Durant ces dernières années, la modélisation en physique est restée aveugle aux développements de disciplines sœurs ; en particulier la mécanique ou plutôt la robotique qui développe des outils puissants comme la cinématique inverse et les moteurs physiques (ou moteurs de jeux). Ces techniques sont couramment employées dans les jeux vidéo pour des résultats très réalistes. Je propose ici de montrer que nous pouvons simuler des assemblages d'ADN et de protéines (fibre de chromatine et à plus grande échelle des chromosomes) comme des systèmes articulés avec un moteur physique. Je montre aussi qu'il est possible d'étendre le thermostat local de Langevin à un thermostat global pour accélérer l'échantillonnage de l'espace des configurations du système ADN-protéines dans l'ensemble canonique. Ce nouveau thermostat est particulièrement intéressant lorsqu'il est utilisé avec un moteur physique. Plus précisément, je montrerai que la simulation que j'ai développée reproduit les résultats expérimentaux de manipulation de molécules uniques sous pinces magnétiques et permet de faire des prédictions. Enfin, cette simulation offre des perspectives intéressantes pour la modélisation des noyaux d'organismes allant de la drosophile à l'humain et la compréhension des toutes dernières données sur l'architecture des génomes.

This thesis presents the benchmarking and development of a method to study ground state properties of hydrogen clusters using molecular dynamics. Benchmark studies are performed on our Path Integral Molecular Dynamics code using the Langevin equation for finite temperature studies and our Langevin equation Path Integral Ground State code to study systems in the zero-temperature limit when all particles occupy their nuclear ground state. A simulation is run on the first 'real' system using this method, a parahydrogen molecule interacting with a fixed water molecule using a trivial unity trial wavefunction. We further develop a systematic method of optimizing the necessary parameters required for our ground state simulations and introduce more complex trial wavefunctions to study parahydrogen clusters and their isotopologues orthodeuterium and paratritium. The effect of energy convergence with parameters is observed using the trivial unity trial wavefunction, a Jastrow-type wavefunction that represents a liquid-like system, and a normal mode wavefunction that represents a solid-like system. Using a unity wavefunction gives slower energy convergence and is inefficient compared to the other two. Using the Lindemann criterion, the normal mode wavefunction acting on floppy systems introduces an ergodicity problem in our simulation, while the Jastrow does not. However, even for the most solid-like clusters, the Jastrow and the normal mode wavefunctions are equally efficient, therefore we choose the Jastrow trial wavefunction to look at properties of a range of cluster sizes. The energetic and structural properties obtained for parahydrogen and orthodeuterium clusters are consistent with previous studies, but to our knowledge, we may be the first to predict these properties for neutral paratritium clusters. The results of our ground state simulations of parahydrogen clusters, namely the distribution of pair distances, are used to calculate Raman vibrational shifts and compare to experiment. We investigate the accuracy of four interaction potentials over a range of cluster sizes and determine that, for the most part, the ab initio derived interaction potentials predict shifts more accurately than the empirically based potentials for cluster sizes smaller than the first solvation shell and the trend is reversed as the cluster size increases. This work can serve as a guide to simulate any system in the nuclear ground state using any trial wavefunction, in addition to providing several applications in using this ground state method.

The transport of a biomolecule through a nanopore occurs in many biological functions such as, DNA or RNA transport across nuclear pores and the translocation of proteins across the eukaryotic endoplasmic reticulum. In addition to the biological processes, it has potential applications in technology such as, drug delivery, gene therapy, and single molecule sensing. The DNA translocation through a synthetic nanopore device is considered as the basis for cheap and fast sequencing technology. Motivated by the experimental advances, many theoretical models have been developed. In this thesis, we explore the dynamics of driven translocation of a semiflexible polymer through a nanopore in two dimensions (2D) using Langevin dynamics (LD) simulation. By carrying out extensive simulation as a function of different parameters such as, driving force, length and rigidity of the chain, viscosity of the solvent, and diameter of the nanopore, we provide a detailed description of the translocation process. Our studies are relevant for fundamental understanding of the translocation process which is essential for making accurate nano-pore based devices.

