Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

How systems transit between different stable states under external perturbation is an important practical issue. We discuss here how a recently developed energy optimization method for identifying the minimal disturbance necessary to reach the basin boundary of a stable state is connected to the instanton trajectory from large deviation theory of noisy systems. In the context of the one-dimensional Swift–Hohenberg equation, which has multiple stable equilibria, we first show how the energy optimization method can be straightforwardly used to identify minimal disturbances—minimal seeds—for transition to specific attractors from the ground state. Then, after generalizing the technique to consider multiple, equally spaced-in-time perturbations, it is shown that the instanton trajectory is indeed the solution of the energy optimization method in the limit of infinitely many perturbations provided a specific norm is used to measure the set of discrete perturbations. Importantly, we find that the key features of the instanton can be captured by a low number of discrete perturbations (typically one perturbation per basin of attraction crossed). This suggests a promising new diagnostic for systems for which it may be impractical to calculate the instanton.

It is known that typical open billiards distribution of transit times is an exponentially decaying function, possibly with a power-law tail. In the paper we show that on small scales some of such distributions change their appearance. These distributions contain a quasiperiodic thin structure, which carries a significant amount of information about the system. Origin and properties of this structure are discussed.

By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity ${\mu }_B$ and displacement thresholds $\vec{\nabla }{P}_c$ evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with $\eta =2$, where fractal dimensions are found between 1.5 and 1.6 for the patterns.

We employ numerical simulations and finite-size scaling techniques to investigate the properties of the dynamic phase transition that is encountered in the Blume-Capel model subjected to a periodically oscillating magnetic field. We mainly focus on the study of the two-dimensional system for various values of the crystal-field coupling in the second-order transition regime. Our results indicate that the present nonequilibrium phase transition belongs to the universality class of the equilibrium Ising model and allow us to construct a dynamic phase diagram, in analogy with the equilibrium case, at least for the range of parameters considered. Finally, we present some complementary results for the three-dimensional model, where again the obtained estimates for the critical exponents fall into the universality class of the corresponding three-dimensional equilibrium Ising ferromagnet.

We investigate the critical properties of the three-dimensional antiferromagnetic ${\mathrm{RP}}^{N-1}$ model, which is characterized by a global $\mathrm{O}(N$) symmetry and a discrete ${\mathbb{Z}}_2$ gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general ${\mathrm{\Phi }}^4$ theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For $N=4$ no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of $\mathrm{O}(N$) symmetric models with a discrete ${\mathbb{Z}}_2$ gauge symmetry.

Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.

A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that real networks typically have more bridges than their completely randomized counterparts, but they have a fraction of bridges that is very similar to their degree-preserving randomizations. We define an edge centrality measure, called bridgeness, to quantify the importance of a bridge in damaging a network. We find that certain real networks have a very large average and variance of bridgeness compared to their degree-preserving randomizations and other real networks. Finally, we offer an analytical framework to calculate the bridge fraction and the average and variance of bridgeness for uncorrelated random networks with arbitrary degree distributions.

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

As an important intracellular signal, $\mathrm{C}{\mathrm{a}}^{2+}$ ions control diverse cellular functions. In this paper, we discuss the $\mathrm{C}{\mathrm{a}}^{2+}$ signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate ($\mathrm{I}{\mathrm{P}}_3$) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large $\mathrm{C}{\mathrm{a}}^{2+}$ diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological $\mathrm{C}{\mathrm{a}}^{2+}$ signaling systems.

We investigate triblock-homopolymer blends of types A1BA2/A and A1BA2/B, using a lattice Monte Carlo method. While the simulated triblock chains are compositionally symmetric in terms of the A-to-B volume ratio, the A1 block is significantly shorter than the A2 block. For the pure A1BA2 melt and the A1BA2 solutions in selective solvent the phase behavior is relatively well known, including existence and stability of the interstitial micelles which were discovered in previous Monte Carlo simulations. In this paper we study the stability of the interstitial micelles as a function of triblock volume fraction in selective homopolymers of either type A or type B, using two significantly different homopolymer chain lengths. We found that adding selective homopolymer of type A shifts the stability of the interstitial micelles into significantly higher temperatures. We also obtained, via self-assembly, intriguing new nanostructures which can be identified as ordered truncated octahedra. Finally, we established that the phase behavior of the triblock-homopolymer blends depends relatively weakly on the chain length of the added homopolymer.

Immediately before adsorption to a horizontal substrate, sinking polymer-coated colloids can undergo a complex sequence of landing, jumping, crawling, and rolling events. Using video tracking, we studied the soft adhesion to a horizontal flat plate of micron-size colloids coated by a controlled molar fraction $f$ of the poly(lysine)-grafted-poly(N-isopropylacrylamide) (PLL-g-PNIPAM) which is a temperature-sensitive polymer. We ramp the temperature from below to above $T_c=32\pm 1^{\circ }\mathrm{C}$, at which the PNIPAM polymer undergoes a transition, triggering attractive interaction between microparticles and surface. The adsorption rate, the effective in-plane ($x\text{−}y$) diffusion constant, and the average residence time distribution over $z$ were extracted from the Brownian motion records during last seconds before immobilization. Experimental data are understood within a rate-equations-based model that includes aging effects and includes three populations: the untethered, the rolling, and the arrested colloids. We show that preadsorption dynamics casts a characteristic scaling function $\alpha \left(f\right)$ proportional to the number of available PNIPAM patches met by soft contact during Brownian rolling. In particular, the increase of in-plane diffusivity with increasing $f$ is understood: The stickiest particles have the shortest rolling regime prior to arrest, so that their motion is dominated by the untethered phase.

