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作者： Johan Bylin Uppsala University

学位级别：硕士

In this thesis, a numerical study of simulating and computing the magnetocaloric properties of magnetic materials is presented. The main objective was to deduce the optimal procedure to obtain the isothermal change in entropy of magnetic systems, by evaluating two different formulas of entropy extraction, one relying on the magnetization of the material and the other on the magnet's heat capacity. The magnetic systems were simulated using two different Monte Carlo algorithms, the metropolis and Wang-Landau procedures. The two entropy methods proved to be comparably similar to one another. Both approaches produced reliable and consistent results, though finite size effects could occur if the simulated system became too small. Erroneous fluctuations that invalidated the results did not seem stem from discrepancies between the entropy methods but mainly from the computation of the heat capacity itself. Accurate determination of the heat capacity via an internal energy derivative generated excellent results, while a heat capacity obtained from a variance formula of the internal energy rendered the extracted entropy unusable. The results acquired from the metropolis algorithm were consistent, accurate and dependable, while all of those produced via the Wang-Landau method exhibited intrinsic fluctuations of varying severity. The Wang-Landau method also proved to be computationally ineffective compared to the metropolis algorithm, rendering the method not suitable for magnetic simulations of this type.

关键词： Magnetocaloric effect Thermodynamics Statistical mechanics Monte Carlo simulations metropolis algorithm Wang-Landau method Isothermal change in entropy Adiabatic change in temperature Numerical methods Effective spin models Condensed Matter Physics

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Effect of increasing the energy gap between the two lowest energy states on the mixing time of the metropolis algorithm

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INFORMATION PROCESSING LETTERS 2012年第23期112卷 922-927页

作者： Nakade, Apurv Biswas, Somenath IIT Kanpur Dept Comp Sci & Engn Kanpur 208016 Uttar Pradesh India Chennai Math Inst Kelambakkam 603103 Siruseri India

In order to understand what makes natural proteins fold rapidly. Sali, Shakhnovich and Karplus (1994) [6,7] had used the metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the metropolis algorithm would find the minimum energy conformation of a chain of beads within an acceptable time scale if and only if there is a large gap between the energies of the minimum energy conformation and that of the second minimum. Clote (1999) [1] attempted to support this conclusion by a proof that the mixing time of the underlying Markov chain would decrease as the gap in energies of the minimum energy conformation and that of the second minimum increased. He was able to show that an upper bound on the mixing time does indeed decrease as the energy gap increases. We show in this paper that the mixing time itself, however, is a non-decreasing function of the value of the energy gap. Therefore, our result contradicts what Clote had attempted to prove. (C) 2012 Elsevier B.V. All rights reserved.

关键词： metropolis algorithm Markov chain mixing time Protein folding Randomized algorithms

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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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Robust adaptive metropolis algorithm with coerced acceptance rate

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STATISTICS AND COMPUTING 2012年第5期22卷 997-1008页

作者： Vihola, Matti Univ Jyvaskyla Dept Math & Stat Jyvaskyla 40014 Finland

The adaptive metropolis (AM) algorithm of Haario, Saksman and Tamminen (Bernoulli 7(2):223-242, 2001) uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance rate. The adaptation rule is computationally simple adding no extra cost compared with the AM algorithm. The adaptation strategy can be seen as a multidimensional extension of the previously proposed method adapting the scale of the proposal distribution in order to attain a given acceptance rate. The empirical results show promising behaviour of the new algorithm in an example with Student target distribution having no finite second moment, where the AM covariance estimate is unstable. In the examples with finite second moments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation.

关键词： Acceptance rate Adaptive Markov chain Monte Carlo Ergodicity metropolis algorithm Robustness

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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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The accuracy of AVA approximations in isotropic media assessed via synthetic numerical experiments: Implications for the determination of porosity

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2018年 170卷 563-575页

作者： Abbasi, Fayyaz-Ur-Rehman Ali, Aamir Alves, Tiago M. Rehman, Khaista Quaid I Azam Univ Dept Earth Sci Islamabad 45320 Pakistan Cardiff Univ Sch Earth & Ocean Sci Seism Lab 3D Cardiff CF10 3AT S Glam Wales Univ Peshawar Natl Ctr Excellence Geol Peshawar 25120 Pakistan

