Diffusion of particles in confined domains with absorbing spots on the otherwise reflecting boundaries is ubiquitous in nature and technology. Because of nonuniform boundary conditions, the problem of finding the mean first passage time (MFPT) of the particle to one of the spots is extremely complicated. We show how the difficulties can be overcome by means of boundary homogenization when the domain is a circular disk whose boundary contains $n$ nonoverlapping identical absorbing arcs, which may occupy an arbitrary fraction of the boundary. We find the MFPT as a function of the fraction of the boundary occupied by the arcs (i) for $n$ evenly spaced arcs and (ii) for two arcs arbitrarily located on the boundary. As the arc length tends to zero, our approximate solution reduces to the known asymptotic formula for the MFPT rigorously derived in studies devoted of the narrow escape problem.

Phase-2 re-entry is thought to underlie many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. In this paper, we study under which circumstances a region of depolarized tissue can re-excite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. For this purpose, we use a simplified ionic model that reproduces well the ventricular action potential. With the help of this model, we analyze the conditions that lead to very short action potentials (APs), as well as possible mechanisms for re-excitation in a cable. We then study the induction of re-entrant waves (spiral waves) in simulations of AP propagation in the heart ventricles. We show that re-excitation takes place via a slow pulse produced by calcium current that propagates into the region of short APs until it encounters excitable tissue. We calculate analytically the speed of the slow pulse, and also give an estimate of the minimal tissue size necessary for allowing reexcitation to take place.

Patterns of Taylor spirals observed in the counter-rotating Couette-Taylor system are described by complex Ginzburg-Landau equations (CGLE) and have been investigated using spatiotemporal diagrams and complex demodulation technique. We have determined the real coefficients of the CGLE and their variations versus the control parameters, i.e., the rotation frequency of cylinders.

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution ${32768}^2$. By forcing the system at intermediate scales, narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two Kolmogorov laws for structure functions are simultaneously observed. The inverse cascade spectrum is found to be consistent with Kolmogorov-Kraichnan prediction and is robust with respect the presence of an enstrophy flux. The direct cascade is found to be more sensible to finite size effects: the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution.

An algorithm for an adaptive boundary condition for the simulation of fully developed, pressure driven flows using the lattice-Boltzmann method is introduced. The method simulates the effect of the solid walls confining a structure with dual periodicity, such as used in microfluidic devices. We combine a recently introduced boundary condition by Kim and Pitsch [Phys. Fluids 19, 108101 (2007)] for the treatment of pressure driven flows in periodic structures with a controller loop that adjusts a perpendicular pressure gradient to suppress any net momentum perpendicular to the outer walls. The method’s accuracy in asymmetric geometries is tested against a periodic array structure that uses regularized zero-velocity boundary conditions as outer walls.

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.

This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a $d$-dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common—yet arbitrary—motion pattern; each particle has its own random propagation parameters—emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles’ displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles’ underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.

This paper compares results from lattice-Boltzmann and Brownian-dynamics simulations of polymer migration in confined flows bounded by planar walls. We have considered both a uniform shear rate and a constant pressure gradient. Lattice-Boltzmann simulations of the center-of-mass distribution agree quantitatively with Brownian-dynamics results, contradicting previously published results. The mean end-to-end distance of the extended polymer is more sensitive to grid resolution $\Delta x$ and time-step $\Delta t$. Nevertheless, for sufficiently small $\Delta x$ and $\Delta t$, convergent results for the polymer stretch are obtained which agree with Brownian dynamics within statistical uncertainties. The Brownian-dynamics simulations incorporate a mobility matrix for a confined polymer that is both symmetric and positive definite for all physically accessible configurations.

Biological membranes are involved in numerous intriguing biophysical and biological cellular phenomena of different length scales, ranging from nanoscale raft formation, vesiculation, to microscale shape transformations. With extended length and time scales as compared to atomistic simulations, solvent-free coarse-grained membrane models have been exploited in mesoscopic membrane simulations. In this study, we present a one-particle-thick fluid membrane model, where each particle represents a cluster of lipid molecules. The model features an anisotropic interparticle pair potential with the interaction strength weighed by the relative particle orientations. With the anisotropic pair potential, particles can robustly self-assemble into fluid membranes with experimentally relevant bending rigidity. Despite its simple mathematical form, the model is highly tunable. Three potential parameters separately and effectively control diffusivity, bending rigidity, and spontaneous curvature of the model membrane. As demonstrated by selected examples, our model can naturally simulate dynamics of phase separation in multicomponent membranes and the topological change of fluid vesicles.

The effect of foldability on protein’s evolvability is analyzed by a two-prong approach consisting of a self-consistent mean-field theory and Monte Carlo simulations. Theory and simulation models representing protein sequences with binary patterning of amino acid residues compatible with a particular foldability criteria are used. This generalized foldability criterion is derived using the high temperature cumulant expansion approximating the free energy of folding. The effect of cumulative point mutations on these designed proteins is studied under neutral condition. The robustness, protein’s ability to tolerate random point mutations is determined with a selective pressure of stability $\left(\Delta \Delta G\right)$ for the theory designed sequences, which are found to be more robust than that of Monte Carlo and mean-field-biased Monte Carlo generated sequences. The results show that this foldability criterion selects viable protein sequences more effectively compared to the Monte Carlo method, which has a marked effect on how the selective pressure shapes the evolutionary sequence space. These observations may impact de novo sequence design and its applications in protein engineering.

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton’s equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton’s equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the solution, are in favorable agreement with recent near-tip measurements.

