Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model

2017 ◽  
Vol 9 (4) ◽  
pp. 964-989 ◽  
Author(s):  
Xu Qian ◽  
Hao Fu ◽  
Songhe Song
Keyword(s):  
Dirac Equation ◽  
Theoretical Analysis ◽  
Conservation Laws ◽  
Numerical Experiments ◽  
Quantum Physics ◽  
Structure Preserving ◽  
Splitting Technique ◽  
Nonlinear Dirac Equation

AbstractThe nonlinear Dirac equation is an important model in quantum physics with a set of conservation laws and a multi-symplectic formulation. In this paper, we propose energy-preserving and multi-symplectic wavelet algorithms for this model. Meanwhile, we evidently improve the efficiency of these algorithms in computations via splitting technique and explicit strategy. Numerical experiments are conducted during long-term simulations to show the excellent performances of the proposed algorithms and verify our theoretical analysis.

Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

2014 ◽  
Vol 6 (4) ◽  
pp. 494-514 ◽  
Author(s):  
Yaming Chen ◽  
Songhe Song ◽  
Huajun Zhu
Keyword(s):  
Dirac Equation ◽  
Hamiltonian System ◽  
Numerical Experiments ◽  
Pseudospectral Method ◽  
Splitting Methods ◽  
Fourier Pseudospectral Method ◽  
Composition Method ◽  
Nonlinear Dirac Equation ◽  
Symplectic Scheme ◽  
Symplectic System

AbstractIn this paper, we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac (NLD) equation. Based on its multi-symplectic formulation, the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system. Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem, respectively. And the nonlinear subsystem is solved by a symplectic scheme. Finally, a composition method is applied to obtain the final schemes for the NLD equation. We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly. Numerical experiments are presented to show the effectiveness of the proposed methods.

DISCRETE COMPRESSIVE SOLUTIONS OF SCALAR CONSERVATION LAWS

2004 ◽  
Vol 01 (03) ◽  
pp. 493-520
Author(s):  
BRUNO DESPRÉS
Keyword(s):  
Theoretical Analysis ◽  
Conservation Laws ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Scalar Conservation Laws ◽  
Initial Profile ◽  
Fully Discrete ◽  
Discrete Approach ◽  
Scalar Conservation ◽  
Proof Of Convergence

We prove the convergence of numerical approximations of compressive solutions for scalar conservation laws with convex flux. This new proof of convergence is fully discrete and does not use Kuznetsov's approach. We recover the well-known rate of convergence in O(Δx½). With the same fully discrete approach, we also prove a rate of convergence in O(Δx) uniformly in time, if the initial data is a shock, or asymptotically after the compression of the initial profile. Numerical experiments confirm the theoretical analysis.

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals Solitary waves in the nonlinear Dirac equation in the presence of external driving forces

2016 ◽  
Vol 49 (6) ◽  
pp. 065402 ◽  
Author(s):  
Franz G Mertens ◽  
Fred Cooper ◽  
Niurka R Quintero ◽  
Sihong Shao ◽  
Avinash Khare ◽  
...  
Keyword(s):  
Dirac Equation ◽  
Solitary Waves ◽  
Driving Forces ◽  
Nonlinear Dirac Equation ◽  
External Driving

Theoretical Analysis of the Mass Transport in the Powder Charge in Long-Term Bulk SiC Growth

2004 ◽  
Vol 457-460 ◽  
pp. 67-70 ◽  
Author(s):  
A.V. Kulik ◽  
M.V. Bogdanov ◽  
S.Yu. Karpov ◽  
M.S. Ramm ◽  
Yuri N. Makarov
Keyword(s):  
Theoretical Analysis ◽  
Mass Transport ◽  
Powder Charge

scholarly journals Multivalued Discrete Tomography Using Dynamical System That Describes Competition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Takeshi Kojima ◽  
Tetsushi Ueta ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Numerical Experiments ◽  
Nonlinear Dynamical System ◽  
Reconstructed Image ◽  
Optimization Approach ◽  
Discrete Tomography ◽  
Nonlinear Dynamical ◽  
Time Optimization

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.

scholarly journals Performance Analysis of Maximum Likelihood Estimation for Transmit Power Based on Signal Strength Model

2018 ◽  
Vol 7 (3) ◽  
pp. 38 ◽  
Author(s):  
Xiao-Li Hu ◽  
Pin-Han Ho ◽  
Limei Peng
Keyword(s):  
Maximum Likelihood ◽  
Performance Analysis ◽  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Likelihood Estimation ◽  
Signal Strength ◽  
Strength Model ◽  
Transmit Power ◽  
Ml Estimation ◽  
Theoretical Performance

We study theoretical performance of Maximum Likelihood (ML) estimation for transmit power of a primary node in a wireless network with cooperative receiver nodes. The condition that the consistence of an ML estimation via cooperative sensing can be guaranteed is firstly defined. Theoretical analysis is conducted on the feasibility of the consistence condition regarding an ML function generated by independent yet not identically distributed random variables. Numerical experiments justify our theoretical discoveries.

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