Construction of exact dynamical invariants of two-dimensional classical system

A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates (z, _z ^- ). A fourth-order potential equation is obtained whose solutions directly provide a large class of integrable systems. The potential equation is tested with an interesting example which admits second constants of motion.     

High-frequency Waves in Gravitational Theories with Fourth-order Derivative Equations

For Einstein's gravitational equations with fourth-order corrections being proportional to the square of an elementary length l, we discuss the behaviour of high-frequency waves. It is shown that (1) only waves with lengths λ ? can generate a macroscopic avarage background (for λ < l, only the terms αl² are decisive such that one has the same situation as in a pure fourth-order theory without Einstein term which cannot be interpreted as gravitational theory), (2) for λ ? l the background metric is purely determined via the second-order derivative Einstein tensor (formally one obtains the same equations for the background as in the non-modified Einsteinian theory), and (3) only waves corresponding to the massless and the massive spin-two gravitons contribute to background curvature; in the geometrical-optics approximation, these both particle sorts are moving independent of each other and satisfy a conservation law for the total number of m = 0 and massive spin-two gravitons, respectively. The results obtained in this paper corroborate partly the conclusions drawn in the weak-field approximation [11, 15, 18].     

Thermodynamic perturbation theory for simple polar fluids,I

The application of thermodynamic perturbation theory to the computation of the properties of simple polar fluids is considered. The Helmholtz free energy of a fluid of molecules interacting via a Stockmayer potential v ^S is computed through fourth order in μ, where μ is the dipole moment. Numerical results are obtained on the basis of both the ‘exact’ Monte-Carlo computations for a Lennard-Jones system and the Verlet-Weis perturbation-theoretic computations for that system. The results obtained on the latter basis are then compared with results for a fluid of molecules interacting via a central-force potential v ^ES that is conformal with the Lennard-Jones 6–12 potential and equivalent to the Stockmayer potential through order μ⁴. To facilitate the comparison the v ^ES results are computed according to the Verlet-Weis method. The v ^ES results and the fourth-order (in μ) v ^S results constitute two different approximations to the thermodynamics of the Stockmayer potential; the compressibility factors as well as the free energies of the two approximations are compared.

It is concluded that the thermodynamic contribution of the dipole term of v ^S is significant over the whole liquid region when μ²=εσ³, where ε and σ are the usual Lennard-Jones parameters. For this μ, the two approximations we consider give results in close agreement.     

二维半线性扩散反应方程的高精度全隐格式及其多重网格方法

针对二维非定常半线性扩散反应方程，空间导数项采用四阶紧致差分公式离散，时间导数项采用四阶向后Euler公式进行离散，提出一种无条件稳定的高精度五层全隐格式.格式截断误差为O（τ⁴+τ²h²+h⁴），即时间和空间均具有四阶精度.对于第一、二、三时间层采用Crank-Nicolson方法进行离散，并采用Richardson外推公式将启动层时间精度外推到四阶.建立适用于该格式的多重网格方法，加快在每个时间层上迭代求解代数方程组的收敛速度，提高计算效率.最后通过数值实验验证格式的精确性和稳定性以及多重网格方法的高效性.     

黏性激波管的有限体积WENO格式数值模拟

本文采用OpenFOAM软件下实现的一种可实现任意阶数,可应用于非结构网格的有限体积WENO格式对黏性激波管问题进行模拟.模拟中对流项离散采用3阶精度、4阶精度该类WENO格式,网格形式采用结构网格和三角形非结构网格.结果表明,采用该类格式,三角形非结构网格的算精度、效率优于结构网格,3阶精度格式计算效率优于4阶精度....     

MBPT studies of van der Waals molecules

The many-body perturbation theory is employed for the calculation of the interaction potential for the F^- … He system in the framework of the supermolecule method. A particular attention is paid to the choice of the basis set functions for the two subsystems and the related basis set superposition effects. It has been found that the main features of the interaction potential are recovered in the SCF approximation. The SCF potential has its minimum at the distance R = 6·4 a ₀ with the interaction energy of 53 cm^-1. The complete fourth-order MBPT method gives the potential minimum position and depth equal to 6·5 a ₀ and 64 cm^-1, respectively. The basis set superposition effects estimated by using the counterpoise technique are negligibly small for the SCF interaction potential, while at the correlated level their magnitude is comparable to the value of the total correlation contribution to the interaction energy. The basis set superposition effect in calculations of the electron correlation contribution to weak intermolecular interactions is found to be the major factor limiting the reliability of the corresponding theoretical data.     

