An improved method of detecting and processing for the beacon in satellite-to-ground laser communication links

In satellite-to-ground laser communication links, the motion and vibration of the satellite are important factors that affect the real-time requirements of pointing, acquiring, and tracking. In order to acquire again the beacon quickly and accurately after losing it for a short time, we propose an improved method of detecting and processing for the beacon. In contrast to the conventional design of processing systems for the beacon, the advantage of the system we designed is provided by the spatial environment, where the optical communication terminal is located, and the motion trace of the beacon can be predicted effectively. We perform numerical simulations and simulation experiments, with a sampling frequency of the CCD in a system of 60 Hz and frequency and amplitude of the simulation vibration signal of 1 Hz and 0.1 mrad, respectively. We assume the motion of the satellite to be of translation type. The prediction precision is not more than 6 pixels of the CCD after the algorithm converges and the experimental results correspond fairly to the numerical simulation.     

Lifting the singular nature of a model for peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. Due to the constraint between the pull force, peel angle and the peel force, the equations of motion derived earlier fall into the category of differential-algebraic equations (DAE) requiring an appropriate algorithm for its numerical solution. By including the kinetic energy arising from the stretched part of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics itself, thus circumventing the need to use any special algorithm. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier singular equations. We find that mass has a strong influence on the dynamics of the model rendering periodic solutions to chaotic and vice versa. Apart from the rich dynamics, the model reproduces several qualitative features of the different waveforms of the peel force function as also the decreasing nature of force drop magnitudes.     

Simulating the motion of a quantum particle at constant temperature

The extended system method of Nosé and Hoover for the control of temperature of a classical ensemble if applied to the de Broglie-Bohm-Vigier formulation of quantum mechanics. This allows for the simulation of the motion of a quantum particle at a constant preset temperature. A specific algorithm for numerical solution of the resulting equations of motion, based on the application of the methods of molecular dynamics simulation, is provided.     

非线性动力系统分岔图中的暗线

基于非线性动力系统混沌运动的回归特性，构造了一种对分岔图中穿过混沌区的暗线进行研究的数值回归算法。运用该算法求得抛物线映射的暗线，并与通过暗线方程精确求得的暗线进行比较，验证了算法的有效性。对Brussel振子系统和分段线性单级齿轮动力系统的暗线进行了研究。通过对非线性动力系统分岔图中暗线的研究，由其切点可以得到嵌在混沌区中的周期窗口，由其交点可以得到混沌吸引子的激变点。研究结果表明该算法有助于分析系统的动力学行为和控制混沌运动。     

利用卫星云图反演云导风的新思路

本文首先借助于近年来发展起来的数值微分方法,从图像灰度中提取出图像梯度信息;然后利用正则化方法,实现了云导风反演;最后采用仿真和实际试验两种方法,对云图中有扰动时加入灰度梯度信息和未加入灰度梯度信息的风场反演结果进行比较.结果表明,加入图像灰度梯度信息所实施的新反演方法可有效减小图像干扰的影响,同时也大大提高了风矢量反演的精度,为卫星云图反演云导风探索一条新路子. 关键词： 云导风 数值微分 图像灰度梯度 正则化     

From Nosé–Hoover chain to Nosé–Hoover network: design of non-Hamiltonian equations of motion for molecular-dynamics with multiple thermostats

A systematic algorithm to design multiple thermostat systems in the framework of the Nosé–Hoover type non-Hamiltonian formulation is presented. Using ‘non uniform’ time transformations in a generalised Hamiltonian equation, we develop the non-Hamiltonian equations of motion for multiple thermostat systems having an arbitrary number of thermostats and arbitrary connections between a physical system and thermostats (‘Nosé–Hoover network’). We then present the algorithm to construct the Nosé–Hoover network equations based on a simple diagram only. On the basis of this algorithm, recursively attached Nosé–Hoover thermostats are introduced as an example of the Nosé–Hoover network and its high efficiency in sampling the canonical distribution for an one-dimensional double-well system is illustrated by numerical calculations.     

