A free dendrite growth under forced fluid flow is analyzed for solidification of a nonisothermal binary system. Using an approach to dendrite growth developed by Bouissou and Pelcé [Phys. Rev. A 40, 6673 (1989)], the analysis is presented for the parabolic dendrite interface with small anisotropy of surface energy growing at arbitrary Péclet numbers. The stable growth mode is obtained from the solvability condition giving the stability criterion for the dendrite tip velocity $V$ and dendrite tip radius $\rho$ as a function of the growth Péclet number, flow Péclet number, and Reynolds number. In limiting cases, the obtained stability criterion presents known criteria for small and high growth Péclet numbers of the solidifying system with and without convective fluid flow.

In studying the dehydration of surface-moistened fumed silica Aerosil powders, we found a conductivity percolation transition at low hydration levels. Both the percolation exponent and the threshold are typical for correlated site-bond transitions in complex two-dimensional (2D) systems. The exponent values, 0.94–1.10, are indicative of severe heterogeneity in the conducting medium. The surface moisture at the percolation threshold takes on a universal value of 0.65 mg${}_{\left[\mathrm{H}2\mathrm{O}\right]}$/m${}^2$${}_{\left[\mathrm{silica}\right]}$, independent of the silica grain size, and equivalent to twice the first hydration monolayer. This level is just sufficient to sustain a quasi-2D, hydrogen-bonded water network spanning the silica surface.

We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic, or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly related to the Lyapunov exponents of the dynamical system. This signature is a horizon of coherence, i.e., a preliminary duration without decoherence followed by a rapid decoherence process.

Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale $L$ increases with time. The so-called coarsening exponent $n$ characterizes the time dependence of the scale of the pattern, $L\left(t\right)\approx t^n$, and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of $D\left(\lambda \right)$, the phase diffusion coefficient, as a function of the wavelength $\lambda$ of the base steady state $u_0\left(x\right)$. $D$ carries all information about coarsening dynamics and, through the relation $\left|D\left(L\right)\right|\simeq L^2/t$, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a orward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved.

Finding the densest sphere packing in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or “extreme” lattices) to gain insight about the nature of the topography of the “density” landscape.

A similarity transformation is utilized to reduce the generalized nonlinear Schrödinger (NLS) equation with variable coefficients to the standard NLS equation with constant coefficients, whose rogue wave solutions are then transformed back into the solutions of the original equation. In this way, Ma breathers, the first- and second-order rogue wave solutions of the generalized equation, are constructed. Properties of a few specific solutions and controllability of their characteristics are discussed. The results obtained may raise the possibility of performing relevant experiments and achieving potential applications.

Recent numerical results on classical dimers with weak aligning interactions have been theoretically justified via a Coulomb gas representation of the height random variable. Here, we propose a completely different representation, the interacting fermions picture, which avoids some difficulties of the Coulomb gas approach and provides a better account of the numerical findings. Besides, we observe that the Peierls argument explains the behavior of the system in the strong interaction case.

Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral and formal stability criteria in the form of necessary and sufficient conditions. These criteria determine stability of spatially inhomogeneous solutions whose stability has not been decided correctly by using a less refined formal stability criterion. It is shown that some of such solutions can be found in a family of stationary solutions to the Vlasov equation, which is parametrized with macroscopic quantities and has a two-phase coexistence region in the parameter space.

We introduce a superdiffusive one-dimensional epidemic process model on which infection spreads through a contact process. Healthy ($A$) and infected ($B$) individuals can jump with distinct probabilities $D_A$ and $D_B$ over a distance $\ell$ distributed according to a power-law probability $P\left(\ell \right)\propto 1/{\ell }^{\mu }$. For $\mu \ge 3$ the propagation is equivalent to diffusion, while $\mu <3$ corresponds to Lévy flights. In the $D_A>D_B$ diffusion regime, field-theoretical results have suggested a first-order transition, a prediction not supported by several numerical studies. An extensive numerical study of the critical behavior in both the diffusive ($\mu \ge 3$) and superdiffusive ($\mu <3$) $D_A>D_B$ regimes is also reported. We employed a finite-size scaling analysis to obtain the critical point as well as the static and dynamic critical exponents for several values of $\mu$. All data support a second-order phase transition with continuously varying critical exponents which do not belong to the directed percolation universality class.

