A simple analytic hydrodynamic model for expanding fireballs

A simple analytic solution is presented for the non-linear hydrodynamic equations describing a free isentropic expansion into vacuum. A “break-up” concept is introduced yielding a well-defined break-up time, density, temperature and final state inclusive particle spectrum.     

Dilepton production in an expanding baryon-rich quark-gluon fireball

From the full stopping scenario, the dilepton production in a baryon-rich quark-gluon fireball has been studied based on a relativistic hydrodynamic model. Due to the influence of the phase boundary on the evolution of the system, the quark phase gives the dominant contribution to the dilepton spectrum. In particular, with increasing initial baryon density, the total dilepton yield first rapidly rises when the initial hadronic system goes to the initial quark system, then goes down owing to the suppression of the dilepton production, thus making a characteristic peak signaling the formation of the baryon-rich quark-gluon matter which appears in the total yield. These characteristics can be tested in future experiments at CERN and Brookhaven.     

On the possibility of an analytic solution of the three-body problem

Three-body Faddeev equations in the Noyes-Fiedeldey form are rewritten as a matrix analog of a one-dimensional nonrelativistic Schrödinger equation. Unlike the method of K-harmonics, where a similar equation was obtained by expansion of a three-body Schrödinger equation wavefunction into the orthogonal set of functions of two variables (K-harmonics), the use of the Noyes-Fiedeldey form of Faddeev equations allows us to limit ourselves to the expansion in functions of one variable only. The solutions of the above mentioned matrix equation are obtained. These solutions converge uniformly within every interval of continuity of the matrix, which corresponds to the potential of that equation. Their asymptotic behavior for large interparticle distances is discussed. The solutions for the harmonic oscillator, inverse-square, and Coulomb-Kepler potentials are found. It is shown that energy levels in the last case may be calculated from a simple formula which is very similar to the corresponding formula for the two-body Coulomb-Kepler problem. This formula can be easily generalized to the case of n particles interacting with inverse distance potentials.     

An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation

An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities.     

Simple analytic solution of fireball hydrodynamics

A new family of simple analytic solutions of hydrodynamics is found for slowly expanding, rotationally symmetric fireballs assuming an ideal gas equation of state. The temperature profile is position-independent only in the collisionless gas limit. The Zimányi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamic particle sources are recovered as special cases. The results are applied to predict new features of proton correlations and spectra for 1.93 AGeV Ni+Ni collisions.     

Tunneling from a 3-dimensional quantum well in an electric field: an analytic solution

We derive the stationary tunneling solution for charged particles moving in a spherical, 3-dimensional zero-range potential plus a constant electric field. From the analytic expression for the wave function we calculate the distribution of the current inside and outside the vacuum barrier. At low field strengths there is a constant spreading of the tunnel current orthogonal to the direction of the applied field. At intermediate field strengths the exact results for the current distribution behave different from the semiclassical predictions.     

Thermodynamic properties of cubic boron nitride based on an analytic mean field approach

We present a detailed derivation of the analytic expressions for the equation of state (EOS) and internal energy of Morse model solids based on an analytic mean field potential (AMFP) method. The formalism is applied to cubic boron nitride (c-BN). One set of potential parameters are determined by fitting the experimental P-V-T data of c-BN up to 160 GPa at 295 K and 80 GPa in the range 500–900 K. Various physical quantities including the isothermals, thermal expansion, isochoric heat capacity, Helmholtz free energy and internal energy are calculated and analyzed. The theoretical results are consistent with the available experimental data and those calculated by others. These results presented in this paper verify that the AMFP method is a useful approach to consider the anharmonic effect at high temperature. Numerous reasonable predictions and the change trend of the properties for c-BN at extreme conditions have been given.     

地-气耦合动力系统的近似解析解

本文研究了一类地-气耦合系统的非线性模式.利用同伦映射方法，将问题转化为线性问题求解.最后得到了原非线性问题的近似表示式. 关键词： 非线性 地-气耦合 动力系统 同伦映射     

On the analytic solution of the lane-emden equation

The Lane-Emden equation describing temperature in a star in hydrostatic equilibrium was recently solved analytically by N.T. Shawagfeh [1] with highly accurate results using decomposition [1–9]. Further consideration suggests some computational advantage, avoidance of the initial transformations, possible generalizations in astrophysics, and a measurement to determine masses of the cepheids.     

