We report a strong discontinuous orientational transition (anchoring transition) of liquid-crystal molecules with a large transverse dipole moment. A perfluoropolymer was used as an alignment layer and the transition was observed from planar to homeotropic with decreasing temperature in the nematic phase. Conversely a gradual variation in tilt angle from homeotropic to conical was observed in a liquid crystal with a comparatively smaller transverse dipole moment on the same alignment layer. The experimental results clearly demonstrate the competition between a short-range dipolar force and long-range van der Waals force at the interfacial region. Using discontinuous anchoring transition in the sample, we demonstrate a possible bistable device for memory and light-driven display.

In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, $\gamma \equiv T_B/T_F$, which is the ratio of the ecosystem biological time scales $T_B$ and the flow time scales $T_F$. We integrate this system numerically for different values of $\gamma$ until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on $\gamma$. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio $\gamma$. For small $\gamma$ the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As $\gamma$ increases the plankton concentration is more influenced by the advection processes. In the largest $\gamma$ cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, ${⟨1/K⟩}^{-1}$. We derive asymptotic approximations for the cases of small and large $\gamma$. We also look at the dependence of the power spectra exponent, $\beta$, on $\gamma$ where the power spectrum of plankton is $\propto k^{-\beta }$. We find that the power spectra exponent closely obeys $\beta =1+2/\gamma$ as predicted by earlier studies using simple models of chaotic advection.

We study a matrix model of RNA in which an external perturbation on $n$ nucleotides is introduced in the action of the partition function of the polymer chain. The effect of the perturbation appears in the exponential generating function of the partition function as a factor $\text{exp}\left(1-n\alpha /L\right)$ (where $\alpha$ is the ratio of strengths of the original to the perturbed term and $L$ is the length of the chain). The asymptotic behavior of the genus distribution functions as a function of length for the matrix model with interaction is analyzed numerically for all $n\le L$. It is found that as $n\alpha /L$ is increased from 0 to 1, the term $3^L$ in the number of diagrams $a_{L,g,\alpha }^{\prime }$ at a fixed length $L$, genus $g$ and $\alpha$, goes to $2^L$ [${\left(3-\frac{n\alpha }{L}\right)}^L$ for any $n\alpha /L$] and the total number of diagrams ${\mathcal{N}}_{\alpha }^{\prime }$ at a fixed length $L$ and $\alpha$ but independent of genus $g$, undergoes a change in the factor $\text{exp}\left(\sqrt{L}\right)$ to 1 ($\text{exp}\left[\right(1-n\alpha /L\left)\sqrt{L}\right]$ for any $n\alpha /L$). However the exponent $L$ of the dominant length dependent term in $a_{L,g,\alpha }^{\prime }$ stays unchanged. Hence the universality is robust to changes in the interaction $\left(\alpha \right)$. The distribution functions also exhibit unusual behavior at small lengths.

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{\text{max}}$ in Newman-Watts networks with the long-range connection probability $p$, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of $p$ or $R_{\text{max}}$, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing $p$ or $R_{\text{max}}$. These results are similar to recent results of Reichenbach et al. [Nature (London) 448, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.

This is a continuation of our paper [Phys. Rev. E 79, 046202 (2009)] devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs average of a chosen observable. Good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes in eigenstates across quantum spectra of general systems.

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin-1/2 antiferromagnetic $XYX$ model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is “derived” from the tensor network representation of the system’s ground-state wave functions.

An on- and off-lattice analog of the driven lattice gas has been studied by molecular-dynamics simulation. In the model, particles move on a two-dimensional lattice potential under a constant driving force. They also interact with each other by an attractive square-well pair potential. A heat bath removes as heat the work done by the driving field. The case of zero field recovers equilibrium two-dimensional lattice and continuous-space results. With nonzero field and a strong lattice potential, the system is comparable to the driven lattice gas. As in the driven lattice gas, the anisotropic single-strip configuration persists to higher kinetic energy as the field strength increases. In the case of zero lattice strength, the model reduces to an off-lattice two-dimensional driven square-well fluid. Single-strip steady states are not observed off lattice.

