No description available.

Dans le tokamak Tore Supra, le champ magnétique qui assure le confinement est rendu stochastique à la périphérie du plasma par l'application d'une perturbation résonante. Cette perturbation est créée par un ensemble de six bobines hélicoïdales, le divertor ergodique, situé à l'intérieur de la chambre à vide. La première partie de notre étude est l'analyse du transport des particules et de l'énergie dans un plasma de fusion en présence d'un champ magnétique stochastique, sans paroi matérielle. Le transport effectif des électrons, i.e. de la chaleur, est fortement augmenté et, dans une moindre mesure, celui des ions. Cette différence produit un champ électrique radial moyen. Dans une seconde partie, l'influence d'une paroi matérielle est considérée. Grâce au code<br />numérique Mastoc, la topologie de la connexion magnétique sur la paroi est détenninée précisément. Il est ainsi possible de décrire le transport des particules et de l'énergie depuis le plasma confiné jusqu'aux éléments de paroi. Cette étude éclaire certaines des principales observations de l'expérience Tore Supra en configuration divertor ergodique : l'étalement du dépôt de puissance sur les différents éléments de la paroi sans concentration anormale, la robustesse de cette configuration vis-à-vis de défauts d'alignement, les structures visibles en lumière Ha lors de réattachement de plasma. Afin d'étudier le transport des ions impuretés, une approche variationnelle par minimum de production d'entropie a été développée. Ce principe variationnel est appliqué au calcul de la diffusion néoclassique des ions impuretés dans le champ électrique radial moyen. Ce champ électrique déconfine les ions si le profil de pression n'est pas équilibré par une force de Laplace, c'est-à-dire si le plasma est bloqué en rotation, poloïdale et toroïdale, par une perturbationmagnétiqueou une force friction.

Une nouvelle approche non-perturbative à la Onsager en systèmes intégrables quantiques est développée, dont les idées maîtresses prennent leurs racines dans l'article de L. Onsager (1944) portant sur la solution exacte du modèle d'Ising en deux dimensions. L'intérêt de cette approche repose sur le fait qu'elle est applicable de façon systématique dans le cas oú d'autres méthodes usuelles échouent. Celle-ci repose sur l'étude de quatres éléments capitaux: (i) L'identification de l'algèbre non-Abélienne de dimension infinie généralisant l'algèbre de Onsager et représentant la condition d'intégrabilité du modèle; (ii) La construction d'une hiérarchie de quantités en involution formant une sous-algèbre Abélienne; (iii) L'étude des réalisations et représentations de dimension finie et infinie de cette algèbre; (iv) La résolution du modèle à l'aide de ces données. Pour un modèle de référence - la chaîne de spin XXZ de taille finie avec conditions aux bords intégrables - la nouvelle approche basée sur l'algèbre q-Onsager introduite par P. Terwilliger est utilisée pour résoudre le problème spectral (spectre en énergie et états propres) dans le régime de paramètres génériques où l'ansatz de Bethe est inapplicable. Certaines étapes essentielles à l'obtention des fonctions de corrélations dans la limite thermodynamique du modèle sont aussi franchies, s'inspirant de la méthode de M. Jimbo et al.. La généralisation associée à toute algèbre de Lie affine de l'algèbre q-Onsager est proposée, et permet de classifier toutes les conditions d'intégrabilité dans les théories de Toda affines avec bord. Diverses perspectives sont enfin présentées.

This dissertation examines the motion of colloids in a temperature gradient, a non-equilibrium phenomenon also known as thermophoresis. Chapter 1 gives an introduction to the existing applications and basic concepts of thermophoresis and outlines some of the experimental and theoretical challenges that serve as a motivation for this PhD project. In Chapter 2, a general theoretical description for thermophoresis is formulated using the theory of non-equilibrium thermodynamics. The colloidal flux is split up into an interfacial single-colloid contribution and a bulk contribution, followed by a determination of transport coefficients based on Onsager’s reciprocal relations. It is further shown how the phenomenological expression of the thermophoretic flux can be recovered when the fluid is at steady-state. The results issuing from this description are then discussed and compared to other existing approaches, some of which are shown to neglect the hydrodynamic character of colloidal thermophoresis. Chapter 3 is dedicated to the validation of the introduced theoretical framework by means of computer simulations, using a simulation technique known as multi-particle collision dynamics. More specifically, the dependence of the thermophoretic force on different system parameters is examined and deviations from the theoretical prediction are explained by an advective distortion of interfacial fluid properties at the colloidal surface. Chapter 4 presents steady-state measurements of functionalised colloids in a temperature gradient, showing how the addition of molecular surface groups increases the experimental complexity of thermophoretic motion. The relaxation process behind this steady-state is also studied, to determine how the relaxation speed depends on the applied temperature gradient. In chapter 5, a general conclusion is drawn from the presented work and its implications are briefly discussed in relation to the current state of knowledge. Finally, the discussion is closed with an outlook on remaining challenges in understanding colloidal motion that could be the subject of future research.

