We analyze the constructive interference of input signals in nonlinear, discrete, two-dimensional media. The media consist of inductor-capacitor lattices with saturating, voltage-dependent capacitors. We find that nonlinearity significantly boosts the ability of such media to generate large-amplitude output signals from small-amplitude inputs. To understand this boosting, we develop a general perturbative method suitable for finding the steady-state solution of a damped $N\times N$ nonlinear lattice that is driven at a single frequency. We verify our theory using extensive numerical simulations.

We show that a consistent modeling of porous flows needs at least one free collision relaxation rate to avoid a nonlinear dependency of the numerical errors on the viscosity. This condition is necessary to get the viscosity-independent permeability from the Stokes flow and to parametrize properly (with nondimensional physical numbers) the lattice Boltzmann Brinkman schemes. The two-relaxation-time (TRT) collision operator controls all coefficients of the higher-order corrections in steady solutions with a specific combination of its two collision rates, a possibility lacking for the Bhatnagar-Gross-Krook (BGK)-based single-relaxation-time schemes. The analysis is based on exact recurrence equations of the evolution equation and illustrated for the exact solutions of the Brinkman scheme in simply oriented parallel and diagonal channels. The apparent viscosity coefficient of the TRT Stokes-Brinkman scheme in arbitrary flow is only approximated. The compatibility of one-dimensional arbitrarily rotated flows with the nonlinear (Navier-Stokes) equilibrium is examined. An explicit dependency for all coefficients on the relaxation rates is presented for the infinite steady state Chapman-Enskog expansion.

We develop a theory of first passage processes in stochastic nonequilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in conjunction with the eikonal approximation. In this way the problem is reduced to finding the optimal path to extinction: a heteroclinic trajectory of an effective multidimensional classical Hamiltonian system. We compute this trajectory and mean extinction time of the disease numerically and uncover a nonmonotone, spiral path to extinction of a disease. We also obtain analytical results close to a bifurcation point, where the problem is described by a Hamiltonian previously identified in one-species population models.

Glasses exist because they are not able to relax in a laboratory time scale toward the most stable structure: a crystal. At the same time, glasses present low-frequency vibrational-mode (LFVM) anomalies. We explore in a systematic way how the number of such modes influences thermal relaxation in one-dimensional models of glasses. The model is a Fermi-Pasta-Ulam chain with nonlinear springs that join second neighbors at random, which mimics the adding of bond constraints in the rigidity theory of glasses. The corresponding number of LFVMs decreases linearly with the concentration of these springs, and thus their effect upon thermal relaxation can be studied in a systematic way. To do so, we performed numerical simulations using lattices that were thermalized and afterwards placed in contact with a zero-temperature bath. The results indicate that the time required for thermal relaxation has two contributions: one depends on the number of LFVMs and the other on the localization of modes due to disorder. By removing LFVMs, relaxation becomes less efficient since the cascade mechanism that transfers energy between modes is stopped. On the other hand, normal-mode localization also increases the time required for relaxation. We prove this last point by comparing periodic and nonperiodic chains that have the same number of LFVMs.

Equilibrium wetting of ethanol onto chemically patterned nanostripes has been investigated using environmental atomic force microscopy (AFM) in noncontact mode. The chemical patterns are composed of COOH-terminated “wetting” regions and ${\text{CH}}_3$-terminated “nonwetting” regions. A specially designed environmental AFM chamber allowed for accurate measurements of droplet height as a function of the temperature offset between the substrate and a macroscopic ethanol reservoir. At saturation, the height dependence scales with droplet width according to $w^{1/2}$, in excellent agreement with the augmented Young equation (AYE) modeled with dispersive, nonretarded surface potentials. At small under- and oversaturations, the AYE model accurately fits the data if an effective $\Delta T$ is used as a fitting parameter. There is a systematic difference between the measured $\Delta T$ and the values extracted from the fits to the data. In addition to static measurements, we present time-resolved measurements of the droplet height which enable the study of condensation-evaporation dynamics of nanometer-scale drops.

During the past decade, phase-transition phenomena in the random 3-satisfiability ($3$-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random $3$-SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature $T\to 0$. The reweighting parameter $y$ of the cavity theory is allowed to approach infinity together with the inverse temperature $\beta$ with fixed ratio $r=y∕\beta$. Focusing on the system’s space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling, and we obtain the entropy density $s\left(r\right)$ and complexity $\Sigma \left(r\right)$ of zero-energy clusters at different $r$ values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of $s\left(r\right)$ and $\Sigma \left(r\right)$ with $r$, we can judge whether a certain type of initial condition is appropriate at a given $r$ value. This work complements and confirms the results of several other very recent theoretical studies.