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquidlike systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results, e.g., for hard spheres or sticky hard spheres (all the more that in the agreement with the notorious Landau statement, there is no physical small parameter for liquids). Instead of it being guided by the experimental data we are solving the Ornstein-Zernike equation with a trial (variational) form of the interparticle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. Our method is developed for spherically symmetric scattering objects, and our numeric code is written for such a case. However, it can be extended (at the expense of more involved computations and a larger amount of required experimental input information) for nonspherical particles. What is important for our approach is that it is sufficient to know experimental data in a relatively narrow range of the scattering wave vectors ($q$) to compute the static structure factor in a much broader range of $q$. We illustrate by a few model and real experimental examples of the x-ray and neutron scattering data how the approach works.

In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer α-(4-cyanobiphenyl-4′-yloxy)-ω-(1-pyrenimine-benzylidene-4′-oxy) heptane (CBO7O.Py) throughout both nematic and smectic-A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition ($T_{\mathrm{g}}$) temperatures: The higher $T_{\mathrm{g}}$ is due to the freezing of the molecular motions responsible for the relaxation mode with the lowest frequency (${\mu }_{1\mathrm{L}}$); the lower $T_{\mathrm{g}}$ is due to the motions responsible for the two relaxation modes with highest frequencies (${\mu }_{1\mathrm{H}}$ and ${\mu }_2$), which converge just at their corresponding $T_{\mathrm{g}}$. It is shown how the three modes follow a critical-like description via the dynamic scaling model. The two modes with lowest frequencies (${\mu }_{1\mathrm{L}}$ and ${\mu }_{1\mathrm{H}}$) are cooperative in the whole range of the mesophases, whereas the highest frequency mode (${\mu }_2$) is cooperative just below some crossover temperature. In terms of fragility, at the glass transition, the ensemble (${\mu }_{1\mathrm{H}}+{\mu }_2$) presents a value of the steepness index and ${\mu }_{1\mathrm{L}}$ a different one, meaning that fragility is a property intrinsic to the molecular motion itself. Finally, the steepness index seems to have a universal behavior with temperature for the dielectric relaxation modes of liquid crystal dimers, being almost constant at high temperatures and increasing drastically when cooling the compound down to the glass transition from a temperature about $\frac{3}{4}{T}_{NI}$.

Equations are derived that describe the growth and subsequent damped oscillation of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid. It is assumed that the nucleation and the growth of the bubble are caused by an initial negative pressure in the cavity. The liquid is treated as viscous and compressible. The obtained equations allow one to model, by numerical computation, the growth and the oscillation of the bubble in the cavity and the oscillation of the cavity surface. It is shown that the equilibrium radius reached by the growing bubble decreases when the absolute magnitude of the initial negative pressure decreases. It is also found that the natural frequency of the bubble oscillation increases with increasing bubble radius. This result is of special interest because in an unbounded liquid, the natural frequency of a bubble is known to behave oppositely, namely it decreases with increasing bubble radius.

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using two-dimensional (2D) and three-dimensional (3D) numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes to be more easily destabilized in 3D than in 2D. It is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble density increases with the wave number and small-scale bubbles carry a larger mass flux of mixed material.

I study an autonomous quantum Maxwell's demon based on two exchange-coupled quantum dots attached to the spin-polarized leads. The principle of operation of the demon is based on the coherent oscillations between the spin states of the system which act as a quantum iSWAP gate. Due to the operation of the iSWAP gate, one of the dots acts as a feedback controller which blocks the transport with the bias in the other dot, thus inducing the electron pumping against the bias; this leads to the locally negative entropy production. Operation of the demon is associated with the information transfer between the dots, which is studied quantitatively by mapping the analyzed setup onto the thermodynamically equivalent auxiliary system. The calculated entropy production in a single subsystem and information flow between the subsystems are shown to obey a local form of the second law of thermodynamics, similar to the one previously derived for classical bipartite systems.

We use Monte Carlo simulations to study the finite temperature behavior of vortices in the XY model for tangent vector order on curved backgrounds. Contrary to naive expectations, we show that the underlying geometry does not affect the proliferation of vortices with temperature respect to what is observed on a flat surface. Long-range order in these systems is analyzed by using two-point correlation functions. As expected, in the case of slightly curved substrates these correlations behave similarly to the plane. However, for high curvatures, the presence of geometry-induced unbounded vortices at low temperatures produces the rapid decay of correlations and an apparent lack of long-range order. Our results shed light on the finite-temperature physics of soft-matter systems and anisotropic magnets deposited on curved substrates.

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.

We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to $L=1600$. As a check, also simulations of the spin-$\frac{1}{2}$ Ising model are performed. We find $f_{\sigma \sigma \epsilon }=1.051\left(1\right)$ and $f_{\epsilon \epsilon \epsilon }=1.533\left(5\right)$ for operator product expansion coefficients. These results are consistent with but less precise than those recently obtained by using the bootstrap method. An important ingredient in our simulations is a variance reduced estimator of $N$-point functions. Finite size corrections vanish with $L^{-{\mathrm{\Delta }}_{\epsilon }}$, where $L$ is the linear size of the lattice and ${\mathrm{\Delta }}_{\epsilon }$ is the scaling dimension of the leading $Z_2$-even scalar $\epsilon$.