This work uses Ginzburg-Landau theory derived from a recent structural phase-field-crystal model of binary alloys developed by the authors to study the roles of concentration, temperature, and pressure on the interfacial energy anisotropy of a solid-liquid front. It is found that the main contribution to the change in anisotropy with concentration arises from a change in preferred crystallographic orientation controlled by solute-dependent changes in the two-point density correlation function of a binary alloy, a mechanism that leads to such phenomena as solute-induced elastic strain and dislocation-assisted solute clustering. Our results are consistent with experimental observations in recent studies by Rappaz et al. [J. Fife, P. Di Napoli, and M. Rappaz, Metall. Mater. Trans. A 44, 5522 (2013)]. This is the first PFC work, to our knowledge, to incorporate temperature, pressure, and density into the thermodynamic description of alloys.

Droplet patterns condensing on solid substrates (breath figures) tend to evolve into a self-similar regime, characterized by a bimodal droplet size distribution. The distributions comprise a bell-shaped peak of monodisperse large droplets and a broad range of smaller droplets. The size distribution of the latter follows a scaling law characterized by a nontrivial polydispersity exponent. We present here a numerical model for three-dimensional droplets on a one-dimensional substrate (fiber) that accounts for droplet nucleation, growth, and merging. The polydispersity exponent retrieved using this model is not universal. Rather it depends on the microscopic details of droplet nucleation and merging. In addition, its values consistently differ from the theoretical prediction by Blackman and Brochard [Phys. Rev. Lett. 84, 4409 (2000)]. Possible causes of this discrepancy are pointed out.

It is well known that hydrophobic surfaces may become superhydrophobic when their surface is properly roughened. However, the role of roughness is not yet very clear, notwithstanding several theoretical and experimental investigations. In the present paper, we propose a relatively simple theory aiming at calculating the apparent contact angle (ACA) and the contact area occurring in the case of drops gently deposited on two-dimensional randomly rough surfaces. Our theory applies both to isotropic and anisotropic rough surfaces, although in the latter case the predicted ACA has to be interpreted as the average contact angle at the triple line. We assume large separation of scales, i.e., that the spectral content of the surface lies in a range of wavelengths much smaller than the size of the apparent liquid-solid contact area. Results show that anisotropy negligibly affects the ACA, and a very reasonable agreement is obtained between theoretical ACA values and experimental data.

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains $O$(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

A model providing an accurate estimate of the charge accumulation on the surface of a metallic target irradiated by a high-intensity laser pulse of fs–ps duration is proposed. The model is confirmed by detailed comparisons with specially designed experiments. Such a model is useful for understanding the electromagnetic pulse emission and the quasistatic magnetic field generation in laser-plasma interaction experiments.

An analytical expression for the fluctuation-rounded stretch-coil transition of semiflexible polymers in extensional flows is derived. The competition between elasticity and tension is known to cause a buckling instability in filaments placed near hyperbolic stagnation points and the effect of thermal fluctuations on this transition has yet to receive full quantitative treatment. Motivated by the findings of recent experiments as well as our simulations, we solve for the amplitude of the first buckled mode near the onset of the instability. This reveals a stochastic supercritical bifurcation, which is in excellent agreement with full numerical simulations.

The relaxation dynamics of a system described by a Langevin equation with pulse multiplicative noise sources with different correlation properties is considered. The solution of the corresponding Fokker-Planck equation is derived for Gaussian white noise. Moreover, two pulse processes with regulated periodicity are considered as a noise source: the dead-time-distorted Poisson process and the process with fixed time intervals, which is characterized by an infinite correlation time. We find that the steady state of the system is dependent on the correlation properties of the pulse noise. An increase of the noise correlation causes the decrease of the mean value of the solution at the steady state. The analytical results are in good agreement with the numerical ones.

