Infinite Compressibility States in the Hierarchical Reference Theory of Fluids. I. Analytical Considerations

In its customary formulation for one-component fluids, the Hierarchical Reference Theory yields a quasilinear partial differential equation (PDE) for an auxiliary quantity f that can be solved even arbitrarily close to the critical point, reproduces non-trivial scaling laws at the critical singularity, and directly locates the binodal without the need for a Maxwell construction. In the present contribution we present a systematic exploration of the possible types of behavior of the PDE\ for thermodynamic states of diverging isothermal compressibility _T as the renormalization group theoretical momentum cutoff approaches zero. By purely analytical means we identify three classes of asymptotic solutions compatible with infinite _T, characterized by uniform or slowly varying bounds on the curvature of f, by monotonicity of the build-up of diverging _T, and by stiffness of the PDE in part of its domain, respectively. These scenarios are analzyed and discussed with respect to their numerical properties. A seeming contradiction between two of these alternatives and an asymptotic solution derived earlier [Parola et al., Phys. Rev. E 48:3321 (1993)] is easily resolved.     

Numerical integration of the fluctuating hydrodynamic equations

An approach to numerically integrate the Landau-Lifshitz fluctuating hydrodynamic equations is outlined. The method is applied to one-dimensional systems obeying the nonlinear Fourier equation and the full hydrodynamic equations for a dilute gas. Static spatial correlation functions are obtained from computer-generated sample trajectories (time series). They are found to show the emergence of long-range behavior whenever a temperature gradient is applied. The results are in very good agreement with those obtained from solving the correlation equations directly.     

Asymptotic properties of coupled nonlinear langevin equations in the limit of weak noise. II: Transition to a limit cycle

We apply the singular perturbation technique, developed in the companion paper, to the study of the fluctuations at the onset of a limit cycle, both for the cases of a soft and a hard transition. The technique and results are illustrated on the Poincaré model (soft transition) and on the Van der Pol oscillator (hard transition).     

A Remark on the Use of Differential Forms for the Skyrme Problem

We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S³ _r R⁴, and S³ ₁ is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R₀ (3/2, 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = 2.     

Simulation of Stochastic Differential Equations Through the Local Linearization Method. A Comparative Study

A new local linearization (LL) scheme for the numerical integration of nonautonomous multidimensional stochastic differential equations (SDEs) with additive noise is introduced. The numerical scheme is based on the local linearization of the SDE's drift coefficient by means of a truncated Ito–Taylor expansion. A comparative study with the other LL schemes is presented which shows some advantanges of the new scheme over other ones.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. II. The Charged System and the Two-Component Burgers Equations

We further study the stochastic model discussed in ref. 2 in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.     

Numerical investigation of the partial oxidation process in porous media based reformer

Numerical investigation of the thermal partial oxidation process of Methane in porous media based reformer is performed. A finite volume based CFD code, including radiation modeling, in combination with a detailed chemical kinetics scheme is used to perform the numerical simulation. A heterogeneous approach for the heat transport modeling in porous media (separate coupled energy equations for the gas and solid phases) was used. Validation of the model with experimental data is also performed. The model was able to predict the temperature behavior in the reformer reasonably well. However, the concentrations of H₂ and CO were under predicted while the H₂O concentration was over predicted.     

双辉光放电静电场数值模拟及场分布边角效应分析

根据双辉光放电3个电极极板上的电势,利用边界元积分方程建立以面电荷密度为未知量的离散方程,通过求解线性方程组计算3个电极极板上面电荷的不均匀分布.由极板上的不均匀面电荷分布计算在真空状态下空间任意一点的电势和电场的空间分布,利用数值解对真空状态下双辉光离子渗金属实验装置场分布边角效应进行了分析.     

A Numerical Study of the Dynamics of Vector-Born Viral Plant Disorders Using a Hybrid Artificial Neural Network Approach

Most plant viral infections are vector-borne. There is a latent period of disease inside the vector after obtaining the virus from the infected plant. Thus, after interacting with an infected vector, the plant demonstrates an incubation time before becoming diseased. This paper analyzes a mathematical model for persistent vector-borne viral plant disease dynamics. The backpropagated neural network based on the Levenberg—Marquardt algorithm (NN-BLMA) is used to study approximate solutions for fluctuations in natural plant mortality and vector mortality rates. A state-of-the-art numerical technique is utilized to generate reference data for obtaining surrogate solutions for multiple cases through NN-BLMA. Curve fitting, regression analysis, error histograms, and convergence analysis are used to assess accuracy of the calculated solutions. It is evident from our simulations that NN-BLMA is accurate and reliable.     

Numerical analysis of the mechanism of carrier transport in organic light—emitting devces

The mechanism of carrier transport in organic light-emitting devices is numerically studied,on the basis of trappedcharge-limited conduction with an exponential trap distribution.The spatial distributions of the electrical potential,field and carrier density in the organic layer are calculated and analysed.Most carriers are distributed near the two electrodes,only a few of them are distributed over the remaining part of the orgaic layer,The carriers are accumulated near the electrodes,and the remaining region is almost exhausted of carriers.When the characteristic energy of trap distribution is greater than 0.3eV.it leads to a reduction of current density.In order to improve the device efficiency,organic materials with minor traps and low characteristic energy should be chosen.The diffusion current is the dominant component near the injection electrode.whereas the drift current dominates the remaining region of the organic layer.     

