We present numerical studies of electrical breakdown in disordered materials using a two-dimensional thermal fuse model with heat diffusion. A conducting fuse is heated locally by a Joule heating term. Heat diffuses to neighboring fuses by a diffusion term. When the temperature reaches a given threshold, the fuse breaks and turns into an insulator. The time dynamics is governed by the time scales related to the two terms, in the presence of quenched disorder in the conductances of the fuses. For the two limiting domains, when one time scale is much smaller than the other, we find that the global breakdown time $t_r$ follows $t_r\sim I^2$ and $t_r\sim L^2$, where $I$ is the applied current and $L$ is the system size. However, such power law does not apply in the intermediate domain where the competition between the two terms produces a subtle behavior.

Taylor’s fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor’s FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor’s law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.

We study the number of propagating Bloch modes $N_B$ of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wave number $k$ in systems with a non-null measure of ballistic trajectories and going like $\sim \sqrt{k}$ in diffusive systems. We have calculated numerically $N_B$ for a waveguide with cosine-shaped walls exhibiting strongly diffusive dynamics. The semiclassical prediction for diffusive systems is verified to good accuracy and a connection between this result and the universality of the parametric variation of energy levels is presented.

The dynamics of a Taylor bubble rising in stagnant liquids is numerically investigated using a front tracking coupled with finite difference method. Parametric studies on the dynamics of the rising Taylor bubble including the final shape, the Reynolds number $\left({\text{Re}}_T\right)$, the Weber number $\left({\text{We}}_T\right)$, the Froude number (Fr), the thin liquid film thickness $\left(w/D\right)$, and the wake length $\left(l_w/D\right)$ are carried out. The effects of density ratio $\left(\eta \right)$, viscosity ratio $\left(\lambda \right)$, Eötvös number (Eo), and Archimedes number (Ar) are examined. The simulations demonstrate that the density ratio and the viscosity ratio under consideration have minimal effect on the dynamics of the Taylor bubble. Eötvös number and Archimedes number influence the elongation of the tail and the wake structures, where higher Eo and Ar result in longer wake. To explain the sudden extension of the tail, a Weber number $\left({\text{We}}_l\right)$ based on local curvature and velocity is evaluated and a critical ${\text{We}}_l$ is detected around unity. The onset of flow separation at the wake occurs in between $\text{Ar}=2\times {10}^3$ and $\text{Ar}=1\times {10}^4$, which corresponds to ${\text{Re}}_T$ between 13.39 and 32.55. Archimedes number also drastically affects the final shape of Taylor bubble, the terminal velocity, the thickness of thin liquid film, as well as the wall shear stress. It is found that $w/D=0.32{\text{Ar}}^{-0.1}$.

Efficient coverage algorithms are essential for information search or dispersal in all kinds of networks. We define an extended coverage problem which accounts for constrained resources of consumed bandwidth $\mathcal{B}$ and time $\mathcal{T}$. Our solution to the network challenge is here studied for regular grids only. Using methods from statistical mechanics, we develop a coverage algorithm with proliferating message packets and temporally modulated proliferation rate. The algorithm performs as efficiently as a single random walker but $\mathcal{O}\left({\mathcal{B}}^{\left(d-2\right)/d}\right)$ times faster, resulting in significant service speed-up on a regular grid of dimension $d$. The algorithm is numerically compared to a class of generalized proliferating random walk strategies and on regular grids shown to perform best in terms of the product metric of speed and efficiency.

We linearize the Uehling-Uhlenbeck equation for bosonic gases close to thermal equilibrium under the assumption of a contact interaction characterized by a scattering length $a$. We show that the spectrum of relaxation rates is similar to that of a classical hard-sphere gas. However, the relaxation rates show a significant dependence on the fugacity $z$ of the gas, increasing by as much as 60% of their classical value for $z$ approaching 1. The relaxation modes are also significantly altered at higher values of $z$. The relaxation rates and modes are determined by the eigenvalues and eigenvectors of a Fredholm integral operator of the second kind. We derive an analytical form for the kernel of this operator and present numerical results for the first few eigenvalues and eigenvectors.

