Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).     

Collective dynamics near a phase transition in confined fluids

We performed molecular dynamics simulations in the microcanonical ensemble (MEMD) for a "simple" fluid confined between two solid substrates. From the calculation of the intermediate scattering function F(k( parallel ),t) and through the memory function formalism, we extract material ( i.e. transport and thermodynamics) coefficients in the vicinity of the liquid-gas phase transition. Our results show that approaching the limit of stability ( i.e. the spinodal), the dynamics of the system changes markedly.     

X-ray study of the PZT solid solutions near the morphotropic phase transition

In the solid solutions Pb(Zr_xTi_1?x)O₃ it is stated that for x ? 0.55 there is a morphotropic phase change. Thermodynamically, it is expected that there will be a region of x, in which the two phases coexist and obey the leverage law. By X-ray diffraction, we found that the two phases coexist for x between 0.49 and 0.64. In this range the lattice parameters do not change, and the leverage law is obeyed. We conclude that an adequate explanation of the particular properties of the PZT solutions has to be found.     

On the dynamics of Heisenberg magnets with lattice anisotropy near the phase transition

The kinetic theory (mode-mode coupling theory) is applied to lattice anisotropic Heisenberg ferromagnets and anti-ferromagnets in the paramagnetic region near the phase transition. The distinction of a hydrodynamic and a critical region is refined by introducing regimes of essentially lower-dimensional (1-d or 2-d) behavior and three-dimensional behavior of the magnet. In the regime of 3-d behavior the scaling function of the line-width of the dynamic spin correlation function is discussed extensively.     

Kurtosis and compressibility near the chiral phase transition

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second-order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of mπ$m_{\pi }$. For physical mπ$m_{\pi }$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large mπ$m_{\pi }$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1$2+1$ flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop.     

Microscopic mean-field boson approach to the shape transition in Sm isotopes

The phase transition from spherical to deformed shape in nuclei ^146–156Sm is analyzed within the mean-field approximation applied to the Dyson boson image of the shell-model hamiltonian. No quasiparticle transformation is involved in the present approach and the Pauli principle in the physical boson subspace is approximately taken into account. The low-energy spectra, B(E2; 0₁⁺→ 2₁⁺) values and the corresponding transition densities are calculated. The results provide a reasonable explanation of the shape transition in the Sm isotopes. The role of bosons with different angular momenta is investigated and it is found that the g-bosons (J = 4) cannot be neglected in the transitional region. Comparison of the present results with those of other approaches is given as well.     

Controlling traffic flow near the transition to the synchronous flow phase

For constant incoming flow far upstream of a freeway on-ramp, the flow downstream (throughput) and the rate of merging are studied with simulations using a generalized optimal velocity model. For large enough merge rates, a transition to synchronous flow occurs and the throughput is reduced by 0.5–0.7 vehicle on average for each vehicle that merges. For smaller merge rates there is free flow on the freeway and the throughput is the sum of the merge rate and the flow upstream of the on-ramp. Thus, there is an optimum merge rate that maximizes the throughput for a given incoming flow rate. These results hold for a wide range of initial vehicle position and velocity profiles and for single- as well as double-lane freeways. The results show that the transition to synchronous flow is due to the dynamics of the merge process, rather than to a limitation on the capacity of the downstream portion of the freeway. As a consequence, a new on-ramp metering algorithm, which controls the merge rate to prevent the transition to synchronous flow and concomitantly to maximize flow, has been developed.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

Pyroelectric and elastic properties of lead magnesium niobate-and barium titanate-based solid solutions near a phase transition

The pyroelectric, elastic, and electrostrictive properties of lead magnesium niobate-and barium titanate-based solid solutions were studied under a dc electric field near a phase transition. The results obtained for a relaxor transition (in a lead magnesium scandium niobate solid solution) are compared with those derived for a conventional ferroelectric transition (in a barium strontium titanate solid solution). The dielectric and electromechanical contributions to the induced pyroelectric effect are discussed.     

Crystal shape near the faceting phase transition point

The critical behavior of an equilibrium shape of a crystal with the size much larger than the capillary length is studied near the faceting phase transition point.     

Pion propagation near the QCD chiral phase transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.     

Comments on the paper “X-ray study of the PZT solid solutions near the morphotropic phase transition”

The statement of Ari-Gur's and Benguigui's paper about invariability of the lattice parameters in the interval of tetragonal and rhombohedric phases coexistence in the Pb(Zr, Ti)O₃ system is criticized. The influence of the concentration fluctuations on the width of the phases coexistence interval and the concentration dependence of the lattice parameters is discussed.     

Lattice dynamics and debye-waller factor near the 195 K phase transition in RbCaF3

The experimental temperature dependence of the mean square amplitudes of atoms in RbCaF₃ is compared with the theoretical values calculated from both an harmonic and a quasi rigid ion model. In the light of these results the anhamonicity of the cubic phase is discussed.     

Analytic approach to the motion of cosmological phase transition fronts

We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account the different hydrodynamic modes of propagation. We obtain analytical approximations for the velocity by using the thin wall approximation and the bag equation of state. We compare our results to those of numerical calculations and discuss the range of validity of the approximations. We analyze the structure of the stationary solutions. Multiple solutions may exist for a given set of parameters, even after discarding non-physical ones. We discuss which of these will be realized in the phase transition as the stationary wall velocity. Finally, we discuss on the saturation of the friction at ultra-relativistic velocities and the existence of runaway solutions.     

Network traffic behaviour near phase transition point

We explore packet traffic dynamics in a data network model near phase transition point from free flow to congestion. The model of data network is an abstraction of the Network Layer of the OSI (Open Systems Interconnect) Reference Model of packet switching networks. The Network Layer is responsible for routing packets across the network from their sources to their destinations and for control of congestion in data networks. Using the model we investigate spatio-temporal packets traffic dynamics near the phase transition point for various network connection topologies, and static and adaptive routing algorithms. We present selected simulation results and analyze them.