We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spect...
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We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.
Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second ...
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Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a nondifferentiable term due to the frictional contact. We prove that these C^0 DG methods are consis tent and st able, and derive optimal order error estima tes for the quadratic element. A numerical example is presented to show the performance of the C^0 DG methods;and the numerical convergence orders confirm the theoretical prediction.
We examine the derivation of eddy-diffusivity equations for transport of passive scalars in a turbulent velocity field. Our main contention is that, in the long-time–large-distance limit, the eddy-diffusivity equatio...
We examine the derivation of eddy-diffusivity equations for transport of passive scalars in a turbulent velocity field. Our main contention is that, in the long-time–large-distance limit, the eddy-diffusivity equations can take very different forms according to the statistical properties of the subgrid velocity, and that these equations depend very sensitively on the interplay between spatial and temporal velocity fluctuations. Such crossovers can be represented in a ‘‘phase diagram’’ involving two relevant statistical parameters. Strikingly, the Kolmogorov-Obukhov statistical theory is shown to lie on a phase-transition boundary.
Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different...
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We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and speci...
We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is estab...
We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is established due to the formation of discontinuities of the temperature gradient in the form of thermal ripples between contiguous convective cells. The results support the applicability of Sivashinsky's model equation beyond its mathematical limit of validity.
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperatu...
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ET≊k−7/5 and E≊k−11/5, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.
We present a physical model constructed from the Navier-Stokes equation to describe the evolution of the probability distribution function of transverse velocity gradients in 3D isotropic turbulence. Quanitative agree...
We present a physical model constructed from the Navier-Stokes equation to describe the evolution of the probability distribution function of transverse velocity gradients in 3D isotropic turbulence. Quanitative agreement with data from direct numerical simulations of isotropic turbulence for a wide range of Reynolds number is obtained. The model is based on a concrete physical picture of self-distortion of structures and interaction between random eddies and structures; the dynamical balance explains the non-Gaussian equilibrium probability distributions.
Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusi...
Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusive media are treated. Rotating-wave solutions are found to be discretely selected by the system and an isolated, complex-conjugate pair of eigenmodes is shown to cause instability of these waves. The instability arises at the point of zero curvature on the spiral interface and results in wavelike disturbances which propagate from this point along the interface.
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