We consider the evolution of sessile droplets of a nonvolatile perfectly wetting liquid on differentially radially heated solid substrates. The heating induces thermocapillary Marangoni forces that affect the contact line dynamics. Our experiments involving a particular heating pattern reveal that the Marangoni effect suppresses the spreading of a drop, typical for perfectly wetting liquids. The result is a rather slow receding motion and a distinctive thinning of the liquid layer in the region close to the contact line. Our theoretical model, based on the lubrication approximation and incorporating the Marangoni effect, recovers the main features observed in the experiments, and in addition predicts novel features that are still to be observed.

Collective response of DNA to terahertz electric fields is studied in a simple pair bond model. We confirm, with some caveats, a previous observation of destabilizing DNA breather modes and explore the parameter dependence of these modes. It is shown that breather modes are eliminated under reasonable physical conditions and that thermal effects are significant.

Supernormal conduction (SNC) in excitable cardiac tissue refers to an increase of pulse (or action potential) velocity with decreasing distance to the preceding pulse. Here we employ a simple ionic model to study the effect of SNC on the propagation of action potentials (APs) and the phenomenology of alternans in excitable cardiac tissue. We use bifurcation analysis and simulations to study attraction between propagating APs caused by SNC that leads to AP pairs and bunching. It is shown that SNC stabilizes concordant alternans in arbitrarily long paced one-dimensional cables. As a consequence, spiral waves in two-dimensional tissue simulations exhibit straight nodal lines for SNC in contrast to spiraling ones in the case of normal conduction.

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems—e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent that it is interpreted as a damped harmonic oscillator at finite temperature—such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects of finite sampling rate and sampling time for these models as well.

In this work the renormalized jellium model of colloidal suspensions, originally proposed by Trizac and Levin [Phys. Rev. E 69, 031403 (2004)], is extended to study mechanisms of charge renormalization in binary mixtures of charged colloids. We here apply our recent reformulation that introduces the requirement of self-consistency directly into the Poisson-Boltzmann equation, i.e., the background charge is explicitly replaced by the effective one, thus facilitating the whole charge renormalization scheme. We briefly discuss the reformulated model for monodisperse charged suspensions composed of either spheres or rods. In particular, we put emphasis on the effects of the surface charge variation, mixture composition, and particle size on the charge regulation of charge-stabilized colloidal suspensions.

Fast electron generation in the presence of coronal plasma in front of a solid target (typically referred to as preformed plasma) in laser-matter interaction in the intensity range of 10${}^{19}$–10${}^{21}$ W/cm${}^2$ is studied in a one-dimensional slab approximation with particle-in-cell (PIC) simulations. Three different preformed plasma density scale lengths of 1, 5, and 15 μm are considered. We report an increase in both mean and maximum energy of generated fast electrons with an increase in the preformed plasma scale length (in the range 1–15 μm). The heating of plasma electrons is predominantly due to their stochastic motion in counterpropagating electromagnetic (EM) waves (incident and reflected waves) and the presence of a longitudinal electric field produced self-consistently inside the preformed plasma. The synergetic effects of this longitudinal electric field and EM waves responsible for the efficient preformed plasma electrons heating are discussed.

For multiscale gas flows, the kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different theoretical frameworks. In particular, it is not easy to recover the nonequilibrium information required by the kinetic method, which is lost by the continuum model at the coupling interface. Therefore, we present a multiscale lattice Boltzmann (LB) method that deploys high-order LB models in highly rarefied flow regions and low-order ones in less rarefied regions. Since this multiscale approach is based on the same theoretical framework, the coupling precess becomes simple. The nonequilibrium information will not be lost at the interface as low-order LB models can also retain this information. The simulation results confirm that the present method can achieve modeling accuracy with reduced computational cost.

The damped Kuramoto-Sivashinsky equation has emerged as a fundamental tool for the understanding of the onset and evolution of secondary instabilities in a wide range of physical phenomena. Most existing studies about this equation deal with its asymptotic states on one-dimensional settings or on periodic square domains. We utilize a large-scale numerical simulation to investigate the asymptotic states of the damped Kuramoto-Sivashinsky equation on annular two-dimensional geometries and three-dimensional domains. To this end, we propose an accurate, efficient, and robust algorithm based on a recently introduced numerical methodology, namely, isogeometric analysis. We compared our two-dimensional results with several experiments of directed percolation on square and annular geometries, and found qualitative agreement.

The relaxation dynamics of a Blume-Capel model with a quenched diluted crystal field is formulated by a method combining the statistical equilibrium theory and the thermodynamics of linear irreversible processes. Using a mean-field approximation for the magnetic Gibbs free-energy production, a generalized force and a current are defined within the irreversible thermodynamics. Next the kinetic equation for the magnetization is obtained within linear response theory. Finally, the temperature dependence of the relaxation time in the neighborhood of the phase-transition points is obtained by solving the kinetic equation of the magnetization. We find that the relaxation time of the order parameter diverges near the critical and multicritical points, which corresponds to the familiar critical slowing down. On the other hand, it displays different behavior at the first-order phase transitions. It has a jump discontinuity at the first-order phase-transition temperatures. Moreover, the $z$ dynamic critical exponent is calculated and compared with the $z$ values obtained for a diverse class of systems, and good agreement is found with our results.

