Rogue waves: New forms enabled by GPU computing

A method to determine parameters governing periodic Riemann theta function rogue-wave solutions to the nonlinear Schrödinger equation is presented. A map of parameter values leading to candidate solutions is developed. In addition to candidate solutions, an overview of qualitative aspects of the solution space can be gained from this map. Based on these findings, several new extreme wave solutions are presented. Although the computations required to determine the map are quite demanding, it is shown that these computations can be efficiently accelerated with a parallel computing architecture. A general purpose computing on a graphics processor unit (GPGPU) implementation yielded a 400× acceleration over a single threaded high level implementation. This acceleration enabled exploration and examination of the solution space, which otherwise would not have been possible. In addition, the solution methodology presented here can be extended to explore other classes of solutions.     

Stress wave propagation in maxwell fluid contained in rigid spherical shells

For stress wave propagation in a rigid spherical shell containing Maxwell fluid subjected to translational and rotational acceleration, the solutions to the governing equations are obtained by employing a finite difference technique, when the input acceleration is a unit step function. The solutions can be extended to accelerations which are general functions of time with the proper discretization of the input acceleration curve. The radial and temporal distribution of the stress waves in both cases are presented. The solutions are also specialized for the case of purely viscous fluids. The applicability of this model for brain injury simulation is briefly discussed.     

Particle dynamics during adiabatic expansion of a plasma bunch

The renormalization-group approach is used to obtain an exact solution to the self-consistent Vlasov kinetic equations for plasma particles in the quasi-neutral approximation. This solution describes the one-dimensional adiabatic expansion of a plasma bunch into a vacuum for arbitrary initial particle velocity distributions. Ion acceleration is studied for two-temperature Maxwellian and super-Gaussian initial electron distributions, which predetermine distinctly different ion spectra. The solution found is used to describe the acceleration of ions of two types. The relative acceleration efficiency of light and heavy ions as a function of atomic weights and number densities is analyzed. The solutions obtained are of practical importance in describing ion acceleration during the interaction of an ultrashort laser pulse with nanoplasma, for example, cluster plasma or plasma produced when thin foils are irradiated by a laser.     

Rotating,charged, and uniformly accelerating mass in general relativity

A new general class of solutions of the Einstein-Maxwell equations is presented. It depends on seven arbitrary parameters that group in a natural way into three complex parameters m + in, a + ib, e + ig, and the cosmological constant λ. They correspond to mass, NUT parameter, angular momentum per unit mass, acceleration, and electric and magnetic charge. The metric is in general stationary and axially symmetric. These solutions are of type D and contain as special cases all known solutions of type D belonging to this class. The known solutions are recovered by performing limiting transitions. An appropriate limit of our solutions describes an electromagnetic field in flat spacetime. We investigate the properties of that field. Its singular region corresponds in general to two circles moving with uniform acceleration in the positive and negative directions along the axis of symmetry. One can easily extend our solutions to the complex domain. Then it turns out that the metric can be written in a double Kerr-Schild form.     

Preliminary study of a niobium quarter-wave prototype cavity for a heavy-ion superconducting linac

Superconducting quarter-wave resonators,due to their compactness and their convenient shape for tuning and coupling,are very attractive for low-β beam acceleration.In this paper,two types of cavities with different geometry have been numerically simulated the first type with larger capacitive load in the beam line and the second type of lollipop-shape for 100 MHz,β=0.06 beams then the relative electromagnetic parameters and geometric sizes have been compared.It is found that the second type,whose structural design is optimized with the conical stem and shaping drift-tube,can support the better accelerating performance.At the end of the paper,some structural deformation effects on frequency shifts and appropriate solutions have been discussed.     

Einige Lösungen der Einsteinschen Feldgleichungen mit idealer Flüssigkeit,die sich in einen fünfdimensionalen flachen Raum einbetten lassen

All solutions of the Einstein equations for a perfect fluid are given, which are invariantly characterized by: embedding class one, Petrov typeD, zero acceleration of matter. Among these solutions are inhomogeneous cosmological models and special solutions with spherical symmetry.     