We study generic aspects of bubble dynamics in DNA under time-dependent perturbations, for example, temperature change, by mapping the associated Fokker-Planck equation to a quantum time-dependent Schrödinger equation with imaginary time. In the static case we show that the eigenequation is exactly the same as that of the $\beta$-deformed nuclear liquid drop model, without the issue of noninteger angular momentum. A universal breathing dynamics is demonstrated by using an approximate method in quantum mechanics. The calculated bubble autocorrelation function qualitatively agrees with experimental data. Under time-dependent modulations, utilizing the adiabatic approximation, bubble properties reveal memory effects.

Turbulence induced by Rayleigh-Taylor instability is a ubiquitous phenomenon with applications ranging from atmospheric physics and geophysics to supernova explosions and plasma confinement fusion. Despite its fundamental character, a phenomenological theory has been proposed only recently and several predictions are untested. In this Rapid Communication we confirm spatiotemporal predictions of the theory by means of direct numerical simulations at high resolution and we extend the phenomenology to take into account intermittency effects. We show that scaling exponents are indistinguishable from those of Navier-Stokes turbulence at comparable Reynolds number, a result in support of the universality of turbulence with respect to the forcing mechanism. We also show that the time dependence of Rayleigh, Reynolds, and Nusselt numbers realizes the Kraichnan scaling regime associated with the ultimate state of thermal convection.

We study the Loschmidt echo $F\left(t\right)$ for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) $1-F_g$, where $F_g$ scales as $F_g\left(\alpha ,ϵ,\eta \right)=f_{\text{cl}}\left({\chi }_{\text{cl}}\equiv {\eta }^{3-\alpha }/ϵ\right)$; $\alpha$ is the order of singularity of the potential, $\eta$ is the spread of the initial phase-space density, and $ϵ$ is the perturbation strength. Instead, the quantum echo gap is insensitive to $\alpha$, described by a scaling law $F_g=f_q\left({\chi }_q={\eta }^2/ϵ\right)$ which can be captured by a random matrix theory modeling of critical systems. We trace this quantum-classical discrepancy to strong diffraction effects that dominate the dynamics.

We study the effects of intrinsic noise on chemical reaction systems, which in the deterministic limit approach a limit cycle in an oscillatory manner. Previous studies of systems with an oscillatory approach to a fixed point have shown that the noise can transform the oscillatory decay into sustained coherent oscillations with a large amplitude. We show that a similar effect occurs when the stable attractors are limit cycles. We compute the correlation functions and spectral properties of the fluctuations in suitably comoving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Rössler system. Analytical results are confirmed convincingly in numerical simulations. The effect is quite general, and occurs whenever the Floquet multipliers governing the stability of the limit cycle are complex, with the amplitude of the oscillations increasing as the instability boundary is approached.

We have performed extensive experimental and numerical studies of spontaneous percolation of small beads through an unconsolidated porous media made with large glass beads. In this paper, an experimental setup and a fast “discrete element method” algorithm are presented to deal with large numbers of particles during our interparticle percolation phenomenon studies. In all the experimental and numerical analyses, the size ratio between the moving beads and the stable packing was chosen larger than the geometrical trapping threshold: ${\xi }_c={\left(\frac{2}{\sqrt{3}}-1\right)}^{-1}=6.464\dots$. We measure the longitudinal and transverse dispersion coefficients versus the height of the porous medium or the number of falling small beads. The influence of bead properties such as density, diameter, or restitution coefficients was investigated by using either steel or glass beads. The individual description of these effects and their explanations were made possible by confrontation and coupling between experimental and numerical results. Indeed, with our numerical model, individual analysis of the effects of these mechanical or geometrical parameters were made possible and carried out.

Dynamical heterogeneities exist ubiquitously in materials near a dynamical arrest transition, such as glass formation or gelation. Among the readily discernible features of heterogeneous dynamics is a non-Gaussian exponential component in the distribution of the constituent particle displacements that is not understood at the single-particle level. We present an experimental study of particle dynamics and self–van Hove functions $G_s\left(r,t\right)$ in a colloid-polymer system approaching gelation. We show experimental evidence, in the special case of a gelation transition, for exponentially distributed times for anomalously large displacements, and confirm that an exponential tail in $G_s$ arises from rare events with associated Poisson statistics. We focus on the role of the anomalous large displacements and analyze their time scales, relating them to other time scales typically used to describe structural relaxation in gels and glasses: the time to cage breakup and the time for re-emergence of Fickian behavior at long times. Furthermore, we search for a structural origin of the dynamical heterogeneity. Various quantities characterizing local structure are examined. We found evidence of a strong correlation between local structure and local dynamics, in contrast to what has been found in supercooled liquids.

