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Numerical equivalence between sph and probabilistic mass transfer methods for lagrangian simulation of dispersioni

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arXiv 2018年

作者： Sole-Mari, Guillem Schmidt, Michael J. Pankavich, Stephen D. Benson, David A. Universitat Politècnica de Catalunya Barcelona Spain UPC-CSIC Barcelona Spain Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401 United States Hydrologic Science and Engineering Program Department of Geology and Geological Engineering Colorado School of Mines GoldenCO80401 United States

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length ` = √2D∆t, at least given a "dense enough" distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute’s displacement Copyright © 2018, The Authors. All rights reserved.

关键词： Mass transfer

Theory of thin-film-mediated exfoliation of van der Waals bonded layered materials

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Physical Review Materials 2018年第9期2卷 094004-094004页

作者： Haoye Sun Eric W. Sirott James Mastandrea Hannah M. Gramling Yuzhi Zhou Max Poschmann Hayden K. Taylor Joel W. Ager D. C. Chrzan Department of Materials Science and Engineering University of California Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Mechanical Engineering University of California Berkeley California 94720 USA Laboratory of Computational Physics Huayuan Road 6 Beijing 100088 People's Republic of China Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing 100094 People's Republic of China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing 100088 People's Republic of China

Tape-mediated mechanical exfoliation of layered materials is known to require multiple exfoliation steps and to produce small, irregularly shaped monolayer samples. Recently, it has been demonstrated experimentally that deposition of a thin layer of Au on the layer to be exfoliated prior to application of the tape can yield large monolayer samples of transition metal dichalcogenides in one exfoliation step. Here the mechanism underlying these improvements is explored using atomic scale total energy calculations to study thin-film-assisted mechanical exfoliation of both MoS2 and graphene. This study focuses on the influence of epitaxially induced biaxial strain on the exfoliated layer and how this impacts monolayer selectivity during exfoliation. For graphite modeled with a reactive empirical bond order (REBO) plus a Lennard-Jones potential, tensile biaxial strain favors monolayer exfoliation, whereas compressive strain favors multilayer exfoliation. For graphite modeled with a more accurate registry-dependent potential and for MoS2 modeled with a REBO plus a Lennard-Jones potential, both compressive and tensile biaxial strains favor monolayer exfoliation. A simple model based on the interlayer potential is introduced to explain these observations, and a linear stability analysis of this model shows that the differences between the thin-film-assisted exfoliation of the considered materials arise from the stacking structure of the layered material and the details of the interlayer potential. The potential for using this simple model to screen suitable metal films for exfoliation of other 2D materials is discussed.

关键词： 2-dimensional systems Transition metal dichalcogenides

On the expansion complexity of sequences over finite fields

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arXiv 2017年

作者： Gómez-Pérez, Domingo Mérai, László Niederreiter, Harald Department of Mathematics University of Cantabria Santander39005 Spain Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenberger Straße 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenberger Straße 69 LinzA-4040 Austria

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for certain applications. We analyze both, the classical and the modified expansion complexity. Moreover, we also study the expansion complexity of the explicit inversive congruential generator. Copyright © 2017, The Authors. All rights reserved.

关键词： Expansion

Rethinking CO antibiosignatures in the search for life beyond the solar system

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arXiv 2019年

作者： Schwieterman, Edward W. Reinhard, Christopher T. Olson, Stephanie L. Ozaki, Kazumi Harman, Chester E. Hong, Peng K. Lyons, Timothy W. Department of Earth Sciences University of California RiversideCA United States NASA Postdoctoral Program Universities Space Research Association ColumbiaMD United States NASA Astrobiology Institute Alternative Earths & Virtual Planetary Laboratory Teams United States Blue Marble Space Institute of Science SeattleWA United States School of Earth and Atmospheric Sciences Georgia Institute of Technology AtlantaGA United States Department of Geophysical Sciences University of Chicago ChicagoIL United States Department of Environmental Science Toho University Tokyo Japan NASA Goddard Institute for Space Studies New YorkNY United States Department of Applied Mathematics and Applied Physics Columbia University New YorkNY United States Planetary Exploration Research Center Chiba Institute of Technology 2-17-1 Tsudanuma Narashino Chiba275-0016 Japan

Some atmospheric gases have been proposed as counter indicators to the presence of life on an exoplanet if remotely detectable at sufficient abundance (i.e., antibiosignatures), informing the search for biosignatures and potentially fingerprinting uninhabited habitats. However, the quantitative extent to which putative antibiosignatures could exist in the atmospheres of inhabited planets is not well understood. The most commonly referenced potential antibiosignature is CO, because it represents a source of free energy and reduced carbon that is readily exploited by life on Earth and is thus often assumed to accumulate only in the absence of life. Yet, biospheres actively produce CO through biomass burning, photooxidation processes, and release of gases that are photochemically converted into CO in the atmosphere. We demonstrate with a 1D ecosphere-atmosphere model that reducing biospheres can maintain CO levels of ~100 ppmv even at low H2fluxes due to the impact of hybrid photosynthetic ecosystems. Additionally, we show that photochemistry around M dwarf stars is particularly favorable for the buildup of CO, with plausible concentrations for inhabited, oxygen-rich planets extending from hundreds of ppm to several percent. Since CH4buildup is also favored on these worlds, and because O2and O3are likely not detectable with the James Webb Space Telescope, the presence of high CO (>100 ppmv) may discriminate between oxygen-rich and reducing biospheres with near-future transmission observations. These results suggest that spectroscopic detection of CO can be compatible with the presence of life and that a comprehensive contextual assessment is required to validate the significance of potential antibiosignatures. Copyright © 2019, The Authors. All rights reserved.