Rapid reaction of a molten metal with an oxide is the key to understanding recently discovered fast reactions in nanothermite composites. We have investigated the thermite reaction of ${\text{Fe}}_2{\text{O}}_3$ with aluminum by molecular dynamics simulations with interatomic forces calculated quantum mechanically in the framework of the density functional theory. A redox reaction to form iron metal and ${\text{Al}}_2{\text{O}}_3$ initiates with the rapid formation of Al-O bonds at the interface within 1 ps, followed by the propagation of the combustion front with a velocity of 70 $\text{m}/\text{s}$ for at least 5 ps at 2000 K. The reaction time for an oxygen atom to change character from ${\text{Fe}}_2{\text{O}}_3$ type to ${\text{Al}}_2{\text{O}}_3$ type at the interface is estimated to be $1.7\pm 0.9\text{ps}$, and bond-overlap population analysis has been used to calculate reaction rates.

We study the growth of fractal clusters in the dielectric breakdown model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent ${\alpha }_{min}$) as a function of the growth exponent $\eta$ of the DBM model. We do not find evidence for a phase transition from fractal to nonfractal growth for a finite $\eta$ value. Simultaneously, we observe that the limit of nonfractal growth $(D\to 1)$ is consistent with ${\alpha }_{min}\to 1∕2$. Finally, using an optimization principle, we give a recipe on how to estimate the effective value of $\eta$ from temporal growth data of fractal aggregates.

The homogenization procedure is applied to the problem of wave propagation in the biphasic mode in porous media saturated with a Newtonian fluid. The local problems corresponding to the solid and fluid phases have been solved separately for complex three-dimensional media. The effective rigidity tensor, some effective coefficients, the dynamic permeability, the celerities, and the attenuation of the three waves are systematically determined. The characteristic length $\Lambda$ was successfully used to gather results for the dynamic permeability as well as for the attenuation coefficients for all media.

Radiation hydrodynamics simulations were used to study the effect of plastic ablators in laser-driven shock experiments. The sensitivity to composition and equation of state was found to be 5%–10% in ablation pressure. As was found for metals, a laser pulse of constant irradiance gave a pressure history which decreased by several percent per nanosecond. The pressure history could be made more constant by adjusting the irradiance history. The impedance mismatch with the sample gave an increase $o\left(100\%\right)$ in the pressure transmitted into the sample, for a reduction of several tens of percent in the duration of the peak load applied to the sample, and structured the release history by adding a release step to a pressure close to the ablation pressure. Algebraic relations were found between the laser pulse duration, the ablator thickness, and the duration of the peak pressure applied to the sample, involving quantities calculated from the equations of state of the ablator and sample using shock dynamics.

In nonideal gas lattice Boltzmann (LB) models, obtaining the correct form of the pressure tensor is essential in determining many of the statistical mechanical properties such as the surface tension and the density profile. Here we outline a general approach for calculating the pressure tensor in LB models with interactions beyond nearest neighbors. The statistical mechanical properties calculated from such a pressure tensor are shown to agree very well with those measured from numerical experiments. Comparisons with alternative theories are also made.

We present a model for a polymer molecule in solution based on smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)]. This method is a thermodynamically consistent version of smoothed particle hydrodynamics able to discretize the Navier-Stokes equations and, at the same time, to incorporate thermal fluctuations according to the fluctuation-dissipation theorem. Within the framework of the method developed for mesoscopic multiphase flows by Hu and Adams [J. Comput. Phys. 213, 844 (2006)], we introduce additional finitely extendable nonlinear elastic interactions between particles that represent the beads of a polymer chain. In order to assess the accuracy of the technique, we analyze the static and dynamic conformational properties of the modeled polymer molecule in solution. Extensive tests of the method for the two-dimensional (2D) case are performed, showing good agreement with the analytical theory. Finally, the effect of confinement on the conformational properties of the polymer molecule is investigated by considering a 2D microchannel with gap $\mathit{H}$ varying between 1 and $10\mu \text{m}$, of the same order as the polymer gyration radius. Several SDPD simulations are performed for different chain lengths corresponding to $N=20–100$ beads, giving a universal behavior of the gyration radius ${\mathit{R}}_{\mathit{G}}$ and polymer stretch $\mathit{X}$ as functions of the channel gap when normalized properly.

We revisit the classic shot noise of Campbell and Schottky—a stochastic process governed by Ornstein-Uhlenbeck dynamics driven by a Poissonian noise. Exploring the order statistics of the shot magnitudes composing its stationary noise level, we show that classic shot noise is intrinsically fractal. This fractality is manifested by $\left(\mathbf{i}\right)$ intrinsic Paretian and scale-invariant structures; $\left(\mathbf{ii}\right)$ an intrinsic power-law scaling; $\left(\mathbf{iii}\right)$ an intrinsic statistical resilience to random power-law perturbations.

