Transport in heterogeneous media can be described by partial differential equations, which exhibit convolutions with time and/or space memory kernels. In this work, we characterize the full time spectrum of time-memory kernels by applying a nonparametric inversion algorithm to macroscopic synthetic data for heterogeneous porous media, Our findings put into evidence the inherent nonuniqueness of the transport parameters for nonlocal transport models. Notably, we find that the Péclet number can be interpreted as an ancillary parameter of a family of probability distribution functions that characterizes the memory kernels of transport.

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e., when the population is not synchronous. This demonstration is facilitated by the construction of a nonequilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in $1∕N$, where $N$ is the number of oscillators. The $N\to \infty$ limit of this theory is what is traditionally called mean field theory for the Kuramoto model.

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modeled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating superradiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section, and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and the degree of chaos inside the system.

Motivated by recent experimental results on model binary colloidal mixtures, especially for the glass transition, we investigate the phase diagram of two models of asymmetric binary mixtures: the hard sphere and the Asakura-Oosawa mixtures. This includes the binodals and the glass transition line, computed in the effective one-component representation using the corresponding potentials of mean force at infinite dilution. The reference hypernetted chain approximation is used for computing the static properties and the glass transition line is computed in the mode coupling approximation. The similarities and the differences between the two models are discussed for different size ratios. It is shown that while both models follow a universal behavior at large asymmetry, the hard sphere mixture model leads to more original results at moderate size ratio. These results show that a modeling beyond generic effective potentials might be necessary for an appropriate description of the complete phase diagram.

We study the dynamics of oscillators that are mutually coupled via dissimilar (or “conjugate”) variables and find that this form of coupling leads to a regime of amplitude death. Analytic estimates are obtained for coupled Landau-Stuart oscillators, and this is supplemented by numerics for this system as well as for coupled Lorenz oscillators. Time delay does not appear to be necessary to cause amplitude death when conjugate variables are employed in coupling identical systems. Coupled chaotic oscillators also show multistability prior to amplitude death, and the basins of the coexisting attractors appear to be riddled. This behavior is quantified: an appropriately defined uncertainty exponent in the coupled Lorenz system is shown to be zero.

A mapping called a connectivity graph is proposed to visualize the complicated networks between local minima via saddles on many-dimensional potential energy surfaces. With this mapping, the effect of the topography of a complex potential energy surface on the dynamics is studied in model funnel potentials and a Lennard-Jones cluster. We present strong evidence that energetically expensive but dynamically relevant saddles are indispensable for kinetic dynamics. The results show that the connectivity graphs provide a sound basis for understanding nonequilibrium dynamics.

An analytical fluid model is proposed for the generation of strong quasistatic magnetic fields during normal incidence of a short ultraintense Gaussian laser pulse with a finite spot size on an overdense plasma. The steepening of the electron density profile in the originally homogeneous overdense plasma and the formation of electron cavitation as the electrons are pushed inward by the laser are included self-consistently. It is shown that the appearance of the cavitation plays an important role in the generation of quasistatic magnetic fields: the strong plasma inhomogeneities caused by the formation of the electron cavitation lead to the generation of a strong axial quasistatic magnetic field $B_z$. In the overdense regime, the generated quasistatic magnetic field increases with increasing laser intensity, while it decreases with increasing plasma density. It is also found that, in a moderately overdense plasma, highly intense laser pulses can generate magnetic fields $\sim 100\text{MG}$ and greater due to the transverse linear mode conversion process.

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When the nonlinearity is of the cubic type, this amplitude is shown to be nonzero for all velocities and therefore small-amplitude solitons moving without emitting radiation do not exist. In the case of a saturable nonlinearity, on the other hand, the radiation is found to be completely suppressed when the soliton moves at one of certain isolated “sliding velocities.” We show that a discrete soliton moving at a general speed will experience radiative deceleration until it either stops and remains pinned to the lattice or—in the saturable case—locks, metastably, onto one of the sliding velocities. When the soliton’s amplitude is small, however, this deceleration is extremely slow; hence, despite losing energy to radiation, the discrete soliton may spend an exponentially long time traveling with virtually unchanged amplitude and speed.

The ${\varphi }^4$ scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.

This paper gives sufficient conditions for the output of $1∕{\omega }^{\alpha }$ noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the $1∕{\omega }^{\alpha }$ condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of $1∕\omega$ noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct $1∕{\omega }^{\alpha }$ noise which also has a long memory.

We investigate heat transport in a spin-$\frac{1}{2}$ Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate quantum master equations. The standard microscopic derivation of the weak-coupling Lindblad equation in the secular approximation is considered, and shown to be inadequate for the description of stationary nonequilibrium properties like a nonvanishing energy current. Furthermore, we derive an alternative master equation that is capable of describing a stationary energy current and, at the same time, leads to a completely positive dynamical map. This paves the way for efficient numerical investigations of heat transport in larger systems based on Monte Carlo wave function techniques.

We consider the analytical investigation of the heat current in the steady state of the quantum harmonic chain of oscillators with alternate masses and self-consistent reservoirs. We analyze the thermal conductivity $\kappa$ and obtain interesting properties: in the high temperature regime, where quantum and classical descriptions coincide, $\kappa$ does not change with temperature, but it is quite sensitive to the difference between the alternate masses; and contrasting with this behavior, in the low temperature regime, $\kappa$ becomes an explicit function of the temperature, but its dependence on the masses difference disappears. Our results reinforce the message that quantum effects cannot be neglected in the study of heat conduction in low temperatures.

