We study the pair correlations between prime numbers in an interval M ≤ p ≤ M + L with M → ∞, L/M → β > 0. By analyzing the structure factor, we prove, conditionally on the Hardy-Littlewood conjecture on prim...
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The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in devel...
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作者:
Ma, ZhengTorquato, SalvatoreDepartment of Physics
Princeton University and Princeton New Jersey08544 United States Department of Chemistry
Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
Studies of random organization models of monodisperse (i.e., identical) spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical s...
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Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macromolecules. In a cryo-EM experiment, t...
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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 propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position a...
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We propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position and *** boundary conditions and basis functions are chosen to be commensurate with the bulk *** observe that the ordered nature of modulated structures stabilizes the interface,which enables us to obtain optimal interfacial structures by searching local minima of the free energy *** framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and *** types of novel complex interfacial structures emerge from the calculations.
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is the task of estimating the 3D structure of a molecule from a set of noisy 2D projections, taken from unknown viewing directions. Many algor...
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—In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications, such as 3-D reconstruction using correlation analysis in X-ray free electron laser (XFEL) single molecule imagi...
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This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of...
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