scholarly journals Renormalized analytic solution for the enstrophy cascade in two-dimensional quantum turbulence

2020 ◽  
Vol 5 (7) ◽  
Author(s):  
Andrew Forrester ◽  
Han-Ching Chu ◽  
Gary A. Williams
Keyword(s):  
Analytic Solution ◽  
Quantum Turbulence ◽  
Two Dimensional ◽  
Enstrophy Cascade

scholarly journals Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence

2017 ◽  
Vol 119 (18) ◽  
Author(s):  
Matthew T. Reeves ◽  
Thomas P. Billam ◽  
Xiaoquan Yu ◽  
Ashton S. Bradley
Keyword(s):  
Quantum Turbulence ◽  
Two Dimensional ◽  
Enstrophy Cascade

Study on the Analytic Solution of Two-Dimensional Transient Heat Conduction

2016 ◽  
Author(s):  
Youzhen Yang ◽  
Hu Wang ◽  
Hailong Ma ◽  
Wenguo Ma ◽  
Shenhu Ding ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytic Solution ◽  
Transient Heat Conduction ◽  
Two Dimensional

QUANTUM DYNAMICS OF WAVE PACKET IN HARMONIC POTENTIAL

2005 ◽  
Vol 19 (24) ◽  
pp. 3745-3754
Author(s):  
ZHAN-NING HU ◽  
CHANG SUB KIM
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Analytic Solution ◽  
Nonlinear Differential Equations ◽  
Time Dependent ◽  
Dimensional System ◽  
Two Dimensional ◽  
Vibrational States

In this paper, the analytic solution of the time-dependent Schrödinger equation is obtained for the wave packet in two-dimensional oscillator potential. The quantum dynamics of the wave packet is investigated based on this analytic solution. To our knowledge, this is the first time we solve, analytically and exactly this kind of time-dependent Schrödinger equation in a two-dimensional system, in which the Gaussian parameters satisfy the coupled nonlinear differential equations. The coherent states and their rotations of the system are discussed in detail. We find also that this analytic solution includes four kinds of modes of the evolutions for the wave packets: rigid, rotational, vibrational states and a combination of the rotation and vibration without spreading.

scholarly journals Abrupt Transition between Three-Dimensional and Two-Dimensional Quantum Turbulence

2020 ◽  
Vol 124 (13) ◽  
Author(s):  
Nicolás P. Müller ◽  
Marc-Etienne Brachet ◽  
Alexandros Alexakis ◽  
Pablo D. Mininni
Keyword(s):  
Quantum Turbulence ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Abrupt Transition

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Abir Chaouk ◽  
Maher Jneid
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Fractional Pdes ◽  
Differential Transform ◽  
Computational Work ◽  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

scholarly journals Unitary-quantum-lattice algorithm for two-dimensional quantum turbulence

2011 ◽  
Vol 84 (4) ◽  
Author(s):  
Bo Zhang ◽  
George Vahala ◽  
Linda Vahala ◽  
Min Soe
Keyword(s):  
Quantum Turbulence ◽  
Two Dimensional ◽  
Quantum Lattice ◽  
Lattice Algorithm

scholarly journals Inverse Energy Cascade in Forced Two-Dimensional Quantum Turbulence

2013 ◽  
Vol 110 (10) ◽  
Author(s):  
Matthew T. Reeves ◽  
Thomas P. Billam ◽  
Brian P. Anderson ◽  
Ashton S. Bradley
Keyword(s):  
Quantum Turbulence ◽  
Energy Cascade ◽  
Two Dimensional ◽  
Inverse Energy Cascade

scholarly journals Comparisons of Two Types of Particle Tracking Models Including the Effects of Vertical Velocity Shear

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3535
Author(s):  
Inhwan Park ◽  
Jaehyun Shin ◽  
Hoje Seong ◽  
Dong Sop Rhee
Keyword(s):  
Particle Tracking ◽  
Analytic Solution ◽  
Initial Period ◽  
Computation Method ◽  
Two Dimensional ◽  
Fick’S Law ◽  
Dispersion Process ◽  
Fick's Law ◽  
Shear Dispersion ◽  
Tracking Model

In this study, two types of particle tracking models were presented to investigate the applicability in the two-dimensional solute mixing simulations. The conventional particle tracking model, denoted as PTM, was developed based on Fick’s law, which adopted the dispersion coefficient to calculate the random displacements. The other model is the particle dispersion model (PDM), which computes the shear dispersion process by dividing into two computation procedures as the shear translation and the vertical mixing. The PTM and the PDM included the effects of vertical profiles of velocity in the computation of dispersion coefficients and the shear translation step, respectively. The main difference between the two models is whether the shear dispersion process is reproduced using Fick’s law or the direct computation method. These differences were clearly revealed by comparing with the analytic solution of the advection-dispersion equation. The concentration curve resulting from the PTM shows the Gaussian curves, which were well-fitted with the analytic solution in both initial and Taylor periods. Meanwhile, the PDM presented skewed curves in the initial period and gradually turned to the symmetric shape in the Taylor period. The inherent differences of the two particle tracking models were scrutinized against the two-dimensional tracer test results, which show the non-Fickian mixing properties. The comparisons of concentration–time curves reveal that the PDM reproduced a more accurate shape of the curves than the results by the PTM by demonstrating skewed concentration curves.

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