向内发射同轴虚阴极振荡器波束互作用的数值模拟研究

对向内发射同轴虚阴极振荡器微波主频进行了解析求解, 利用稳态相对论流体Maxwell方程组得到了微波主频所满足的方程; 同时使用MAFIA程序的TS3模块对向内发射同轴虚阴极振荡器中波束互作用进行了全三维PIC数值模拟研究, 通过对微波输出圆波导中5个传输模式的监测,得到了各模式的频谱分布及输出功率. 结果表明, 在有阳极反射板存在时, 构成的准腔结构能够有效地改善频谱, 从而提高能量转换效率.     

New Developments in the Eight Vertex Model II. Chains of Odd Length

We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity pointsη=mK/L with m odd the transfer matrix is known to satisfy the famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(υ) matrix is qualitatively different from the case of evenN and in particular they satisfy a previously unknown equation which is more general than what is often called ‘‘Bethe’s equation.’’ For the case of even m where no Q(υ) matrix is known we demonstrate that there are many states which are not obtained from the formalism of the SOS model but which do satisfy the TQ equation. The ground state for the particular case of η=2K/3 and N odd is investigated in detail.     

Blood flow of Jeffrey fluid in a catherized tapered artery with the suspension of nanoparticles

Current letter deals with the mathematical models of Jeffrey fluid via nanoparticles in the tapered stenosed atherosclerotic arteries. The convection effects of heat transfer with catheter are also taken into account. The nonlinear coupled equations of nanofluid model are simplified under mild stenosis. The solutions for concentration and temperature are found by using homotopy perturbation method, whereas for velocity profile the exact solution is calculated. Moreover, the expressions for flow impedance and pressure rise are computed and discussed through graphs for different physical quantities of interest. The streamlines have also been presented to discuss the trapping bolus discipline.     

Experimental and Numerical Investigation of the Effect of Turbulator on Heat Transfer in a Concentric-type Heat Exchanger

This article experimentally and numerically analyzes the effect of turbulators with different geometries (Type I, Type II, Type III, and Type IV) located at the inlet of the inner pipe in a concentric-type heat exchanger. Experiments were performed at parallel-flow conditions in the same and opposite directions to investigate the impact of manufactured turbulators on heat transfer and pressure drop. In the numerical study, ANSYS 12.0 Fluent code program was used, and basic protection equations were solved in the steady-state, three-dimensional, and turbulence-flow conditions. Results were obtained from numerical analysis conducted at different flow values of air (7, 8, 9, 10, 11, and 12 m³/h). The distribution of temperature, velocity, and pressure was demonstrated as a result of numerical analyses. Experimental and numerical results were compared, and it was observed that they were in conformity with each other. When the data obtained from the analyses were examined, the highest heat transfer, pressure drop, and friction factor increase were detected to be in the Type IV turbulator.     

Ergodic theory of the mixmaster universe in higher space-time dimensions. II

The topological dynamics of the mixmaster models in space-time dimension d+1 are investigated. We use a new parametrization to reduce the mixmaster map to a translation combined with an appropriate isometry or a dilating inversion. For d9, we show that the mixmaster map is ergodic and topologically mixing. For d10, the mixmaster map reduces to the identity after a finite number of iterations, except for a set of initial data with zero Lebesgue measure.Chargé de recherches au Fonds National de la Recherche Scientifique.     

Theory of the Robin quantum wall in a linear potential. II. Thermodynamic properties

A theoretical analysis of the thermodynamic properties of the Robin wall characterized by the extrapolation length Λ in the electric field that pushes the particle to the surface is presented both in the canonical and two grand canonical representations and in the whole range of the Robin distance with the emphasis on its negative values which for the voltage‐free configuration support negative‐energy bound state. For the canonical ensemble, the heat capacity at exhibits a nonmonotonic behavior as a function of the temperature T with its pronounced maximum unrestrictedly increasing for the decreasing fields as and its location being proportional to . For the Fermi‐Dirac distribution, the specific heat per particle is a nonmonotonic function of the temperature too with the conspicuous extremum being preceded on the T axis by the plateau whose magnitude at the vanishing is defined as , with N being a number of the particles. The maximum of is the largest for and, similar to the canonical ensemble, grows to infinity as the field goes to zero. For the Bose‐Einstein ensemble, a formation of the sharp asymmetric feature on the ‐T dependence with the increase of N is shown to be more prominent at the lower voltages. This cusp‐like dependence of the heat capacity on the temperature, which for the infinite number of bosons transforms into the discontinuity of , is an indication of the phase transition to the condensate state. Some other physical characteristics such as the critical temperature and ground‐level population of the Bose‐Einstein condensate are calculated and analyzed as a function of the field and extrapolation length. Qualitative and quantitative explanation of these physical phenomena is based on the variation of the energy spectrum by the electric field.     

Kinetic Theory of Area-Preserving Maps. Application to the Standard Map in the Diffusive Regime

The evolution of the distribution function of a dynamical system governed by a general two-dimensional area-preserving iterative map is studied by the methods of nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines the angle-averaged distribution function (the density profile). The complementary, angle-dependent part (the fluctuations) is expressed as a non-Markovian functional of the density profile. Whenever there exist two widely separated intrinsic time scales, the master equation can be markovianized, yielding an asymptotic kinetic equation. The general theory is applied to the standard map in the diffusive regime, i.e., for large stochasticity parameter and large scale length. The non-Markovian master equation can be written and solved analytically in this approximation. The two characteristic time scales are exhibited. This permits the thorough study of the evolution of the density profile, its tendency toward the Markovian approximation, and eventually toward a diffusive Gaussian packet. The evolution of the fluctuations is also described in detail. The various relaxation processes are governed asymptotically by a single diffusion coefficient, which is calculated analytically. This model appears as a testing bench for the study of kinetic equations. The various previous approaches to this problem are reviewed and critically discussed.