Phase-separation dynamics of polymer thin-film mixtures of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are observed while an in-plane electric field is applied, instead of the out-of-plane fields usually employed previously. The phase separation is accompanied by the formation of PS dewetting holes at zero or weak fields. The dewetting velocity at $0.25\mu \text{m}/\text{min}$ is a few times slower than that seen in regular bilayer dewetting. With the increasing of the field strength, we observe the formation of PS droplets in PMMA matrix, a reversal from zero- or low-field conditions. The PS dewetting holes are also suppressed. At further increased fields, PS droplets quickly penetrate up to the top of the PMMA matrix, leading to smaller and more irregular final PS droplets. This is manifested in the dramatic decrease in the growth exponent of the droplet size $\mathcal{L}$ from $\mathcal{L}\sim t^{1.5}$ to $\mathcal{L}\sim t^{0.1}$. These morphology changes are explained by the electrostatic energy resulted from the PS and PMMA dielectric contrast.

We consider a coarse-grained description of a collection of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low-density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.

Cells must continuously sense and respond to time-varying environmental stimuli. These signals are transmitted and processed by biochemical signaling networks. However, the biochemical reactions making up these networks are intrinsically noisy, which limits the reliability of intracellular signaling. Here we use information theory to characterize the reliability of transmission of time-varying signals through elementary biochemical reactions in the presence of noise. We calculate the mutual information for both instantaneous measurements and trajectories of biochemical systems for a Gaussian model. Our results indicate that the same network can have radically different characteristics for the transmission of instantaneous signals and trajectories. For trajectories, the ability of a network to respond to changes in the input signal is determined by the timing of reaction events, and is independent of the correlation time of the output of the network. We also study how reliably signals on different time scales can be transmitted by considering the frequency-dependent coherence and gain-to-noise ratio. We find that a detector that does not consume the ligand molecule upon detection can more reliably transmit slowly varying signals, while an absorbing detector can more reliably transmit rapidly varying signals. Furthermore, we find that while one reaction may more reliably transmit information than another when considered in isolation, when placed within a signaling cascade the relative performance of the two reactions can be reversed. This means that optimizing signal transmission at a single level of a signaling cascade can reduce signaling performance for the cascade as a whole.

We investigate the origins of salt damage in sandstones for the two most common salts: sodium chloride and sulfate. The results show that the observed difference in damage between the two salts is directly related to the kinetics of crystallization and the interfacial properties of the salt solutions and crystals with respect to the stone. We show that, for sodium sulfate, the existence of hydrated and anhydrous crystals and specifically their dissolution and crystallization kinetics are responsible for the damage. Using magnetic resonance imaging and optical microscopy we show that when water imbibes sodium sulfate contaminated sandstones, followed by drying at room temperature, large damage occurs in regions where pores are fully filled with salts. After partial dissolution, anhydrous sodium sulfate salt present in these regions gives rise to a very rapid growth of the hydrated phase of sulfate in the form of clusters that form on or close to the remaining anhydrous microcrystals. The rapid growth of these clusters generates stresses in excess of the tensile strength of the stone leading to the damage. Sodium chloride only forms anhydrous crystals that consequently do not cause damage in the experiments.

A two-phase flow model with liquid-solid transformation [M. Hütter, Phys. Rev. E 64, 011209 (2001)] is discussed, focusing on two elements: (1) the driving force for nucleation and growth and (2) the contribution of phase interfaces to the momentum balance. According to the model, nucleation and growth are partly driven by deviations from the equilibrium pressure difference between the phases, obtained as the surface tension times the ratio of the rates of change of two structural variables: the interfacial area per unit volume and the solid volume fraction. This is shown to be the proper extension of Laplace’s law to nondilute conditions. Contrary to the classical result, the equilibrium pressure difference changes sign at a volume fraction around 50% because the amount of interfacial area lost due to impingement starts to outweigh the amount gained by growth. Hütter did not notice this and consequently misinterpreted a source term in his evolution equation for the momentum density. This term involves the surface tension times the interfacial area per unit volume, which is always nonnegative and hence not related to Laplace’s law, as assumed in earlier two-phase models [M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow (Eyrolles, Paris, 1975); J. Ni and C. Beckermann, Metall. Trans. B 22, 349 (1991)]. An alternative derivation of the interfacial momentum source is presented here, which shows that Hütter’s result correctly expresses the balance of forces on a representative volume element and should have been presented as a correction, rather than a corroboration, of the previous works mentioned.

