In this Rapid Communication, results on smectic layer thickness, using synchrotron radiation x-ray diffraction, for different mixtures of ferroelectric and antiferroelectric liquid crystals are given. We find that with an increased ferroelectric component in the mixtures, the layer shrinkage at the de Vries $\text{Sm}{A}^{\ast }\text{-Sm}{C}^{\ast }$ transition increases. This observation can be used to explain our previously observed behaviors [U. Manna, J.-K. Song, Yu. P. Panarin, A. Fukuda, and J. K. Vij, Phys. Rev. E 77, 041707 (2008)] that the soft-mode dielectric strength decreases, the Landau coefficient increases, and the Curie-Weiss temperature range decreases with increased ferroelectric component in the mixture exhibiting de Vries $\text{Sm}{A}^{\ast }\text{-Sm}{C}^{\ast }$ transition.

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance $d$ between the inclusions is decreased from infinity, the variance of the Casimir force decreases as $-1/d^2$. This distance dependence shares a common physical origin with the Casimir force itself.

In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.

A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the $q$-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent $\alpha$ allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the $q=3$ case is very good at high and low temperatures as well as at the critical point. It is shown that the $q>4$ cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting $q=4$ case is shortly discussed.

We present a numerical analysis of the effect of particle elongation on the quasistatic behavior of sheared granular media by means of the contact dynamics method. The particle shapes are rounded-cap rectangles characterized by their elongation. The macroscopic and microstructural properties of several packings subjected to biaxial compression are analyzed as a function of particle elongation. We find that the shear strength is an increasing linear function of elongation. Performing an additive decomposition of the stress tensor based on a harmonic approximation of the angular dependence of branch vectors, contact normals, and forces, we show that the increasing mobilization of friction force and the associated anisotropy are key effects of particle elongation. These effects are correlated with partial nematic ordering of the particles which tend to be oriented perpendicular to the major principal stress direction and form side-to-side contacts. However, the force transmission is found to be mainly guided by cap-to-side contacts, which represent the largest fraction of contacts for the most elongated particles. Another interesting finding is that, in contrast to shear strength, the solid fraction first increases with particle elongation but declines as the particles become more elongated. It is also remarkable that the coordination number does not follow this trend so that the packings of more elongated particles are looser but more strongly connected.

We experimentally address the locations of maximal curvature on crystalline cellular or dendritic interfaces that directionally grow in a thin sample of a transparent material. Local curvatures are determined on the whole dendrite tips by considering the intersection of nearby normals. It is found that, at the location of the curvature maximum, the interface normal points toward a particular direction solely set by the crystal lattice and equal in practice to the dendrite growth direction at large pulling velocity. This property is independent of the growth conditions (thermal gradient, velocity, dendrite spacing, and crystal orientation). It enables crystal orientations to be recovered from dendrite shapes and provides a bridge to understand the implications of anisotropy on the forms and orientations of directionally solidified dendrites.

We demonstrate the existence of steadily translating filaments in the Belousov-Zhabotinsky reaction. The filaments have self-reinforcing shapes tracing planar hairpins and constant velocities that are inversely proportional to their width. These features are well described by an analytical solution of the mean curvature flow problem. Using numerical simulations based on an excitable reaction-diffusion model, we also probe the solution’s large basin of attraction and show that entangled hairpins reconnect during collisions.

An outstanding problem in quantum nonlinear dynamics concerns about the energy-level statistics in experimentally accessible relativistic quantum systems. We demonstrate, using chaotic graphene confinements where electronic motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are those given by Gaussian orthogonal ensemble (GOE) random matrices. Weak magnetic field can change the level-spacing statistics to those of Gaussian unitary ensemble for electrons in graphene. For sufficiently strong magnetic field, the GOE statistics are restored due to the appearance of Landau levels.

Stability of planar “frozen” fronts propagating through a cylindrical shell reactor in reaction-diffusion and reaction-diffusion-advection systems is studied numerically using the reactor perimeter $\left(S\right)$ as a bifurcation parameter. For both systems rigid rotating patterns superimposed on axially propagating fronts were shown to emerge in $S$ gaps between one-wave and two-wave solutions. The rotating motion is surprising since the linear analysis predicts formation of stationary patterns which are sustained in the plane, and emerges due to the periodic azimuthal boundary conditions.

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles—membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for prebiotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations even when the number of constituents is quite large. These oscillations are spatiotemporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.

The paper presents the analytic study of energy exchange in a system of coupled nonlinear oscillators subject to superharmonic resonance. The attention is given to complete irreversible energy transfer that occurs in a system with definite initial conditions corresponding to a so-called limiting phase trajectory (LPT). We show that the energy imparted in the system is partitioned among the principal and superharmonic modes but energy exchange can be due to superharmonic oscillations. Using the LPT concept, we construct approximate analytic solutions describing intense irreversible energy transfer in a harmonically excited Duffing oscillator and a system of two nonlinearly coupled oscillators. Numerical simulations confirm the accuracy of the analytic approximations.