The kinetics of spinodal-assisted crystallization in a region of the phase diagram where the dynamics is controlled by the critical slow down was studied by means of a Cahn-Hilliard model. The length-scale selectivity conducted by the spinodal process led to the formation of a filamentary network of density fluctuations that resemble the scarred states found in quantum-chaos systems. The present work reveals that the early structure of density fluctuations acts such as a precursor for crystallization and deeply affects the orientational and translational correlation between growing crystals. At deep quenches the network of fluctuations is deeply modified and the classical picture of spinodal decomposition is recovered.

In this paper, the curvature changes and fission routes of the lipid domains in a multicomponent vesicle are studied by dissipative particle dynamics. Under different conditions of asymmetric distribution of lipids in two leaflets of lipid bilayer and area-to-volume ratio of the vesicle, we obtained different configurations of the domain in the vesicle: three typical curvature characters of the lipid domain, namely, positive, negative, and invariable curvatures compared to the vesicle are observed. Furthermore, some other morphologies of the domain and two vesicle fission routes (i.e., exocytic and endocytic fissions) are also obtained in our simulations. Particular emphasis is put on the formation of the negative curvature domain and on the behavior of endocytic fission. Based on our simulations, it is indicated that water plays an important role in the invagination and endocytic fission processes of the domain in a vesicle. For endocytic fission, domains of different sizes are evolved according to different routes under the effect of the water. Additionally, we find that both the spontaneous curvature of lipid molecules and area-to-volume ratio can promote or restrain the shape deformation of the lipid domain. Under the competition of these two factors, another possible route of endocytic fission is observed in our simulations, in that only a part of the lipid domain invaginates into the interior of the vesicle to complete the endocytic fission. Our study is helpful for understanding the possible mechanism of the shape transformation of the cellular membrane and the difference of several kinds of routes of vesicle fission.

It is pointed out that the Casimir energy in a medium can be obtained most directly from the zero-point energy of the electromagnetic field because of its reduced propagation velocity. This brings to the fore again the old problem related to how the principle of relativity is combined with the Maxwell field equations in a continuous medium.

The critical behavior of the contact process is studied in annealed scale-free networks by mapping it on the random-walk problem. We obtain the analytic results for the critical scaling using the event-driven dynamics approach. These results are confirmed by numerical simulations. The disorder fluctuation induced by the sampling disorder in annealed networks is also explored. Finally, we discuss over a possible discrepancy of the finite-size-scaling theory in annealed and quenched networks in spirit of the droplet size scale and the linking disorder fluctuation.

Propagation of waves through Cantor-set media is investigated by renormalization-group analysis. For specific values of wave numbers, transmission coefficients are shown to be governed by the logistic map and, in the chaotic region, they show sensitive dependence on small changes in parameters of the system such as the index of refraction. For other values of wave numbers, our numerical results suggest that light transmits completely or reflects completely by the Cantor-set media ${\text{C}}_{\infty }$. It is also shown that transmission coefficients exhibit a local scaling behavior near complete transmission if the complete transmission is achieved at a wave number $\kappa ={\kappa }^{\ast }$ with a rational ${\kappa }^{\ast }/\pi$. The scaling function is obtained analytically by using the Euler totient function, and the local scaling behavior is confirmed numerically.

In this work, wave breaking for general non-quasi-static oscillations in warm plasma is investigated using Lagrangian methods. In particular, the effects of secular behavior on wave-breaking limits are explored, and it is shown that thermal effects can sometimes prevent wave breaking by curbing secular behavior. The oscillation equations for fully relativistic warm plasma are cast into Lagrangian form, and wave-breaking limits are derived for waves in warm plasma having nonconstant density. These results have important applications in electron acceleration schemes that employ a wakefield or a slow beat wave propagating down a density gradient.