We present an experimental study of thin-sample directional solidification (T-DS) in impure biphenyl. The platelike growth shape of the monoclinic biphenyl crystals includes two low-mobility (001) facets and four high-mobility {110} facets. Upon T-DS, biphenyl plates oriented with (001) facets parallel to the sample plane can exhibit either a strong growth-induced plastic deformation (GID), or deformation-free weakly faceted (WF) growth patterns. We determine the respective conditions of appearance of these phenomena. GID is shown to be a long-range thermal-stress effect, which disappears when the growth front has a cellular structure. An early triggering of the cellular instability allowed us to avoid GID and study the dynamics of WF patterns as a function of the orientation of the crystal.

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from instability onsets, is conducted using spatial dynamics and numerical continuations. The selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model. Accordingly, we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves (including solitary) against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory Hopf instability. Consequently, the resulting pattern selection is qualitatively different from the symmetric finite wavenumber Turing or Hopf instabilities.

We consider surface diffusion of a single particle, which performs site-to-site underbarrier hopping, fulfils intrasite motion between the ground and the first-excited states within a quantum well, and interacts with surface phonons. We obtain a chain of quantum-kinetic equations for one-particle distribution functions and nonequilibrium hopping probabilities. The generalized diffusion coefficients are derived, and the generic non-Markovian diffusion equation is written down both for the infinite lattice model and in the continuous media limit. In the latter case, the one-particle distribution function obeys the telegrapher’s equation, which could give us a nonmonotonic behavior of the intermediate distribution functions at large spatial gradients. In a weak-coupling limit, if the energy of level splitting is comparable with the temperature, there are also pronounced oscillations of the generalized diffusion coefficients. The recrossing/multiple crossing phenomena, a problem of long tails of the generalized diffusion coefficients, as well as a mapping into the next- to the nearest-neighbors hopping regime, are discussed.

The effect of multiplicative noise on a system described by two modes close to a bifurcation point is investigated. The bifurcation is assumed stationary and noise acts as random coupling between these modes. An analytic formula that predicts the onset of instability is derived, and the domain of existence of on-off intermittency is calculated based on an eigenvalue problem. This approach, confirmed by numerical simulations of the Langevin equations, allows quantifying the possible effects of the noise. The stability and the on-off behavior are shown to be very sensitive to deviations of the deterministic system from the case where both modes grow with equal rate and the system displays a continuous symmetry associated to rotation in phase space. In general, a noise term that breaks this continuous symmetry will increase the domain of instability of the system while a noise term that preserves the symmetry reduces the domain of instability.

We report a detailed theoretical analysis of quadrupolar interactions observed between islands, which are disklike inclusions of extra layers, floating in thin, freely suspended smectic-$C$ liquid crystal films. Strong tangential anchoring at the island boundaries results in a strength $+1$ chiral defect in each island and a companion $-1$ defect in the film—these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral-island-defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the interisland potential and the trajectories of the $-1$ defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with $\epsilon$ expansion that this transition belongs to the same universality class as directed percolation.

Study of reversible catalytic reaction networks is important not only as an issue for chemical thermodynamics but also for protocells. From extensive numerical simulations and theoretical analysis, slow relaxation dynamics to sustain nonequlibrium states are commonly observed. These dynamics show two types of salient behaviors that are reminiscent of glassy behavior: slow relaxation along with the logarithmic time dependence of the correlation function and the emergence of plateaus in the relaxation-time course. The former behavior is explained by the eigenvalue distribution of a Jacobian matrix around the equilibrium state that depends on the distribution of kinetic coefficients of reactions. The latter behavior is associated with kinetic constraints rather than metastable states and is due to the absence of catalysts for chemicals in excess and the negative correlation between two chemical species. Examples are given and generality is discussed with relevance to bottleneck-type dynamics in biochemical reactions as well.

The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next-nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin-spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization-group calculations.

The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.

A means of swimming in a viscous fluid is presented, in which a swimmer with only two links rotates around a joint and then rehinges in a periodic fashion in what is here termed rehinging locomotion. This two-link rigid swimmer is shown to locomote with an efficiency similar to that of Purcell’s well-studied three-link swimmer, but with a simpler morphology. The hydrodynamically optimal stroke of an analogous flexible biflagellated swimmer is also considered. The introduction of flexibility is found to increase the swimming efficiency by up to 520% as the body begins to exhibit wavelike dynamics, with an upper bound on the efficiency determined by a degeneracy in the limit of infinite flexibility.

The sedimentation of particles in a vigorously convecting fluid is a process of great interest in various geophysical and industrial settings. Using a classical Rayleigh-Bénard setup with salty water as a working fluid and PMMA particles, we systematically quantify the progressive settling of a large number of heavy particles initially distributed homogeneously through the tank. Our two control parameters are the Rayleigh number Ra characterizing the vigor of convection and the density ratio between the particles and the fluid $\frac{\Delta \rho }{\rho }$. In all our experiments, the time evolution of the solid fraction of suspended particles is correctly described by a diffusion-convection equation, taking into account a constant settling velocity given by the classical Stoke’s law with an apparent viscosity due to small-scale turbulent motions, as well as a time-independent diffusive flux of particles from the bottom of the tank. We define scaling laws for this diffusive flux as well as for the equilibrium value of the suspended particles solid fraction as a function of Ra and $\frac{\Delta \rho }{\rho }$, in agreement with the experimental results.

