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作者： Zhang, Jianing Texas A&M University

学位级别：Ph.D.

Surface roughness, a fundamental characteristic of atmospheric ice particles, is essential for defining an appropriate particle morphology model to simulate optical properties of atmospheric particles. This dissertation presents a dynamic stochastic parameterization approach based on combining the discrete differential geometry and stochastic partial differential equations to generate particle overall shapes and the degree of surface roughness. The scattering of light by particles modeled as Gaussian spheroids with size parameters up to 300 is simulated with the Invariant Imbedding T-Matrix (II-TM) method to investigate the effect of particle surface roughness on the single-scattering properties, including the phase matrix, single-scattering albedo, and extinction efficiency. It is shown that high-frequency oscillations of the phase matrix with respect to scattering angle are gradually suppressed as the degree of roughness increases. The dissertation presents a more thorough method of roughened particles in light scattering computation than various ad hoc methods reported in the literature. We discuss how surface roughness influences the Muller matrix patterns of ice particles. These results also enable better understanding of microphysics on ice surface and more accurate parameterization of atmospheric ice particles. We show that surface irregularity changes the phase matrix elements dramatically. An analysis of optical modeling of mineral dust aerosols as Gaussian spheroids is presented. The modeling results are compared with experimental measurements of feldspar to validate the applicability of roughened model particles. The Gaussian spheroids shows better data fitting than smooth spheroids. Furthermore, we analyze population density and shape distributions of Gaussian spheroid for different mineral dust species. In addition to the scattering study, we propose a new Monte Carlo method for radiative transfer based on the metropolis algorithm.

关键词： Spectral method T-Matrix Surface roughness Random field metropolis algorithm Thesis

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A HIERARCHICAL MULTIVARIATE BAYESIAN APPROACH TO ENSEMBLE MODEL OUTPUT STATISTICS IN ATMOSPHERIC PREDICTION

A HIERARCHICAL MULTIVARIATE BAYESIAN APPROACH TO ENSEMBLE MO...

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作者： Robert D. T. Wendt NAVAL POSTGRADUATE SCHOOL

学位级别：博士

Previous research in statistical post-processing has found systematic deficiencies in deterministic forecast guidance. As a result, ensemble forecasts of sensible weather variables often manifest biased central tendencies and anomalous dispersion. In this way, the numerical weather prediction community has largely focused on upgrades to upstream model components to improve forecast performance-that is, innovations in data assimilation, governing dynamics, numerical techniques, and various parameterizations of subgrid-scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to ensemble model output statistics. This technique directly parameterizes meteorological phenomena with probability distributions that describe the intrinsic structure of observable data. Bayesian posterior beliefs in model parameter were conditioned on previous observations and dynamical predictors available outside of the parent ensemble. An adaptive variant of the random-walk metropolis algorithm was used to complete the inference scheme with block-wise multiparameter updates. This produced calibrated multivariate posterior predictive distributions (PPD) for 24-hour forecasts of diurnal extrema in surface temperature and wind speed. These Bayesian PPDs reliably characterized forecast uncertainty and outperformed the parent ensemble and a classical least-squares approach to multivariate multiple linear regression using both measures-oriented and distributions-oriented scoring rules.

关键词： ensemble model output statistics statistical post-processing multivariate multiple linear regression Bayesian data analysis Bayesian hierarchical modeling Markov chain Monte Carlo methods metropolis algorithm machine learning atmospheric prediction

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Path Integral Monte Carlo Simulation of Helium-4 Nanodroplets

Path Integral Monte Carlo Simulation of Helium-4 Nanodroplet...