Shock waves and shock-induced phase transitions are theoretically and numerically studied on the basis of the system of Euler equations with caloric and thermal equations of state for a system of hard spheres with internal degrees of freedom. First, by choosing the unperturbed state (the state before the shock wave) in the liquid phase, the Rankine-Hugoniot conditions are studied and their solutions are classified on the basis of the phase of the perturbed state (the state after the shock wave), being a shock-induced phase transition possible under certain conditions. With this regard, the important role of the internal degrees of freedom is shown explicitly. Second, the admissibility (stability) of shock waves is studied by means of the results obtained by Liu in the theory of hyperbolic systems. It is shown that another type of instability of a shock wave can exist even though the perturbed state is thermodynamically stable. Numerical calculations have been performed in order to confirm the theoretical results in the case of admissible shocks and to obtain the actual evolution of the wave profiles in the case of inadmissible shocks (shock splitting phenomena).

We study a nonautonomous Toda lattice, with a periodically switched on-off coupling coefficient, describing a pulsating strength of neighbor particle interaction. It is shown that when the uncoupled oscillations are linear and under appropriate conditions for the duration of the time intervals where the coupling is switched off, breather solutions can be obtained analytically. Their dynamics and collisions are related to the soliton dynamics of the corresponding autonomous Toda lattice, while a “ratchet” effect is shown to result in breather deceleration, providing a mechanism for breather velocity and collision control.

In this paper, a lattice kinetic algorithm is presented to simulate nonisothermal magnetohydrodynamics in the low-Mach number incompressible limit. The flow and thermal fields are described by two separate distribution functions through respective scalar kinetic equations and the magnetic field is governed by a vector distribution function through a vector kinetic equation. The distribution functions are only coupled via the macroscopic density, momentum, magnetic field, and temperature computed at the lattice points. The novelty of the work is the computation of the thermal field in conjunction with the hydromagnetic fields in the lattice Boltzmann framework. A 9-bit two-dimensional (2D) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated in a 5-bit 2D lattice. Simulation of Hartmann flow in a channel provides excellent agreement with corresponding analytical results.

The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter’s variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

The appearance of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon. We study the coexistence profile between poor and rich fluid phases and we show that for a suitable choice of the parameters nonmonotonic interfaces show up at coexistence.

Closed weakly bound bipartite quantum systems typically exhibit relaxation behavior with respect to the smaller subsystem. Here, we investigate a model composed of a finite spin network with one interfacing spin being coupled to a single electromagnetic field mode via the Jaynes-Cummings interaction. The initial pure state of the system can be chosen such that the resulting thermodynamical relaxation process is lasing/nonlasing relaxation or energy back flow from the field mode. We examine the properties of the field mode with quantum optical methods. During the lasing process, the field mode is in a phase-diffused Glauber state with no optical coherence. The thermodynamical analysis of our system is consistent with this finding: The total energy exchanged between both subsystems is found to be heat only. Yet the mapping of this function onto a thermodynamic heat engine appears to be of limited value.

Lipid monolayers have been shown to represent a powerful tool in studying mechanical and thermodynamic properties of lipid membranes as well as their interaction with proteins. Using Einstein’s theory of fluctuations we here demonstrate that an experimentally derived linear relationship both between transition entropy $S$ and area $A$ as well as between transition entropy and charge $q$ implies a linear relationships between compressibility ${\kappa }_T$, heat capacity $c_{\pi }$, thermal expansion coefficient ${\alpha }_T$, and electric capacity $C_T$. We demonstrate that these couplings have strong predictive power as they allow calculating electrical and thermal properties from mechanical measurements. The precision of the prediction increases as the critical point $T_C$ is approached.

We study collective helping behavior and bystander effects in a coevolving helping network model. A node and a link of the network represents an agent who renders or receives help and a friendly relation between agents, respectively. A helping trial of an agent depends on relations with other involved agents and its result (success or failure) updates the relation between the helper and the recipient. We study the network link dynamics and its steady states analytically and numerically. The full phase diagram is presented with various kinds of active and inactive phases and the nature of phase transitions are explored. We find various interesting bystander effects, consistent with the field study results, of which the underlying mechanism is proposed.