We derive the three-dimensional telegrapher's equation out of a random walk model. The model is a three-dimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take. We set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher's equation in three dimensions. We generalize the isotropic model and the telegrapher's equation to include fractional anomalous transport in three dimensions.

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time $t$ is represented by a discrete stochastic variable $k\left(t\right)\in \{0,1\}$ such that the rate of absorption is $\gamma [1-k(t\left)\right]$, with $\gamma$ a positive constant. The variable $k\left(t\right)$ evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant $\sqrt{D/\gamma }$, where $D$ is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

The nature of emergent collective behaviors of moving interacting physical agents is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and the degree of order in a collection of diffusively moving noisy oscillators. We address this by constructing a generic hydrodynamic theory for active phase fluctuations in a collection of a large number of nearly-phase-coherent moving oscillators in two dimensions. Our theory describes the general situation where phase fluctuations and oscillator mobility mutually affect each other. We show that the interplay between the active effects and the mobility of the oscillators leads to a variety of phenomena, ranging from synchronization with long-range, nearly-long-range, and quasi-long-range orders to instabilities and desynchronization with short-range order of the oscillator phases. We highlight the complex dependences of synchronization on the active effects. These should be testable in wide-ranging systems, e.g., oscillating chemical reactions in the presence of different reaction inhibitors and facilitators, live oriented cytoskeletal extracts, and vertebrate segmentation clocks.

The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favoring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial role in these cooperative dynamics. We consider a susceptible-infected-removed-type model with two mutually cooperative pathogens: An individual already infected with one disease has an increased probability of getting infected by the other. We present a heterogeneous mean-field theoretical approach to the coinfection dynamics on generic uncorrelated power-law degree-distributed networks and validate its results by means of numerical simulations. We show that, when the second moment of the degree distribution is finite, the epidemic transition is continuous for low cooperativity, while it is discontinuous when cooperativity is sufficiently high. For scale-free networks, i.e., topologies with diverging second moment, the transition is instead always continuous. In this way we clarify the effect of heterogeneity and system size on the nature of the transition, and we validate the physical interpretation about the origin of the discontinuity.

One of the major difficulties in employing phase-field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work, we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free-energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite-element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A comparable experimental observation is made on a column of bubbles under forced drainage, clearly exhibiting the expected line slip.

In this paper, we propose a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework that describes the transport in random systems by taking into account two different scenarios: particles can work as mobile obstacles, whereas particles of one species move in the opposite direction to the particles of the other species, or particles of a given species work as fixed obstacles remaining in their places during the time evolution. We conduct a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming are also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observe in our study the formation of patterns of lanes which reach the steady state regardless of the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principles modeling.

Using Brownian motion in periodic potentials $V\left(x\right)$ tilted by a force $f$, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation $q$, and in order to limit the output fluctuation within a relative uncertainty $\epsilon$, at least $2k_{B}T/{\epsilon }^2$ of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium $[f\ll V^{\prime }\left(x\right)]$ but also at far-from-equilibrium $[f\gg V^{\prime }\left(x\right)]$, more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat $\left({\sigma }_q^2\right)$ increases with its mean $\left({\mu }_q\right)$, and it cannot be smaller than $2k_{B}T{\mu }_q$.

We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the eigenstate energy differences and show that it is in accordance with the eigenstate thermalization hypothesis ansatz.

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the $XYZ$ spin chain. First, we identify the Ising order along $\widehat{x}$ or $\widehat{y}$ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy $\lambda$ of the $XY$ interaction and the coupling $\mathrm{\Delta }$ of the $\mathrm{\Delta }{\sigma }^z{\sigma }^z$ interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the $XYZ$ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number $\pm 1$, depending on whether the Ising order parameter is along $\widehat{x}$ or $\widehat{y}$ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the $XYZ$ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the $XYZ$ model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

The time-reversal properties of charged systems in a constant external magnetic field are reconsidered in this paper. We show that the evolution equations of the system are invariant under a new symmetry operation that implies a new signature property for time-correlation functions under time reversal. We then show how these findings can be combined with a previously identified symmetry to determine, for example, null components of the correlation functions of velocities and currents and of the associated transport coefficients. These theoretical predictions are illustrated by molecular dynamics simulations of superionic AgI.

We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into account explicitly the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wave vectors. It is shown that within a short time interval a long-wavelength deformation excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Conversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.

