International Journal of Modern Physics B

In this work, we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicsek's original results. In this work, we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.

We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered (CO) ground states (Wigner and Peierls) as the strength of the longer range interactions is varied. At lower energies, the two CO states drive different spin-ordered ground states (Heisenberg antiferromagnet and dimerised respectively), reminiscent of the phase diagram of the TMTTF and TMTSF organic charge transfer salts. Several response functions computed in the quantum critical regime bear a remarkable resemblance to recent experimental observations related to CO in the organic TMTTF systems. RPA studies of coupled chains reveal a phase diagram with the ordered phase extended to finite temperatures and a phase boundary ending at a quantum critical point (QCP). Critical quantum fluctuations at the QCP enhance the transverse dispersion, leading to a dimensional crossover and a T = 0 deconfinement transition from insulating chains to anisotropic metallic planar behavior. Numerical estimates for the hierarchy of energy scales associated with charge and spin order and the dimensional crossover compare well with the values obtained experimentally. This leads us to propose that the TMTTF and TMTSF systems are proximate to a QCP associated with T = 0 charge order.

In this brief report, two one-dimensional interacting particles interacting with a delta interaction in a harmonic trap is discussed. For strong interactions, we derive the asymptotic expressions for all the energy levels. In addition, the variational method is used to obtain asymptotic ground state energy and wave function. The variational results are compared with the exact solution and they turn out to agree very well.

A spin-rotation symmetry in spin-orbit coupled two-dimensional electron systems gives rise to a long-lived spin excitation that is robust against short-range impurity scattering. The influence of a constant in-plane electric field on this persistent spin helix is studied. To probe the field-induced eigen-modes of the spin-charge coupled system, a surface acoustic wave is exploited that provides the wave-vector for resonant excitation. The approach takes advantage of methods worked out in the field of space-charge waves. Sharp resonances in the field dependence of the in-plane and out-of-plane magnetization are identified.

A systematic theoretical study of the structural properties and stabilities for neutral Si_nO(n = 1-13) clusters and their ions has been carried out using the full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method and the Amsterdam Density Functional (ADF) program with TZ2P basis set in conjunction with self-consistent field (SCF). Their ionization potentials (IPs), electron affinities (EAs), dipole moments μ, constant volume heat capacity C_v are computed. Based on the Mulliken population analyses, it is found that part of electronic charge is transferred from the Si atoms into the oxygen atom. Compared with other structures, the adsorption structures with an edge or a surface O atom are more stable. Calculations also show that the Si_nO clusters with larger HOMO–LUMO gap exhibit high stability.

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.

Based on the one-parameter Lie group theory, we established a modified symmetry reduction method in solving nonlinear variable coefficient equations. Our study shows that the modified method can be applied in solving or reducing various nonlinear variable coefficient equations. In our initial applications, we have successfully obtained some exact solutions to the equations of nonlinear variable coefficients KdV and KP.

The purpose of this study is to obtain some information about the viscoelastic properties of the material and to see the effect of the addition of plasticizer on these properties. In particular, we try to study the loss of plasticizer, caused by ageing under conditions of utilization, on the properties of material at the neighborhood of vitreous transition.

Using a viscoelastimeter, the study of a polyamide-11 (PA11) at the neighborhood of its temperature of vitreous transition Tv has shown that the increase of the plasticizer rate clearly improves the properties of the material by decreasing its Tv temperature. The comparison of the curves giving the modulus of elasticity E' of the various samples showed that the mechanical properties of the material improve with the increase of the concentration of plasticizer, but ageing reduces this improvement by causing the loss of plasticizer, thus, the temperature range of utilization of material is reduced.

Ca_2.7Bi_0.3Co₄O₉ samples have been sintered in temperature range of 1183–1243 K by conventional solid-state reaction method. XRD and SEM investigations show that c-axis-oriented structure could be formed in these samples and Lotgering factors increase with the increase of sintering temperature when it is below 1223 K, from 52% for the sample sintered at 1183 K to 86% for the sample sintered at 1223 K. Due to decomposition of Ca_2.7Bi_0.3Co₄O₉, however, the c-axis-oriented structure was destroyed in the sample sintered at 1243 K although Ca_2.7Bi_0.3Co₄ O₉ phase could be recovered at the cooling stage. The size of grains in all samples increases with the increase of sintering temperature, but the relative densities are almost kept unchanged for the samples sintered at the temperature higher than 1183 K. Due to the highly textured structure, the transport properties of the sample sintered at 1223 K are anisotropic and its ZT values in the ab plane are obviously larger than those along the c-axis.

In this paper we have studied the dynamics of thermal broadband noise-driven dynamical system in terms of information entropy at both the nonstationary and stationary states. Here, a unified description of fluctuating force is considered in a thermodynamically closed system. Based on the Fokker–Planck description of stochastic processes and the entropy balance equation, we have calculated the time-dependence of the information entropy production and entropy flux in the presence and absence of nonequilibrium constraint. Our calculation considers how the time evolution of these quantities is affected if the characteristic of noise changes from white to red or green and red to green in a unified scheme.

The resistive–capacitive–inductive-shunted (RCL-shunted) Josephson junction (RCLSJJ) shows chaotic behavior under some parameter conditions. This paper studies chaos control in the RCLSJJ based on the delayed feedback theory. Numerical results demonstrate that chaotic states in this junction can be controlled into stable periodic states by appropriately adjusting the feedback intensity and delay time.

A variable-coefficient variant Boussinesq (VCVB) model describes the propagation of long waves in shallow water, the nonlinear lattice waves, the ion sound waves in plasmas, and the vibrations in a nonlinear string. With the help of symbolic computation, a VCVB model is investigated for its integrability through the Painlevé analysis. Then, by truncating the Painlevé expansion at the constant level term with two singular manifolds, the dependent variable transformations are obtained through which the VCVB model is bilinearized. Furthermore, the corresponding N-solitonic solutions with graphic analysis are given by the Hirota method and Wronskian technique. Additionally, a bilinear Bäcklund transformation is constructed for the VCVB model, by which a sample one-solitonic solution is presented.