from one side of the particle to the other based on Darcy's law, which is in good agreement with experiments.

The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.

An accurate method for time propagation of the coupled Maxwell and time-dependent Kohn-Sham (TDKS) equation is presented. The new approach uses a simultaneous fourth-order Runge-Kutta–based propagation of the vector potential and the Kohn-Sham orbitals. The approach is compared to the conventional fourth-order Taylor propagation and predictor-corrector methods. The calculations show several computational and numerical advantages, including higher computational performance, greater stability, better accuracy, and faster convergence.

A laminar flow control technique based on spanwise mean velocity gradients (SVGs) has recently proven successful in delaying transition in boundary layers. Here we take advantage of a well-known nonlinear effect, namely, the interaction of two oblique waves at high amplitude, to produce spanwise mean velocity variations. Against common belief we are able to fully master the first stage of this nonlinear interaction to generate steady and stable streamwise streaks, which in turn trigger the SVG method. Our experimental results show that the region of laminar flow can be extended by up to 230%.

Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-$\frac{1}{2}$ particle interacting with a bath of up to 32 spin-$\frac{1}{2}$ particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-$\frac{1}{2}$ particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.

Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the biologically relevant high-scoring region, where the probabilities are exponentially small. For gapless local alignments of infinitely long sequences this distribution is known analytically to follow a Gumbel distribution. Distributions for gapped local alignments and global alignments of finite lengths can only be obtained numerically. To obtain result for the small-probability region, specific statistical mechanics-based rare-event algorithms can be applied. In previous studies, this was achieved for pairwise alignments. They showed that, contrary to results from previous simple sampling studies, strong deviations from the Gumbel distribution occur in case of finite sequence lengths. Here we extend the studies to multiple sequence alignments with gaps, which are much more relevant for practical applications in molecular biology. We study the distributions of scores over a large range of the support, reaching probabilities as small as ${10}^{-160}$, for global and local (sum-of-pair scores) multiple alignments. We find that even after suitable rescaling, eliminating the sequence-length dependence, the distributions for multiple alignment differ from the pairwise alignment case. Furthermore, we also show that the previously discussed Gaussian correction to the Gumbel distribution needs to be refined, also for the case of pairwise alignments.

Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al., Soft Matter 7, 2352 (2011)]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles [Dzubiella et al., Phys. Rev. E 65, 021402 (2002)]. Here we use computer simulation to assess the generality of lane formation with respect to variation of particle type and dynamical protocol. We find that laning results from rectification of diffusion on the scale of a particle diameter: oppositely driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with the Péclet number, a prediction confirmed by our numerics over a range of model parameters. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely driven nonattractive colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas [Katz, Leibowitz, and Spohn, J. Stat. Phys. 34, 497 (1984)]. These features include long-ranged correlations in the disordered regime, a critical regime characterized by a change in slope of the particle current with the Péclet number, and fluctuations that grow with system size. By analogy, we suggest that lane formation in the driven colloid system is a phase transition in the macroscopic limit, but that macroscopic phase separation would not occur in finite time upon starting from disordered initial conditions.

The standard theory of induced-charge electro-osmosis (ICEO) often overpredicts experimental values of ICEO velocities. Using a nonsteady direct multiphysics simulation technique based on the coupled Poisson-Nernst-Planck and Stokes equations for an electrolyte around a conductive cylinder subject to an ac electric field, we find that a phase delay effect concerning an ion response provides a fundamental mechanism for electrokinetic suppression. A surprising aspect of our findings is that the phase delay effect occurs even at much lower frequencies (e.g., 50 Hz) than the generally believed charging frequency of an electric double layer (typically, 1 kHz) and it can decrease the electrokinetic velocities in one to several orders. In addition, we find that the phase delay effect may also cause a change in the electrokinetic flow directions (i.e., flow reversal) depending on the geometrical conditions. We believe that our findings move toward a more complete understanding of complex experimental nonlinear electrokinetic phenomena.

We report an experimental study of bubble dynamics in a non-Newtonian fluid subjected to a pressure decrease. The fluid is a hydrogel, composed of water and a synthetic clay, prepared and sandwiched between two glass plates in a Hele-Shaw geometry. The rheological properties of the material can be tuned by the clay concentration. As the imposed pressure decreases, the gas initially dissolved in the hydrogel triggers bubble formation. Different stages of the process are observed: bubble nucleation, growth, interaction, and creation of domains by bubble contact or coalescence. Initially bubble behave independently. They are trapped and advected by the mean deformation of the hydrogel, and the bubble growth is mainly driven by the diffusion of the dissolved gas through the hydrogel and its outgassing at the reactive-advected hydrogel-bubble interface. In this regime, the rheology of the fluid does not play a significant role on the bubble growth. A model is proposed and gives a simple scaling that relates the bubble growth rate and the imposed pressure. Carbon dioxide is shown to be the gas at play, and the hydrogel is degassing at the millimeter scale as a water solution does at a smaller scale. Later, bubbles are not independent anymore. The growth rate decreases, and the morphology becomes more anisotropic as bubbles interact because they are separated by a distance smaller than the individual stress field extension. Our measurements show that the interaction distance scales with the bubbles' size.

We discuss the energy distribution of free-electron Fermi-gas, a problem with a textbook solution of Gaussian energy fluctuations in the limit of a large system. We find that for a small system, characterized solely by its heat capacity $C$, the distribution can be solved analytically, and it is both skewed and it vanishes at low energies, exhibiting a sharp drop to zero at the energy corresponding to the filled Fermi sea. The results are relevant from the experimental point of view, since the predicted non-Gaussian effects become pronounced when $C/k_{\text{B}}\lesssim {10}^3$ ($k_{\text{B}}$ is the Boltzmann constant), a regime that can be easily achieved for instance in mesoscopic metallic conductors at sub-kelvin temperatures.

We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015)], we show that mobile two-particle predictions of the probability of dimerization $P_{\mathrm{dimer}}$, equilibrium constant $K$, and 2D osmotic pressure ${\mathrm{\Pi }}_{2\mathrm{D}}$ as a function of the particle area fraction ${\varphi }_{\mathrm{A}}$ correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.