In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

We derive analytical solutions for the autocorrelation and cross-correlation functions of the kinetic, potential, and total energy of a Langevin oscillator. These functions are presented in both the time and frequency domains and validated by independent numerical simulations. The results are applied to address the long-standing issue of temperature fluctuations in canonical systems.

We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and Essam, and it can be used to find exact or very accurate approximations of the critical density. The criterion that follows is related to the criterion used by Scullard and Jacobsen to find precise approximate thresholds, and our work provides a different perspective on their approach.

We study the spread of a persuasive new idea through a population of continuous-time random walkers in one dimension. The idea spreads via social gatherings involving groups of nearby walkers who act according to a biased “majority rule”: After each gathering, the group takes on the new idea if more than a critical fraction $\frac{1-\varepsilon }{2}<\frac{1}{2}$ of them already hold it; otherwise they all reject it. The boundary of a domain where the new idea has taken hold expands as a traveling wave in the density of new idea holders. Our walkers move by Lévy motion, and we compute the wave velocity analytically as a function of the frequency of social gatherings and the exponent of the jump distribution. When this distribution is sufficiently heavy tailed, then, counter to intuition, the idea can propagate faster if social gatherings are held less frequently. When jumps are truncated, a critical gathering frequency can emerge which maximizes propagation velocity. We explore our model by simulation, confirming our analytical results.

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the crossover mode between the bending and the slipping to a larger value. As the vesicle parameters approach the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.

Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.

The vertical drying of a colloidal film containing rodlike particles was studied by means of kinetic Monte Carlo (MC) simulation. The problem was approached using a two-dimensional square lattice, and the rods were represented as linear $k$-mers (i.e., particles occupying $k$ adjacent sites). The initial state before drying was produced using a model of random sequential adsorption (RSA) with isotropic orientations of the $k$-mers (orientation of the $k$-mers along horizontal $x$ and vertical $y$ directions are equiprobable). In the RSA model, overlapping of the $k$-mers is forbidden. During the evaporation, an upper interface falls with a linear velocity of $u$ in the vertical direction and the $k$-mers undergo translation Brownian motion. The MC simulations were run at different initial concentrations, $p_i$, ($p_i\in [0,p_j]$, where $p_j$ is the jamming concentration), lengths of $k$-mers ($k\in [1,12]$), and solvent evaporation rates, $u$. For completely dried films, the spatial distributions of $k$-mers and their electrical conductivities in both $x$ and $y$ directions were examined. Significant evaporation-driven self-assembly and orientation stratification of the $k$-mers oriented along the $x$ and $y$ directions were observed. The extent of stratification increased with increasing value of $k$. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of $p_i$, $k$, and $u$.

We use a discrete-element method simulation and analytical considerations to study the dynamics of a self-energized object, modeled as a disk, oscillating horizontally within a two-dimensional bed of denser and smaller particles. We find that, for given material parameters, the immersed object (IO) may rise, sink, or not change depth, depending on the oscillation amplitude and frequency, as well as on the initial depth. With time, the IO settles at a specific depth that depends on the oscillation parameters. We construct a phase diagram of this behavior in the oscillation frequency and velocity amplitude variable space. We explain the observed rich behavior by two competing effects: climbing on particles, which fill voids opening under the disk, and sinking due to bed fluidization. We present a cavity model that allows us to derive analytically general results, which agree very well with the observations and explain quantitatively the phase diagram. Our specific analytical results are the following. (i) Derivation of a critical frequency, $f_c$, above which the IO cannot float up against gravity. We show that this frequency depends only on the gravitational acceleration and the IO size. (ii) Derivation of a minimal amplitude, $A_{\text{min}}$, below which the IO cannot rise even if the frequency is below $f_c$. We show that this amplitude also depends only on the gravitational acceleration and the IO size. (iii) Derivation of a critical value, $g_c$, of the IO's acceleration amplitude, below which the IO cannot sink. We show that the value of $g_c$ depends on the characteristics of both the IO and the granular bed, as well as on the initial IO's depth.

We introduce a minimal geometric partial differential equation framework to understand pattern formation from interacting, counterpropagating fronts. Our approach concentrates on the interfaces between different states in a system, and relies on both nonlocal interactions and mean-curvature flow to track their evolution. As an illustration, we use this approach to describe a phenomenon in bacterial colony formation wherein sibling colonies can arrest each other's growth. This arrested motion leads to static separations between healthy, growing colonies. As our minimal model faithfully recovers the geometry of these competing colonies, it captures and elucidates the key leading-order mechanisms responsible for such patterned growth.

