The short-time behavior of the turbulent viscosity is inferred from the immediate response of the Reynolds stress deduced by Crow [1] for the problem of isotropic turbulence subjected to a mean strain at time t=0. The...
In this paper, a spectral method is formulated as a numerical solution for the stochastic Ginzburg-Landau equation driven by space-time white noise. The rates of pathwise convergence and convergence in expectation in ...
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A second moment turbulence closure model of the type used before for flows with density stratification, frame rotation and streamline curvature is augmented to describe MHD flows with small magnetic Reynolds number. I...
Kinetic Monte Carlo(KMC)is a stochastic model used to simulate crystal ***,most KMC models rely on a pre-defined lattice that neglects dislocations,lattice mismatch and strain *** this paper,we investigate the use of ...
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Kinetic Monte Carlo(KMC)is a stochastic model used to simulate crystal ***,most KMC models rely on a pre-defined lattice that neglects dislocations,lattice mismatch and strain *** this paper,we investigate the use of a 3D off-lattice KMC *** test this method by investigating impurity diffusion in a strained FCC *** faster than a molecular dynamics simulation,the most general implementation of off-lattice KMC is much slower than a lattice-based *** improved procedure is achieved for weakly strained systems by precomputing approximate saddle point locations based on unstrained lattice *** this way,one gives up some of the flexibility of the general method to restore some of the computational speed of lattice-based *** addition to providing an alternative approach to nano-materials simulation,this type of simulation will be useful for testing and calibrating methods that seek to parameterize the variation in the transition rates for lattice-based KMC using continuum modeling.
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...
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Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
Robertson and Seymour prove that a set of graphs of bounded tree-width is well-quasi-ordered by the graph minor relation. By extending their methods to matroids, Geelen, Gerards, and Whittle prove that a set of matroi...
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The results of numerical simulations of random-force-driven Navier-Stokes turbulence designed to test predictions of the renormalization group theory of turbulence are presented. By specially choosing the random force...
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The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use...
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The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. ''Counting lemmas'' for the non-selfadjoint operator L, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite disc D in the complex eigenvalue plane. The radius of the disc D is controlled by the H-1 norm of the potential q. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds - ''whiskered tori'' for the NLS pde. The Floquet discriminant DELTA(lambda;q) used to introduce a natural sequence of NLS constants of motion, [F(j)(q) = DELTA(lambda = lambda(j)c(q);q), where lambda(j)c denotes the j(th) critical point of the Floquet discriminant DELTA(lambda)]. A Taylor series expansion of the constants F(j)(q), with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of F(j)(q), which themselves are expressed in terms of quadratic products of eigenfunctions of L. The second variation permits identification, within the disc D, of important bifurcations m the spectral configurations of the operator L. The constant F(j)(q), as the height of the Floquet discriminant over the critical point lambda(j)c, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, {F(j)(q)}\j\>N, which is associated with critical points outside the disc D. Within this disc, the interpretation is only valid locally, with the s
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Me...
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Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface(PES)is the philosopher's stone for unraveling the nature of matter via atomistic *** has b...
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Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface(PES)is the philosopher's stone for unraveling the nature of matter via atomistic *** has been particularly challenging for multi-component alloy systems due to the complex and non-linear nature of the associated *** this work,we develop an accurate PES model for the Al-Cu-Mg system by employing deep potential(DP),a neural network based representation of the PES,and DP generator(DP-GEN),a concurrent-learning scheme that generates a compact set of ab initio data for *** resulting DP model gives predictions consistent with first-principles calculations for various binary and ternary systems on their fundamental energetic and mechanical properties,including formation energy,equilibrium volume,equation of state,interstitial energy,vacancy and surface formation energy,as well as elastic *** benchmark shows that the DP model is ready and will be useful for atomistic modeling of the Al-Cu-Mg system within the full range of concentration.
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