Numerical solutions of matrix Riccati equations for radiative transfer in a plane-parallel geometry

Abstract

In this paper, we conduct numerical experiments with matrix Riccati equations (MREs) which describe the reflection (R) and transmission (T) matrices of the specific intensities in a layer containing randomly distributed scattering particles. The theoretical formulation of MREs is discussed in our previous paper where we show that R and T for a thick layer can be efficiently computed by successively doubling R and T matrices for a thin layer (with small optical thickness τ_Δ). We can compute R(τ_Δ) and T(τ_Δ) very accurately using either a fourth-order Runge–Kutta scheme or the fourth-order iterative solution. The differences between these results and those computed by the eigenmode expansion technique (EMET) are very small (<0.1%). Although the MRE formulation cannot be extended to handle the inhomogeneous term (source term) in the differential equation, we show that the force term can be reformulated as an equivalent boundary condition which is consistent with MRE methods. MRE methods offer an alternative way of solving plane-parallel radiative transport problems. For large problems that do not fit into computer memory, the MRE method provides a significant reduction in computer memory and computational time.     

NUMERICAL STUDY ON TUNNELING SPLITTING IN BIAIXAL SPIN SYSTEMS

Numerical study on tunneling splitting in biaxial spin systems is done by performing diagonalization of the Hamilton operator. It is found that the calculated energy splitting agrees quantitatively with theoretical prediction of instanton method. Our result shows that both the instanton method and the large spin limit work well for the total spin around 10. By including the fourth-order term in Hamiltonian, experimental observation can be re-covered quantitatively.     

四阶Colpitts混沌振荡器

提出了一种新的四阶Colpitts混沌振荡器.理论设计与电路实验表明,在三阶Colpitts混沌振荡器中的电感两端并联一个电容器C₃,可构建出一种四阶Colpitts混沌振荡器.当C₃的取值变化时,电路的谐振频率随之改变,从而使该振荡器经过倍周期分岔进入混沌状态.对四阶Colpitts混沌振荡器的平衡点、分岔和李氏指数等基本动力学问题进行了分析.最后通过数值仿真和电路实验证实了这一方法的可行性. 关键词： 四阶Colpitts混沌振荡器 混沌吸引子 电路实现     

On Internucleon Interaction of Composite Nucleon

We discuss the low energy nucleon-nucleon interaction leading to a bound state, namely the deuteron problem. The currently known method of calculating internucleon interactions is the boson exchange potential model, where the Klein-Gordon equation for a virtual pseudoscalar boson with a single point-like nucleon source is solved using the Green function method. This method is known to be inadequate in particular to the internucleon problem leading to a bound state. As an alternative we propose to solve internucleon potential problems, including the bound state, by solving the Klein-Gordon equation in which the interaction term has been introduced in a more invariant way. In the place of the single source term used in the standard method the interaction term is introduced in the covariant derivative form in the spirit of the minimum coupling scheme. It turns out that this method is not only mathematically satisfactory (gauge and Lorentz invariant formalism aspect), but also gives a more physically satisfactory interpretation of the internucleon interaction mechanism. For a deuteron bound state problem can then be solved approximately using the variational calculus. We obtain the analytic expression for the internucleon potential as a function of internucleon distances. The minimum energy value 2,2 MeV, the binding energy of the deuteron, is found to be at equilibrium distance of r_ab = ?_φ = 2 × 10^?13 cm.     

Soliton solutions in an effective action for SU(2) Yang—Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model, which is an O(3) σ model in three dimensional space, upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second-derivative term perturbatively and show that the SFN model with the second-derivative term possesses soliton solutions. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

带三次非线性项的四阶Schr(o)dinger方程的分裂多辛算法

对一类带三次非线性项的四阶Schr(o)dinger方程提出分裂多辛格式.其基本思想是将多辛算法和分裂方法相结合,既具有多辛格式固有的保多辛几何结构的特性,又发挥了分裂方法在计算上灵活高效的特点.数值实验结果表明,分裂多辛格式比其它传统的多辛格式更节约计算时间和计算机的内存,从而更加优越.     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.     

