We consider a viscous flow on an inclined plate, such that the liquid’s depth far upstream is larger than that far downstream, resulting in a “smoothed-shock wave” steadily propagating downstream. Our numerical simulations show that in a large section of the problem’s parameter space all initial conditions overturn (i.e., the liquid’s surface becomes vertical at some point) and thus no steady solution exists. The overturning can only be stopped by a sufficiently strong surface tension.

The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

The coupled translation-rotation activated dynamics in dense suspensions of attractive homogeneous and Janus uniaxial dicolloids are studied using microscopic statistical mechanical theory. Multiple kinetic arrest transitions and reentrant phenomena are predicted that are associated with fluid, gel, repulsive glass, attractive glass, plastic glass, and novel glass-gel states. The activated relaxation rate is a nonuniversal nonmonotonic function of attraction strength at high volume fractions due to the consequences of a change of the transient localization mechanism from caging to physical bonding.

We analyze critical phenomena on networks generated as the union of hidden variable models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small worlds similar to those à la Watts and Strogatz, but with a heterogeneous degree distribution. We prove that the critical behavior (thermal or percolative) remains completely unchanged by the presence of finite loops (or finite clustering). Then, we show that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature. Quite interestingly, if $\gamma$ is the exponent for the power-law distribution of the vertex degree, for $\gamma ⩽3$ and with or without short-range couplings, such strong correlations persist even in the thermodynamic limit, contradicting the common opinion that, in mean-field models, correlations always disappear in this limit. Finally, we provide the optimal choice of rewiring under which percolation phenomena in the rewired network are best performed, a natural criterion to reach best communication features, at least in noncongested regimes.

The characteristics of the deterministic Nagel–Schreckenberg model with traffic-light boundary conditions are investigated and elucidated in a mostly theoretically way. First, precise analytical results of the outflow are obtained for cases in which the duration of the red phase is longer than one step. Then, some results are found and studied for cases in which the red phase equals one step. The main findings include the following. The maximum outflow is “road-length related” if the inflow is saturated; otherwise, if the inbound cars are generated stochastically, multiple theoretical outflow volumes may exist. The findings indicate that although the traffic-light boundary can be implemented in a simple and deterministic manner, the deterministic Nagel–Schreckenberg model with such a boundary has some unique and interesting behaviors.

The behavior of hysteretic, coupled elastic and fluid systems is modeled. The emphasis is on quasistatic equilibrium in response to prescribed chemical potential ($\mu$) protocols and prescribed stress ($\sigma$) protocols. Hysteresis arises in these models either from the presence of hysterons or from the presence of self-trapping internal fields. This latter mechanism is modeled in finite element calculations which serve to illustrate the creation of hysteresis in a range of circumstances that go from conventionally hysteretic systems, a sandstone, to systems like a wood fiber. An essential ingredient in the behavior of these systems, the interaction between the mechanical variables and the fluid variables, is accorded special attention. The proper venue for the exploration of these systems is $(\mu ,\sigma )$ space and appropriate $\mu$ protocols, $\sigma$ protocols, and combined $\mu -\sigma$ protocols.

The present paper investigates the global instability mechanisms of arrayed-cellular growth with asymptotic approach. We find that the system of directional solidification involves two types of global instability mechanisms: the low-frequency instability and the global oscillatory instability, which are profoundly similar to that found in the system of viscous fingering and free dendritic growth. Based on these global instabilities, the neutral mode selection principle for the limiting state of growth is proposed; the origin and essence of side branching on the interface are elucidated with the so-called global trapped wave mechanism, which involves the interfacial wave reflection and amplification along the interface. It is demonstrated that side branching is self-sustaining and can persist without continuously applying the external noise; the effect of the anisotropy of interfacial energy is not essential for the selection of steady cellular growth and for the origin and formation of side branching at the interface. The comparisons of theoretical results are made with the most recent experimental works and the numerical simulations which show very good quantitative agreement.

The mechanism of the solidification of compound materials, such as oxide crystals, in a vapor-liquid-solid (VLS) system is investigated by model molecular dynamics simulation. A simple model for the VLS growth of a compound crystal is proposed to clarify the general mechanism of how a liquid solvent catalyzes the growth rate. We find that the nucleation process at the solid surface is responsible for limiting the growth rate, and that the solvent catalyzes the nucleation by reducing the critical nucleation size at the liquid-solid interface. Our theoretical suggestion that the ratio of the vapor-solid (VS) growth rate to the VLS growth rate strongly depends on the supply rate qualitatively agrees well with the experimental result. Finally, we simulate the entire process of VLS nanowire formation.

We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant $D_{\mathrm{r}}$ of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern, with characteristic length $\ell$, grows with self-similarity in three dimensions over time with an $\ell ~t^{1/4}$ scaling law. In the late stage, the rotational diffusion becomes significant, leading to a crossover of the growth exponent from 1/4 to 1/2. This crossover time is estimated to be on the order of $t~D_{\mathrm{r}}^{-1}$. We also examined the time evolution of a pair of disclinations placed in a confined system by solving the same time-dependent Ginzburg-Landau equations in two dimensions. If the initial distance between the disclinations is shorter than some critical length, they approach and annihilate each other; however, at larger initial separations, they are stabilized.

