We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.

Generation of intense coherent THz radiation by obliquely incidenting an intense laser pulse on a wire target is studied using particle-in-cell simulation. The laser-accelerated fast electrons are confined and guided along the surface of the wire, which then acts like a current-carrying line antenna and under appropriate conditions can emit electromagnetic radiation in the THz regime. For a driving laser intensity $\sim 3\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$ and pulse duration $\sim 10$ fs, a transient current above 10 KA is produced on the wire surface. The emission-cone angle of the resulting $\sim 0.15$ mJ ($\sim 58$ GV/m peak electric field) THz radiation is $\sim {30}^{\circ }$. The conversion efficiency of laser-to-THz energy is $\sim 0.75\%$. A simple analytical model that well reproduces the simulated result is presented.

An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.

The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.

We study the dynamics of the out-of-equilibrium nonlinear $q$-voter model with two types of susceptible voters and zealots, introduced in Mellor et al. [Europhys. Lett. 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1\ne q_2$ and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the nonequilibrium stationary state of the system in terms of its probability distribution, nonvanishing currents, and unequal-time two-point correlation functions. We also study the switching time properties of the model by exploiting an approximate mapping onto the model of Mobilia [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and we outline some properties of the model near criticality.

The entanglement entropy $\mathcal{S}$ is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension $\mathcal{S}$ generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the $Q$-state quantum Potts chain for $Q>4$ and calculate $\mathcal{S}$ across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point $\mathcal{S}$ shows a jump, which is expected to vanish for $Q\to 4^{+}$. This jump is calculated in leading order as $\mathrm{\Delta }\mathcal{S}=lnQ[1-4/Q-2/(QlnQ)+O(1/Q^2)]$.

We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.

Multistrategy evolutionary games are studied on a square lattice when the pair interactions are composed of coordinations between strategy pairs and an additional term with self-dependent payoff. We describe a method for determining the strength of each elementary coordination component in $n$-strategy potential games. Using analytical and numerical methods, the presence and absence of Ising-type order-disorder phase transitions are studied when a single pair coordination is extended by some types of self-dependent elementary games. We also introduce noise-dependent three-strategy equivalents of the $n$-strategy elementary coordination games.

This paper examines the behavior of the dimensionless dissipation rate $C_{\varepsilon }$ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for $C_{\varepsilon }$ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote $C_{\varepsilon ,\infty }$ lie between $0.193\le C_{\varepsilon ,\infty }\le 0.268$ for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure $C_{\varepsilon ,\infty }=0.223$.

We develop an approach for computing the hydrodynamic friction tensor and scalar friction coefficient for an aerosol fractal aggregate in the transition regime. Our approach involves solving the Bhatnagar-Gross-Krook equation for the velocity field around a sphere and using the velocity field to calculate the force on each primary sphere in the aggregate due to the presence of the other spheres. It is essentially an extension of Kirkwood-Riseman theory from the continuum flow regime to the entire Knudsen range (Knudsen number from 0.01 to 100 based on the primary sphere radius). Our results compare well to published direct simulation Monte Carlo results, and they converge to the correct continuum and free molecule limits. Our calculations for clusters with up to 100 spheres support the theory that aggregate slip correction factors collapse to a single curve when plotted as a function of an appropriate aggregate Knudsen number. This self-consistent-field approach calculates the friction coefficient very quickly, so the approach is well-suited for testing existing scaling laws in the field of aerosol science and technology, as we demonstrate for the adjusted sphere scaling method.

The majority-vote model with noise was studied on the 11 Archimedean lattices by the Monte Carlo method and finite-size scaling. The critical noises and critical exponents were obtained with precision. Contrary to some previous reports, we confirmed that the majority-vote model on the Archimedean lattices belongs to the two-dimensional Ising universality class. It was shown that very precise determination of the critical noise is required to obtain proper values of the critical exponents.

The Giardinà-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time evolution of the population probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a two-state model.

Theory predicts that parametrically excited oscillators, tuned to operate under resonant condition, are capable of large-amplitude oscillation useful in diverse applications, such as signal amplification, communication, and analog computation. However, due to amplitude saturation caused by nonlinearity, lack of robustness to model uncertainty, and limited sensitivity to parameter modulation, these oscillators require fine-tuning and strong modulation to generate robust large-amplitude oscillation. Here we present a principle of self-tuning parametric feedback excitation that alleviates the above-mentioned limitations. This is achieved using a minimalistic control implementation that performs (i) self-tuning (slow parameter adaptation) and (ii) feedback pumping (fast parameter modulation), without sophisticated signal processing past observations. The proposed approach provides near-optimal amplitude maximization without requiring model-based control computation, previously perceived inevitable to implement optimal control principles in practical application. Experimental implementation of the theory shows that the oscillator self-tunes itself near to the onset of dynamic bifurcation to achieve extreme sensitivity to small resonant parametric perturbations. As a result, it achieves large-amplitude oscillations by capitalizing on the effect of nonlinearity, despite substantial model uncertainties and strong unforeseen external perturbations. We envision the present finding to provide an effective and robust approach to parametric excitation when it comes to real-world application.

