We investigate the stability of an excited domain in a two-component reaction-diffusion system in two dimensions and correct the previous results obtained by one of the authors [L. M. Pismen, Patterns and Interfaces in Dissipative Dynamics (Springer, Berlin, 2006); L. M. Pismen, Phys. Rev. Lett. 86, 548 (2001)].

In this paper we develop a common theoretical framework for the dynamics of thin featureless interfaces. We explicitly demonstrate that the same phase field and velocity dependent one-scale models characterizing the dynamics of relativistic domain walls, in a cosmological context, can also successfully describe, in a friction dominated regime, the dynamics of nonrelativistic interfaces in a wide variety of material systems. We further show that a statistical version of the von Neumann’s law applies in the case of scaling relativistic interface networks, implying that, although relativistic and nonrelativistic interfaces have very different dynamics, a single simulation snapshot is not able to clearly distinguish the two regimes. We highlight that crucial information is contained in the probability distribution function for the number of edges of domains bounded by the interface network and explain why laboratory tests with nonrelativistic interfaces can be used to rule out cosmological domain walls as a significant dark energy source.

A variant of the standard voter model, where a randomly selected site of a one-dimensional lattice ($d=1$) adopts the state of another site placed at a distance $r$ from the previous one, is proposed and studied by means of numerical simulations that are rationalized with the aid of dynamical and finite-size scaling arguments. The distance between the two sites is also selected randomly with a probability given by $P(r)\propto r^{-(d+\sigma )}$, where $\sigma$ is a control parameter. In this way one can study how the introduction of these long-range interactions influences the dynamic behavior of the standard voter model with nearest-neighbor interactions. It is found that the dynamics strongly depends on the range of the interactions, which is parameterized by $\sigma$, leading to an interesting effective multidimensional crossover behavior, as follows. (a) For $\sigma <1$ ordering is no longer observed and the average interface density [$\rho (t)$] assumes a steady state in the thermodynamic limit. Instead, for finite-size systems an exponential decay with a characteristic time ($\tau$) that increases with the size is observed. This behavior resembles the scenario corresponding to the short-range voter model for $d>2$, as well as the case of both scale-free and small-world networks. (b) For $\sigma >1$, an ordering dynamics is observed, such that $\rho (t)\propto t^{-\alpha }$, where the exponent $\alpha$ increases with $\sigma$ until it reaches the value $\alpha =1/2$ for $\sigma ⩾5$, which corresponds to the behavior of the standard voter model with short-range interactions in $d=1$. (c) Finally, for $\sigma \approx 1$ we show evidence of a critical-type behavior as in the case of the critical dimension ($d_c=2$) of the standard voter model.

A light-scattering goniometer for evanescent-wave dynamic light scattering (EWDLS) measurements at a liquid-fluid interface is introduced, and used for measurements on two charge-stabilized polystyrene colloid systems adsorbed to alkane-water interfaces. The goniometer allows an independent variation of the penetration depth and the scattering vector components parallel and perpendicular to a liquid-fluid interface. The possible illumination geometries are compared. Ellipsometry at the liquid-fluid interface is implemented as a complementary tool. In EWDLS measurements, the absence of diffusive motion perpendicular to the interface is demonstrated, which confirms the adsorption of the particles. The two-step decay of the autocorrelation function is interpreted in terms of diffusion within a two-dimensional interface lattice of colloidal particles, stabilized by repulsive electrostatic interactions, and a desorption process. A significant slowing down of the in-plane diffusion of the colloids as compared to the bulk diffusion is observed.

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair-correlation function $g(x)~x^{-a}$. Applying the field-theoretical renormalization group approach in $d$ dimensions, we analyze different scenarios of scaling behavior working to first order of a double $\varepsilon =4-d$, $\delta =4-a$ expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion-controlled reactions in the vicinity of absorbing traps placed on polymers as well as the effective short-distance interaction between star copolymers.

In this Rapid Communication we propose a most general equation to study pattern formation for one-species populations and their limit domains in systems of length $L$. To accomplish this, we include nonlocality in the growth and competition terms, where the integral kernels now depend on characteristic length parameters $\alpha$ and $\beta$. Therefore, we derived a parameter space $(\alpha ,\beta )$ where it is possible to analyze a coexistence curve ${\alpha }^{*}={\alpha }^{*}(\beta )$ that delimits domains for the existence (or absence) of pattern formation in population dynamics systems. We show that this curve is analogous to the coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations.

Silk fibers are semicrystalline nanocomposite protein fibers with an extraordinary mechanical toughness that changes with humidity. Diffusive or overdamped motion on a molecular level is absent in dry silkworm silk, but present in humid silk at ambient temperature. This microscopic diffusion distinctly depends on the externally applied macroscopic tensile force. Quasielastic and inelastic neutron-scattering data as a function of humidity and of tensile strain on humid silk fibers support the model that both the adsorbed water and parts of the amorphous polymers participate in diffusive motion and are affected by the tensile force. It is notable that the quasielastic linewidth of humid silk at 100% relative humidity increases significantly with the applied force. The effect of the tensile force is discussed in terms of an increasing alignment of the polymer chains in the amorphous fraction with increasing tensile stress which changes the geometrical restrictions of the diffusive motions.

In this Brief Report we present an extension of the recent fluid deformation (RFD) closure introduced by Chevillard and Meneveau [L. Chevillard and C. Meneveau, Phys. Rev. Lett. 97, 174501 (2006)] which was developed for modeling the time evolution of Lagrangian fluctuations in incompressible Navier-Stokes turbulence. We apply the RFD closure to study the evolution of magnetic and passive scalar fluctuations. This comparison is especially interesting since the stretching term for the magnetic field and for the gradient of the passive scalar are similar but differ by a sign such that the effect of stretching and compression by the turbulent velocity field is reversed. Probability density functions (PDFs) of magnetic fluctuations and fluctuations of the gradient of the passive scalar obtained from the RFD closure are compared against PDFs obtained from direct numerical simulations.

