The neutron-rich isotope ${}^{22}$Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of ${}^{22}$Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semianalytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two-component carbon and oxygen systems. This suggests that small amounts of ${}^{22}$Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher $\Gamma$) in our MD simulations compared to the semianalytic model. This difference seems to grow with impurity parameter $Q_{\text{imp}}$ and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semianalytic model.

The principle of mixed convolved action provides a new rigorous weak variational formalism for a broad range of initial value problems in mathematical physics and mechanics. Here, the focus is initially on classical single-degree-of-freedom oscillators incorporating either Kelvin-Voigt or Maxwell dissipative elements and then, subsequently, on systems that utilize fractional-derivative constitutive models. In each case, an appropriate mixed convolved action is formulated, and a corresponding weak form is discretized in time using temporal shape functions to produce an algorithm suitable for numerical solution. Several examples are considered to validate the mixed convolved action principles and to investigate the performance of the numerical algorithms. For undamped systems, the algorithm is found to be symplectic and unconditionally stable with respect to the time step. In the case of dissipative systems, the approach is shown to be robust and to be accurate with good convergence characteristics for both classical and fractional-derivative based models. As part of the derivations, some interesting results in the calculus of Caputo fractional derivatives also are presented.

The entropy time rate of systems described by nonlinear Fokker-Planck equations—which are directly related to generalized entropic forms—is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

We show that the limiting eigenvalue density of the product of $n$ identically distributed random matrices from an isotropic unitary ensemble is equal to the eigenvalue density of $n$th power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation, one can derive the limiting density of the product of $n$ independent identically distributed non-Hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of $n$ Girko-Ginibre matrices and the product of $n$ truncated unitary matrices. We also provide evidence that the result holds also for isotropic orthogonal ensembles.

A stochastic model is used to assess the effect of external parameters on the development of submerged biofilms on smooth and rough surfaces. The model includes basic cellular mechanisms, such as division and spreading, together with an elementary description of the interaction with the surrounding flow and probabilistic rules for extracellular polymeric substance matrix generation, cell decay, and adhesion. Insight into the interplay of competing mechanisms such as the flow or the nutrient concentration change is gained. Erosion and growth processes combined produce biofilm structures moving downstream. A rich variety of patterns are generated: shrinking biofilms, patches, ripplelike structures traveling downstream, fingers, mounds, streamerlike patterns, flat layers, and porous and dendritic structures. The observed regimes depend on the carbon source and the type of bacteria.

Here we have studied the nonequilibrium thermodynamic response of a voltage-gated Shaker potassium ion channel using a stochastic master equation. For a constant external voltage, the system reaches equilibrium indicated by the vanishing total entropy production rate, whereas for oscillating voltage the current and entropy production rates show dynamic hysteretic behavior. Here we have shown quantitatively that although the hysteresis loop area vanishes in low and high frequency domains of the external voltage, they are thermodynamically distinguishable. In the very low frequency domain, the system remains close to equilibrium, whereas at high frequencies it goes to a nonequilibrium steady state (NESS) associated with a finite value of dissipation function. At NESS, the efficiency of the ion conduction can also be related with the nonlinear dependence of the dissipation function on the power of the external field. Another intriguing aspect is that, at the high frequency limit, the total entropy production rate oscillates at NESS with half of the time period of the external voltage.

We investigate the multifractal properties in the dynamics of domain walls of a ferromagnetic film. We apply the Multifractal Detrended Fluctuation Analysis method in experimental Barkhausen noise time series measured in a 1000-nm-thick Permalloy film under different driving magnetic field frequencies, and calculate the fluctuation function $F_q\left(s\right)$, generalized Hurst exponent $h\left(q\right)$, multifractal scaling exponent $\tau \left(q\right)$, and the multifractal spectrum $f\left(\alpha \right)$. Based on this procedure, we provide experimental evidence of multifractality in the dynamics of domain walls in ferromagnetic films and identify a rich and strong multifractal behavior, revealed by the changes of the scaling properties of over the entire Barkhausen noise signal, independently of the driving magnetic field rate employed in the experiment.

