High‐order long‐time approximation of ( N  + 1)‐level systems with near‐resonance control

2021 ◽  
Author(s):  
Ru Geng ◽  
Jian Zu
Keyword(s):  
High Order ◽  
Time Approximation ◽  
Near Resonance ◽  
Long Time ◽  
Resonance Control

Evolution of solitary waves in a two-pycnocline system

2009 ◽  
Vol 642 ◽  
pp. 235-277 ◽  
Author(s):  
M. NITSCHE ◽  
P. D. WEIDMAN ◽  
R. GRIMSHAW ◽  
M. GHRIST ◽  
B. FORNBERG
Keyword(s):  
Solitary Waves ◽  
Initial Conditions ◽  
Oscillation Period ◽  
Resonance Phenomenon ◽  
Numerical Code ◽  
Asymptotic Model ◽  
Narrow Region ◽  
Near Resonance ◽  
Long Time ◽  
The Waves

Over two decades ago, some numerical studies and laboratory experiments identified the phenomenon of leapfrogging internal solitary waves located on separated pycnoclines. We revisit this problem to explore the behaviour of the near resonance phenomenon. We have developed a numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on two separated pycnoclines in a three-layer stratified fluid bounded by rigid horizontal top and bottom walls. We study the dependence of the solution on input system parameters, namely the three fluid densities and the two interface thicknesses, for fixed initial conditions describing isolated mode-two disturbances on each pycnocline. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. However, in a narrow region of parameter space, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is only quasi-periodic, as each wave loses energy into its respective dispersive tail, which causes the spatial oscillation magnitude and period to increase until the waves eventually separate. We record the separation time, oscillation period and magnitude, and the final amplitudes and celerity of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

Long-Time Coherent Integration for Weak Maneuvering Target Detection and High-Order Motion Parameter Estimation Based on Keystone Transform

2016 ◽  
Vol 64 (15) ◽  
pp. 4013-4026 ◽  
Author(s):  
Penghui Huang ◽  
Guisheng Liao ◽  
Zhiwei Yang ◽  
Xiang-Gen Xia ◽  
Jing-Tao Ma ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Target Detection ◽  
High Order ◽  
Motion Parameter ◽  
Maneuvering Target ◽  
Motion Parameter Estimation ◽  
Keystone Transform ◽  
Coherent Integration ◽  
Long Time

scholarly journals FINITE ELEMENT ALGORITHM BASED ON HIGH-ORDER TIME APPROXIMATION FOR TIME FRACTIONAL CONVECTION-DIFFUSION EQUATION

2018 ◽  
Vol 8 (1) ◽  
pp. 229-249 ◽  
Author(s):  
Xin Fei Liu ◽  
◽  
Yang Liu ◽  
Hong Li ◽  
Zhi Chao Fang ◽  
...  
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
High Order ◽  
Time Approximation ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
High Order Time ◽  
Element Algorithm

Long-time simulation of the phase-field crystal equation using high-order energy-stable CSRK methods

2020 ◽  
Vol 364 ◽  
pp. 112981 ◽  
Author(s):  
Jaemin Shin ◽  
Hyun Geun Lee ◽  
June-Yub Lee
Keyword(s):  
Phase Field ◽  
High Order ◽  
Order Energy ◽  
Time Simulation ◽  
Long Time ◽  
Energy Stable ◽  
Phase Field Crystal

A “long-time” approximation for the intensity decay equation in diffusion-limited fluorescence quenching reactions

1989 ◽  
Vol 160 (4) ◽  
pp. 457-463 ◽  
Author(s):  
N. Periasamy ◽  
G.C. Joshi ◽  
Ranjan Das
Keyword(s):  
Fluorescence Quenching ◽  
Time Approximation ◽  
Diffusion Limited ◽  
Long Time ◽  
Intensity Decay

Continued fraction representation for slow neutron scattering. II

1970 ◽  
Vol 48 (5) ◽  
pp. 616-629 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Cross Sections ◽  
Continued Fraction ◽  
Linear Response Theory ◽  
Liquid Argon ◽  
Slow Neutron ◽  
New Approach ◽  
Time Approximation ◽  
Long Time ◽  
Scattering Cross Sections

The calculation of slow neutron scattering cross sections for simple classical liquids by means of Mori's continued fraction representation was discussed in a previous article on the basis of the long-time approximation. In the present work it is shown that by going beyond the long-time approximation one can eliminate certain difficulties that arose in the previous work. This new approach yields results equivalent to those found by Kadanoff and Martin, and others, from linear response theory. Numerical calculations are made for liquid argon and compared with available experimental data.

Long-time stable high-order absorbing boundary conditions for elastodynamics

2012 ◽  
Vol 241-244 ◽  
pp. 20-37 ◽  
Author(s):  
Daniel Baffet ◽  
Jacobo Bielak ◽  
Dan Givoli ◽  
Thomas Hagstrom ◽  
Daniel Rabinovich
Keyword(s):  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary ◽  
Long Time
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