Optical oscillator strengths for atomic nitrogen based upon an analytic IPM model

An analytic atomic independent particle model is used to generate optical oscillator strengths for a variety of transitions in atomic nitrogen. The results generally compare favorably with those obtained from Hartree-Fock-Slater calculations and experiment. Where differences arise, it would appear that the parameter adjustment technique of this IPM model insures a closer representation of the properties of excited atomic states.     

A Studying for the Dilepton Mass Spectrum from an Expanding Hot Quark Matter

The relativistic hydrodynamic equations derived from the energy-momentum conservation,are generalized to include the equation of the particle number.The influences of the latent heat and particle distribution on the spectrum are studied on the basis of the generalized formalism.It is shown that these influences should be included,in order to get a reasonable prediction for the formation of the quark matter.     

Exact cosmological solution with particle creation in JBD theory

Exact solutions are sought by taking the generated particles of spin 1/2 (according to the creation rate of Schäfer and Dehnen [1]) as matter sources of the Cosmological equations of JBD theory. There exists one exact solution for which the gravitational constant decreases linearly with time and the mass of the universe increases proportionally to the square of its age (Dirac's hypotheses). The radius of curvature increases linearly with time while the density decreases inversely with it. It is found that for an age of the universe 10^–22 sec only two particles have populated the universe. This is assumed to be the initial state of the model. The calculated present particle number and their density are in agreement with the observed data. This model implies that all present matter (excluding the two initial particles) has been created by the expansion of the universe.Supported in part by CONACYT grant No. 11358.     

The energy of the analytic lump solution in SFT

Journal of High Energy Physics - We study $ \mathcal{N} = 1 $ Minkowski vacua in compactifications of type II string theory in the language of exceptional generalized geometry (EGG). We find the...     

同轴型强流电子束二极管的一种解析近似

从描述电子束运动的基本方程出发,引入一定条件下的近似,获得了一种实用的同轴二极管电流、电压与几何参数关系的近似解析解。给出了同轴二极管阻抗、间隙电压分布与二极管外加电压以及结构参数之间的关系式,并与1维模型精确数值解进行比较分析。采用了PIC数值模拟方法对该理论分析结果在常用参数范围内的准确性进行了验证,获得了一致的结果。与相对论条件下的实验结果数据相比,在二极管电压为300～700 kV时实验结果与该理论估算值非常接近。     

Exact analytic self-similar solution of a wave attractor field

Stratified and rotating fluids support obliquely propagating internal waves. A symmetry-breaking shape of the fluid domain focuses them on a wave attractor. For a trapezoidal basin, it is here shown how to determine the internal wave field analytically. This requires solving the wave equation on a closed domain-an ill-posed Cauchy problem-whose solution exhibits a remarkable self-similar spatial structure. These results are relevant for mixing and mean flow generation in oceans, atmospheres and stars whose symmetry is generally broken and where internal waves are tidally forced.     

同轴型强流电子束二极管的一种解析近似

 从描述电子束运动的基本方程出发,引入一定条件下的近似,获得了一种实用的同轴二极管电流、电压与几何参数关系的近似解析解。给出了同轴二极管阻抗、间隙电压分布与二极管外加电压以及结构参数之间的关系式,并与1维模型精确数值解进行比较分析。采用了PIC数值模拟方法对该理论分析结果在常用参数范围内的准确性进行了验证,获得了一致的结果。与相对论条件下的实验结果数据相比,在二极管电压为300～700 kV时实验结果与该理论估算值非常接近。     

追踪问题轨迹的解析解

关于追踪目标问题,一般文献仅计算了追上所用的时间,或者在给定位置追上的条件下,追踪者与目标的速度比的取值.而获得追踪者运动轨迹的解析解,显然更重要也更困难.本文在追踪问题一般表述的基础上,通过建立并求解追踪者运动的二阶微分方程,得到追踪轨迹的解析解,最后顺便简捷地推导了追上的地点、时间以及在给定位置追上时二者的速度比.