A method of synchronization is presented which, unlike existing methods, can, for generic dynamical systems, force all conditional Lyapunov exponents to go to $-\infty$. It also has improved noise immunity compared to existing methods, and unlike most of them it can synchronize hyperchaotic systems with almost any single coupling variable from the drive system. Results are presented for the Rossler hyperchaos system and the Lorenz system.

We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity ${\left|u_l\right|}^{\sigma }{u}_l$ for different values of $\sigma$. We perform extensive numerical simulations where wave packets are evolved (a) without and (b) with dephasing in normal-mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{\alpha }$. The dependence of the numerically computed exponent $\alpha$ on $\sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $\sigma \ge 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos and observe destruction of Anderson localization in the packet tails for small values of $\sigma$.

The time evolution of a thin conducting liquid film flowing down a porous inclined substrate is investigated when an electric field acts normal to the substrate. It is assumed that the flow through the porous medium is governed by Darcy’s law together with Beavers-Joseph condition. Under the assumption of small permeability relative to the thickness of the overlying fluid layer, the flow is decoupled from the filtration flow through the porous medium. A slip condition at the bottom is used to incorporate the effects of the permeability of the substrate. From the set of exact averaged equations derived using integral boundary method for the film thickness and for the flow rate, a nonlinear evolution equation for the film thickness is derived through a long-wave approximation. A linear stability analysis of the base flow is performed and the critical Reynolds number is obtained. The results reveal that the substrate porosity in general destabilizes the liquid film flow and the presence of the electric field enhances this destabilizing effect. A weakly nonlinear stability analysis divulges the existence of supercritical stable and subcritical unstable zones in the wave number/Reynolds number parameter space and the results demonstrate how the neutral curves change as the intensity of the electric filed or the permeability of the porous medium is varied. The numerical solution of the nonlinear evolution equation in a periodic domain reveals that the base flow yields to surface structures that are either time independent waves of permanent form that propagate or time-dependent modes that oscillate slightly in the amplitude. Further, it is observed that the shape and amplitude of long-time waveforms are influenced by the permeability of the porous medium as well as by the applied electric field. The results reveal that the destabilization induced by the electric field in an otherwise stable film over a porous medium is exhibited in the form of traveling waves of finite amplitude. The presence of the porous substrate promotes the oscillatory behavior of the long-time waveform; however, the electric field has a tendency to suppress this oscillatory behavior.

Shear banding in the cetylpyridinium chloride/sodium salicylate micellar system is investigated using electrical conductivity measurements parallel to the velocity and parallel to the vorticity in a cylindrical Couette cell. The measurements show that the conductivity parallel to the velocity (vorticity) increases (decreases) monotonically with applied shear rate. The shear-induced anisotropy is over one order of magnitude lower than the anisotropy of the $N_c$ nematic phase. The steady-state conductivity measurements indicate that the anisotropy of the shear induced low-viscosity (high shear rate) phase is not significantly larger than the anisotropy of the high viscosity (low shear rate) phase. We estimate that the micelles in the shear induced low viscosity band are relatively short, with a characteristic length to diameter ratio of 5–15. The relaxation behavior following the onset of shear is markedly different above and below the first critical value ${\dot{\gamma }}_1$, in agreement with results obtained by other methods. The transient measurements show that the overall anisotropy of the sample decreases as the steady state is approached, i.e., the micellar length/the degree of order decrease.

Dispersion energy of a system out of equilibrium containing two molecules and substrate in different thermostats is calculated taking into account nonlocal optical effects. A resonance increase of energy due to three-body interaction in a system out of equilibrium is shown. In particular, dispersion energy of a two-body subsystem of the three-body system out of equilibrium may be essentially larger than the energy of the same subsystem in equilibrium. A necessary condition of the resonance increase is a closeness of eigenfrequencies of the subsystems composing the whole system. It is shown that different nonlocal reflectivities of surface corresponding to different additional boundary conditions lead to similar results in resonance magnification of dispersion interaction of subsystems in a system out of equilibrium.

The wave-vector dependent shear viscosities for butane and freely jointed chains have been determined. The transverse momentum density and stress autocorrelation functions have been determined by equilibrium molecular dynamics in both atomic and molecular hydrodynamic formalisms. The density, temperature, and chain length dependencies of the reciprocal and real-space viscosity kernels are presented. We find that the density has a major effect on the shape of the kernel. The temperature range and chain lengths considered here have by contrast less impact on the overall normalized shape. Functional forms that fit the wave-vector-dependent kernel data over a large density and wave-vector range have also been tested. Finally, a structural normalization of the kernels in physical space is considered. Overall, the real-space viscosity kernel has a width of roughly 3–6 atomic diameters, which means that generalized hydrodynamics must be applied in predicting the flow properties of molecular fluids on length scales where the strain rate varies sufficiently in the order of these dimensions (e.g., nanofluidic flows).

We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent ${\alpha }_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find ${\alpha }_c=3/2$. Frequency entrainment and phase ordering are discussed as a function of $\alpha \ge 1$. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the $d$-dimensional problem.

We demonstrated very recently [Lenz et al., New J. Phys. 11, 083035 (2009)] that an ensemble of particles in the driven elliptical billiard shows a surprising crossover from subdiffusion to normal diffusion in momentum space. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. In this work, we consider three different driving modes of the elliptical billiard and perform a comprehensive analysis of the corresponding four-dimensional phase space. The composition of this phase space is different in the high-velocity regime compared to the low-velocity regime. We will show, among others, by investigating periodic orbits and probability distributions of laminar phases that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change in the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion.