Application of reverse Monte Carlo simulations to diatomic molecules. Part 1. Noncomplete radial distribution functions

The reverse Monte Carlo (RMC) method generates sets of points in space which yield radial distribution functions (RDFS) that approximate those of the system of interest. Such sets of configurations should, in principle, be sufficient to determine the structural properties of the system. In this work we apply the RMC technique to fluids of hard diatomic molecules. The experimental RDFs of the hard-dimer fluid were generated by the conventional MC method and used as input in the RMC simulations. Our results indicate that the RMC method is only satisfactory in determining the local structure of the fluid studied by means of only mono-variable RDF. Also we suggest that the use of multi-variable RDFs would improve the technique significantly. However, the accuracy of the method turned out to be very sensitive to the variance of the input experimental RDF. © 1995.

Local Earthquake Tomography by trans-dimensional Monte Carlo Sampling

In this study a new, fully non-linear, approach to Local Earthquake Tomography is presented. Local Earthquakes Tomography (LET) is a non-linear inversion problem that allows the joint determination of earthquakes parameters and velocity structure from arrival times of waves generated by local sources. Since the early developments of seismic tomography several inversion methods have been developed to solve this problem in a linearized way. In the framework of Monte Carlo sampling, we developed a new code based on the Reversible Jump Markov Chain Monte Carlo sampling method (Rj-McMc). It is a trans-dimensional approach in which the number of unknowns, and thus the model parameterization, is treated as one of the unknowns. I show that our new code allows overcoming major limitations of linearized tomography, opening a new perspective in seismic imaging. Synthetic tests demonstrate that our algorithm is able to produce a robust and reliable tomography without the need to make subjective a-priori assumptions about starting models and parameterization. Moreover it provides a more accurate estimate of uncertainties about the model parameters. Therefore, it is very suitable for investigating the velocity structure in regions that lack of accurate a-priori information. Synthetic tests also reveal that the lack of any regularization constraints allows extracting more information from the observed data and that the velocity structure can be detected also in regions where the density of rays is low and standard linearized codes fails. I also present high-resolution Vp and Vp/Vs models in two widespread investigated regions: the Parkfield segment of the San Andreas Fault (California, USA) and the area around the Alto Tiberina fault (Umbria-Marche, Italy). In both the cases, the models obtained with our code show a substantial improvement in the data fit, if compared with the models obtained from the same data set with the linearized inversion codes.

Modeling the heterogeneous ice and gas coma of Comet 103P/Hartley 2

The spectacular images of Comet 103P/Hartley 2 recorded by the Medium Resolution Instrument (MRI) and High Resolution Instrument (HRI) on board of the Extrasolar Planet Observation and Deep Impact Extended Investigation (EPOXI) spacecraft, as the Deep Impact extended mission, revealed that its bi-lobed very active nucleus outgasses volatiles heterogeneously. Indeed, CO2 is the primary driver of activity by dragging out chunks of pure ice out of the nucleus from the sub-solar lobe that appear to be the main source of water in Hartley 2's coma by sublimating slowly as they go away from the nucleus. However, water vapor is released by direct sublimation of the nucleus at the waist without any significant amount of either CO2 or icy grains. The coma structure for a comet with such areas of diverse chemistry differs from the usual models where gases are produced in a homogeneous way from the surface. We use the fully kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J. 685, 659-677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J. 732, 104-120) applied to Comet 103P/Hartley 2 including sublimating icy grains to reproduce the observations made by EPOXI and ground-based measurements. A realistic bi-lobed nucleus with a succession of active areas with different chemistry was included in the model enabling us to study in details the coma of Hartley 2. The different gas production rates from each area were found by fitting the spectra computed using a line-by-line non-LTE radiative transfer model to the HRI observations. The presence of icy grains with long lifetimes, which are pushed anti-sunward by radiation pressure, explains the observed OH asymmetry with enhancement on the night side of the coma.

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659−677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ∼30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241−248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.

Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Monte Carlo approaches to nonlinear optimal control

This paper explores the use of Monte Carlo techniques in deterministic nonlinear optimal control. Inter-dimensional population Markov Chain Monte Carlo (MCMC) techniques are proposed to solve the nonlinear optimal control problem. The linear quadratic and Acrobot problems are studied to demonstrate the successful application of the relevant techniques.

跨大气层飞行器姿态控制相关三维稀薄气体流动的Monte Carlo模拟

本文利用直接模拟Monte Carlo位置元(DSMC-PE)方案模拟了跨大气层飞行器姿态控制相关的两个典型的稀薄气体流动,真空轴对称射流冲击平板和楔形垂直相交平板稀薄气体绕流。真空轴对称射流在附近平板表面的压力、剪应力和热流分布的计算结果,与Legge(1991)和D(?)ring(1990)的测量数据一致;楔形垂直相交平板表面压力分布计算结果,与Allegre和Raffin(1992)实验数据的比较,也令人满意。上述计算表明,DSMC-PE是处理航天领域稀薄气流的有力工具。

Configuration optimization of hypersonic vehicles under transitional flow conditions

The rarefied gas effects on several configurations are investigated under hypersonic flow conditions using the direct simulation Mont Carlo method. It is found that the Knudsen number, the Mach number, and the angle of attack all play a mixed role in the aerodynamics of a flat plate. The ratio of lift to drag decreases as the Knudsen number increases. Studies on 3D delta wings show that the ratio of lift to drag could be increased by decreasing the wing thickness and/or by increasing the wing span. It is also found that the waveriders could produce larger ratio of lift to drag as compared with the delta wing having the same length, wing span, and cross section area.

Direct simulation of proton-coupled electron transfer reaction dynamics and mechanisms

Proton-coupled electron transfer (PCET) reactions are ubiquitous throughout chemistry and biology. However, challenges arise in both the the experimental and theoretical investigation of PCET reactions; the rare-event nature of the reactions and the coupling between quantum mechanical electron- and proton-transfer with the slower classical dynamics of the surrounding environment necessitates the development of robust simulation methodology. In the following dissertation, novel path-integral based methods are developed and employed for the direct simulation of the reaction dynamics and mechanisms of condensed-phase PCET.

Monte Carlo studies of quantum and classical annealing on a double well

We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the path integral Monte Carlo approach is found to yield nontrivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a "relativistic" kinetic energy form, leading to a higher probability of long real-space jumps, can be considerably more effective than the standard nonrelativistic one.