Most previous studies on spreading dynamics on complex networks are based on the assumption that a node can transmit infection to any of its neighbors with equal probability. In realistic situations, an infected node can preferentially select a targeted node and vice versa. We develop a first-order correction to the standard mean-field theory to address this type of more realistic spreading dynamics on complex networks. Our analysis reveals that, when small-degree nodes are selected more frequently as targets, infection can spread to a larger part of the network. However, when a small set of hub nodes dominates the dynamics, spreading can be severely suppressed. Our analysis yields more accurate predictions for the spreading dynamics than those from the standard mean-field approach.

The coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback. For the case of a weakly nonlinear oscillator, we discuss the validity of a previously determined phase equation. For the case of a strongly nonlinear oscillator, we derive a phase equation and analyze its bifurcation diagram. Our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback.

The development of immiscible viscous fingering patterns in a rotating Hele-Shaw cell is investigated. We focus on understanding how the time evolution and the resulting morphologies are affected by the action of the Coriolis force. The problem is approached analytically and numerically by employing a vortex sheet formalism. The vortex sheet strength and a linear dispersion relation are derived analytically, revealing that the most relevant Coriolis force contribution comes from the normal component of the averaged interfacial velocity. It is shown that this normal velocity, uniquely due to the presence of the Coriolis force, is responsible for the complex-valued nature of the linear dispersion relation making the linear phases vary with time. Fully nonlinear stages are studied through intensive numerical simulations. A suggestive interplay between inertial and viscous effects is found, which modifies the dynamics, leading to different pattern-forming structures. The inertial Coriolis contribution plays a characteristic role: it generates a phase drift by deviating the fingers in the sense opposite to the actual rotation of the cell. However, the direction and intensity of finger bending is predominantly determined by viscous effects, being sensitive to changes in the magnitude and sign of the viscosity contrast. The finger competition behavior at advanced time stages is also discussed.

We present molecular-dynamics calculations of the shear viscosity of three-dimensional strongly coupled Yukawa liquids which are frequently used as a model system of complex plasmas. The results obtained using two independent nonequilibrium simulation methods are critically compared with each other and with earlier published data for a wide range of plasma coupling $\left(\Gamma \right)$ and screening $\left(\kappa \right)$ parameters. The non-Newtonian behavior of the liquid, manifested as a descrease of the shear viscosity with increasing shear rate (shear thinning), and the validity of the Stokes-Einstein relation at high coupling strength are also demonstrated.

The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa systems are investigated by molecular dynamics simulations. Using both the asymptotic behavior of the mean-squared displacement of the particles and the long-time tail of the velocity autocorrelation function as indicators of superdiffusion, we confirm the existence of a transition from normal diffusion to superdiffusion in systems changing from a three-dimensional to a two-dimensional character. A connection between superdiffusion and dimensionality is established by the behavior of the projected pair distribution function.

We present experimental and numerical studies of the properties of a capacitively coupled $13.56\mathrm{MHz}$ discharge in a mixture of Ar and ${\mathrm{C}}_2{\mathrm{H}}_2$ with growing nanosize particles. It is found that at the initial stage of the growth, nanoparticles are accumulated near the sheath-plasma boundaries, where the ionization by electrons is maximal. The nanoparticles suppress the ionization due to the absorbing fast electrons and stimulate a quick change of the plasma parameters followed by a transition between different modes of discharge operation. At that moment the peaked distribution of the dust particles transforms into a flat one.

Accurate evaluation of damping in laterally oscillating microstructures is challenging due to the complex flow behavior. In addition, device fabrication techniques and surface properties will have an important effect on the flow characteristics. Although kinetic approaches such as the direct simulation Monte Carlo (DSMC) method and directly solving the Boltzmann equation can address these challenges, they are beyond the reach of current computer technology for large scale simulation. As the continuum Navier-Stokes equations become invalid for nonequilibrium flows, we take advantage of the computationally efficient lattice Boltzmann method to investigate nonequilibrium oscillating flows. We have analyzed the effects of the Stokes number, Knudsen number, and tangential momentum accommodation coefficient for oscillating Couette flow and Stokes’ second problem. Our results are in excellent agreement with DSMC data for Knudsen numbers up to $\mathrm{Kn}=\mathcal{O}\left(1\right)$ and show good agreement for Knudsen numbers as large as 2.5. In addition to increasing the Stokes number, we demonstrate that increasing the Knudsen number or decreasing the accommodation coefficient can also expedite the breakdown of symmetry for oscillating Couette flow. This results in an earlier transition from quasisteady to unsteady flow. Our paper also highlights the deviation in velocity slip between Stokes’ second problem and the confined Couette case.

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau–de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase, and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic-nematic interface, illustrate the anisotropic character of droplets in the nucleation regime, and validate dynamical scaling in the coarsening regime.

In a range of physical systems, the first instability in Rayleigh-Bérnard convection between nearly thermally insulating horizontal plates is large scale. This holds for thermal convection of fluids saturating porous media. Large-scale thermal convection in a horizontal layer is governed by remarkably similar equations both in the presence of a porous matrix and without it, with only one additional term for the latter case, which, however, vanishes under certain conditions (e.g., two-dimensional flows or infinite Prandtl number). We provide a rigorous derivation of long-wavelength equations for a porous layer with inhomogeneous heating and possible pumping.

