Molecular dynamics simulation of the spherical electrical double layer of a soft nanoparticle. Effect of the surface and counterion valence

Molecular dynamics simulations were performed to study the ion and water distribution around a spherical charged nanoparticle. A soft nanoparticle model was designed using a set of hydrophobic interaction sites distributed in six concentric spherical layers. In order to simulate the effect of charged functionalyzed groups on the nanoparticle surface, a set of charged sites were distributed in the outer layer. Four charged nanoparticle models, from a surface charge value of −0.035 Cm−2 to − 0.28 Cm−2, were studied in NaCl and CaCl2 salt solutions at 1 M and 0.1 M concentrations to evaluate the effect of the surface charge, counterion valence, and concentration of added salt. We obtain that Na + and Ca2 + ions enter inside the soft nanoparticle. Monovalent ions are more accumulated inside the nanoparticle surface, whereas divalent ions are more accumulated just in the plane of the nanoparticle surface sites. The increasing of the the salt concentration has little effect on the internalization of counterions, but significantly reduces the number of water molecules that enter inside the nanoparticle. The manner of distributing the surface charge in the nanoparticle (uniformly over all surface sites or discretely over a limited set of randomly selected sites) considerably affects the distribution of counterions in the proximities of the nanoparticle surface.

Structural modelling of liquid ZrO2 and glassy B2O3 by using AB INITIO Molecular Dynamics method

Atomic structure of ZrO2 and B2O3 was investigated in this work. New data under extreme conditions (T = 3100 K) was obtained for the liquid ZrO2 structure. A fractional number of boron was investigated for glassy structure of B2O3. It was shown that it is possible to obtain an agreement for the fractional number between NMR and DFT techniques using a suitable initial configuration.

Mechanical design and optics simulation of the illuminated Volvo Iron mark

Utilization of light and illumination systems in automotive industry for different purposes has been increased significantly in recent years. Volvo as one of the leading companies in manufacturing of luxury cars has found the great capacity in this area. The performance of such an illumination systems is one of the challenges that engineers in this industry are facing with. In this study an effort has been made to design a system to make the iron mark of Volvo being illuminated and the system is being evaluated by optics simulation in software using Ray optics method. At the end, results are assessed and some optimizations are carried out. Different kind of light guides, front side of the iron mark and some possible arrangement for LED also evaluated and different materials tested. The best combination from uniformity, color and amount of luminance aspect selected as a possible solution for this special project which can be used as a base for further studies in Volvo.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

New simulation schemes for the Heston model

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

Numerical simulation of magnetic field enhanced plasma immersion ion implantation

The behavior of plasma and sheath characteristics under the action of an applied magnetic field is important in many applications including plasma probes and material processing. Plasma immersion ion implantation (PIII) has been developed as a fast and efficient surface modification technique of complex shaped three-dimensional objects. The PIII process relies on the acceleration of ions across a high-voltage plasma sheath that develops around the target. Recent studies have shown that the sheath dynamics is significantly affected by an external magnetic field. In this work we describe a two-dimensional computer simulation of magnetic field enhanced plasma immersion implantation system. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded cylindrical vacuum chamber filled with uniform nitrogen plasma. An axial magnetic field is created by a solenoid installed inside the cylindrical target. The computer code employs the Monte Carlo method for collision of electrons and neutrals in the plasma and a particle-in-cell (PIC) algorithm for simulating the movement of charged particles in the electromagnetic field. Secondary electron emission from the target subjected to ion bombardment is also included. It is found that a high-density plasma region is formed around the cylindrical target due to the intense background gas ionization by the magnetized electrons drifting in the crossed ExB fields. An increase of implantation current density in front of high density plasma region is observed. (C) 2007 Elsevier B.V. All rights reserved.

Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method

There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed.

Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^

Refined method of potential enhancement in the equilibria characterization of activated carbon. Comparison with GCMC and DFT

In this paper, we present a technique for equilibria characterization of activated carbon having slit-shaped pores. This method was first developed by Do (Do, D. D. A new method for the characterisation of micro-mesoporous materials. Presented at the International Symposium on New Trends in Colloid and Interface Science, September 24-26, 1998 Chiba, Japan) and applied by his group and other groups for characterization of pore size distribution (PSD) as well as adsorption equilibria determination of a wide range of hydrocarbons. It is refined in this paper and compared with the grand canonical Monte Carlo (GCMG) simulation and density functional theory (DFT). The refined theory results in a good agreement between the pore filling pressure versus pore width and those obtained by GCMG and DFT. Furthermore, our local isotherms are qualitatively in good agreement with those obtained by the GCMC simulations. The main advantage of this method is that it is about 4 orders of magnitude faster than the GCMC simulations, making it suitable for optimization studies and design purposes. Finally, we apply our method and the GCMG in the derivation of the PSD of a commercial activated carbon. It was found that the PSD derived from our method is comparable to that derived from the GCMG simulations.