Multiple Quantum Well in static magnetic field and intense laser pulses

The energy spectrum and dipole matrix elements of a multiple quantum well (MQW) system has been calculated numerically by solving the time-independent Schrödinger equation using finite difference method, in the presence of magnetic field. The effect of barrier width is also investigated. The energy difference between the levels of various minibands and the energy difference between various levels of the same miniband is calculated for different number of wells in the MQW. Finally, the dynamics of the system in short laser pulses has been calculated numerically by solving the time-dependent Schrödinger equation. The effect of magnetic field on the dynamics is clearly shown and explained.     

A Poisson–Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid

We introduce a second-order solver for the Poisson–Boltzmann equation in arbitrary geometry in two and three spatial dimensions. The method differs from existing methods solving the Poisson–Boltzmann equation in the two following ways: first, non-graded Quadtree (in two spatial dimensions) and Octree (in three spatial dimensions) grid structures are used; Second, Neumann or Robin boundary conditions are enforced at the irregular domain’s boundary. The irregular domain is described implicitly and the grid needs not to conform to the domain’s boundary, which makes grid generation straightforward and robust. The linear system is symmetric, positive definite in the case where the grid is uniform, nonsymmetric otherwise. In this case, the resulting matrix is an M-matrix, thus the linear system is invertible. Convergence examples are given in both two and three spatial dimensions and demonstrate that the solution is second-order accurate and that Quadtree/Octree grid structures save a significant amount of computational power at no sacrifice in accuracy.     

微振动激励作用下编组站镜架对光束指向的影响

 编组站是靶场光路传输系统的重要组成部分,编组站镜架的稳定性对光路的传输有着直接的影响。为了分析微振动对光束指向性的影响,采用有限元分析软件建立镜架的有限元模型,将数字式地震仪测得的镜架安装平台的速度功率谱密度函数作为载荷施加到分析模型上,计算得到了编组站光学元件（A,B,C,D）在基座微振动激励作用下的转角漂移分别为0.338,0.327,0.289,0.241 mrad,均小于稳定性指标0.460 mrad的要求;采用加速度传感器对光学元件A的转角漂移测试结果为0.340 mrad,与分析结果的误差为0.6%,说明所采用的计算分析方法是有效的,为精密镜架的设计分析提供了有效的方法。     

Random Motions at Finite Speed in Higher Dimensions

We present a general method of studying the transport process , t≥0, in the Euclidean space ℝ ^m , m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions of are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function (Fourier transform) of in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic function of in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions for the governing partial differential equations, is given. We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m. We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions are considered and some known results are derived as the particular cases of our general model by means of the method developed.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

Ultrasound simulation of real-time temperature estimation during radiofrequency ablation using finite element models

Radiofrequency ablation is the most common minimally invasive therapy used in the United States to treat hepatocellular carcinoma and liver metastases. The ability to perform real-time temperature imaging while a patient is undergoing ablation therapy may help reduce the high recurrence rates following ablation therapy. Ultrasound echo signals undergo time shifts with increasing temperature due to sound speed and thermal expansion, which are tracked using both 1D cross correlation and 2D block matching based speckle tracking methods. In this paper, we present a quantitative evaluation of the accuracy and precision of temperature estimation using the above algorithms on both simulated and experimental data.A finite element analysis simulation of radiofrequency ablation of hepatic tissue was developed. Finite element analysis provides a method to obtain the exact temperature distribution along with a mapping of the tissue displacement due to thermal expansion. These local displacement maps were combined with the displacement due to speed of sound changes and utilized to generate ultrasound radiofrequency frames at specified time increments over the entire ablation procedure. These echo signals provide an ideal test-bed to evaluate the performance of both speckle tracking methods, since the estimated temperature results can be compared directly to the exact finite element solution. Our results indicate that the 1D cross-correlation (CC) method underestimates the cumulative displacement by 0.20 mm, while the underestimation with 2D block matching (BM) is about 0.14 mm after 360 s of ablation. The 1D method also overestimates the size of the ablated region by 5.4% when compared to 2.4% with the 2D method after 720 s of ablation. Hence 2D block matching provides better tracking of temperature variations when compared to the 1D cross-correlation method over the entire duration of the ablation procedure. In addition, results obtained using 1D cross-correlation diverge from the ideal finite element results after 7 min of ablation and for temperatures greater than 65 °C.In a similar manner, experimental results presented using a tissue-mimicking phantom also demonstrate that the maximum percent difference with 2D block matching was 5%, when compared to 31% with the 1D method over the 700 s heating duration on the phantom.     

Finite-size scaling and the renormalization group

Renormalization group calculations ind = 4 andd = 4 – are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this allows a sensible expansion in fluctuations. A combination of Ewald and Poisson sum techniques is used to produce explicit numerical results for the specific heat ind = 4 which, with the setting of two nonuniversal metrical factors and the fourth-order coupling constant may be compared with simulations. The numerical visibility of logarithmic corrections is investigated. The universal scaling function for the specific heat to relativeO() is also evaluated numerically.     

Thermal effects in high-power Nd:YAG disk-type solid state laser

An investigation of thermal effects in a high-power Nd:YAG disk-type solid state laser pumped with different pump beam transverse profiles is carried out by numerical simulation based on the finite element method (FEM). Impact of the heat sink on the thermal effects is included in the simulation. The distribution of first principle stress, thermally induced birefringence, including the distribution and variation of the birefringence loss, are studied. The characteristics of the phase variation are analyzed with consideration of the temperature gradient, deformation, strain and thermal stress. Thermal lensing is explored as a function of pump power and of the radius pumped with different pump beam transverse profiles. The non-parabolic part of optical phase distortion is simulated. Furthermore, the characteristics of the bi-focus of the disk laser are also studied. Experiments on the maximum tensile stress distribution and depolarization loss are carried out. The presented calculations are in qualitative agreement with the experimental observations.     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

Thickness and local field effects on energy transfer rate in coupled quantum wells system: Linear regime

We investigate theoretically the dependence of energy transfer rate in Double-Quantum-Well system on the well thickness by using the balance equation formalism. Also, by including the local field correction in our calculations through the zero- and finite-temperature Hubbard approximations, we study the effect of the short-range interactions on the energy transfer phenomenon. Calculations consider both the static and dynamic screening approximations. Our numerical results predict that the energy transfer rate increases considerably by increasing the layers' thicknesses and by taking into account the short-range interactions, as well.