The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasistatic velocities proportional to the external loading rate to velocities larger than the shear wave speed. The way system parameters influence front speed is still poorly understood. Here we study steady-state rupture propagation in a one-dimensional (1D) spring-block model of an extended frictional interface for various friction laws. With the classical Amontons-Coulomb friction law, we derive a closed-form expression for the steady-state rupture velocity as a function of the interfacial shear stress just prior to rupture. We then consider an additional shear stiffness of the interface and show that the softer the interface, the slower the rupture fronts. We provide an approximate closed form expression for this effect. We finally show that adding a bulk viscosity on the relative motion of blocks accelerates steady-state rupture fronts and we give an approximate expression for this effect. We demonstrate that the 1D results are qualitatively valid in 2D. Our results provide insights into the qualitative role of various key parameters of a frictional interface on its rupture dynamics. They will be useful to better understand the many systems in which spring-block models have proved adequate, from friction to granular matter and earthquake dynamics.

A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the model is a strongly overdamped oscillator described by a harmonic restoring force for small displacements that reversibly yields to stress under sufficiently large displacement. This simple dynamical system also reveals unexpectedly rich behavior—exhibiting a series of dynamical transitions and analogies with equilibrium thermodynamic phase transitions. The effects of noise and of inertia are briefly considered and described.

We study the dynamical behaviors of two types of spiral- and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling $G_j$ and (2) the number $N_f$ of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) $G_j$ is large or (b) the maximum possible number of fibroblasts per myocyte $N_f^{\max }$ is large. We also observe that the minimum value of $G_j$, for the transition from the ST to the RS state, decreases as $N_f^{\max }$ increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) $G_j$ increases, with fixed $N_f^{\max }$, and (2) $N_f^{\max }$ increases, with fixed $G_j$. We obtain the boundary between ST and RS stability regions in the $N_f^{\max }\text{−}{G}_j$ plane. In particular, for low values of $N_f^{\max }$, the value of $G_j$, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as $N_f^{\max }$ increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral- and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem, finding phase transitions of different kinds. Distinct phases are associated with different arrangements of the connections, but the need of drastic topological changes does not determine the presence or the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.

Properties of the coupled particles with spin 3/2 (quartits) in a constant magnetic field, as a working substance in the quantum Otto cycle of the heat engine, are considered. It is shown that this system as a converter of heat energy in work (i) shows the efficiency 1 at the negative absolute temperatures of heat baths, (ii) at the temperatures of the opposite sign the efficiency approaches 1, (iii) at the positive temperatures of heat baths antiferromagnetic interaction raises efficiency threefold in comparison with uncoupled particles.

This paper starts with a systematic rederivation of the statistical thermodynamic equations of motion for dislocation-mediated plasticity proposed in 2010 by Langer, Bouchbinder, and Lookman [Acta Mat. 58, 3718 (2010)]. It then uses that theory to explain the anomalous rate-hardening behavior reported in 1988 by Follansbee and Kocks and to explore the relation between hardening rate and grain size reported in 1995 by Meyers et al. A central theme is the need for physics-based, nonequilibrium analyses in developing predictive theories of the strength of polycrystalline materials.

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time $t$. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.

We calculate the local dielectric function $\varepsilon \left(r\right)$ inside the hydration layer around a spherical solute (i) from molecular dynamics simulations including explicit solutes and (ii) theoretically using the nonlocal dielectric function of bulk water which includes the radial electric field, but not the explicit solute. The observed agreement between the two concepts shows that while $\varepsilon \left(r\right)$ is strongly different from bulk, this difference is not due to restructuring of the hydrogen bond network but is mostly a consequence of the field geometry. The dielectric response differs for anions and cations, yielding a natural explanation for the well-known charge asymmetry of ionic solvation in agreement with experimental data.

The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.

Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

The phase structure of a single self-interacting homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the chain in the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high-temperature limit the homopolymer chain is in the self-avoiding random walk phase. At very low temperatures two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space-filling conformation. But when the attractive interactions weaken, there is a low-temperature unfolding transition and the chain becomes like a straight rod. Between the high- and low-temperature limits, several intermediate states are observed, including the $\theta$ regime and pseudogap state, which is a novel form of phase state in the context of polymer chains. Applications to polymers and proteins, in particular collagen, are suggested.

The stochastic process of gene expression is commonly controlled at the level of RNA transcription. The synthesis of messenger RNA (mRNA) is a multistep process, performed by RNA polymerase II and controlled by many transcription factors. Although mRNA transcription is intensively studied, real-time in vivo dynamic rates of a single transcribing polymerase are still not available. A popular method for examining transcription kinetics is the fluorescence recovery after photobleaching (FRAP) approach followed by kinetic modeling. Such analysis has yielded a surprisingly broad range of transcription rates. As transcription depends on many variables such as the chromatin state, binding and unbinding of transcription factors, and cell phase, transcription rates are stochastic variables. Thus, the distribution of rates is expected to follow Poissonian statistics, which does not coincide with the wide range of transcription rate results. Here we present an approach for analyzing FRAP data for single-gene transcription. We find that the transcription dynamics of a single gene can be described with a constant rate for all transcribing polymerases, while cell population transcription rates follow a fat-tailed distribution. This distribution suggests a larger probability for extreme rates than would be implied by normal distribution. Our analysis supports experimental results of transcription from two different promoters, and it explains the puzzling observation of extreme average rate values of transcription.

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the past few decades. A theoretical model was proposed by [T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the model of Vicsek et al., in this paper, we consider a group of animals as particles moving freely in a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle $\phi =\varphi /2$ $(\varphi$ is called the angle of view) of a circle centered at its position of radius $R$. We obtained a phase diagram in the space $\left(\phi ,{\eta }_c\right)$ with ${\eta }_c$ being the critical noise. We show that the phase transition exists only in the case of a wide view's angle $\phi \ge 0.5\pi$. The flocking of animals is a universal behavior of the species of prey but not the one of the predator. Our simulation results are in good agreement with experimental observation [C. Beccoa et al., Physica A 367, 487 (2006)].

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The $\mathrm{C}\to \mathrm{U}$ deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.

We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise noncompact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yields further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.

The stability of networks is greatly influenced by their degree distributions and in particular by their breadth. Networks with broader degree distributions are usually more robust to random failures but less robust to localized attacks. To better understand the effect of the breadth of the degree distribution we study two models in which the breadth is controlled and compare their robustness against localized attacks (LA) and random attacks (RA). We study analytically and by numerical simulations the cases where the degrees in the networks follow a bi-Poisson distribution, $P\left(k\right)=\alpha e^{-{\lambda }_1}\frac{{\lambda }_1^k}{k!}+(1-\alpha )e^{-{\lambda }_2}\frac{{\lambda }_2^k}{k!},\alpha \in [0,1]$, and a Gaussian distribution, $P\left(k\right)=A\text{exp}(-\frac{{(k-\mu )}^2}{2{\sigma }^2}),$ with a normalization constant $A$ where $k\ge 0$. In the bi-Poisson distribution the breadth is controlled by the values of $\alpha$, ${\lambda }_1$, and ${\lambda }_2$, while in the Gaussian distribution it is controlled by the standard deviation, $\sigma$. We find that only when $\alpha =0$ or $\alpha =1$, i.e., degrees obeying a pure Poisson distribution, are LA and RA the same. In all other cases networks are more vulnerable under LA than under RA. For a Gaussian distribution with an average degree $\mu$ fixed, we find that when ${\sigma }^2$ is smaller than $\mu$ the network is more vulnerable against random attack. When ${\sigma }^2$ is larger than $\mu$, however, the network becomes more vulnerable against localized attack. Similar qualitative results are also shown for interdependent networks.