Analyses of seismic amplitude vs. angle are widely used to estimate hydrocarbon reservoir properties. This paper investigates the accuracy of existing approximations based on the Zoeppritz equation, using synthetic numerical experiments that correlate P-wave reflectivity in isotropic media with reservoir porosity. An effective medium non-interacting approach (NIA) in rock physics modelling was used to compute the properties of fluid-saturated (water + gas) reservoir, which were then used in seismic modelling. In parallel, a Bayesian approach was used to estimate reservoir porosities from angle-dependent reflection coefficients and seismic amplitudes. A Maximum a posteriori solution of the Bayesian approach was also utilised to obtain an inverted porosity distribution in the reservoir model. The results of our forward models are important as they suggest that most of the approximations deviate from the exact Zoeppritz solutions with increasing angles of incidence of seismic waves. The results from the Bayesian inversion show that the Ruger and Bortfeld approximations agree with the exact Zoeppritz solutions to accurately estimate reservoir porosity. All the other approximations, except for Smith's, underestimate reservoir porosity and should be used in pre-stack inversion with caution. Smith's and Fatti's approximations failed to estimate reservoir porosity because of associated uncertainties.

关键词： Seismic amplitude vs. angle Rock physics modelling Non-interacting approach Bayesian approach metropolis algorithm Pre-stack seismic inversion

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Improving accuracy of vehicle-terrain interface algorithms for wheeled vehicles on fine-grained soils through Bayesian calibration

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JOURNAL OF TERRAMECHANICS 2018年 77卷 59-68页

作者： Dettwiller, Ian Vahedifard, Farshid Rais-Rohani, Masoud Mason, George L. Priddy, Jody D. US Army ERDC 3909 Halls Ferry Rd Vicksburg MS 39180 USA Mississippi State Univ Dept Aerosp Engn Mississippi State MS 39762 USA Mississippi State Univ CAVS Mississippi State MS 39762 USA Mississippi State Univ Dept Civil & Environm Engn Mississippi State MS 39762 USA Univ Maine Dept Mech Engn Orono ME 04469 USA

The Vehicle-Terrain Interface (VTI) model for off-road vehicle performance is often used in virtual prototyping to support preliminary vehicle design. Five VTI algorithms for wheeled vehicles on fine-grained soils are calibrated in this study using a Bayesian calibration technique and the Database Records for Off-road Vehicle Environments (DROVE): powered and unpowered sinkage, drawbar pull, motion resistance, and gross traction. These algorithms are improved through a two-stage Bayesian calibration technique utilizing the metropolis algorithm with three separate calibration strategies. The VII and proposed algorithms are compared for performance in coefficient of determination and root-mean square error. The results from each algorithm were validated through k-fold cross validation with five folds. The final algorithms from the best performing strategy after accounting for increased complexity for each of the five performance parameters are reported as calibrated algorithms. Validated improvements in coefficient of determination are recorded for all five parameters: 7.8% for powered sinkage, 1.4% for unpowered sinkage, 6.4% for drawbar pull, 0.9% for motion resistance, and 12.5% for gross traction. Improvements are also seen in the normalized root-mean square error performance: 13.4% for powered sinkage, 1.9% for unpowered sinkage, 7.6% for drawbar pull, 17.5% for motion resistance, and 23.2% for gross traction. (C) 2018 ISTVS. Published by Elsevier Ltd. All rights reserved.

关键词： Off-road mobility Vehicle Terrain Interface (VTI) model Bayesian calibration metropolis algorithm Fine-grained soils Sinkage Drawbar pull Traction Motion resistance Database Records for Off-road Vehicle Environments (DROVE)

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Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves

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Physical Review E 2019年第1期100卷 012132-012132页

作者： Wei Zhong Debabrata Panja Gerard T. Barkema Department of Information and Computing Sciences Utrecht University Princetonplein 5 3584 CC Utrecht the Netherlands

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times 1≲t≲Lzc, where zc=4−η=15/4 is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.

