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...
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...
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This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
The detection and unfolding of degenerate local bifurcations provides one of very few generally applicable analytical tools for studying complex dynamics in systems of arbitrarily high dimension. Using the Brusselator...
The detection and unfolding of degenerate local bifurcations provides one of very few generally applicable analytical tools for studying complex dynamics in systems of arbitrarily high dimension. Using the Brusselator partial differential equations (PDEs) (Prigogine and Lefever, 1968) as motivation and main example, we critically review this method. We extend and correct previous calculations, presenting explicit formulae from which normal forms accurate to third order may be computed, and for the first time we carefully compare bifurcations and dynamics of these normal forms with those of the untransformed systems restricted to a center manifold, and with Galerkin and finite difference approximations of the original PDE. While judicious use of symbolic manipulations makes feasible such high-order center manifold and normal form calculations, we show that the conclusions drawn from them are of limited use in understanding spatio-temporal complexity and chaos. As Guckenheimer (1981) argued, the method permits proof of existence of quasi-periodic motions and, under mild genericity assumptions, Sil'nikov chaos (sub-shifts of finite type), but the parameter and phase space ranges in which these results may be applied are extremely small.
Stealthy hyperuniform (SHU) many-particle systems are distinguished by a structure factor that vanishes not only at zero wavenumber (as in "standard" hyperuniform systems) but also across an extended range o...
Stealthy hyperuniform (SHU) many-particle systems are distinguished by a structure factor that vanishes not only at zero wavenumber (as in "standard" hyperuniform systems) but also across an extended range of wavenumbers near the origin. We generate disordered SHU packings of identical and ‘nonoverlapping’ spheres in d-dimensional Euclidean space using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. Compared to SHU packings without soft-core repulsions, these SHU packings are ultradense with packing fractions ranging from 0.67-0.86 for d = 2 and 0.47-0.63 for d = 3, spanning a broad spectrum of structures depending on the stealthiness parameter χ. We consider two-phase media composed of hard particles derived from ultradense SHU packings (phase 2) embedded in a matrix phase (phase 1), with varying stealthiness parameter χ and packing fractions . Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely, the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes at a small wavenumber, implying perfect transparency for the corresponding wavevectors. While a larger packing fraction yields a smaller transparency interval, we show that it also displays a reduced height of the attenuation peak. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media, showing that one leads to infor
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.
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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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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In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionalit...
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In secure multi-party computations (SMC), parties wish to compute a function on their private data without revealing more information about their data than what the function reveals. In this paper, we investigate two ...
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The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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