I have developed time-varying coefficient models for recurrent event data to evaluate the temporal profiles for recurrence rate and covariate effects. There are three major parts in this dissertation. The first two parts propose a mixed Poisson process model with gamma frailties for single type recurrent events. The third part proposes a Bayesian joint model based on multivariate log-normal frailties for multi-type recurrent events. In the first part, I propose an approach based on penalized B-splines to obtain smooth estimation for both time-varying coefficients and the log baseline intensity. An EM algorithm is developed for parameter estimation. One issue with this approach is that the estimating procedure is conditional on smoothing parameters, which have to be selected by cross-validation or optimizing certain performance criterion. The procedure can be computationally demanding with a large number of time-varying coefficients. To achieve objective estimation of smoothing parameters, I propose a mixed-model representation approach for penalized splines. Spline coefficients are treated as random effects and smoothing parameters are to be estimated as variance components. An EM algorithm embedded with penalized quasi-likelihood approximation is developed to estimate the model parameters. The third part proposes a Bayesian joint model with time-varying coefficients for multi-type recurrent events. Bayesian penalized splines are used to estimate time-varying coefficients and the log baseline intensity. One challenge in Bayesian penalized splines is that the smoothness of a spline fit is considerably sensitive to the subjective choice of hyperparameters. I establish a procedure to objectively determine the hyperparameters through a robust prior specification. A Markov chain Monte Carlo procedure based on Metropolis-adjusted Langevin algorithms is developed to sample from the high-dimensional distribution of spline coefficients. The procedure includes a joint sampling scheme to achieve better convergence and mixing properties. Simulation studies in the second and third part have confirmed satisfactory model performance in estimating time-varying coefficients under different curvature and event rate conditions. The models in the second and third part were applied to data from a commercial truck driver naturalistic driving study. The application results reveal that drivers with 7-hours-or-less sleep prior to a shift have a significantly higher intensity after 8 hours of on-duty driving and that their intensity remains higher after taking a break. In addition, the results also show drivers' self-selection on sleep time, total driving hours in a shift, and breaks. These applications provide crucial insight into the impact of sleep time on driving performance for commercial truck drivers and highlights the on-road safety implications of insufficient sleep and breaks while driving. This dissertation provides flexible and robust tools to evaluate the temporal profile of intensity for recurrent events. / PHD / The overall objective of this dissertation is to develop models to evaluate the time-varying profiles for event occurrences and the time-varying effects of risk factors upon event occurrences. There are three major parts in this dissertation. The first two parts are designed for single event type. They are based on approaches such that the whole model is conditional on a certain kind of tuning parameter. The value of this tuning parameter has to be pre-specified by users and is influential to the model results. Instead of pre-specifying the value, I develop an approach to achieve an objective estimate for the optimal value of tuning parameter and obtain model results simultaneously. The third part proposes a model for multi-type events. One challenge is that the model results are considerably sensitive to the subjective choice of hyperparameters. I establish a procedure to objectively determine the hyperparameters. Simulation studies have confirmed satisfactory model performance in estimating the temporal profiles for both event occurrences and effects of risk factors. The models were applied to data from a commercial truck driver naturalistic driving study. The results reveal that drivers with 7-hours-or-less sleep prior to a shift have a significantly higher intensity after 8 hours of on-duty driving and that their driving risk remains higher after taking a break. In addition, the results also show drivers’ self-selection on sleep time, total driving hours in a shift, and breaks. These applications provide crucial insight into the impact of sleep time on driving performance for commercial truck drivers and highlights the on-road safety implications of insufficient sleep and breaks while driving. This dissertation provides flexible and robust tools to evaluate the temporal profile of both event occurrences and effects of risk factors.

This thesis investigates the integration of Stein Variational Gradient Descent (SVGD) with Joint Energy Models (JEMs), comparing its performance to Stochastic Gradient Langevin Dynamics (SGLD). We incorporated a generative loss term with an entropy component to enhance diversity and a smoothing factor to mitigate numerical instability issues commonly associated with the energy function in energy-based models. Experiments on the CIFAR-10 dataset demonstrate that SGLD, particularly with Sharpness-Aware Minimization (SAM), outperforms SVGD in classification accuracy. However, SVGD without SAM, despite its lower classification accuracy, exhibits lower calibration error underscoring its potential for developing well-calibrated classifiers required in safety-critical applications. Our results emphasize the importance of adaptive tuning of the SVGD smoothing factor ($alpha$) to balance generative and classification objectives. This thesis highlights the trade-offs between computational cost and performance, with SVGD demanding significant resources. Our findings stress the need for adaptive scaling and robust optimization techniques to enhance the stability and efficacy of JEMs. This thesis lays the groundwork for exploring more efficient and robust sampling techniques within the JEM framework, offering insights into the integration of SVGD with JEMs. / Master of Science / This thesis explores advanced techniques for improving machine learning models with a focus on developing well-calibrated and robust classifiers. We concentrated on two methods, Stein Variational Gradient Descent (SVGD) and Stochastic Gradient Langevin Dynamics (SGLD), to evaluate their effectiveness in enhancing classification accuracy and reliability. Our research introduced a new mathematical approach to improve the stability and performance of Joint Energy Models (JEMs). By leveraging the generative capabilities of SVGD, the model is guided to learn better data representations, which are crucial for robust classification. Using the CIFAR-10 image dataset, we confirmed prior research indicating that SGLD, particularly when combined with an optimization method called Sharpness-Aware Minimization (SAM), delivered the best results in terms of accuracy and stability. Notably, SVGD without SAM, despite yielding slightly lower classification accuracy, exhibited significantly lower calibration error, making it particularly valuable for safety-critical applications. However, SVGD required careful tuning of hyperparameters and substantial computational resources. This study lays the groundwork for future efforts to enhance the efficiency and reliability of these advanced sampling techniques, with the overarching goal of improving classifier calibration and robustness with JEMs.