Sonoluminescence (SL) radiation from an argon bubble in water and in different concentrations of sulfuric acid has numerically been studied to quantify the effects of vapor pressure and viscosity of the liquid on cavitation luminescence in a liquid with controllable vapor pressure and viscosity. For the solutions containing the noble gas with low partial pressure (about 4 Torr), it is shown that there exists an optimum acid solution in which both the temperature and the intensity of SL radiation become maximum. The calculations show that the maximum SL radiation is achieved from the solution of around 65% (wt.) ${\text{H}}_2{\text{SO}}_4$, which is in agreement with available experimental results.

We study the existence and stability of localized modes in the two-dimensional (2D) nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation with a symmetric four-well potential. Using the corresponding four-mode approximation, we trace the parametric evolution of the trapped stationary modes, starting from the linear limit, and thus derive a complete bifurcation diagram for families of the stationary modes. This provides the picture of spontaneous symmetry breaking in the fundamental 2D setting. In a broad parameter region, the predictions based on the four-mode decomposition are found to be in good agreement with full numerical solutions of the NLS/GP equation. Stability properties of the stationary states coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of unstable modes is explored by means of direct simulations. Finally, in addition to the full analysis for the case of the self-attractive nonlinearity, the bifurcation diagram for the case of self-repulsion is briefly considered too.

A sampling algorithm is presented that generates spin-glass configurations of the two-dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson’s algorithm [D. B. Wilson, Proceedings of the Eighth Symposium on Discrete Algorithms (SIAM, Philadelphia, 1997), p 258] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin-glass samples. This algorithm is recursive: it computes probabilities for spins along a “separator” that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination rather than Gaussian elimination for sampling dimer configurations. For $n$ spins and given floating point precision, the algorithm has an asymptotic run-time of $O\left(n^{3/2}\right)$; it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to $n={128}^2$, with fixed and periodic boundary conditions.

We formulate a coarse-grained molecular-dynamics model of polymer chains in solution that includes hydrodynamic interactions, thermal fluctuations, nonlinear elasticity, and topology-preserving solvent mediated excluded volume interactions. The latter involve a combination of potential forces with explicit geometric detection and tracking of chain entanglements. By solving this model with numerical and computational methods, we study the physics of polymer knots in a strong extensional flow (Deborah number $\text{De}=1.6$). We show that knots slow down the stretching of individual polymers by obstructing via entanglements the “natural,” unraveling, and flow-induced chain motions. Moreover, the steady-state polymer length and polymer-induced stress values are smaller in knotted chains than in topologically trivial chains. We indicate the molecular processes via which the rate of knot tightening affects the rheology of the solution.

Neuronal cells in isolation or as an assembly exhibit bursting behavior on two different time scales. We introduce a simple one-dimensional model which requires only one phase variable to describe the phenomenon of parabolic bursting. The analysis in the continuum limit reveals that for any unimodal distribution of frequencies, the qualitative properties of the full and the reduced model are identical. Further, we derive analytically an exact low-dimensional description of a globally coupled network of bursting oscillators for our model. Study of the stability for this low-dimensional model reveals different dynamical signatures in the parameter space. We demonstrate that the structure of the parameter space remains independent of the number of spikes per burst.

We investigate the six-state clock model with nearest-neighbor interactions on the square lattice. We obtain the density of states of the finite systems up to $L=28$ using the Wang-Landau sampling. With the density of states and the Fisher zero approach, we successfully find two different critical temperatures 0.632(2) and 0.997(2) for the clock model. It seems that this study supports the recent results by [Lapilli et al.Phys. Rev. Lett. 96, 140603 (2006)] that the transitions are not of Kosterlitz and Thouless type.

Emergence of noise-induced regularity or coherence resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance $\left(V_N\right)$ of interspike time intervals, which is a measure of regularity in such systems, has a unimodal profile. Our semianalytic treatment of the associated spiking process produces a general yet simple formula for $V_N$, which we show is in very good agreement with numerics in two test cases, namely, the FitzHugh-Nagumo model and the chemical oscillator model.

New powerful soft x-ray sources may be able to access intensities needed for backward Raman amplification (BRA) of x-ray pulses in plasmas. However, high plasma densities, needed to provide enough coupling between the pump and seed x-ray pulses, cause strong damping of the Langmuir wave that mediates energy transfer from the pump to the seed pulse. Such damping could reduce the coupling, thus making efficient BRA impossible. This work shows that efficient BRA can survive despite the Langmuir wave damping significantly exceeding the linear BRA growth rate. Moreover, the strong Langmuir wave damping can automatically suppress deleterious instabilities of BRA to the thermal noise. The class of “quasitransient” BRA regimes identified here shows that it may be feasible to observe x-ray BRA within available x-ray facilities.

For the resistive pressure-gradient-driven turbulence model, the transition from laminar regime to fully developed turbulence is not simple and goes through several phases. For low values of the plasma parameter $\beta$, a single quasicoherent structure forms. As $\beta$ increases, several of these structures may emerge and in turn take the dominant role. Finally, at high $\beta$, fully developed turbulence with a broad spectrum is established. A suitable characterization of this transition can be given in terms of topological properties of the flow. Here, we analyze these properties that provide an understanding of the turbulence-induced transport and give a measure of the breaking of the homogeneity of the turbulence. To this end, an approach is developed that allows discriminating between topological properties of plasma turbulence flows that are relevant to the transport dynamics and the ones that are not. This is done using computational homology tools and leads to a faster convergence of numerical results for a fixed level of resolution than previously presented in Phys. Rev. E 78, 066402 (2008).