关键词： Free energy

Scaling laws of ion acceleration in ultrathin foils driven by laser radiation pressure

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arXiv 2018年

作者： Shen, X.F. Qiao, B. He, H. Xie, Y. Zhang, H. Zhou, C.T. Zhu, S.P. He, X.T. Center for Applied Physics and Technology HEDPS State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University Beijing100871 China Shanghai Jiao Tong University Shanghai200240 China Department of Physics Fudan University Shanghai200433 China Shanghai Institute of Laser Plasma CAEP Shanghai201800 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

Scaling laws of ion acceleration in ultrathin foils driven by radiation pressure of intense laser pulses are investigated by theoretical analysis and two-dimensional particle-in-cell simulations. Considering the instabilities are inevitable during laser plasma interaction, the maximum energy of ions should have two contributions: the bulk acceleration driven by radiation pressure and the sheath acceleration in the moving foil reference induced by hot electrons. A theoretical model is proposed to quantitatively explain the results that the cutoff energy and energy spread are larger than the predictions of "light sail" model, observed in simulations and experiments for a large range of laser and target parameters. Scaling laws derived from this model and supported by the simulation results are verified by the previous experiments. Copyright © 2018, The Authors. All rights reserved.

关键词： Ions

Path-based spectral clustering: Guarantees, robustness to outliers, and fast algorithms

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arXiv 2017年

作者： Little, Anna Maggioni, Mauro Murphy, James M. Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Applied Mathematics and Statistics Department of Mathematics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics Tufts University MedfordMA02139 United States

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensional clusters in high-dimensional space, in the presence of a large number of high-dimensional outliers. By combining these results with spectral clustering with respect to LLPD, we provide conditions under which the Laplacian eigengap statistic correctly determines the number of clusters for a large class of data sets, and prove guarantees on the labeling accuracy of the proposed algorithm. Our methods are quite general and provide performance guarantees for spectral clustering with any ultrametric. We also introduce an efficient, easy to implement approximation algorithm for the LLPD based on a multiscale analysis of adjacency graphs, which allows for the runtime of LLPD spectral clustering to be quasilinear in the number of data points. Copyright © 2017, The Authors. All rights reserved.

关键词： Clustering algorithms

Efficient algorithms for T-distributed stochastic neighborhood embedding

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arXiv 2017年

作者： Linderman, George C. Rachh, Manas Hoskins, Jeremy G. Steinerberger, Stefan Kluger, Yuval Applied Mathematics Program Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States Department of Pathology and Applied Mathematics Program Yale University School of Medicine New HavenCT06511 United States

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Numerical approximation to benjamin type equations. Generation and stability of solitary waves

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arXiv 2017年

作者： Dougalis, Vassilios A. Duran, Angel Mitsotakis, Dimitrios Mathematics Department University of Athens Zographou15784 Greece Institute of Applied and Computational Mathematics FO.R.T.H. Heraklion71110 Greece Applied Mathematics Department University of Valladolid Valladolid47011 Spain School of Mathematics and Statistics Victoria University of Wellington PO Box 600 Wellington6140 New Zealand

This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge-Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves. Copyright © 2017, The Authors. All rights reserved.

关键词： Solitons

Dynamical Sampling with Random Noise

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Dynamical Sampling with Random Noise

International Conference on Sampling Theory and Applications

作者： Akram Aldroubi Longxiu Huang Ilya Krishtal Roy Lederman Department of Mathematics Vanderbilt University Department of Mathematics Northern Illinois University Program in Applied and Computational Mathematics Princeton University

ISBN: (纸本)9781538615669

In this paper we consider a system of dynamical sampling, i.e. sampling a signal f that evolves in time under the action of an evolution operator A. We discuss the error in the recovery of the original signal when the samples are corrupted by additive, independent and identically distributed (i.i.d) noise. We focus on the study of the mean squared error E(‖ε_n‖_2~2) between the original signal and the reconstructed signal obtained by solving a least squares problem. In the theoretical part, we give a formula for E(‖ε_n‖_2~2) and prove that E(‖ε_n‖_2~2) decreases as the number of the samples increases. In addition, we discuss several numerical experiments that verify the theoretical results.

关键词： original signal random noise time action formula Identically distributed Mean square error signals