Consideration of the Lifshitz expression for the Casimir free energy on the real frequency axis rather than the imaginary Matsubara frequencies as is customary sheds light on the ongoing debate regarding the thermodynamical consistency of this theory in combination with common permittivity models. It is argued that when permittivity is temperature independent over a temperature interval including zero temperature, a cavity made of causal material with continuous dispersion properties separated by vacuum cannot violate Nernst’s theorem (the third law of thermodynamics). The purported violation of this theorem pertains to divergencies in the double limit in which frequency and temperature vanish simultaneously. While any model should abide by the laws of thermodynamics within its range of applicability, we emphasize that the Nernst heat theorem is a relevant criterion for choosing among candidate theories only when these theories are fully applicable at zero temperature and frequency.

Exact expressions for first- and higher-order residence time statistics, count statistics, and spectral properties of a bistable system driven by dichotomous colored noise are put forward and discussed. The employed method is based on a discrete kinetic scheme and is valid for a wide range of parameter values of the colored noise. This permits a detailed analysis of the effects of noise correlations for arbitrary correlation times. It is found that at a characteristic correlation time of the dichotomous noise, the residence time sequence becomes Poissonian; in particular, all correlations between residence times disappear. We also find that correlations become strongest for a finite strength of the driving force. The analytical results can also be used to infer the underlying driving parameters in the case of noise with long-range temporal correlations.

We calculate exactly the first cumulants of the integrated current and of the activity (which is the total number of changes of configurations) of the symmetric simple exclusion process on a ring with periodic boundary conditions. Our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form, with the same scaling function for both quantities. This scaling function can be understood either by an analysis of Bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim.

A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.

We explore the equilibrium mechanics of a binary lipid membrane that wraps around a spherical or cylindrical particle. One of the lipid membrane components induces a positive spontaneous curvature, while the other induces a negative local curvature. Using a Hamiltonian approach, we derive the equations governing the membrane shape and lipid concentrations near the wrapped object. Asymptotic expressions and numerical solutions for membrane shapes are presented. We determine the regimes of bending rigidity, surface tension, intrinsic lipid curvature, and effective receptor binding energies that lead to efficient wrapping and endocytosis. Our model is directly applicable to the study of invagination of clathrin-coated pits and receptor-induced wrapping of colloids such as spherical virus particles.

The temperature equilibration rate between electrons and protons in dense hydrogen has been calculated with molecular dynamics simulations for temperatures between 10 and $600\mathrm{eV}$ and densities between ${10}^{20}{\mathrm{cm}}^{-3}\text{to}{10}^{24}{\mathrm{cm}}^{-3}$. Careful attention has been devoted to convergence of the simulations, including the role of semiclassical potentials. We find that for Coulomb logarithms $\mathcal{L}\gtrsim 1$, a model by Gericke-Murillo-Schlanges (GMS) [D. O. Gericke et al., Phys. Rev. E 65, 036418 (2002)] based on a $T$-matrix method and the approach by Brown-Preston-Singleton [L. S. Brown et al., Phys. Rep. 410, 237 (2005)] agrees with the simulation data to within the error bars of the simulation. For smaller Coulomb logarithms, the GMS model is consistent with the simulation results. Landau-Spitzer models are consistent with the simulation data for $\mathcal{L}>4$.

We use Green’s function molecular dynamics to evaluate the effectiveness of asperity models when describing the contact mechanics of elastic solids with self-affine surfaces. Surfaces are created with the help of a Fourier filtering algorithm, and the interactions between the solids are modeled via hard-wall potentials. We illustrate how the real area of contact $A_{\text{real}}$ is formed by a set of contact clusters. Two different regimes are identified when the normal force per cluster $L_c$ is plotted as a function of its area $A_c$. Small clusters satisfy a Hertzian-type law $L_c\sim A_c^{3∕2}$, while large clusters display a linear $L_c\sim A_c$ behavior. It is shown how the area $A_c^{*}$, where the crossover between the two regimes takes place, depends only on the roughness at the smallest length scale if the longitudinal dimension of the surface remains unaltered. Moreover, our results display a distribution of cluster sizes $P\left(A_c\right)$ remaining nearly constant for areas smaller than $A_c^{*}$, while showing power law decay above such a critical value. Furthermore, we found the heights of the contacting atoms to be normally distributed with width inversely proportional to the surface roughness.

We consider two mutually coupled oscillators, where we have independent control over the magnitude, sign, and delay of the coupling signal. For appropriate tuning of the coupling constants, there is a coupling-induced resonance where the amplitude becomes large. We investigate the role of nonlinear dissipation and amplitude-dependent frequency correction on the coupling resonance. With delayed coupling, we track the deformation of the resonant bifurcation equation through imperfect bifurcations and the generation of isolas, which generate intervals of multistability between oscillations of different amplitudes. The resonance should be observable in coupled-oscillator systems, where the amplitude remains an important dynamical variable, but not in limit-cycle oscillators modeled by phase-only descriptions.

We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather “turbulent” system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. The Newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin—its backbone consists of several Smale horseshoe repellers, well approximated by intrinsic local one-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.

Optical Tamm states, a kind of interface modes, are also called Tamm plasmon-polaritons. They are experimentally observed in photonic heterostructures based on microstrip transmission lines. The position of optical Tamm states can be designed exactly under effective impedance match and effective phase shift match conditions. Our results show that the photonic band gaps can have the effect of negative-permittivity or negative-permeability media in constructing the interface modes. The simulations and experimental results agree with each other quite well.

When new composite optical materials are developed experimentally or studied in numerical simulations, it is essential to have a set of fundamental constraints that the optical constants of such materials must satisfy. In this paper I argue that positivity of the imaginary part of the magnetic permeability may not be one of such constraints, particularly in naturally occurring diamagnetics and in artificial materials that exhibit diamagnetic response to low-frequency or static magnetic fields.