The self-similar propagation of asymptotic optical beams in semiconductor waveguides doped with quantum dots is reported. The possibility of controlling the shape of output asymptotic optical beams is demonstrated. The analytical results are confirmed by numerical simulations. We give a possible experimental protocol to generate the obtained asymptotic parabolic beams in realistic waveguides. As a generalization to the present work, the self-similar propagation of asymptotic optical beams is proposed in a power-law nonlinear medium.

The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models. Nevertheless, these stochastic models overlooked the influence of rational decisions on the outcome of the process. For instance, different levels of trust in acquaintances do play a role in information spreading, and actors may change their spreading decisions during the information diffusion process accordingly. Here, we study an information-spreading model in which the decision to transmit or not is based on trust. We explore the interplay between the propagation of information and the trust dynamics happening on a two-layer multiplex network. Actors' trustable or untrustable states are defined as accumulated cooperation or defection behaviors, respectively, in a Prisoner's Dilemma setup, and they are controlled by a memory span. The propagation of information is abstracted as a threshold model on the information-spreading layer, where the threshold depends on the trustability of agents. The analysis of the model is performed using a tree approximation and validated on homogeneous and heterogeneous networks. The results show that the memory of previous actions has a significant effect on the spreading of information. For example, the less memory that is considered, the higher is the diffusion. Information is highly promoted by the emergence of trustable acquaintances. These results provide insight into the effect of plausible biases on spreading dynamics in a multilevel networked system.

Because of the holonomic constraints, the kinetic energy contribution in the partition function of an inextensible polymer chain is difficult to find, and it has been systematically ignored. We present the first thermodynamic calculation incorporating the kinetic energy of an inextensible polymer chain with the bending energy. To explore the effect of the translation-rotation degrees of freedom, we propose and solve a statistical model of a fully flexible chain of $N+1$ linked beads which, in the limit of smooth bending, is equivalent to the well-known wormlike chain model. The partition function with the kinetic and bending energies and correlations between orientations of any pair of links and velocities of any pair of beads are found. This solution is precise in the limits of small and large rigidity-to-temperature ratio $b/T$. The last exact solution is essential as even very “harmless” approximation results in loss of the important effects when the chain is very rigid. For very high $b/T,$ the orientations of different links become fully correlated. Nevertheless, the chain does not go over into a hard rod even in the limit $b/T\to \infty$: While the velocity correlation length diverges, the correlations themselves remain weak and tend to the value $\propto T/(N+1).$ The $N$ dependence of the partition function is essentially determined by the kinetic energy contribution. We demonstrate that to obtain the correct energy and entropy in a constrained system, the $T$ derivative of the partition function has to be applied before integration over the constraint-setting variable.

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size $L\times L$ and in the thermodynamic limit $L\to \infty$, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

We evaluate the effect of the aspect ratio, i.e., the distance between the propellers $H$ divided by the diameter $D$, on the slow dynamics of a von Kármán swirling flow driven by two propellers in a closed cylinder. We use a cell with a fixed diameter $D$ but where the distance between the propellers can be turned continuously and where the inertia from the propellers can also be changed using different gears. No change on the dynamics is observed when the momentum of inertia is modified. Some dramatic changes of the shear layer position are observed modifying the aspect ratio $\mathrm{\Gamma }=H/D$. A bifurcation of the shear layer position appears. Whereas for low $\mathrm{\Gamma }$ the shear layer position has a smooth evolution when turning the asymmetry between the rotation frequency of the propellers, for high $\mathrm{\Gamma }$ the transition becomes abrupt and a symmetry breaking appears. Secondly we observe that the spontaneous reversals with large residence times already observed in this experiment for $\mathrm{\Gamma }=1$ [de la Torre and Burguete, Phys. Rev. Lett. 99, 054101 (2007)] exist only in a narrow window of aspect ratio. We show using an experimental study of the mean flow structure and a numerical approach based on a Langevin equation with colored noise that the shear layer position seems to be decided by the mean flow structure, whereas the reversals are linked to the spatial distribution of the turbulent fluctuations in the cell.