We studied the phase behavior of a mixture of two semiflexible negatively charged polyelectrolytes, giant DNA and alginate, under crowded condition in a cell-sized sphere (5–40 $\mu$m in diameter), where the persistence length of giant DNA is 50 nm and that of alginate is 5 nm. Through microscopic observation, we found that the polymer mixture exhibits a unique phase behavior, which depends on the size of the sphere, whereas the mixture remains homogeneous and isotropic in bulk solution. When the sphere is small, DNA is completely depleted on the surface. When the sphere is medium sized, a portion of the DNA is depleted on the surface, and the remainder stays within the sphere. By introducing a curvature-dependent term for the interaction between DNA and the surface into the Flory-Huggins model, we interpret the observed characteristics of the phase behavior in terms of the relative importance of the surface-to-volume effect.

Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists often use distinctive keywords to quantify the dynamics of information spreading in societies harboring strong culture centers. One prominent example, which is addressed here, is Kyoto’s historical impact on Japanese culture. We construct a minimal model, based on shared properties of linguistic maps, to address the interplay between information flow and geography. We show that spreading of information over Japan in the premodern time can be described by an Eden growth process with noise levels corresponding to coherent spatial patches of sizes given by a single day’s walk ($~$15 km), and that new words appear in Kyoto at times comparable to the time between human generations ($~$30 yr).

A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutions corresponding to these potentials are then studied. Also, properties of a few solutions and physical applications of interest to the field are discussed. Finally, the stability of the solitary wave solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed numerically; the results reveal that the solitary waves can propagate in a stable way under slight disturbance of the constraint conditions and the initial perturbation of white noise.

In the area of bipedal locomotion, the spring-loaded inverted pendulum model has been proposed as a unified framework to explain the dynamics of a wide variety of gaits. In this paper, we present an analysis of the mathematical model and its dynamical properties. We use the perspective of hybrid dynamical systems to study the dynamics and define concepts such as partial stability and viability. With this approach, on the one hand, we identify stable and unstable regions of locomotion. On the other hand, we find ways to exploit the unstable regions of locomotion to induce gait transitions at a constant energy regime. Additionally, we show that simple nonconstant angle of attack control policies can render the system almost always stable.

Nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules. In this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics. We find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these. Our result offers a possible solution to the long-standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters.

The simultaneous effect of thermal noise and time-periodic spin torques on magnetic multilayers are treated in this work. Using two commonly studied magnetic systems with multiple stable states at zero temperature as examples, we show that periodic spin torques can enhance the stability of the system and suppress the noise due to interwell transitions. In the case of weak periodic spin torques, stochastic resonance, which is usually associated with ac magnetic fields, is also manifested for nonconservative torques. In more complex systems with a relatively low energy barrier, it is shown that high-frequency spin torques can inhibit interwell transitions and in effect suppress the telegraph noise due to the switching between neighboring states.

Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional flow fields with particle-scale resolution, we calculate the time evolving broken-links network and find that a giant component of this network is formed as shear is applied to this system. We implement a model of link breakages where the probability of a link breaking is proportional to the average rate of longitudinal strain (elongation) in the direction of the edge and find that the model demonstrates qualitative agreement with the data when studying the onset of the giant component. We note, however, that the broken-links network formed in the model is less clustered than our experimental observations, indicating that the model reflects less localized breakage events and does not fully capture the dynamics of the granular flow.

The Kelvin equation relates the vapor pressure of a volatile liquid to the curvature of the liquid surface. It describes phenomena such as capillary condensation, capillary adhesion, nucleation, and the adsorption of vapors into porous media. Here we propose an extension of the Kelvin equation, which takes into account changes of the vapor pressure due to electric fields. The presence of electric fields reduces the saturation vapor pressure and leads to field-induced condensation. Field-induced condensation can explain the presence of water bridges in scanning probe nanolithographic methods such as anodic oxidation.

The mechanical response to electrical stimulation was investigated in a chiral smectic elastomer. The two-dimensional strain tensor in an elastomer film was precisely measured by tracking fluorescent beads dispersed on the film. Shear deformation in the film was clearly observed when an electric field was applied perpendicular to the film surface. The temperature dependence of the strain tensor was also investigated, and the origin of the electric-field-induced shear strain in the chiral smectic-$C$ phase was mainly attributed to the Nambu-Goldstone mode.

We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order parameter, and orientational correlation functions using the transfer-matrix method if some simplifying assumptions are applied for either the orientational freedom or the contact distance between two needles. The two-state Zwanzig model accounts for the orientational ordering, but it produces unphysical pressure at high densities and there is no orientational correlation. The four-state Zwanzig model gives reasonable results for orientational correlation function, but the pressure is still poorly represented at high densities. In the continuum limit, apart from the orientational correlation length it is managed to reproduce all relevant bulk properties of the hard needles using an approximate formula for the contact distance. The results show that the orientational correlation length diverges at zero and infinite pressures. The high-density behavior of the fluid of needles is not resolved.