We present an analytical expression for the first return time (FRT) probability density function of a stationary correlated signal. Precisely, we start by considering a stationary discrete-time Ornstein-Uhlenbeck (OU) process with exponential decaying correlation function. The first return time distribution for this process is derived by adopting a well-known formalism typically used in the study of the FRT statistics for nonstationary diffusive processes. Then, by a subordination approach, we treat the case of a stationary process with power-law tail correlation function and diverging correlation time. We numerically test our findings, obtaining in both cases a good agreement with the analytical results. We notice that neither in the standard OU nor in the subordinated case a simple form of waiting time statistics, like stretched-exponential or similar, can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior.

A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in different directions with respect to the orientation of the stripes. Depending on the strength and density of the substrate disorder, we find that there can be pronounced anisotropy in the transport produced by different dynamical flow phases. We also find a disorder-induced “peak effect” similar to that observed for superconducting vortex systems, which is marked by a transition from elastic depinning to a state where the stripe structure fragments or partially disorders at depinning. Under the sudden application of a driving force, we observe pronounced metastability effects similar to those found near the order-disorder transition associated with the peak effect regime for three-dimensional superconducting vortices. The characteristic transient time required for the system to reach a steady state diverges in the region where the flow changes from elastic to disordered. We also find that anisotropy of the flow persists in the presence of thermal disorder when thermally induced particle hopping along the stripes dominates. The thermal effects can wash out the effects of the quenched disorder, leading to a thermally induced stripe state. We map out the dynamical phase diagram for this system, and discuss how our results could be explored in electron liquid crystal systems, type-1.5 superconductors, and pattern-forming colloidal assemblies.

A protein-folding model is proposed at the amino acid level, in which the folding process is divided into two successive stages: the rate-determining step, dominated by the “stochastic interactions”of solvent molecules, and the rapid phase, dominated by the “order interactions”among atoms in polypeptide. The master equation approach is used to investigate the folding kinetics, and an analytical treatment of the master equation yields a simple three-parameter expression for folding time. It is found that both two-state and downhill protein-folding kinetics can be described by a unifying model.

Many systems in nature, society, and technology can be described as networks, where the vertices are the system’s elements, and edges between vertices indicate the interactions between the corresponding elements. Edges may be weighted if the interaction strength is measurable. However, the full network information is often redundant because tools and techniques from network analysis do not work or become very inefficient if the network is too dense, and some weights may just reflect measurement errors and need to be be discarded. Moreover, since weight distributions in many complex weighted networks are broad, most of the weight is concentrated among a small fraction of all edges. It is then crucial to properly detect relevant edges. Simple thresholding would leave only the largest weights, disrupting the multiscale structure of the system, which is at the basis of the structure of complex networks and ought to be kept. In this paper we propose a weight-filtering technique based on a global null model [Global Statistical Significance (GloSS) filter], keeping both the weight distribution and the full topological structure of the network. The method correctly quantifies the statistical significance of weights assigned independently to the edges from a given distribution. Applications to real networks reveal that the GloSS filter is indeed able to identify relevant connections between vertices.

In systems exhibiting transient chaos in coexistence with periodic attractors, the inclusion of weak noise might give rise to noise-induced chaotic attractors. When the noise amplitude exceeds a critical value, an extended attractor appears along the fractal unstable manifold of the underlying nonattracting chaotic set. A further increase of noise leads to a fuzzy nonfractal pattern. By means of the concept of snapshot attractors and random maps, we point out that the fuzzy pattern can be decomposed into well-defined fractal components, the snapshot attractors belonging to a given realization of the noise and generated by following an ensemble of noisy trajectories. The pattern of the snapshot attractor and its characteristic numbers, such as the finite time Lyapunov exponents and numerically evaluated fractal dimensions, change continuously in time. We find that this temporal fluctuation is a robust property of the system which hardly changes with increasing ensemble size. The validity of the Kaplan-Yorke formula is also investigated. A superposition of about 100 snapshot attractors provides a good approximant to the fuzzy noise-induced attractor at the same noise strength.

We propose a methodology for swimming at low-Reynolds-number flows based on ciliary motion of a microswimmer using magnetic actuation of artificial cilia. By solving the coupled magnetic-elastic-hydrodynamic problem, we demonstrate nonreciprocal effective and recovery strokes for cilia that nicely mimic natural cilia beating. Cilia drag forces, microswimmer net displacement, velocity, and efficiency are calculated, and we show the model can swim using a prespecified magnetic actuation. The proposed methodology can be used for devising biomedical microdevices that swim in viscous flows inside the human body.