The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.

We study, numerically and experimentally, three different methods to suppress the trajectories of strongly collapsing and sonoluminescent bubbles in a highly viscous sulfuric acid solution. A new numerical scheme based on the window method is proposed to account for the history force acting on a spherical bubble with variable radius. We could quantify the history force, which is not negligible in comparison with the primary Bjerknes force in this type of problem, and results are in agreement with the classical primary Bjerknes force trapping threshold analysis. Moreover, the present numerical implementation reproduces the spatial behavior associated with the positional and path instability of sonoluminescent argon bubbles in strongly gassed and highly degassed sulfuric acid solutions. Finally, the model allows us to demonstrate that spatially stationary bubbles driven by biharmonic excitation could be obtained with a different mode from the one used in previous reported experiments.

The quantities entropy and diffusion are measured for two- and three-dimensional (3D) dust clusters in the fluid state. Entropy and diffusion are predicted to be closely linked via unstable modes. The method of instantaneous normal modes is applied for various laser-heated clusters to determine these unstable modes and the corresponding diffusive properties. The configurational entropy is measured for 2D and 3D clusters from structural rearrangements. The entropy shows a threshold behavior at a critical temperature for the 2D clusters, allowing us to estimate a configurational melting temperature. Further, the entropic disorder increases for larger clusters. Finally, the predicted relation between entropy and unstable modes has been confirmed from our experiments for 2D systems, whereas 3D systems do not show such a clear correlation.

From the nonlinear Vlasov equation, a nonlinear turbulence scattering term is found to describe stochastic dissipation on a time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined by the well-understood unperturbed motion of charged particles, with the effects of the fluctuating part of fields described by the turbulence scattering term. In the present framework, one can identify various important physics, from the linear and quasilinear regimes to the nonlinear regime, in particular, the connections between the widely used Kadomtsev-Pogutse equation [B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1970), pp. 368–387] and the Frieman-Chen equation [Frieman and Chen, Phys. Fluids 25, 502 (1982)]. The nonlinear scattering term indicates the Onsager symmetry relation of turbulent transport and a nonlinear frequency or $\mathit{k}$ spectrum shift of a resonantly excited wave.

The electroclinic (EC) effect is the tilt of the optical axis of a liquid crystal in the plane perpendicular to an applied electric field. Chirality plays a key role for its emergence. Based on the molecular and phase symmetry we derive a molecular expression for the EC coefficient, the material property that quantifies the linear coupling between tilt and electric field, in nematic liquid crystals. Modeling the relevant molecular properties (shape, electric dipole moment, and polarizability) with atomic resolution, we calculate the EC coefficient for prototype molecular structures. We demonstrate that molecular chirality, needed for the occurrence of the EC effect in nematics with a uniform director, is not a necessary requirement in the presence of a twisted director. Our results show that in the latter case conformational deracemization, invoked to explain recent experiments, is not the only mechanism.

The effect of complex dynamics of solitons on the output noise of the system (thermal jitter) is studied in the frame of the driven underdamped Frenkel-Kontorova model. In contrast to the continuous case, we have observed a dramatic splash of the jitter. It is demonstrated that this jitter increase is related to the joining of an initial soliton with the one generated by large amplitude oscillations of the Cherenkov radiation tail, which results in the establishment of a unified soliton structure.