We describe a method which allows the treatment of high orders of replica symmetry breaking (RSB) at low temperatures as well as at $T=0$ directly, without a need for approximations or scaling assumptions. It yields the low-temperature order function $q\left(a,T\right)$ in the full range $0\le a<\infty$ and is complete in the sense that all observables can be calculated from it. The behavior of some observables and the finite RSB theory itself is analyzed as the continuous RSB limit is approached. The validity and applicability of the traditional continuous formulation is then scrutinized and a continuous formulation for treating RSB in the Parisi gauge directly at $T=0$ is proposed.

A general Bayesian framework is introduced for the inference of time-varying parameters in nonstationary, nonlinear, stochastic dynamical systems. Its convergence is discussed. The performance of the method is analyzed in the context of detecting signaling in a system of neurons modeled as FitzHugh-Nagumo (FHN) oscillators. It is assumed that only fast action potentials for each oscillator mixed by an unknown measurement matrix can be detected. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) variables of the FHN oscillators, to determine the model parameters, to detect stepwise changes of control parameters for each oscillator, and to follow continuous evolution of the control parameters in the adiabatic limit.

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when they are time-varying is considered in the context of online decoding of physiological information from neuron signaling activity. To model the spiking of neurons, a set of FitzHugh-Nagumo (FHN) oscillators is used. It is assumed that only a fast dynamical variable can be detected for each neuron, and that the monitored signals are mixed by an unknown measurement matrix. The Bayesian framework introduced in paper I (immediately preceding this paper) is applied both for reconstruction of the model parameters and elements of the measurement matrix, and for inference of the time-varying parameters in the nonstationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) slow variables of the FHN oscillators, to learn to model each individual neuron, and to track continuous, random, and stepwise variations of the control parameter for each neuron in real time.

Colloidal model systems have been used for over three decades for investigating liquids, crystals, and glasses. Colloidal crystal superstructures have been observed in binary systems of repulsive spheres as well as oppositely charged sphere systems showing structures well known from atomic solids. In this work we study the structural transition of colloidal crystals under confinement. In addition to the known sequence of crystalline structures, crystal superstructures with dodecagonal and hexagonal symmetry are observed in one component systems. These structures have no atomic counterpart.

The shape of Escherichia coli is approximately that of a cylinder with hemispherical caps. Since its size is not much larger than optical resolution, it has been difficult to quantify deviations from this approximation. We show that one can bypass this limitation and obtain the cell shape with subpixel accuracy. The resulting contours are shown to deviate from the hemisphere-cylinder-hemisphere shape. In particular, the cell is weakly asymmetric. Its two caps are different from each other and the sides are slightly curved. Most cells have convex sides. We discuss our results in light of several mechanisms that are involved in determining the shape of cells.

We investigate the role of fluctuations in single-molecule measurements of torque-link $\left(t\text{-lk}\right)$ curves. For semiflexible polymers of finite persistence length (i.e., polymers with contour length $L$ comparable to the persistence length $L_P$), the torque versus link curve in the constant-torque (isotorque) ensemble is distinct from the one in the constant-link (isolink) ensemble. Thus, one encounters the conceptually interesting issue of a “free energy of transition” in switching ensembles while making torque-link measurements. We predict the dependence on the semiflexibility parameter $\beta =L/L_P$ of this extra contribution to the free energy, which shows up as an area in the torque-link plane. This can be tested against future torque-link experiments with single biopolymers. We bring out the inequivalence of torque-link curves for a stiff polymer and present explicit analytical expressions for the distinct torque-link relations in the two ensembles and the free-energy difference in switching ensembles in this context. The predictions of our work can be tested against single-molecule experiments on torsionally constrained biopolymers.

We present a detailed dynamic light scattering study of the phase separation in the ocular lens emerging during cold cataract development. Cold cataract is a phase separation effect that proceeds via spinodal decomposition of the lens cytoplasm with cooling. The intensity autocorrelation functions of the lens protein content are analyzed with the aid of two methods, providing information on the populations and dynamics of the scattering elements associated with cold cataract. It is found that the temperature dependence of many measurable parameters changes appreciably at the characteristic temperature $\sim 16\pm 1°\text{C}$ which is associated with the onset of cold cataract. By extending the temperature range of this work to previously inaccessible regimes, i.e., well below the phase separation or coexistence curve at $T_{cc}$, we have been able to accurately determine the temperature dependence of the collective and self-diffusion coefficients of proteins near the spinodal. The analysis showed that the dynamics of proteins bears some resemblance to the dynamics of structural glasses, where the apparent activation energy for particle diffusion increases below $T_{cc}$, indicating a highly cooperative motion. Application of ideas developed for studying the critical dynamics of binary protein-solvent mixtures, as well as the use of a modified Arrhenius equation, enabled us to estimate the spinodal temperature $T_{\text{sp}}$ of the lens nucleus. The applicability of dynamic light scattering as a noninvasive, early-diagnostic tool for ocular diseases is also demonstrated in light of the findings of the present paper.