In the present paper we consider reflection spectra peculiarities of a cholesteric liquid crystal (CLC) cell with two defect layers. We consider both the isotropic and anisotropic defect cases. The problem is solved by Ambartsumian's modified layer addition and Muller's matrix methods. We investigated the influence of the defect layer thicknesses and location changes in the CLC cell on the defect modes and the photonic band gap. In particular, we considered (in detail) the cases when the defect layers are half-wave or quarter-wave plates. We also investigated the influence of dielectric borders on the reflection spectra. We showed that the subject system possesses the property of structural nonreciprocity, and that the system can work as a tunable filter, a mirror, and a low threshold laser. We also showed that the system can work as a light modulator, or as an optical diode, or as a system for getting linearly polarized light with electrically tunable polarization plane rotation, as well as a device for getting linearly polarized light from nonpolarized light, again with electrically tunable polarization plane rotation.

We extended the analysis of a variational theory for nematoacoustics recently proposed by Virga [Phys. Rev. E 80, 031705 (2009)] by allowing the nematic director to vibrate about an average orientation at the frequency of a propagating wave, a periodic motion that we call the director libration. The acoustic susceptibilities, two phenomenological parameters that, in this theory, express the coupling between director and acoustic fields, are estimated along with an extra viscosity coefficient by using available experimental data.

We suggest a governing equation that describes the process of polymer-chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time $t$ after the process has begun, and (ii) a subdiffusive increase of the distribution variance $\Delta (t)$ with elapsed time $\Delta (t)\propto t^{\alpha }$. The latter quantity measures the mean-squared number $s$ of polymer segments that have passed through the pore $\Delta (t)=\langle [s(t)-s(t=0)]{}^2\rangle$, and is known to grow with an anomalous diffusion exponent $\alpha <1$. Our main assumption [i.e., a Gaussian distribution of the translocation velocity $v(t)$] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in $3\text{D}$. We also numerically confirm the predictions made recently that the exponent $\alpha$ changes from $0.91$ to $0.55$ to $0.91$ for short-, intermediate-, and long-time regimes, respectively.

We report a statistical analysis of more than eight thousand songs. Specifically, we investigated the probability distribution of the normalized sound amplitudes. Our findings suggest a universal form of distribution that agrees well with a one-parameter stretched Gaussian. We also argue that this parameter can give information on music complexity, and consequently it helps classify songs as well as music genres. Additionally, we present statistical evidence that correlation aspects of the songs are directly related to the non-Gaussian nature of their sound amplitude distributions.

We investigate the evolution of a light impurity particle in a Lorentz gas where the background atoms are in thermal equilibrium. As in the standard Lorentz gas, we assume that the particle is negligibly light in comparison with the background atoms. The thermal motion of atoms causes the average particle speed to grow. In the case of the hard-sphere particle-atom interaction, the temporal growth is ballistic, while generally it is sublinear. For the particle-atom potential that diverges as $r^{-\lambda }$ in the small separation limit, the average particle speed grows as $t^{\lambda /[2(d-1)+\lambda ]}$ in $d$ dimensions. The particle displacement exhibits a universal growth, linear in time, and the average (thermal) speed of the atoms. Surprisingly, the asymptotic growth is independent of the gas density and the particle-atom interaction. The velocity and position distributions approach universal scaling forms which are non-Gaussian. We determine the velocity distribution in arbitrary dimension and for arbitrary interaction exponent $\lambda$. For the hard-sphere particle-atom interaction, we compute the position distribution and the joint velocity-position distribution.

We study a one-dimensional $\mathit{XX}$ chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in a previous study [M. Žnidarič J. Stat. Mech. (2010) L05002] is extended to arbitrary coupling constants, driving, and a homogeneous magnetic field. All one-, two-, and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not Gaussian. Nevertheless, in the thermodynamic and weak-driving limit it is only weakly correlated and can be described by a matrix product operator ansatz with matrices of fixed dimension $4$. A nonequilibrium phase transition at zero dephasing is also discussed. It is suggested that the scaling of the relaxation time with the system size can serve as a signature of a nonequilibrium phase transition.

In this paper we present a quantum approach to the old problem of temperature fluctuations. We start by observing that according to quantum thermodynamics, fluctuations of intensive parameters like temperature cannot exist. Furthermore, such parameters are not observables, so their estimation has to be done indirectly. The respective temperature estimate based on quantum measurements of the energy is shown to fluctuate according to the well-known formula ${\Delta T}^2=\frac{k_B{T}^2}{C}$, but only within a certain temperature range and if the system is not too small. We also calculate the fourth-order correction term, becoming important at higher temperatures. Finally we illustrate our results with a concrete model of $n$ spins.

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Substrate patterning is shown to be a convenient method to control the adhesion of filaments. The pattern not only permits a control of adhesion, it also leads to an unbinding transition at finite temperatures. The dimensionality of transverse fluctuations controls the continuity of the transition, and in some cases, re-entrant binding is observed as temperature is increased. Unbinding on patterns is found to be easier to observe than unbinding on flat substrates. Finally, experimental conditions under which unbinding could be observable are discussed.

We obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time $t$ and that at $t-\tau$, where $\tau$ is the delay time, is examined. We find that the correlation time diverges at the model’s bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small $\tau$. The correlation time $T$ diverges as $T~a^{-1}$, where $a$ is the control parameter so that $a=0$ is the bifurcation threshold. The small-$\tau$ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time.