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of $K\left(2,2\right)$ Rosenau-Hyman compactons including the collision of two compactons and resultant shock formation. Our approach uses a differencing scheme involving only nearest and next-to-nearest neighbors on a uniform spatial grid. The partial differential equation for the compactons involves first, second, and third partial derivatives in the spatial coordinate and we concentrate on four different fourth-order methods which differ in the possibility of increasing the degree of accuracy (or not) of one of the spatial derivatives to sixth order. A method designed to reduce round-off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order. Simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity. For those problems the different choices lead to different amounts of “spurious” radiation and we compare the virtues of the different choices.

Using an approach based on the time-dependent density-matrix renormalization-group method, we study the thermalization in spin chains locally coupled to an external bath. Our results provide evidence that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well approximated by the grand canonical state. Moreover, the resulting ergodic state in the bulk does not depend on the details of the baths. On the other hand, for integrable systems we found that the invariant state in general depends on the bath and is different from the grand canonical state.

We investigate the quantum transmission through laterally driven single- and double-barrier systems in the nonlinear regime of strong driving. A broad parameter range is explored, distinguishing in particular between different frequency regimes. The applicability of an effective, time independent, potential description in the high-frequency regime is explored. Moreover, we analyze in detail the inelastic processes and their dependence on parameters, resonant tunneling, and photon assisted tunneling. For the single-barrier problem we address driving laws that differ from the purely sinusoidal one. In this context, we encounter reduced spatial and temporal symmetries and demonstrate the corresponding effects on quantum pumping. For the double barrier, the focus of our studies lies on the impact of the variation in the relative phase of the barriers on the transmission.

We present a simple approach to realize truly random number generator based on measuring the phase noise of a single-mode vertical cavity surface emitting laser. The true randomness of the quantum phase noise originates from the spontaneous emission of photons and the random bit generation rate is ultimately limited only by the laser linewidth. With the final bit generation rate of 20 Mbit/s, the truly random bit sequence guaranteed by the uncertainty principle of quantum mechanics passes the three standard randomness tests (ENT, Diehard, and NIST Statistical Test Suites). Moreover, a continuously generated random bit sequence, with length up to 14 Gbit, is verified by two additional criteria for its true randomness.

We study how the degree of ordering depends on the strength of the thermal and quantum fluctuations in frustrated systems by investigating the correlation function of the order parameter. Concretely, we compare the equilibrium spin correlation function in a frustrated lattice which exhibits a nonmonotonic temperature dependence (reentrant type dependence) with that in the ground state as a function of the transverse field that causes the quantum fluctuation. We find the correlation function in the ground state also shows a nonmonotonic dependence on the strength of the transverse field. We also study the real-time dynamics of the spin-correlation function under a time-dependent field. After sudden decrease in the temperature, we found nonmonotonic changes of the correlation function reflecting the static temperature dependence, which indicates that an effective temperature of the system changes gradually. For the quantum system, we study the dependence of changes of the correlation function on the sweeping speed of the transverse field. Contrary to the classical case, the correlation function varies little in a rapid change of the field, though it shows a nonmonotonic change when we sweep the field slowly.

Bistable azimuthal nematic alignment textures have been created in micrometer-scale channels for which one sidewall is smooth and straight and the other possesses a symmetric sawtooth morphology. The optical textures have been observed during dynamic switching between the two stable states in response to dual frequency ac waveform driving of a highly dispersive nematic liquid crystal. The switching processes involves collapsing of filamentlike director reorientation (tilt-wall) loops and the associated motion and annihilation of surface defects along and close to the edge at the sawtooth sidewall. The predictions from both the $n$-director-based Ericksen-Leslie theory and the $Q$-tensor theory are in good agreement with the experimental observations.

We consider optimal vaccination protocol where the vaccine is in short supply. In this case, the endemic state remains dynamically stable; disease extinction happens at random and requires a large fluctuation, which can come from the intrinsic randomness of the population dynamics. We show that vaccination can exponentially increase the disease extinction rate. For a time-periodic vaccination with fixed average rate, the optimal vaccination protocol is model independent and presents a sequence of short pulses. The effect can be resonantly enhanced if the vaccination pulse period coincides with the characteristic period of the disease dynamics or its multiples. This resonant effect is illustrated using a simple epidemic model. The analysis is based on the theory of fluctuation-induced population extinction in periodically modulated systems that we develop. If the system is strongly modulated (for example, by seasonal variations) and vaccination has the same period, the vaccination pulses must be properly synchronized; a wrong vaccination phase can impede disease extinction.

We study the thermally driven denaturation of a double-stranded polymer in the presence of a stretching force via Monte-Carlo simulations. When one strand only is stretched, the denaturation transition is first order, while when both strands are stretched, melting is second order. By revisiting the Poland-Scheraga model for DNA melting, we show that at room temperature, the most likely scenario is that DNA melts as it overstretches. Our results are in general agreement with the most recent experiments and suggest how varying temperature and stretching mode may help settle the question whether S-DNA exists or not.