GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations qn=U＇（qn＋1-qu）-U＇（qn-qn-1）,n∈Z,where qn denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth （Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 （2009）, 3802- 3822）, we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.

Application of ESPRIT in Broad Beam HF Ground Wave Radar Sea Surface Current Mapping

HF surface wave radar system OSMAR2000 is a broad-beam sea-state detecting radar. ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique) algorithm is proposed to apply in DOA (direction of arrival) determination of sea echoes. The algorithm of ESPRIT is briefly introduced first. Then discussions are made on the technique for application in the OSMAR2000 framework. Numerical simulation results are presented to demonstrate the feasibility of radial current mapping based on this method. The algorithm manifests significant performance and computational advantages compared with that of MUSIC. Data acquired by OSMAR2000 are processed to give radial current map and the synthesized vector currents are compared with the in-situ measurement with traditional means. The results show the validity of ESPRIT application in DOA determination for broad-beam radar. Key words HF ground wave radar - sea surface current - ESPRIT - MUSIC CLC number TN 911.72 - TN 958.95 Foundation item: Supported by the National Natural Science Foundation of China (60201003) and the National High Technology Development 863 Program of China (863-818-01-02)Biography: Liu Dan-hong (1976-), female, Master candidate, research direction: radar signal processing.

Estimation of detection threshold in multiple ship target situations with HF ground wave radar

A credible method of calculating the detection threshold is presented for the multiple target situations, which appear frequently in the lower Doppler velocity region during the surveillance of sea with HF ground wave radar. This method defines a whole-peak-outlier elimination （WPOE） criterion, which is based on in-peak-samples correlation of each target echo spectra, to trim off the target signals and abnormal disturbances with great amplitude from the complex spectra. Therefore, cleaned background noise samples are obtained to improve the accuracy and reliability of noise level estimation. When the background noise is nonhomogeneous, the detection samples are limited and often occupied heavily with outliers. In this case, the problem that the detection threshold is overvalued can be solved. In applications on experimental data, it is verified that this method can reduce the miss alarm rate of signal detection effectively in multiple target situations as well as make the adaptability of the detector better.

Estimation of the Direction of Arrival Using Virtual Matrix Method for HF Ground Wave Radar

According to the characteristic of the echo of highfrequency ground wave radar（HF GWR）, which is one-dimensional narrow band signal, a virtual direction of arrival（DOA） matrix is constructed at first, then the DOA of target evaluation is achieved by the method of resolving equations for two-dimensional DOA matrix. And this method bases on the redundancy information of a linear two-row array of antennae. Both the simulation process and the treatment results of measured data （in the case of low SNR echoes and short data series） are given at the end of this paper. By comparing with GPS data of the targets, the validity and practical applicability of the method in this paper is verified.

Solving Schrodinger Equation with Soft Constrained Monotonic Neural Network

Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.

Solving Schrodinger equations using a physically constrained neural network

Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.