Hydrodynamic Evolution of Spherical Fireball in Relativistic Heavy Ion Collisions

Evolution process can be calculated from the relativistic hydrodynamic equation with certain estimated initial conditions about a single spherical fireball here.So one can estimate a kind of initial condition qualitatively with a possible energy density about ε0≈1.9 GeV/fm^3,and to fit the experimental data at thermal freeze-out based on this process.The evolution from a cylindrical fireball is discussed simply.     

Long—Range Effects on the Pyroelectric Coefficient of Ferroelectric Superlattice

Long-range effects on the pyroelectric coefficient of a ferroelectric superlattice consisting of two different ferroelectric materials are investigated based on the transverse Ising model.The effects of the interfacial coupling and the thickness of one period on the pyroelectric coefficient of the ferroelectric superlattics are studied by taking into account the long-range interaction.It is found that with the increase of the strength of the long-range interaction,the pyroelectric coefficient decreases when the temperature is lower than the phase transition temperature;the mumber of the pyroelectric peaks decreases gradually and the phase transition temperature increases,It is also found that with the decrease of the interfacial coupling and the thickness of one period.the phase transition temperature and the number of the pyroelectric peaks decrease.     

Six—Parameter Exponential—Type Potential and the Identity for the Exponential—Type Potentials

We propose a six-parameter exponential-type potential (SPEP),which has been shown to be a shapeinvariant potential with a translation of parameters.For this reducible potential,the exact energy levels are obtained by using the supersymmetric shape invariance technique.Choosing appropriate parameters,four classes of exponential-type potentials and their exact energy spectra are reduced from the SPEP and a general energy level formula,respectively.Each class shows the identity except for the different definitions of parameters.     

Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

Controlling Strong Chaos by an Aperiodic Perturbation in Area Preserving Maps

We demonstrate a method for controlling strong chaos by an aperiodic perturbation in two-dimensional Hamiltonian systems.The method has the advantages that the controlled system remains conservative property and the selection of the perturbation has a considerable diversity.We illustrate this method with two area preserving maps:the non-monotonic twist map which is a mixed system and the perturbed cat map which exhibits hard chaos.Numerical results show that the strong chaos can be effectively controlled into regular motions,and the final states are always quasiperiodic ones.The method is robust against the presence of weak external noise.     

Stability of Crystal Growth Face and Dissolution Face in Crystallization from Solution under Microgravity

The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied.It is proved that the stable shapes of crystal growth face and dissolution face do exist,which are suitably shaped curves with their upper parts inclined backward properly.The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters,Ra,Pr and Sc.It is shown that the stronger the convection relative to the diffusion in solution is,the more backward the upper parts of the stable crystal growth face and dissolution face are inclined.The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.     

Difference Discrete Variational Principle,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures II：Euler—Lagrange Cohomology

In this second paper of a series of papers,we explore the difference discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multiparameter differential approach.In terms of the difference discrete Euler-Lagrange cohomological concepts,we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler-Lagrange or canonical equations erived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrange cohomological conditions are satisfied.     

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state.Our results show that the system state will evolve to a squeezed coherent state under the effect of external source.We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation.When the circuit has no dissipation or there is complete coupling between two meshes,the squeezing amplitude parameter only depends on the capacitance‘s ratio.     

Weak Finite—Size Dependence of Velocity and Strong Phase Dependence of Central Charge

We study the finite-size scaling behavior of velocity and central charge for different coupling constants and different phases in (1 1)-dimensional lattice model in very short chains.Using XXZ spin 1/2 chains with 15 or fewer sites,we demonstrate the weak finite-size dependence of spinon velocity for any magnitude of coupling strength Jz and the strong phase dependence of central charge.This behavior of velocity and central charge in different coupling constants and different phases gives a method to determine phase transitions of (1 1)-dimensional models.This method is simple and efficient by utilizing only the ground state energy of very short finite-size chains.It is also general and powerfur for various one-dimensional lattice models and it uncovers eventhe weakest berezinski-Kosterlitz-Thouless phase transitions.     

Ising Transition in Dimerized XY Quantum Spin Chain

We proposed a simple spin-1/2 model which provides an exactly solvable example to study the Ising criticality with central charge c=1/2.By mapping it onto the real Majorana fermions,the Ising critical behavior in explored explicitly,although its bosonized form is not the double frequency sine-Gordon model.