We describe a model for the simulation of extended two-dimensional in-plane dynamical ruptures and for the rapid calculation of statistical properties of repeated model-seismicity events. The discretization involves first- and second-nearest neighbors and is isotropic in both compression and shear properties. All rupture events obey a fracture criterion in the appropriate coordinate frame and numerical oscillations in slip velocity at crack tips due to discretization are minimized. The rupture velocities of fractures, in cases of homogeneous stress drop equal to the strength, are the supershear $P$-wave velocity in the direction of the prestress and the $S$-wave velocity in the perpendicular direction. We use the model to study the growth and healing of individual faults to understand the formation of propagating slip pulses. We confirm two mechanisms for the generation of isolated rupture pulses that have been proposed, namely, (1) a decrease in the dynamical friction with accelerating slip and (2) the encounter of the growing crack with extended regions of large difference between the threshold fracture stress and the prestress. We describe a third mechanism which is that of a velocity-dependent friction that operates equally on both the phases of increasing and decreasing slip velocities and has a characteristic length scale. It is a proxy for energy loss by radiation in a three-dimensional medium. In the case of an elongated rectangular model fault with an upper free surface and lower rigid boundary, pulses develop due to the influence of stress waves reflected from the rigid bottom boundary. In general, the excess of strength over stress drop controls crack fracture speeds; if it is too large, the crack stops. Under homogeneous stress conditions, isolated slip pulses are controlled by the spatial distribution of heterogeneities and by the velocity-dependent friction parametrization.

The paper authored by Lima et al. [Phys. Rev. E 61, 3260 (2000)] has discussed the dispersion relation and Landau damping of a Langmuir wave in the context of the nonextensive statistics proposed by Tsallis. However, the results obtained in this paper are not appropriate. In this comment on the paper we shall derive the correct analytic formulas for both the dispersion relation and Landau damping in the Tsallis formalism. We hope that this comment will be useful in providing the correct results.

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, we show that a stiff directed line in $1+d$ dimensions undergoes a localization transition with increasing disorder for $d>2/3$. We demonstrate that this transition is accessible by numerical transfer matrix calculations in $1+1$ dimensions and analyze the properties of the disorder-dominated phase. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in $1+d$ dimensions and of directed lines under tension in $1+3d$ dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice and in the presence of thermal noise. The internal degree of freedom of each particle is a periodic variable that is coupled to those of other particles with an attractive $XY$-like interaction. The coupling strength decays with the interparticle separation $r$ in space as $1/r^{\alpha }$; $0<\alpha <1$. We study the dynamics of the model in the continuum limit by considering the Fokker-Planck equation for the evolution of the spatial density of particles. We show that the equation allows a linearly stable stationary state, which is always uniform in space, being nonuniform in the internal degrees below a critical temperature $T=1/2$ and uniform above, with a phase transition between the two at $T=1/2$. The state is the same as the equilibrium state of the mean-field version of the model, obtained by considering $\alpha =0$. Our analysis also allows us to compute the growth and decay rates of spatial Fourier modes of density fluctuations. The growth rates compare very well with numerical simulations.

The recent proliferation of correlated percolation models—models where the addition of edges and/or vertices is no longer independent of other edges and/or vertices—has been motivated by the quest to find discontinuous percolation transitions. The leader in this proliferation is what is known as explosive percolation. A recent proof demonstrates that a large class of explosive percolation-type models does not, in fact, exhibit a discontinuous transition [Riordan and Warnke, Science, 333, 322 (2011)]. Here, we discuss two lesser known correlated percolation models—the $k\ge 3$-core model on random graphs and the counter-balance model in two-dimensions—both exhibiting discontinuous transitions. To search for tricriticality, we construct mixtures of these models with other percolation models exhibiting the more typical continuous transition. Using a powerful rate equation approach, we demonstrate that a mixture of $k=2$-core and $k=3$-core vertices on the random graph exhibits a tricritical point. However, for a mixture of $k$-core and counter-balance vertices in two dimensions, as the fraction of counter-balance vertices is increased, numerics and heuristic arguments suggest that there is a line of continuous transitions with the line ending at a discontinuous transition, i.e., when all vertices are counter-balanced. Interestingly, these heuristic arguments may help identify the ingredients needed for a discontinuous transition in low dimensions. In addition, our results may have potential implications for glassy and jamming systems.

In this work we investigate the late-time steady states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is nonvanishing or equivalently if the relaxation time scales are finite. Using a variety of nonequilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system $=$ system+environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multitime correlations of the open system evolve towards those of the closed system thermal state. Multitime correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.