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作者： Marcus Ahlstrom KTH Royal Institute of Technology

学位级别：硕士

Quantum effects in many-body systems of 4 He at low temperature are studied in a two dimensional droplet geometry using a path integral simulation of worldlines of 4 He atoms. The implementation of an effective metropolis-Hastings algorithm is discussed in some detail. We investigate the dependency on multiple parameters: droplet diameter, worldline lengths, number of particles involved, and investigate their effects on the energy, heat capacity and RMS-distance between particles. The cases of Bose-Einstein and Boltzmann statistics, and of interacting and free systems are compared. We find that Bose-Einstein statistics start affecting the interacting systems around 3K, a much higher temperature than expected. We discuss the implication the finite-size space and low density of the simulation volumes may have on these re- sults. The free systems have small differences in energy, with a larger difference in heat capacity than expected, likely due to finite-size effects. The RMS-distance shows that the lack of periodic boundary allows the particles to escape their re- spective potential wells, and diffuse to the domain walls. We also discuss possible future extensions to three dimensions, calculation of su- perfluid density, and effects of entanglement on the entropy.

关键词： Path Integral Monte Carlo metropolis algorithm helium-4 Bose-Einstein statistics superfluidity

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Monte Carlo Pottsův model

Monte Carlo Pottsův model

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作者： Vlachovský, Karel Charles University of Prague

Potts model is a generalisation of the Ising model which is used in statistical mechanics. Our goal is to sample from the distribution of that model. However, the state space is too large, so we cannot sample from it directly. We will use Markov Chain Monte Carlo methods instead. It means that the markov chain would have Potts distribution as its stationary distribution. We will compare Gibbs sampler, metropolis algorithm, Swendsen-Wang algorithm and significantly we will introduce a new mixing algorithm. We will show that all these algorithms are uniformly ergodic. We will implement them and show that it is wise to use only mixing algorithm and Swendsen-Wang algorithm for larger parameter of temperature for Potts model. 1

关键词： Markov chain MCMC simulation Potts model Gibbs sampler metropolis algorithm Mixing of markov kernels Swendsen-Wang algorithm

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Mechanism of nucleation and incipient growth of Re clusters in irradiated W-Re alloys from kinetic Monte Carlo simulations

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Physical Review B 2017年第9期96卷 094108-094108页

作者： Chen-Hsi Huang Leili Gharaee Yue Zhao Paul Erhart Jaime Marian Department of Materials Science and Engineering University of California Los Angeles California 90095 USA Department of Physics Chalmers University of Technology S-412 96 Gothenburg Sweden Department of Mechanical and Aerospace Engineering University of California Los Angeles California 90095 USA

High-temperature, high-dose, neutron irradiation of W results in the formation of Re-rich clusters at concentrations one order of magnitude lower than the thermodynamic solubility limit. These clusters may eventually transform into brittle W-Re intermetallic phases, which can lead to high levels of hardening and thermal conductivity losses. Standard theories of radiation-enhanced diffusion and precipitation cannot explain the formation of these precipitates and so understanding the mechanism by which nonequilibrium clusters form under irradiation is crucial to predict material degradation and devise mitigation strategies. Here we carry out a thermodynamic study of W-Re alloys and conduct kinetic Monte Carlo simulations of Re cluster formation in irradiated W-2Re alloys. We use a generalized Hamiltonian for crystals containing point defects parametrized entirely with electronic structure calculations. Our model incorporates recently gained mechanistic information of mixed-interstitial solute transport, which is seen to control cluster nucleation and growth by forming quasispherical nuclei after an average incubation time of 13.5(±8.5) s at 1800 K. These nuclei are seen to grow by attracting more mixed interstitials bringing solute atoms, which in turn attracts vacancies leading to recombination and solute agglomeration. Owing to the arrival of both Re and W atoms from the mixed dumbbells, the clusters are not fully dense in Re, which amounts to no more than 50% of the atomic concentration of the cluster near the center. Our simulations are in qualitative agreement with recent atom probe examinations of ion-irradiated W-2Re systems at 773 K.

关键词： Dynamics of phase separation Irradiation effects Microphase separation Alloys 150 ≤ A ≤ 189 Density functional theory First-principles calculations metropolis algorithm Monte Carlo methods

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Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

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Physical Review E 2016年第6期94卷 062407-062407页

作者： H. Salari B. Eslami-Mossallam H. F. Ranjbar M. R. Ejtehadi Department of Physics Sharif University of Technology P.O. Box 11155-9161 Tehran Iran and School of Nano Science Institute for Research in Fundamental Sciences (IPM) Tehran 19395-5531 Iran

Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.