Efficient algorithms for numerical simulation of the motion of earth satellites

We briefly present our results obtained during the development and an investigation of the efficacy of algorithms for numerical prediction of the motion of earth satellites (ESs) using computers of different power. High accuracy and efficiency in predicting ES motion are achieved by using higher-order numerical methods, transformations that regularize and stabilize the equations of motion, and a high-precision model of the forces acting on an ES. This approach enables us to construct efficient algorithms of the required accuracy, both for universal computers with a large RAM and for personal computers with very limited capacity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 62–70, August, 1992.     

A numerical algorithm for viscous incompressible interfacial flows

We present a new algorithm to numerically simulate two-dimensional viscous incompressible flows with moving interfaces. The motion is updated in time by using the backward difference formula through an iterative procedure. At each iteration, the pseudo-spectral technique is applied in the horizontal direction. The resulting semi-discretized equations constitute a boundary value problem in the vertical coordinate which is solved by decoupling growing and decaying solutions. Numerical tests justify that this method achieves fully second-order accuracy in both the temporal variable and vertical coordinate. As an application of this algorithm, we study the motion of Stokes waves in the presence of viscosity. Our numerical results are consistent with the recently published asymptotic solution for Stokes waves in slightly viscous fluids.     

Hamilton's equations for constrained dynamical systems

We derive expressions for the conjugate momenta and the Hamiltonian for classical dynamical systems subject to holonomic constraints. We give an algorithm for correcting deviations of the constraints arising in numerical solution of the equations of motion. We obtain an explicit expression for the momentum integral for constrained systems.     

Algorithm for molecular dynamics simulations of spin liquids

A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard predictor-corrector schemes. The results obtained for time correlation functions demonstrate the evident dynamic interplay between the liquid and magnetic subsystems.     

On the numerical integration of FPU-like systems

This paper concerns the numerical integration of systems of harmonic oscillators coupled by nonlinear terms, like the common FPU models. We show that the most used integration algorithm, namely leap-frog, behaves very gently with such models, preserving in a beautiful way some peculiar features which are known to be very important in the dynamics, in particular the “selection rules” which regulate the interaction among normal modes. This explains why leap-frog, in spite of being a low order algorithm, behaves so well, as numerical experimentalists always observed. At the same time, we show how the algorithm can be improved by introducing, at a low cost, a “counterterm” which eliminates the dominant numerical error.     

A novel mesh regeneration algorithm for 2D FEM simulations of flows with moving boundary

A novel mesh regeneration algorithm is proposed to maintain the mesh structure during a finite element simulation of flows with moving solid boundary. With the current algorithm, a new body-fitted mesh can be efficiently constructed by solving a set of Laplace equations developed to specify the displacements of individual mesh elements. These equations are subjected to specific boundary conditions determined by the instantaneous body motion and other flow boundary conditions. The proposed mesh regeneration algorithm has been implemented on an arbitrary Lagrangian–Eulerian (ALE) framework that employs an operator-splitting technique to solve the Navier–Stokes equations. The integrated numerical scheme was validated by the numerical results of four existing problems: a flow over a backward-facing step, a uniform flow over a fixed cylinder, the vortex-induced vibration of an elastic cylinder in uniformly incident flow, and a complementary problem that compares the transient drag coefficient for a cylinder impulsively set into motion to that measured on a fixed cylinder in a starting flow. Good agreement with the numerical or experimental data in the literature was obtained and new transient flow dynamics was revealed. The scheme performance is further examined with respect to the parameter employed in the mesh regeneration algorithm.     

Two-dimensional lattice models of the Peierls type

Two-dimensional discrete models are used to describe nonlinear interactions of 'atoms' within interface regions. An evolution algorithm is presented for a distribution of dislocations on a plane. Results of numerical simulations illustrate motion of a dislocation kink. A finite-thickness nonlinear interface is studied in two dimensions; it gives a further extension of the mathematical model to the analysis of contact problems with frictional interfaces.     

The target motion parameters estimation based on the acoustic field interference structure similarity match

A spectral sequence matched algorithm based on acoustic field interference structure is proposed to estimate the target motion parameters.According to the longitudinalcorrelation of the acoustic field using the spectral sequences of different frequencies obtained from the target LOFAR spectrogram and the target range solution vector obtained from the two-azimuth and two-range target motion parameters calculation method,a matching cost factor of the spectral sequences similarity is constructed to...     