Detailed analysis of the static structure factor $S\left(Q\right)$ in several glass-forming liquids reveals that the temperature variations of the width of the main diffraction peak $\mathrm{\Delta }Q\left(T\right)$ correlate with the fragility of these liquids. This observation suggests a direct connection between rather subtle structural changes and sharp slowing down of structural relaxation in glass-forming liquids. We show that this observation can be rationalized using the Adam-Gibbs approach, through a connection between temperature variations of structural correlation length, $l_c\sim 2\pi /\mathrm{\Delta }Q$, and the size of cooperatively rearranging regions.

We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.

Dissipative quantum systems are frequently described within the framework of the so-called “system-plus-reservoir” approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well-established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are nonextensive by nature, and the former task may require the use of nonextensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results.

Zero-temperature directed polymer in random potential in $4+1$ dimensions is described. The fluctuation $\mathrm{\Delta }E\left(t\right)$ of the lowest energy of the polymer varies as $t^{\beta }$ with $\beta =0.159\pm 0.007$ for polymer length $t$ and $\mathrm{\Delta }E$ follows $\mathrm{\Delta }E\left(L\right)\sim L^{\alpha }$ at saturation with $\alpha =0.275\pm 0.009$, where $L$ is the system size. The dynamic exponent $z\approx 1.73$ is obtained from $z=\alpha /\beta$. The estimated values of the exponents satisfy the scaling relation $\alpha +z=2$ very well. We also monitor the end to end distance of the polymer and obtain $z$ independently. Our results show that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than $d=4+1$ dimensions.

Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.

Most of the studies on epidemics so far have focused on the growing phase, such as how an epidemic spreads and what are the conditions for an epidemic to break out in a variety of cases. However, we discover from real data that on a large scale, the spread of an epidemic is in fact a recurrent event with distinctive growing and recovering phases, i.e., a hysteresis loop. We show here that the hysteresis loop can be reproduced in epidemic models provided that the infectious rate is adiabatically increased or decreased before the system reaches its stationary state. Two ways to the hysteresis loop are revealed, which is helpful in understanding the mechanics of infections in real evolution. Moreover, a theoretical analysis is presented to explain the mechanism of the hysteresis loop.

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the system undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze the binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at a dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.

The permeation and trapping of soft colloidal particles in the confined space of porous media are of critical importance in cell migration studies, design of drug delivery vehicles, and colloid separation devices. Our current understanding of these processes is however limited by the lack of quantitative models that can relate how the elasticity, size, and adhesion properties of the vesicle-pore complex affect colloid transport. We address this shortcoming by introducing a semianalytical model that predicts the equilibrium shapes of a soft vesicle driven by pressure in a narrow pore. Using this approach, the problem is recast in terms of pressure and energy diagrams that characterize the vesicle stability and permeation pressures in different conditions. We particularly show that the critical permeation pressure for a vesicle arises from a compromise between the critical entry pressure and exit pressure, both of which are sensitive to geometrical features, mechanics, and adhesion. We further find that these results can be leveraged to rationally design microfluidic devices and diodes that can help characterize, select, and separate colloids based on physical properties.

We perform experiments and numerical simulations to investigate spatial distribution of pressure in a sheared dilatant fluid of the Taylor-Couette flow under a constant external shear stress. In a certain range of shear stress, the flow undergoes the shear thickening oscillation around 20 Hz. We find that, during the oscillation, a localized thickened band rotates around the axis with the flow. Based upon experiments and numerical simulations, we show that a major part of the thickened band is under negative pressure even in the case of discontinuous shear thickening, which indicates that the thickening is caused by Reynolds dilatancy; the dilatancy causes the negative pressure in interstitial fluid, which generates contact structure in the granular medium, then frictional resistance hinders rearrangement of the structure and solidifies the medium.

The paper deals with the hexagonal convective flow near the stability threshold in an internally heated fluid layer. In our previous numerical study of convection near the stability threshold in a square box with internal heat generation [Phys. Lett. A 377, 2111 (2013)] for a region of large horizontal extent, it has been shown that at small values of Prandtl number ($\text{Pr}$), convection sets in as a pattern of hexagonal cells with upward motion in the center (up-hexagons), whereas at large $\text{Pr}$, a stable flow pattern is formed by hexagonal cells with a downward motion in the center (down-hexagons). Here, we study axisymmetric convection in a cylinder as a model of motion in a single hexagonal cell. The radius of the cylinder matches the size of hexagons observed in our three-dimensional simulation. The lateral boundary of the cylinder is free and heat insulated. Horizontal bounding surfaces are rigid. The upper boundary is maintained at a constant temperature; the lower one is insulated. Two stable, steady-state motions with the upward and downward flow at the cylinder axis have been attained in calculations, irrespective of $\text{Pr}$. Cylindrical motion with the same direction of circulation as in the stable hexagons has a maximum temperature drop measured along the radius at the bottom of the cell. We suggest maximization of the temperature drop as a selection criterion, which determines the preferred state of motion in an internally heated fluid layer. This new selection principle is validated by the comparative analysis of the dominant nonlinear effects in low- and high-Prandtl number convection.