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a distance $L$. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behavior characterized by a nonuniversal exponent which depends on the ratio of the system size to a dynamic length scale.

We report the results of a combined phenomenological analysis of the data from positron-annihilation-lifetime spectroscopy (PALS) and the relaxation data from broadband dielectric spectroscopy (BDS) on diethyl phthalate (DEP). The ortho-positronium ($o$-Ps) lifetime, ${\tau }_3$, as a function of temperature over a temperature range from $67\mathrm{K}$ up to $300\mathrm{K}$ is compared with the spectral features and the relaxation parameters of the BDS spectra decomposed into the primary $\alpha$ and the secondary $\beta$ processes in the temperature range from $140\mathrm{K}$ up to $380\mathrm{K}$ by using the Williams-Watts scheme. Phenomenological model-free analysis of the ${\tau }_3\text{−}T$ plot provides the three characteristic PALS temperatures, where the two most pronounced ones at $T_g^{\mathrm{PALS}}=185\mathrm{K}$ and $T_{b2}=245\mathrm{K}=1.32T_g^{\mathrm{PALS}}$ are related to the glass-liquid transition and the onset of a quasiplateau region, respectively. In the case of a weaker bend effect at $T_{b1}=210\mathrm{K}=1.14T_g^{\mathrm{PALS}}$, a number of new coincidences with changes in the dielectric $\beta$ process have been found. They concern the changes in width parameter of the distribution function for the $\beta$ relaxation time and the activation energy of the ${\beta }_{\mathrm{eff}}$ process, a crossover from the Arrhenius to the non-Arrhenius type of temperature dependence as well as with the onset of a short-time tail of the $\beta$ relaxation time distribution and finally, with changes in the relaxation strength of the $\alpha$ and ${\beta }_{\mathrm{eff}}$ processes. All these findings indicate a close connection of the $o$-Ps annihilation parameters and relaxation characteristics of BDS response for the DEP matrix.

Magnetic elastica with spontaneous magnetization and superparamagnetic properties are considered. Obtained solutions illustrate the characteristic transformations of their shapes as spontaneous magnetization increases. Solutions are selected on the basis of the stability analysis and results of numerical simulations. A different mechanism of the magnetic relaxation in suspension of ferromagnetic filaments by migration of a loop with antiparallel to the field magnetization is predicted.

The recent development of DNA structure, brought by the elastic rod model, revives the study of the so-called Michell-Zajac instability for isotropic naturally straight elastic rings. The instability states that when subjected to a terminal twist, a manipulation which cuts, rotates, and then seals closed rods, an elastic ring does not writhe until the amount of rotation exceeds a rod-dependent threshold. From the data generated by a finite element method, Bauer, Lund, and White [Proc. Natl. Acad. Sci. USA. 90, 833 (1993)] concluded that the instability becomes extreme for isotropic naturally singly bent, doubly bent, and $O$-ring elastic rings since they writhe immediately as subject to a terminal twist. This paper continues their study for other closed rods. In order to understand DNA structure in DNA-protein interactions, this paper also extends the study to open rods with clamped ends; for such rods, a terminal twist is a manipulation which releases, rotates, and then reclamps one end of the rods. Moreover, the rods under consideration need not be isotropic or may violate Kirchhoff-Clebsch conservation law of total energy. By linearizing the Euler-Lagrange equations which govern equilibrium rods and analyzing the linearized equations, this paper establishes an inequality such that if the initial values of the bending curvatures, their first derivatives, and the twisting density of an equilibrium rod satisfy the inequality, the rod axis deforms immediately as the rod is subject to a terminal twist. Since the initial data dissatisfying the inequality form a hypersurface in the five-dimensional Euclidean space, this paper asserts that a terminal twist makes the axis deformed instantly for almost every equilibrium rod.

Icosahedral shells undergo a buckling transition as the ratio of Young’s modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transition. We define elastic susceptibilities as the response to forces applied at vertices, edges, and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order, and other shell-like structures with icosahedral symmetry.

We propose two-layer architecture of associative memory oscillatory network with directional interlayer connectivity. The network is capable to store information in the form of phase-locked (in-phase and antiphase) oscillatory patterns. The first (input) layer takes an input pattern to be recognized and their units are unidirectionally connected with all units of the second (control) layer. The connection strengths are weighted using the Hebbian rule. The output (retrieved) patterns appear as forced-phase locked states of the control layer. The conditions are found and analytically expressed for pattern retrieval in response on incoming stimulus. It is shown that the system is capable to recover patterns with a certain level of distortions or noises in their profiles. The architecture is implemented with the Kuramoto phase model and using synaptically coupled neural oscillators with spikes. It is found that the spiking model is capable to retrieve patterns using the spiking phase that translates memorized patterns into the spiking phase shifts at different time scales.

A method is proposed to stop the cascade of partial coalescences of a droplet laid on a liquid bath. The strategy consists of vibrating the bath in the vertical direction in order to keep small droplets bouncing. Since large droplets are not able to bounce, they partially coalesce until they reach a critical size. The system behaves as a low pass filter: droplets smaller than the critical size are selected. This size has been investigated as a function of the acceleration and the frequency of the bath vibration. Results suggest that the limit size for bouncing is related to the first mode of the droplet deformation.