The quantum linear response of a dielectric to an external electric field yields expressions for the dielectric susceptibility and the associated impulse response function. These are measured properties that, during analysis, are often “curve-fitted” to diverse forms of parametric functional forms that shall herein be referred to as fit-functions. The main purpose of this paper is to show, from a very general linear response formalism that encompasses virtually all microscopic models of dielectric response, that there are constraints on the forms that the susceptibilities must obey and to examine common parametrizations of the dielectric function in light of these constraints. Naturally these constraints should, whenever possible, be in-built into the fit-functions employed. The linear response approach due to Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)], where the cause is considered to be a uniform external field, ${\mathbf{E}}_{\text{ext}}(t)$, is utilized as it affords a much more straightforward interaction term, viz., $-\mathbf{M}·{\mathbf{E}}_{\text{ext}}(t)$, ($\mathbf{M}$ being the system’s total electric dipole moment operator) than would be the case if the mean internal field (or “Maxwell field”) were taken as the cause. It is shown that this implies definite relations between the quasipermittivity, $\zeta (\omega )$, of the Madden-Kivelson approach and the normal permittivity, $\chi (\omega )\equiv \epsilon (\omega )-{\epsilon }_0$. These relations indicate a condition for the divergence of the normal susceptibility, which, arguably, marks the onset of a ferroelectric transition in “sufficiently polar” dielectrics. Finally, some common parametric “fit-function” forms are investigated as to whether they comply with the constraints that the formalism imposes, and examples are given of their associated Cole-Cole plots in typical cases involving one or more relaxation times.

We numerically solve a discretized model of Lévy random walks on a finite one-dimensional domain with a reflection coefficient $r$ and in the presence of sources. At the domain boundaries, the steady-state density profile is nonanalytic. The meniscus exponent $\mu$, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that $\mu =\alpha /2+r(\alpha /2-1)$, where $\alpha$ is the Lévy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain corresponds to a Lévy walk with negative reflection coefficient.

We investigate the properties of crystalline phantom membranes, at the crumpling transition and in the flat phase, using a nonperturbative renormalization group approach. We avoid a derivative expansion of the effective average action and instead analyze the full momentum dependence of the elastic coupling functions. This leads to a more accurate determination of the critical exponents and further yields the full momentum dependence of the correlation functions of the in-plane and out-of-plane fluctuation. The flow equations are solved numerically for $D=2$ dimensional membranes embedded in a $d=3$ dimensional space. Within our approach we find a crumpling transition of second order which is characterized by an anomalous exponent ${\eta }_c\approx 0.63(8)$ and the thermal exponent $\nu \approx 0.69$. Near the crumpling transition the order parameter of the flat phase vanishes with a critical exponent $\beta \approx 0.22$. The flat phase anomalous dimension is ${\eta }_f\approx 0.85$ and the Poisson’s ratio inside the flat phase is found to be ${\sigma }_f\approx -1/3$. At the crumpling transition we find a much larger negative value of the Poisson’s ratio ${\sigma }_c\approx -0.71(5)$. We discuss further in detail the different regimes of the momentum dependent fluctuations, both in the flat phase and in the vicinity of the crumpling transition, and extract the crossover momentum scales which separate them.

We study oil evaporation from oil in water emulsions, whose oil phases are mixtures of two alkanes of different solubilities in water. The aqueous phase is a colloidal clay suspension that exhibits a yield stress, in which the oil droplets are immobilized. A surfactant-free emulsion is thus formed, providing a convenient model system in which the oil transfer solely occurs through the aqueous phase. When the emulsion is left in contact with the atmosphere, oil evaporation results in the formation of a droplet-free region in the emulsion, and that region grows diffusively with time. We show that the transfer of the more soluble alkane is dramatically retarded when the mixture ratio of the less soluble alkane is increased, as a consequence of entropy loss associated with oil demixing. Using a simple transfer model, which captures well the experimental trends, we study the alkane concentrations both within the oil droplets and within the aqueous phase of the emulsion. We report overshoots in the concentration profiles of the less soluble alkane both in the emulsion and in the droplets, and explain their formation using a qualitative argument.

Biological macromolecules expand with increasing temperature and this dynamic expansion is associated with the onset of function. The expansion is typically characterized by the mean square vibrational displacement (MSD), $\langle u^2\rangle$, of specific constituents such as hydrogen within the macromolecules. The $\langle u^2\rangle$ increases with increasing temperature and the slope of $\langle u^2\rangle$ versus temperature can increase significantly at a temperature $T_D$ identified as a dynamical transition. We illustrate that the observed expansion and change in slope of $\langle u^2\rangle$ with temperature at $T_D$ can be reproduced within a simple model of the vibration, an atom in an anharmonic potential, $V(u)$. Given $V(u)$, only the temperature is varied in the model. A simple Gaussian potential or a potential containing a hard wall is particularly effective is reproducing the observed change in the slope of $\langle u^2\rangle$ with temperature around $T_D$.