关键词： Anomalous diffusion Magnetization dynamics Phase transitions Equilibrium lattice models Lattice models in statistical physics Stochastic dynamical systems Finite-size scaling Ising model metropolis algorithm Monte Carlo methods

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Anisotropic exchange Hamiltonian, magnetic phase diagram, and domain inversion of Nd2Zr2O7

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Physical Review B 2019年第14期99卷 144420-144420页

作者： J. Xu Owen Benton V. K. Anand A. T. M. N. Islam T. Guidi G. Ehlers E. Feng Y. Su A. Sakai P. Gegenwart B. Lake Helmholtz-Zentrum Berlin für Materialien und Energie GmbH Hahn-Meitner-Platz 1 D-14109 Berlin Germany Institut für Festkörperphysik Technische Universität Berlin Hardenbergstraße 36 D-10623 Berlin Germany RIKEN Center for Emergent Matter Science (CEMS) Wako Saitama 351-0198 Japan ISIS facility Rutherford Appleton Laboratory Didcot OX11 0QX United Kingdom Oak Ridge National Laboratory Oak Ridge P.O. Box 2008 Tennessee 37831 USA Jülich Centre for Neutron Science JCNS Forschungszentrum Jülich Outstation at MLZ Lichtenbergstr. 1 D-85747 Garching Germany Center for Electronic Correlations and Magnetism Institute of Physics University of Augsburg D-86135 Augsburg Germany

We present thermodynamic and neutron-scattering measurements on the quantum spin ice candidate Nd2Zr2O7. The parametrization of the anisotropic exchange Hamiltonian is refined based on high-energy-resolution inelastic neutron-scattering data together with thermodynamic data using linear spin-wave theory and numerical linked-cluster expansion. Magnetic phase diagrams are calculated using classical Monte Carlo simulations with fields along [100], [110], and [111] crystallographic directions which agree qualitatively with the experiment. Large hysteresis and irreversibility for [111] is reproduced and the microscopic mechanism is revealed by mean-field calculations to be the existence of metastable states and domain inversion. Our results shed light on the explanations of the recently observed dynamical kagome ice in Nd2Zr2O7 in [111] fields.

关键词： Frustrated magnetism Magnetic interactions Spin ice Inorganic compounds Single crystal materials Cluster methods Crystal growth Holstein-Primakoff method Magnetization measurements metropolis algorithm Specific heat measurements Time-of-flight neutron spectroscopy X-ray powder diffraction

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Spontaneous symmetry lowering of Si (001) towards two-dimensional ferro/antiferroelectric behavior

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Physical Review Materials 2019年第4期3卷 044410-044410页

作者： Chengcheng Xiao Xinwei Wang Xiaodong Pi Shengyuan A. Yang Yuanping Feng Yunhao Lu Shengbai Zhang State Key Laboratory of Silicon Materials School of Materials Science and Engineering Zhejiang University Hangzhou 310027 China Research Laboratory for Quantum Materials Singapore University of Technology and Design Singapore 487372 Singapore Department of Physics National University of Singapore Singapore 117542 Singapore Department of Physics Zhejiang University Hangzhou 310027 China Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA

Electronic polarization, manifested in numerous physical phenomena such as ferroelectricity, piezoelectricity, and pyroelectricity, is of great importance to many technological applications. The presence of ferroelectricity in bulk elemental materials is extremely rare due to the high symmetry of the underlying lattices. However, the presence of a surface lowers the symmetry, which may provide a future avenue for achieving robust ferroelectric polarization. Using first-principles calculations, we show that a spontaneous electrical polarization can be realized on the silicon reconstructed (001) surface. The magnitude of this polarization is 0.45×10−10C/m, comparable to those in benchmarking two-dimensional ferroelectric compounds such as SnTe and SnSe. The symmetry lowering is originated from a Peierls instability that removes the degeneracy of surface dangling bonds, whereby opening a band gap. Although flip-flop of the surface dimers may destroy the ordered phase at elevated temperatures, we find that a modest compressive strain, which increases the local stress and interdimer coupling, can drastically increase the robustness of the ferroelectric state towards room-temperature operations. The technology for processing Si has been well developed and the Si (001) surface has also been widely used in various electronic devices. Our discovery here thus holds high promise in a multitude of fields, ranging from nanoscale random access memory to low power consumption energy storage devices.

关键词： Antiferroelectrics Structural phase transition Elemental semiconductors Surfaces Density functional theory metropolis algorithm Nonequilibrium Green's function Wannier function methods

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