高品质激光尾波场电子加速器

激光尾波场电子加速的加速梯度相比于传统直线加速器高了3—4个量级,对于小型化粒子加速器与辐射源的研制具有重要的意义,成为当今国内外的研究热点.台式化辐射源应用需求的提高,特别是自由电子激光装置的快速发展,对电子束流品质提出了更高的要求,激光尾波场电子加速的束流品质和稳定性是目前实现新型辐射源的首要障碍.本文归纳整理了中国科学院上海光学精密机械研究所电子加速研究团队十年来在研制台式化激光尾波场电子加速器过程中采取的方案和取得的进展.例如率先提出了注入级和加速级分离的级联加速方案,通过实验获得了GeV量级的电子束能量;基于级联加速方式利用能量啁啾控制,实验获得世界最高品质的电子束流;通过优化激光系统稳定性和特殊的气体喷流结构,获得稳定的高品质电子束流输出等.这一系列实验结果有利于进一步推进激光尾波场电子加速器的应用.     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Anomalous Diffusion Equations with Multiplicative Acceleration

A generalization of the model of Lévy walks with traps is considered. The main difference between the model under consideration and the already existing models is the introduction of multiplicative particle acceleration at collisions. The introduction of acceleration transfers the consideration of walks to coordinate–momentum phase space, which allows both the spatial distribution of particles and their spectrum to be obtained. The kinetic equations in coordinate–momentum phase space have been derived for the case of walks with two possible states. This system of equations in a special case is shown to be reduced to ordinary Lévy walks. This system of kinetic equations admits of integration over the spatial variable, which transfers the consideration only to momentum space and allows the spectrum to be calculated. An exact solution of the kinetic equations can be obtained in terms of the Laplace–Mellin transform. The inverse transform can be performed only for the asymptotic solutions. The calculated spectra are compared with the results of Monte Carlo simulations, which confirm the validity of the derived asymptotics.     

多目标粒子群优化算法在交变相位聚焦直线加速器模拟中的应用

现代智能优化算法粒子群算法\,(Particle Swarm Optimization)\,在加速器设计优化上的应用逐渐增多。交变相位聚焦直线加速器\,(Alternative Phase Focused Drift Tube Linac)\,具有节省空间和造价的优点。将交变相位聚焦直线加速器的初步设计方案作为种子,植入粒子群算法中;以加速器的传输效率和束流能量作为目标,得到该方案的Pareto最优解集;在粒子进化过程中,以前沿解集作为粒子的运动方向,以前沿解集的束流径迹作为粒子的参数来源。最终得到了满足能量增益的高传输效率、大接受度的优化方案。The Particle Swarm Optimization(PSO), one of the modern intelligent optimization algorithms,is increasingly employed in the design and optimization of accelerators. Alternative Phase Focused Drift Tube Linac(APF DTL) has an advantage in cost-effecient fabrication and reduced construction space. The preliminary design of APF DTL is involved in the optimization as the anchor; by taking the acceleration efficiency and the beam energy as two fitness functions, the Pareto optimal set is obtained; the evolutionary direction is determined by the Pareto optimal set and the particles’ parameters in the optimization are derived from the simulations of the randomly selected Pareto optimal solutions. A final optimized design with extracted energy of 5.35 MeV/uand acceleration efficiency greater than 83% is acquired.     

A Parallel Quantum Algorithm for the Satisfiability Problem

In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 （2004） 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.     

Gauss-Bonnet as Effective Cosmological Constant

It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant.We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions.Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter.One branch(the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero,in which case the effective cosmological constant becomes identical with the bare value,while the other(i.e.the "+") branch is singular in the same limit,and beyond this singular limit,the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.     