Considering systems of self-propelled polar particles with nematic interactions (“rods”), we compare the continuum equations describing the evolution of polar and nematic order parameters, derived either from Smoluchowski or Boltzmann equations. Our main goal is to understand the discrepancies between the continuum equations obtained so far in both frameworks. We first show that, in the simple case of point-like particles with only alignment interactions, the continuum equations obtained have the same structure in both cases. We further study, in the Smoluchowski framework, the case where an interaction force is added on top of the aligning torque. This clarifies the origin of the additional terms obtained in previous works. Our observations lead us to emphasize the need for a more involved closure scheme than the standard normal form of the distribution when dealing with active systems.

By means of advanced parallel replica-exchange Monte Carlo methods we examine the influence of elasticity and confinement on the structural transitions of linear systems with restricted bonded interaction. For this purpose, we adopt a model for coarse-grained flexible polymers of finite length in the dilute regime. Hyperphase diagrams are constructed using energy-dependent canonical quantities to demonstrate the effects of the changes in the range of the confined interaction on the liquid and solid structural phases. With increasing bonded interaction range we observe the disappearance of the liquid phase and the fusion of the gas-liquid (or $\mathrm{\Theta })$ and the liquid-solid transitions. One of the most remarkable features, the liquid-gas transition, changes from second to first order if the confined interaction range exceeds a threshold that separates polymeric from nonpolymeric systems. The notoriously difficult sampling of the entropically suppressed conformations in the region of very strong first-order transitions is improved by using multiple Gaussian modified ensembles.

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than $\sim 1/L$. In integrable systems with boundary dissipation one typically observes scaling of $\sim 1/L^3$, while in chaotic ones one can have faster relaxation with the gap scaling as $\sim 1/L$ and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, namely the average angular frequency of precession of nanoparticles and their average magnetization, are of interest. Using the Langevin and Fokker-Planck equations, we calculate both analytically and numerically these characteristics in the deterministic and stochastic cases, determine their dependence on the model parameters, and analyze in detail the role of thermal fluctuations.

Viruses and other cellular cargo that lack locomotion must rely on diffusion and cellular transport systems to navigate through a biological cell. Indeed, advances in single particle tracking have revealed that viral motion alternates between (a) diffusion in the cytoplasm and (b) active transport along microtubules. This intermittency makes quantitative analysis of trajectories difficult. Therefore, the purpose of this paper is to construct mathematical methods to approximate intermittent dynamics by effective stochastic differential equations. The coarse-graining method that we develop is more accurate than existing techniques and applicable to a wide range of intermittent transport models. In particular, we apply our method to two- and three-dimensional cell geometries (disk, sphere, and cylinder) and demonstrate its accuracy. In addition to these specific applications, we also explain our method in full generality for use on future intermittent models.

This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number $\mathrm{Ca})$ is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high $\mathrm{Ca}$ such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low $\mathrm{Ca}$ such as rolling, tumbling, kayaking, and flip-flopping.

The information diffusion process in single complex networks has been extensively studied, especially for modeling the spreading activities in online social networks. However, individuals usually use multiple social networks at the same time, and can share the information they have learned from one social network to another. This phenomenon gives rise to a new diffusion process on multiplex networks with more than one network layer. In this paper we account for this multiplex network spreading by proposing a model of information diffusion in two-layer multiplex networks. We develop a theoretical framework using bond percolation and cascading failure to describe the intralayer and interlayer diffusion. This allows us to obtain analytical solutions for the fraction of informed individuals as a function of transmissibility $T$ and the interlayer transmission rate $\theta$. Simulation results show that interaction between layers can greatly enhance the information diffusion process. And explosive diffusion can occur even if the transmissibility of the focal layer is under the critical threshold, due to interlayer transmission.