Binding of ligands to macromolecules is central to many functional and regulatory biological processes. Key parameters characterizing ligand-macromolecule interactions are the stoichiometry, inducing the number of ligands per macromolecule binding site, and the dissociation constant, quantifying the ligand-binding site affinity. Both these parameters can be obtained from analyses of classical saturation experiments using the standard binding equation that offers the great advantage of mathematical simplicity but becomes an approximation for situations of interest when a ligand binds and covers more than one single binding site on the macromolecule. Using the framework of car-parking problem with latticelike macromolecules where each ligand can cover simultaneously several consecutive binding sites, we showed that employing the standard analysis leads to underestimation of binding parameters, i.e., ligands appear larger than they actually are and their affinity is also greater than it is. Therefore, we have derived expressions allowing to determine the ligand size and true binding parameters (stoichiometry and dissociation constant) as a function of apparent binding parameters retrieved from standard saturation experiments.

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius $\ell$. For large $\ell$ the angular velocity decreases for increasing $\ell$. At a specific value of $\ell$ the angular velocity reaches its maximum and, for short $\ell$ it rapidly decreases. Such behavior is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A comparable experimental observation is made on a column of bubbles under forced drainage, clearly exhibiting the expected line slip.

When colloidal particles form a crystal phase on a spherical template, their packing is governed by the effective interaction between them and the elastic strain of bending the growing crystal. For example, if growth commences under appropriate conditions, and the isotropic crystal that forms reaches a critical size, growth continues via the incorporation of defects to alleviate elastic strain. Recently, it was experimentally found that, if defect formation is somehow not possible, the crystal instead continues growing in ribbons that protrude from the original crystal. Here we report on computer simulations in which we observe both the formation of ribbons at short interaction ranges and packings that incorporate defects if the interaction is longer-ranged. The ribbons only form above some critical crystal size, below which the nucleus is disk-shaped. We find that the scaling of the critical crystal size differs slightly from the one proposed in the literature, and we argue that this is because the actual morphology transition is caused by the competition between line tension and elastic stress, rather than the competition between chemical potential and elastic stress.

We explore reshaping of nematoelastic films upon imbibing an isotropic solvent under conditions when isotropic and nematic phases coexist. The structure of the interphase boundary is computed taking into account the optimal nematic orientation governed by interaction of gradients of the nematic order parameter and solvent concentration. This structure determines the effective line tension of the boundary. We further compute equilibrium shapes of deformed thin sheets and cylindrical and spherical shells with the rectilinear or circular shape of the boundary between nematic and isotropic domains. A differential expansion or contraction near this boundary generates a folding pattern spreading out into the bulk of both phases. The hierarchical ordering of this pattern is most pronounced on a cylindrical shell.

Biological locomotion in nature is often achieved by the interaction between a flexible body and its surrounding medium. The interaction of a flexible body with granular media is less understood compared with viscous fluids partially due to its complex rheological properties. In this work, we explore the effect of flexibility on granular propulsion by considering a simple mechanical model in which a rigid rod is connected to a torsional spring that is under a displacement actuation using a granular resistive force theory. Through a combined numerical and asymptotic investigation, we characterize the propulsive dynamics of such a flexible flapper in relation to the actuation amplitude and spring stiffness, and we compare these dynamics with those observed in a viscous fluid. In addition, we demonstrate that the maximum possible propulsive force can be obtained in the steady propulsion limit with a finite spring stiffness and large actuation amplitude. These results may apply to the development of synthetic locomotive systems that exploit flexibility to move through complex terrestrial media.

The linear stability of layered two-phase Poiseuille flows through soft-gel-coated parallel walls is studied in this work. The focus is on determining the effect of the elastohydrodynamic coupling between the fluids and the soft-gel layers on the different instabilities observed in flows between parallel plates. The fluids are assumed Newtonian and incompressible, while the soft gels are modeled as linear viscoelastic solids. A long-wave asymptotic analysis is used to obtain an analytical expression for the growth rate of the disturbances. A Chebyshev collocation method is used to numerically solve the general linearized equations. Three distinct instability modes are identified in the flow: (a) a liquid-liquid long-wave mode; (b) a liquid-liquid short-wave mode; (c) a gel-liquid short-wave mode. The effect of deformability of the soft gels on these three modes is analyzed. From the long-wave analysis of the liquid-liquid mode a stability map is obtained, in which four different regions are clearly demarcated. It is shown that introducing a gel layer near the more viscous fluid has a predominantly stabilizing effect on this mode seen in flows between rigid plates. For parameters where this mode is stable for flow between rigid plates, introducing a gel layer near the less viscous and thinner fluid has a predominantly destabilizing effect. The liquid-liquid short-wave mode is destabilized by the introduction of soft-gel layers. Additional instability modes at the gel-liquid interfaces induced by the deformability of the soft-gel layers are identified. We show that these can be controlled by varying the thickness of the gel layers. Insights into the physical mechanism driving different instabilities are obtained using an energy budget analysis.