Computation of an infinite integral using series acceleration

A numerical computation in crystallography involves an infinite integral depending on one parameter. In a recent article in this journal this computational problem is addressed using Romberg’s method and tools for error control. One observe numerical difficulties with the reported approach both near the parameter’s endpoints and near the parameter interval’s midpoint. In this short note we will present an alternative approach making use of a known infinite series formulation of the problem at hand and a simple and efficient series acceleration technique. If some care is taken to avoid cancellations the numerical results are excellent for all values of the parameter. AMS subject classification 65B05, 65B10, 65D30     

超薄靶激光质子加速实验研究

在超短超强飞秒SILEX-Ⅰ激光装置上,开展了薄膜靶激光质子加速的实验研究。实验发现激光预脉冲、靶厚度对质子加速有很大的影响。在激光强度3×1018~3×1019W/cm2条件下,采用前表面厚度为3μm铜、后表面镀4μm厚CH靶,质子的最大能量达到3.15 MeV。而对190 nm厚CH膜靶,质子的最大能量为0.54 MeV。初步研究了激光偏振对质子加速的影响,相同激光功率条件下,圆偏振激光加速产生的质子最大能量略低于P偏振打靶。这些结果与靶后鞘层加速机制相一致。     

基于多项式外推的Richardson-Lucy算法加速研究

提出一种新的可加速Richardson-Lucy(R-L)图像迭代恢复算法的方法.该方法基于阻尼R-L算法,通过存储阻尼R-L算法的前若干次(n次)迭代运算结果,利用多项式外推法分析这前n次迭代运算结果,并用一个多项式函数近似描述各结果之间的关系.通过该多项式的外推,预测以后的迭代结果,从而减少迭代运算的次数,取得了较好的加速效果.该方法可以实现几乎没有图像失真的复原,并能应用于其他类型的算法.     

用Excel研究单摆测重力加速度实验中的随机误差分布规律

在单摆法测重力加速度实验中,为了能够快速且正确地得到摆球运动周期的随机误差分布规律,本文提出了一种应用Excel软件给出随机误差统计直方图的方法。该方法简单直观,能够加深同学对随机误差统计规律的认识。     

Reciprocal Relativity of Noninertial Frames and the Quaplectic Group

The frame associated with a classical point particle is generally noninertial. The point particle may have a nonzero velocity and force with respect to an absolute inertial rest frame. In time–position–energy–momentum-space {t, q, p, e}, the group of transformations between these frames leaves invariant the symplectic metric and the classical line element ds² = d t². Special relativity transforms between inertial frames for which the rate of change of momentum is negligible and eliminates the absolute rest frame by making velocities relative but still requires the absolute inertial frame. The Lorentz group leaves invariant the symplectic metric and the line elements and . General relativity for particles under only the influence of gravity avoids the issue of noninertial frames as all particles follow geodesics and hence have locally inertial frames. For other forces, the question of the absolute inertial frame remains.) Born conjectured that the line element should be generalized to the pseudo-orthogonal metric . The group leaving this metrics and the symplectic metric invariant is the pseudo-unitary group of transformations between noninertial frames. We show that these transformations also eliminate the need for an absolute inertial frame by making forces relative and bounded by b and so embodies a relativity that is shape reciprocal in the sense of Born. The inhomogeneous version of this group is naturally the semidirect product of the pseudo-unitary group with the nonabelian Heisenberg group. This is the quaplectic group.     

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应用电子与多光子集团非线性Compton散射模型,将入射和散射光作为离子的传输机制,研究了Compton散射下多束相干强耦合激光等离子体中离子的运动,给出了相对论离子动力学方程,并进行了数值模拟。研究发现,散射使光的传播速度减小,系统的矢势和标势增大,由入射和散射光形成的多束相干强耦合激光能使质子加速到5.40GeV的能量,而耦合轴向电场在其中起着关键作用。     

Separation of particles in time-dependent focusing billiards

We consider a family of stadium-like billiards with time-dependent boundaries. Two different cases of time dependence are studied: (i) the fixed boundary approximation and (ii) the exact model which takes into account the motion of the boundary. It is shown that when the billiards possess strong chaotic properties, the sequence of their boundary perturbations is the Fermi acceleration phenomenon which is three times larger than in the case of the fixed boundary approximation. However, weak mixing in such billiards leads to particle separation. Depending on the initial velocity three different things occur: (i) the particle ensemble may accelerate; (ii) the average velocity may stay constant or (iii) it may even decrease.     

Defect clustering in double doped fluorite crystals with Lu and Gd

Abstract

Solid solutions Ca¹ x-^yLu^xGd^y F_2+x+y for 10^?4 ≤ x ≤ 2 × 10^?2 and y=0.0001 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). It has been found that the ITC spectrum from 77 to 420 K is very weak and the main peak is attributed to the relaxation of both Lu³⁺-F^? _x and Gd³⁺F^? _i nn dipoles. No polarizable clusters are present in the temperature range explored here. The EPR spectra show the presence of Gd³⁺ tetragonal and cubic centers due to the local and non local compensation, respectively. The continuous decrease in the molar fraction of Gd³⁺ tetragonal centers together with the low concentration of Lu nn dipoles is an evidence of the existence at these low and intermediate concentrations of large clusters such as the cubo-octahedral hexamer which has been proposed for CaF₂ crystals very highly doped with small trivalent cations.     

Energy analysis of protons emitted from Nd:YAg laser-generated plasmas

Hydrogenated targets have been irradiated in vacuum with the pulsed Nd:YAg laser at intensities of the order of 10¹⁰ W/cm². The laser-generated plasma, produced by the interaction with the solid, emits protons and other ions along the normal to the target surface. Ion collectors and ion energy analyzer were used to measure the current, the angular emission and the energy distributions of the emitted protons. Time-of-flight measurements, Coulomb–Boltzmann-distributions and the fits of experimental data were also used in order to evaluate the equivalent ion plasma temperature and the ion acceleration developed in the non-equilibrium-pulsed plasma.     

Effects of density profile and multi-species target on laser-heated thermal-pressure-driven shock wave acceleration

The shock wave acceleration of ions driven by laser-heated thermal pressure is studied through one-dimensional particle-in-cell simulation and analysis. The generation of high-energy mono-energetic protons in recent experiments （D. Haberberger et al., 2012 Nat. Phys. 8 95） is attributed to the use of exponentially decaying density profile of the plasma target. It does not only keep the shock velocity stable but also suppresses the normal target normal sheath acceleration. The effects of target composition are also examined, where a similar collective velocity of all ion species is demonstrated. The results also give some reference to future experiments of producing energetic heavy ions.