The Asymmetric Inclusion Process (ASIP) is a unidirectional lattice-gas flow model which was recently introduced as an exactly solvable ‘Bosonic’ counterpart of the ‘Fermionic’ asymmetric exclusion process. An iterative algorithm that allows the computation of the probability generating function (PGF) of the ASIP's steady state exists but practical considerations limit its applicability to small ASIP lattices. Large lattices, on the other hand, have been studied primarily via Monte Carlo simulations and were shown to display a wide spectrum of intriguing statistical phenomena. In this paper we bypass the need for direct computation of the PGF and explore the ASIP's asymptotic statistical behavior. We consider three different limiting regimes: heavy-traffic regime, large-system regime, and balanced-system regime. In each of these regimes we obtain—analytically and in closed form—stochastic limit laws for five key ASIP observables: traversal time, overall load, busy period, first occupied site, and draining time. The results obtained yield a detailed limit-laws perspective of the ASIP, numerical simulations demonstrate the applicability of these laws as useful approximations.

We introduce a homogeneous pair approximation to the naming game (NG) model by deriving a six-dimensional Open Dynamics Engine (ODE) for the two-word naming game. Our ODE reveals the change in dynamical behavior of the naming game as a function of the average degree $\langle k\rangle$ of an uncorrelated network. This result is in good agreement with the numerical results. We also analyze the extended NG model that allows for presence of committed nodes and show that there is a shift of the tipping point for social consensus in sparse networks.

We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this “cage-like” dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Nontrivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the “de-caging time” obtained from the study of deviations from Gaussian behavior. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics.

A transition in hydraulically induced granular displacement patterns is studied by means of discrete numerical molecular dynamics simulations. During this transition the patterns change from fractures and fingers to finely dispersed bubbles. The dynamics of the displacement patterns are studied in a rectangular Hele-Shaw cell filled with a dense but permeable two-dimensional granular layer. At one side of the cell the pressure of the compressible interstitial gas is increased. At the opposite side from the inlet of the cell a semipermeable boundary is located. This boundary is only permeable towards the gas phase while preventing grains from leaving the cell. The imposed pressure gradient compacts the grains. In the process we can identify and describe a mechanism that controls the transition of the emerging displacement patterns from fractures and fingers to finely dispersed bubbles as a function of the interstitial gas's properties and the characteristics of the granular phase.

This study experimentally investigates the influence of intruder surface roughness in the Brazil nut effect in a quasi-two-dimensional vertical vibration granular bed. The intruder dynamics are determined using a particle-tracking method. The results show that surface roughness has a crucial role in the intruder rise dynamics; a rougher intruder has more difficulty rising in the bed because of higher kinetic energy dissipation. This study determined that penetration length and drag length are reduced and drag is enhanced as intruder surface roughness increases. The exponential decay of the penetration length with vibration frequency is shown. The results also show that at higher dimensionless vibration acceleration and lower vibration frequency the variation in rise time between smooth and rough intruders is negligible.

We study numerically the influence of confinement on the solid fraction and on the structure of three-dimensional random close-packed granular materials subject to gravity. The effects of grain shape (spherical or polyhedral), material polydispersity, and confining wall friction on this dependence are investigated. In agreement with a simple geometrical model, the solid fraction is found to decrease linearly for increasing confinement no matter the grain shape. Furthermore, this decrease remains valid for bidisperse sphere packings, although the gradient seems to reduce significantly when the proportion of small particles reaches $40\%$ by volume. The confinement effect on the coordination number is also captured by an extension of the aforementioned model.

Periodic flow inversions have been shown as an effective means to eliminate both density (D system) and size (S system) segregation. The frequency of these inversions, however, is the key to applying this technique and is directly related to the inverse of the characteristic time of segregation. In this work, we study size segregation (S system) and adapt a size segregation model to compliment existing work on density segregation and, ultimately, aid in determining the critical forcing frequency for S systems. We determine the impact on mixing and segregation of both the binary size ratio and the length of each leg of a “zigzag chute”. Mixing is observed when $L<\overline{U}{t}_S$, where $L$, $\overline{U}$, and $t_S$ denote the length of each leg of the zigzag chute, the average streamwise flow velocity of the particle, and the characteristic time of segregation, respectively.