关键词： Chain stiffness Persistence length Polymer behavior Polymer conformation & topology DNA Ideal-chain models metropolis algorithm Monte Carlo methods Worm-like chain model

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Wind field reconstruction with adaptive random Fourier features

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PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2021年第2255期477卷 20210236-20210236页

作者： Kiessling, Jonas Strom, Emanuel Tempone, Raul H Ai AB Stockholm Sweden KTH Royal Inst Technol Stockholm Sweden Rhein Westfal TH Aachen Aachen Germany KAUST Thuwal Saudi Arabia

We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model beta(x)= Sigma(K)(k-1) beta(k) e(i omega kx) approximating the velocity field, with randomly sampled frequencies omega(k) and amplitudes beta(k) trained to minimize a loss function. We include a physically motivated divergence penalty vertical bar del. beta(x)vertical bar(2), as well as a penalty on the Sobolev norm of beta. We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.

关键词： random Fourier features metropolis algorithm spatial interpolation machine learning wind field reconstruction flow field estimation

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Classical statistical mechanics in the grand canonical ensemble

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Physical Review E 2021年第1期104卷 014117-014117页

作者： Philipp Ströker Karsten Meier Institut für Thermodynamik Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg Holstenhofweg 85 22043 Hamburg Germany

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

关键词： Classical statistical mechanics Equations of state metropolis algorithm Monte Carlo methods

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Anomalous Ostwald Ripening Enables 2D Polymer Crystals via Fast Evaporation

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Physical Review Letters 2019年第20期123卷 207801-207801页

作者： Qiyun Tang Marcus Müller Christopher Y. Li Wenbing Hu Department of Polymer Science and Engineering State Key Lab of Coordination Chemistry School of Chemistry and Chemical Engineering Nanjing University 210023 Nanjing China Institut für Theoretische Physik Universität Göttingen Friedrich-Hund-Platz 1 37077 Göttingen Germany Department of Materials Science and Engineering Drexel University Philadelphia Pennsylvania 19104 USA

We demonstrate by molecular simulations that the Ostwald ripening of crystalline polymer nuclei within the fast-evaporation-induced 2D skin layer is retarded at suitable temperatures and evaporation rates. Such an anomalous ripening can be attributed to the interplay between the thermodynamically driven diffusion of noncrystalline fragments toward the growing nuclei and the diffusive current away from the free surface caused by the densification in the nonequilibrium skin layer. The growth orientation of the nuclei inside the skin plane can be adjusted during this anomalous ripening process, which is beneficial for fabricating 2D polymer crystals.

关键词： Crystal growth Crystal orientation Gas-liquid interfaces Polymer solutions Semicrystalline polymers metropolis algorithm

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Role of local atomic short-range order distribution in alloys: Why it matters in Si-Ge-Sn alloys

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Physical Review Materials 2023年第11期7卷 L111601-L111601页

作者： Xiaochen Jin Shunda Chen Christopher Lemkan Tianshu Li Department of Civil and Environmental Engineering George Washington University Washington 20052 DC United States

Short-range order (SRO) in alloys refers to deviations from a perfectly random distribution of atoms in lattice sites within a short distance. Conventionally, the degree of the deviations has been quantified using an average SRO parameter, but such a coarse-grained description does not reflect how the deviations occur at a finer level. Here we show the distribution of the local atomic SRO parameter, which describes the occurring frequency of a local structural motif, carries the crucial information for both structures and properties in Si-Ge-Sn alloy system. This is demonstrated through the fact that distinct SRO structures can exhibit the same average SRO parameter but very different distributions and disparate electronic structures. By deliberately creating special structures that explicitly match the structural information at different levels, we show the distribution of local atomic SRO parameters contain critical structural features that are missing in the average SRO parameter but can substantially contribute to material's properties. Our finding thus calls for the need for considering the finer structural details to effectively describe alloys' structures and properties.

关键词： Structural properties Disordered alloys Elemental semiconductors First-principles calculations metropolis algorithm Monte Carlo methods

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