Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential ene...
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Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model f...
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The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400...
The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400. The process has been documented in several eXperimental mvestigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the NavierStokes equations at representative Reynolds numbers, up to 500. A high-order timeaccurate, miXed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vorteX street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vorteX filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vorteX filaments. Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance intermittent phenomena. It is concluded that the wake undergoes transit
We present our recent work on the Weyl-Heisenberg ensemble and its statistical properties [4]. The WH ensemble is a class of determinantal point processes associated with the Schrodinger representation of the Heisenbe...
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ISBN:
(纸本)9781538615669
We present our recent work on the Weyl-Heisenberg ensemble and its statistical properties [4]. The WH ensemble is a class of determinantal point processes associated with the Schrodinger representation of the Heisenberg group. As a special example, WH ensembles include a multi-layer extension of the Ginibre ensemble modeling the distribution of electrons in higher Landau levels. We describe the hyperuniformity of WH ensembles, which characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. Our approach is based on methods from time-frequency analysis. We introduce the main results from [4] highlighting time-frequency techniques and connections to the theory of polyanalytic functions, and also present some small extensions.
We report first results of a large-scale simulation of two-dimensional quantum gravity using the dynamical triangulation model for systems of up to sixteen thousand triangles. Our results for the internal geometry sho...
We report first results of a large-scale simulation of two-dimensional quantum gravity using the dynamical triangulation model for systems of up to sixteen thousand triangles. Our results for the internal geometry show an unexpectedly complicated behavior of the internal volume as function of the internal radius. A simple fractal characterization is inadequate to describe the geometry of the states in the system.
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capaci...
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Deep neural networks have been demonstrated to be vulnerable to adversarial attacks, where small perturbations intentionally added to the original inputs can fool the classifier. In this paper, we propose a defense me...
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We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this ab...
A numerical and phenomenological study of the gradient descent (GD) algorithm for training two-layer neural network models is carried out for different parameter regimes when the target function can be accurately appr...
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Despite their rich information content,electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally *** introduce a transferable high-fidelity neural network representati...
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Despite their rich information content,electronic structure data amassed at high volumes in ab initio molecular dynamics simulations are generally *** introduce a transferable high-fidelity neural network representation of such data in the form of tight-binding Hamiltonians for crystalline *** predictive representation of ab initio electronic structure,combined with machinelearning boosted molecular dynamics,enables efficient and accurate electronic evolution and *** it is applied to a one-dimension charge-density wave material,carbyne,we are able to compute the spectral function and optical conductivity in the canonical *** spectral functions evaluated during soliton-antisoliton pair annihilation process reveal significant renormalization of low-energy edge modes due to retarded electron-lattice coupling beyond the Born-Oppenheimer *** availability of an efficient and reusable surrogate model for the electronic structure dynamical system will enable calculating many interesting physical properties,paving the way to previously inaccessible or challenging avenues in materials modeling.
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