The theory of Brownian motion is a cornerstone of modern physics. In this thesis, we introduce a nonequilibrium extension to this theory, namely an effective Markovian theory of the Brownian motion of a heated nanoparticle. This phenomenon belongs to the class of nonequilibrium steady states (NESS) and is characterized by spatially inhomogeneous temperature and viscosity fields extending in the solvent surrounding the nanoparticle. The first chapter provides a pedagogic introduction to the subject and a concise summary of our main results and summarizes their implications for future developments and innovative applications. The derivation of our main results is based on the theory of fluctuating hydrodynamics, which we introduce and extend to NESS conditions, in the second chapter. We derive the effective temperature and the effective friction coefficient for the generalized Langevin equation describing the Brownian motion of a heated nanoparticle. As major results, we find that these parameters obey a generalized Stokes–Einstein relation, and that, to first order in the temperature increment of the particle, the effective temperature is given in terms of a set of universal numbers. In chapters three and four, these basic results are made explicit for various realizations of hot Brownian motion. We show in detail, that different degrees of freedom are governed by distinct effective parameters, and we calculate these for the rotational and translational motion of heated nanobeads and nanorods. Whenever possible, analytic results are provided, and numerically accurate approximation methods are devised otherwise. To test and validate all our theoretical predictions, we present large-scale molecular dynamics simulations of a Lennard-Jones system, in chapter five. These implement a state-of-the-art GPU-powered parallel algorithm, contributed by D. Chakraborty. Further support for our theory comes from recent experimental observations of gold nanobeads and nanorods made in the the groups of F. Cichos and M. Orrit. We introduce the theoretical concept of PhoCS, an innovative technique which puts the selective heating of nanoscopic tracer particles to good use. We conclude in chapter six with some preliminary results about the self-phoretic motion of so-called Janus particles. These two-faced hybrids with a hotter and a cooler side perform a persistent random walk with the persistence only limited by their hot rotational Brownian motion. Such particles could act as versatile laser-controlled nanotransporters or nanomachines, to mention just the most obvious future nanotechnological applications of hot Brownian motion.

This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.

Le mélange de deux faisceaux laser sur un photo-détecteur permet de générer un signal radiofréquence jusqu'au THz. Par corrélation des deux sources optiques, le signal obtenu peut acquérir la pureté spectrale requise pour les réseaux de communications radio sur fibre. Notre travail porte sur la méthode de corrélation par accrochage optique sur un peigne de fréquences. L'injection optique permet de transférer le bruit de phase d'un laser maître, pris comme référence, à un laser esclave. En utilisant deux harmoniques d'un laser modulé en fréquence comme sources distinctes d'injection, les bruits de phase des deux lasers esclaves sont corrélés et la différence de fréquences est multiple de la fréquence primaire. Nous avons réalisé une étude théorique générale de l'injection dans les lasers semi-conducteur à cavité complexe, en particulier les lasers DFB, en mettant notamment en évidence l'asymétrie géométrique du bruit. Nous avons relié théoriquement le degré de corrélation entre les deux lasers aux paramètres d'injection et au bruit de phase. L'expression a été confirmée par des mesures sur le contraste de franges d'interférences et le spectre du photo-courant hétérodyne. Ces battements temporels ont été mis en regard avec l'optique de Fourier et le speckle. Nous avons étudié la pureté spectrale du battement et établi les limites fondamentales de cette technique en fonction de la qualité de l'oscillateur primaire, des propriétés spectrales des lasers, des paramètres d'injection et de transport sur fibre. Les mesures de bruit de phase sur le signal généré expérimentalement, pour différentes conditions d'injection, sont en très bon accord avec les expressions analytiques.

Ce travail propose une étude expérimentale au niveau fondamental des fluctuations du travail et de la chaleur dans des sytèmes mécaniques hors d'équilibre, en vue de valider les approches théoriques récentes sur le sujet dues à Jarzynski, Crooks, Gallavotti, Cohen, van Zon et leurs collaborateurs. Dans un premier chapitre, nous introduisons ces nouveaux concepts et motivons la nécessité de réaliser des expériences afin de tester ces nouveaux résultats. Le second chapitre est consacré aux principes ainsi qu'à la réalisation du dispositif de mesure: un interféromètre différentiel inspiré de la technique de Nomarski, permettant de mesurer les déplacements thermiques sub-nanométriques de petits oscillateurs mécaniques dissipatifs. Un troisième chapitre détaille le principe ainsi que la réalisation d'une technique de réduction du bruit originale s'inspirant du filtrage de Wiener, dans le but de s'affranchir du bruit environnemental transmis aux systèmes considérés. Dans les deux derniers chapitres, nous étudions expérimentalement et théoriquement les fluctuations du travail ainsi que de la production de chaleur de petits oscillateurs mécaniques dissipatifs portés dans des états hors d'équilibre.

No description available.