The problem of effectively adiabatic control of a collection of classical harmonic oscillators sharing the same time-dependent frequency is analyzed. The phase differences between the oscillators remain fixed during the process. This fact leads us to adopt the coordinates: energy, Lagrangian, and correlation, which have proved useful in a quantum description and which have the advantage of treating both the classical and quantum problem in one unified framework. A representation theorem showing that two classical oscillators can represent an arbitrary collection of classical or quantum oscillators is proved. An invariant, the Casimir companion, consisting of a combination of our coordinates, is the key to determining the minimum reachable energy. We present a condition for two states to be connectable using one-jump controls and enumerate all possible switchings for one-jump effectively adiabatic controls connecting any initial state to any reachable final state. Examples are discussed. One important consequence is that an initially microcanonical ensemble of oscillators will be transformed into another microcanonical ensemble by effectively adiabatic control. Likewise, a canonical ensemble becomes another canonical ensemble.

From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive the corresponding interface description. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. The constitutive equations, connecting the crystallization and diffusion fluxes and forces, decouple in the low-velocity limit and there generate an occasionally negative, but nevertheless thermodynamically consistent friction coefficient. We, moreover, discover a continuous symmetry, which is independent of our model and allows to decouple the constitutive equations for the two components of the alloy for arbitrary growth velocities.

Pseudochaotic properties are systematically investigated in a one-parameter family of irrational triangular billiards (all angles irrational with $\pi$). The absolute value of the position correlation function $C_x\left(t\right)$ decays like $\sim$$t^{-\alpha }$. Fast $(\alpha \approx 1)$ and slow $(0<\alpha <1)$ decays are observed, thus indicating that the irrational triangles do not share a unique ergodic dynamics, which, instead, may vary smoothly between the opposite limits of strong mixing $(\alpha =1)$ and regular behaviors $(\alpha =0)$. Upgrading previous data, spectral statistical properties of the quantized counterparts are computed from $150000$ energy eigenvalues numerically calculated for each billiard. Gaussian orthogonal ensemble spectral fluctuations are observed when $\alpha \approx 1$ and intermediate statistics are found otherwise. Our irrational billiards have zero Kolmogorov-Sinai entropy and essentially infinity genus. Thus, differently from previous works on rational (pseudointegrable) enclosures, our results provide a missing classical-quantum correspondence regarding the ergodic hierarchy for a set of nonchaotic systems that might enjoy the strong mixing property.

We explore the salient features of the different instability modes of a pressure-driven two-layer plane Couette flow confined between a moving wall and a Darcy-Brinkman porous layer. A linear stability analysis of the conservation laws leads to an Orr-Sommerfeld system, which is solved numerically with appropriate boundary conditions to identify the time and length scales of the instability modes. The study reveals that the movement of the confining wall together with the slippage at the porous-liquid interface originating from the flow inside the porous layer can stimulate a pair of finite-wave-number shear modes in addition to the long-wave interfacial mode of instability. The shear modes dominate the interfacial mode, especially when the frictional influence at the liquid layers is smaller due to the movement of the confining plate or due to the larger slippage at the porous-liquid interface. The shear modes are found to be present under all combinations of the viscosity ${\mu }_r$ and thickness $h_r$ ratios of the liquid layers. This is in stark contrast to the two-layer flow confined between nonporous plates where the interfacial (shear) mode is observed only when ${\mu }_r>h_r^2$ (${\mu }_r<h_r^2$). Interestingly, the strength of one of the shear modes is found to increase with the velocity of the bounding moving plate, whereas the other shear mode gains strength in the presence of highly porous, permeable, and thick porous layers. The results reported can be of significant importance in the microscale two-phase flows where the presence of a bounding porous layer or moving wall can expedite the intermixing of layers to improve the multiphase mixing, heat and mass transfer, and emulsification characteristics.

SLE($\kappa ,\vec{\rho }$) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE($\kappa ,\vec{\rho }$) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case $\kappa =2$ and $h_{\rho }=0$ in which $h_{\rho }$ is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ${\xi }_0$ and conditioned by a change of boundary conditions at $x_0$, we find that this probability depends significantly on the factor $x_0-{\xi }_0$. We also present the perturbative general solution for large $x_0$. As a prototype, we apply this formalism to SLE($\kappa ,\kappa -6$) which governs the curves that start from and end on the real axis.