Following an approach by Siggia, we present coefficients $C_n$ relating the moments of the dissipation of kinetic energy $\langle \varepsilon \rangle$ and the longitudinal velocity gradient $\langle \partial u_1/\partial x_1\rangle$ under the assumption of isotropy and continuity. Particularly, we find that the moment $\langle {\varepsilon }^n\rangle$ of order $n$ is completely determined by $\langle {(\partial u_1/\partial x_1)}^{2n}\rangle$ and an order- (and viscosity-) dependent coefficient for all $n$ under the assumption of (local) isotropy. This implies that all theories which specify $\langle {\varepsilon }^n\rangle$ also implicitly determine $\langle {(\partial u_1/\partial x_1)}^{2n}\rangle$ and vice versa. As a corollary to the direct connection between the moments of the dissipation and the longitudinal velocity gradient, the even standardized moments of order $2n$ of $\partial u_1/\partial x_1$ (flatness, hyperflatness, and so on) are directly related to the ratio of the moments $\langle {\varepsilon }^n\rangle /{\langle \varepsilon \rangle }^n$. We compare the theoretical values of the coefficients $C_n$ up to $n=6$ with homogeneous isotropic DNS data ranging from ${\text{Re}}_{\lambda }=88$ to ${\text{Re}}_{\lambda }=529$.

A strongly nonintegrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which has multiple thermal values. We propose that in this case the system is unstable towards forming nearby eigenstates which yield each of the allowed thermal values. We provide strong evidence for this from a numerical study of the two-dimensional transverse-field quantum Ising model.

The temperature dependence of the Soret coefficient $S_T\left(T\right)$ in electrostatically charged magnetic colloids is investigated. Two different ferrofluids, with different particles' mean dimensions, are studied. In both cases we obtain a thermophilic behavior of the Soret effect. The temperature dependence of the Soret coefficient is described assuming that the nanoparticles migrate along the ionic thermoelectric field created by the thermal gradient. A model based on the contributions from the thermoelectrophoresis and variation of the double-layer energy, without fitting parameters, is used to describe the experimental results of the colloid with the bigger particles. To do so, independent measurements of the $\zeta$ potential, mass diffusion coefficient, and Seebeck coefficient are performed. The agreement of the theory and the experimental results is rather good. In the case of the ferrofluid with smaller particles, it is not possible to get experimentally reliable values of the $\zeta$ potential and the model described is used to evaluate this parameter and its temperature dependence.

Based on the reformulation of the boundary integral equations recently derived by Creagh, Hamdin, and Tanner [J. Phys. A: Math. Theor. 46, 435203 (2013)] together with semiclassical (short wavelength) approximation, we theoretically show that low-loss resonances of a fully chaotic dielectric billiard can be related with ray dynamical orbits whose intensities are weighted by the Fresnel reflection and transmission coefficients. In addition, it is revealed that intensity localization spots observed in the phase-space representation of an individual resonance wave function are ray-dynamically correlated.

We consider the problem of ignition of propagating waves in one-dimensional bistable or excitable systems by an instantaneous spatially extended stimulus. Earlier we proposed a method [I. Idris and V. N. Biktashev, Phys. Rev. Lett. 101, 244101 (2008)] for analytical description of the threshold conditions based on an approximation of the (center-)stable manifold of a certain critical solution. Here we generalize this method to address a wider class of excitable systems, such as multicomponent reaction-diffusion systems and systems with non-self-adjoint linearized operators, including systems with moving critical fronts and pulses. We also explore an extension of this method from a linear to a quadratic approximation of the (center-)stable manifold, resulting in some cases in a significant increase in accuracy. The applicability of the approach is demonstrated on five test problems ranging from archetypal examples such as the Zeldovich–Frank-Kamenetsky equation to near realistic examples such as the Beeler-Reuter model of cardiac excitation. While the method is analytical in nature, it is recognized that essential ingredients of the theory can be calculated explicitly only in exceptional cases, so we also describe methods suitable for calculating these ingredients numerically.

A study of the dynamical characteristics of the phase space corresponding to the vibrations of the LiNC-LiCN molecule using an analysis based on the small alignment index (SALI) is presented. SALI is a good indicator of chaos that can easily determine whether a given trajectory is regular or chaotic regardless of the dimensionality of the system, and can also provide a wealth of dynamical information when conveniently implemented. In two-dimensional (2D) systems SALI maps are computed as 2D phase space representations, where the SALI asymptotic values are represented in color scale. We show here how these maps provide full information on the dynamical phase space structure of the LiNC-LiCN system, even quantifying numerically the volume of the different zones of chaos and regularity as a function of the molecule excitation energy.