Solitary wave solutions for the regularized long-wave equation

The regularized long-wave equation has been solved numerically using the collocation method based on the Adams-Moulton method for the time integration and quintic B-spline functions for the space integration. The method is tested on the problems of propagation of a solitary wave and interaction of two solitary waves. The three conserved quantities of motion are calculated to determine the conservation properties of the proposed algorithm. The L _?? error norm is used to measure the difference between exact and numerical solutions. A comparison with the previously published numerical methods is performed.     

A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line

In this article we discuss the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn–Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient.     

Correction of out-of-FOV motion artifacts using convolutional neural network

PurposeSubject motion during MRI scan can result in severe degradation of image quality. Existing motion correction algorithms rely on the assumption that no information is missing during motions. However, this assumption does not hold when out-of-FOV motion happens. Currently available algorithms are not able to correct for image artifacts introduced by out-of-FOV motion. The purpose of this study is to demonstrate the feasibility of incorporating convolutional neural network (CNN) derived prior image into solving the out-of-FOV motion problem.Methods and materialsA modified U-net network was proposed to correct out-of-FOV motion artifacts by incorporating motion parameters into the loss function. A motion model based data fidelity term was applied in combination with the CNN prediction to further improve the motion correction performance. We trained the CNN on 1113 MPRAGE images with simulated oscillating and sudden motion trajectories, and compared our algorithm to a gradient-based autofocusing (AF) algorithm in both 2D and 3D images. Additional experiment was performed to demonstrate the feasibility of transferring the networks to different dataset. We also evaluated the robustness of this algorithm by adding Gaussian noise to the motion parameters. The motion correction performance was evaluated using mean square error (NMSE), peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM).ResultsThe proposed algorithm outperformed AF-based algorithm for both 2D (NMSE: 0.0066 ± 0.0009 vs 0.0141 ± 0.008, P < .01; PSNR: 29.60 ± 0.74 vs 21.71 ± 0.27, P < .01; SSIM: 0.89 ± 0.014 vs 0.73 ± 0.004, P < .01) and 3D imaging (NMSE: 0.0067 ± 0.0008 vs 0.070 ± 0.021, P < .01; PSNR: 32.40 ± 1.63 vs 22.32 ± 2.378, P < .01; SSIM: 0.89 ± 0.01 vs 0.62 ± 0.03, P < .01). Robust reconstruction was achieved with 20% data missed due to the out-of-FOV motion.ConclusionIn conclusion, the proposed CNN-based motion correction algorithm can significantly reduce out-of-FOV motion artifacts and achieve better image quality compared to AF-based algorithm.     

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Unsteady flows of two immiscible Maxwell fluids in a rectangular channel bounded by two moving parallel plates are studied. The fluid motion is generated by a time-dependent pressure gradient and by the translational motions of the channel walls in their planes. Analytical solutions for velocity and shear stress fields have been obtained by using the Laplace transform coupled with the finite sine-Fourier transform. These analytical solutions are new in the literature and the method developed in this paper can be generalized to unsteady flows of n-layers of immiscible fluids. By using the Laplace transform and classical method for ordinary differential equations, the second form of the Laplace transforms of velocity and shear stress are determined. For the numerical Laplace inversion, two accuracy numerical algorithms, namely the Talbot algorithm and the improved Talbot algorithm are used.     

Numerical Computations for the Schramm-Loewner Evolution

We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The second method can be thought of as the inverse problem. Given a simple curve in the half-plane it computes the driving function in the Loewner equation. This algorithm can be used to test if a given random family of curves in the half-plane is SLE by computing the driving process for the curves and testing if it is Brownian motion. More generally, this algorithm can be used to compute the driving process for random curves that may not be SLE. Most of the material presented here has appeared before. Our goal is to give a pedagogic review, illustrate some of the practical issues that arise in these computations and discuss some open problems.     

A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion

We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of the differential equations of relaxation of moments. This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated. The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems studied. Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999