On the T Bloch law in magnets with fourth-order exchange interaction

For the ferromagnets EuS and GdMg, in which fourth-order exchange interactions (i.e. biquadratic, three-spin and four-spin interactions) have been identified, the deviation of the spontaneous magnetization with respect to the T =0 value is shown to follow a T² law instead of the famous T3/2 law expected for a Heisenberg ferromagnet. Moreover, the observed T² law holds for temperatures as large as 0.8T_C and the extrapolated magnetization value for does not conform to ferromagnetic saturation. This is because the fourth-order exchange interactions generate a second order-parameter which is assumed to govern the order of the transverse moment components. These moment components have a finite expectation value for at the expense of the Heisenberg order parameter. Like the spontaneous magnetization, the critical field curves B c ( T ) of the metamagnet EuSe and the antiferromagnet EuTe also start decreasing with a T² term for . It is argued that the T² law is a consequence of the fourth-order exchange interactions. This is shown experimentally by a study of the critical field curves [0pt] pertinent to the longitudinal (Heisenberg) order-parameter in the diamagnetically diluted antiferromagnets Eu_xSr_1-xTe. In this solid solution series a particular composition of x c =0.85 exists at which the different fourth-order interaction processes compensate each other in the high temperature average. As a consequence, an Eu_xSr_1-xTe sample with x =0.85 meets the requirements of a Heisenberg antiferromagnet at least if a quantity is considered for which the high-temperature average over all fourth-order interactions is decisive. This seems to be the case for the critical field curve [0pt] which gives the phase boundary to the paramagnetic phase. In fact, a crossover from a T² to a T3/2 law is observed for [0pt] on approaching x_c. This, we believe, shows the frequently observed T² law is caused by the fourth-order interactions. Received 23 July 1998 and Received in final form 12 October 1998     

Cosmological models with Yang-Mills fields

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.     

The Raman non-gain and self-steepening effects in Raman fiber amplifiers

In Raman fiber amplifiers, due to the strong pump power, the self-steepening effect and Raman non-gain term should be taken into account even for the pico-second pulse's transmission. A model including these effects is established based on the resonant and no-resonant terms of cubic susceptibility tensor (x⁽³⁾). These extra effects will result in the requirement of strict dispersion compensation, which means the second-, third- and fourth-order dispersion should be compensated exactly. Till 95% of the fourth-order dispersion is compensated, 80 fs pulse can keep its shape successfully after 2000 m transmission in Raman amplifiers.     

Extended skyrmion model from quark flavour dynamics

From the effective chiral meson lagrangian derived recently from Nambu-Jona-Lasinio type of quark flavour dynamics, an extended skyrmion model is extracted. This model contains besides the usual Skyrme term further fourth-order derivative terms of the chiral field and in addition the ω meson field. It is shown that the net effect of all fourth-order derivative terms is to destabilize the soliton and to provide the desired medium-range attraction of the nucleon-nucleon interaction, which is responsible for nuclear binding but missing in the original Skyrme model. The soliton is stabilized by the coupling to the ω meson which produces a short-range repulsion. The corresponding equation of state of skyrmion matter is constructed and found to be in qualitative agreement with the equation of state of nuclear matter obtained from effective density-dependent forces.     

Structure factor of charged colloidal suspensions using Brownian-dynamics simulation: Comparison of Yukawa and Sogami pair potentials

Static structure factorsS(Q) are obtained for dilute charged colloidal systems using Brownian dynamics simulation method for the widely used screened Coulomb repulsive Yukawa potential and the recently proposed Sogami pair potential. The latter potential has, in addition to the usual repulsive part, an attractive term which is necessary to understand the reentrant phase transition reported in these colloids. It is shown for the first time thatS(Q) obtained using the Sogami potential for parameters favourable for liquid-like order agrees well with that measured experimentally. Thus it appears that the Sogami potential explains features of a homogeneous liquid as well as phase separated states, whereas Yukawa potential does not.     

Parity-doubling chiral solitons with vector mesons

We argue the presence of new classical solutions with spontaneous parity violation in chiral soliton models coupled with vector fields. Using a variational method, we find that these solutions become stable minima when a coupling of a fourth-order stabilizing term is larger than a critical value. These form an almost degenerate parity doublet via tunneling effects at the semi-classical level.