Macroparticle acceleration by a laser-plasma stream

A physical model is proposed for macroparticle acceleration in an expanding laser plasma. Two acceleration mechanisms are considered, based on absolutely inelastic interaction of the laser-plasma ions with the macroparticle surface: acceleration due to the ion momentum and reactive acceleration due to evaporation of the surface layer. The processes are mathematically described with the aid of the gasdynamics equations with thermal conductivity. Approximate analytic expressions are obtained and permit an estimate of the laser-plasma energy as well as of the quasiparticle momentum as functions of the parameters of the laser pulse, of the target, and of the macroparticle. The analytic solutions are compared with numerical computations using the RAPID program; the comparison confirms that the results agree qualitatively and quantitatively.Quantum Radiophysics Division, Lebedev Physics Institute. Translated from Preprint No. 209 of the Lebedev Physics Institute, Academy of Sciences USSR, Moscow, 1990.     

Singularity-Free Cosmological Solutions with Non-Rotating Perfect Fluids

The paper establishes the result that solutions of the type described in the title of the article are in essence only those that have been already presented in the literature provided the acceleration vector is hypersurface orthogonal. The procedure adopted in the paper is somewhat novel - while the usual practice is to display an exact solution and then to examine whether it is singularity free, the present paper discovers the conditions which a singularity free solution of the desired type must satisfy. There is no attempt to obtain exact solutions. Simply, the conditions that were ad-hoc introduced in the deduction of singularity free solutions are here shown to follow from the requirement of non-singularity.     

Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

Electron acceleration driven by ultrashort and nonparaxial radially polarized laser pulses

Exact closed-form solutions to Maxwell's equations are used to investigate the acceleration of electrons in vacuum driven by ultrashort and nonparaxial radially polarized laser pulses. We show that the threshold power above which significant acceleration takes place is greatly reduced by using a tighter focus. Moreover, electrons accelerated by tightly focused single-cycle laser pulses may reach around 80% of the theoretical energy gain limit, about twice the value previously reported with few-cycle paraxial pulses. Our results demonstrate that the direct acceleration of electrons in vacuum is well within reach of current laser technology.     

Instability of surfactant solution flow in a Taylor cell

The hydrodynamic instability of surfactant solutions between two coaxial cylinders was investigated by using a laser-induced-fluorescence flow visualization technique to clarify the effect of drag-reducing additives on vortex formation in Taylor-Couette flow. The test fluids were Ethoquad O/12 surfactant solutions, which have a gel-like structure called “shear-induced structurer” (SIS). Photographs of the formation of Görtler vortices were taken and compared with these of tap water. In the Taylor number range of 1.2×10⁵≤Ta≤7.1×10⁵, tap water and 10 ppm surfactant solution flows consisted of Taylor vortices and much smaller Görtler vortices at the rotating inner wall. However, for 50 and 100 ppm surfactant solutions, Taylor vortices were not apparent and Görtler vortices were collapsed. Measurements of the wavelength of Görtler vortices lead to the conclusion that surfactant solutions have a stabilizing effect on Görtler instabilities. This effect depends on surfactant concentration and becomes considerable with increasing acceleration of the inner cylinder.     

Pure Kinetic K-essence as the Cosmic Speed-Up

In this paper, we consider three types of k-essence. These k-essence models were presented in the parametric forms. The exact analytical solutions of the corresponding equations of motion are found. It is shown that these k-essence models for the presented solutions can give rise to cosmic acceleration.     

Accelerating universe from an evolving Λ in higher dimension

We find exact solutions in 5D inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial singularity our spacetime is regular everywhere including the centre of the inhomogeneous distribution. We also study the analogous homogeneous universe in (4 + d) dimensions. Here an initially decelerating model is found to give late acceleration in conformity with the current observational demands. We also find that both anisotropy and number of dimensions have a role to play in determining the time of flip, in fact the flip is delayed in multidimensional models. Some astrophysical parameters like the age, luminosity distance, etc., are also calculated and the influence of extra dimensions is briefly discussed. Interestingly our model yields a larger age of the universe compared to many other quintessential models.