<p>This thesis studies infinite dimensional Gaussian measures on Banach spaces. Let $\mu_0$ be a centered Gaussian measure on Banach space $\mathcal B$, and $\mu^\ast$ is a measure equivalent to $\mu_0$. We are interested in approximating, in sense of relative entropy (or KL divergence) the quantity $\frac{d\mu^z}{d\mu^\ast}$ where $\mu^z$ is a mean shift measure of $\mu_0$ by an element $z$ in the so-called ``Cameron-Martin" space $\mathcal H_{\mu_0}$. That is, we want to find the information projection</p> <p><br></p> <p>$$\inf_{z\in \mathcal H_{\mu_0}} D_{KL}(\mu^z||\mu_0)=\inf_{z\in \mathcal H_{\mu_0}} E_{\mu^z} \left(\log \left(\frac{d\mu^z}{d\mu^\ast}\right)\right).$$</p> <p><br></p> <p>We relate this information projection to a mode computation, to an ``open loop" control problem, and to a variational formulation leading to an Euler-Lagrange equation. Furthermore, we use this relationship to establish a kind of Feynman-Kac theorem for systems of ordinary differential equations. We demonstrate that the solution to a system of second order linear ordinary differential equations is the mode of a diffusion, analogous to the result of Feynman-Kac for parabolic partial differential equations. </p>

This examines the interplay of structure and local electrostatic fields in protein-protein and protein-solvent interactions. The partial charges of the protein amino acids and the polarization of the surrounding solvent create a complex system of electrostatic fields at protein-protein and protein-solvent interfaces. An approach incorporating vibrational Stark effect (VSE) spectroscopy, dissociation constant measurements, and molecular dynamics (MD) simulations was used to investigate the electrostatic interactions in these interfaces. Proteins p21Ras (Ras) and Rap1A (Rap) have nearly identical amino acid sequences and structures along the effector-binding region but bind with different affinities to Ral guanine nucleotide dissociation stimulator (RalGDS). A charge reversion mutation at position 31 alters the binding affinity of Ras and Rap with RalGDS from 0.1 [mu]M and 1 [mu]M, to 1 [mu]M and 0.5 [mu]M, respectively. A spectral probe was placed at various locations along the binding interface on the surface of RalGDS as it was docked with Ras and Rap single (position 30 or 31) and double mutants (both positions). By comparing the probes' absorption energies with the respective wild-type (WT) analogs, VSE spectroscopy was able to measure molecular-level electrostatic events across the protein-protein interface. MD simulations provided a basis for deconvoluting the structural and electrostatic changes observed by the probes. The mutation at position 31 was found to be responsible for both structural and electrostatic changes compared to the WT analogs. Furthermore, previous identification of positions N27 and N29 on RalGDS as "hot spots" that help discriminate between structurally similar GTPases was supported. The RalGDS probe-containing variants and three model compounds were placed in aqueous solvents with varying dielectric constants to measure changes in absorption energy. We investigated the ability of the Onsager solvent model to describe the solvent induced changes in absorption energy, while MD simulations were employed to determine the location and solvation of the probes at the protein-solvent interface. The solvent accessible-surface area, a measure of hydration, was determined to correlate well with the change in magnitude of the probe's absorption energy and the displaced solvent by the probe. / text

In 1949, Lars Onsager in his famous note on statistical hydrodynamics conjectured that weak solutions to the 3-D incompressible Euler equations belonging to Hölder spaces with Hölder exponent greater than 1/3 conserve kinetic energy; conversely, he conjectured the existence of solutions belonging to any Hölder space with exponent less than 1/3 which do not conserve kinetic energy. The first part, relating to conservation of kinetic energy, has since been confirmed (cf. Eyink 1994, Constantin-E-Titi 1994). The second part, relating to the existence of non-conservative solutions, remains an open conjecture and is the subject of this dissertation. In groundbreaking work of De Lellis and Székelyhidi Jr. (2012), the authors constructed the first examples of non-conservative Hölder continuous weak solutions to the Euler equations. The construction was subsequently improved by Isett (2012/2013), introducing many novel ideas in order to construct 1/5− Hölder continuous weak solutions with compact support in time. Adhering more closely to the original scheme of De Lellis and Székelyhidi Jr., we present a comparatively simpler construction of 1/5− Hölder continuous non-conservative weak solutions which may in addition be made to obey a prescribed kinetic energy profile. Furthermore, we extend this scheme in order to construct weak non-conservative solutions to the Euler equations whose Hölder 1/3− norm is Lebesgue integrable in time. The dissertation will be primarily based on three papers, two of which being in collaboration with De Lellis and Székelyhidi Jr.

No description available.

Motion of ions under the influence of electric field has been a subject of scientific interest for many decades. Capillary electrophoresis in particular benefited greatly from this research and mathematical models of electromigration applicable to capillary electrophoresis have been developed. As the sophistication of the models grew, so did the computational demands to evaluate them. In order to fully exploit the possibilities of advanced mathematical models a computer implementation capable of solving non-trivial problems at sufficient speed is necessary. This dissertation thesis explores applications of computer implementations of mathematical models re- lated to electromigration in two different areas. The main focus of this thesis is on the topic of linear theory of electromigration. We discuss the extension of the linear theory of electromigration beyond of just acid-base equilibria and computer implementation of this extented theory which is specialized to include complex-forming equilibria in order to be able to deal with affinity capillary electrophoresis prob- lems. Some technical aspects of the computer implementation are also discussed. This is followed upon by investigating certain selected affinity capillary electrophoresis systems. The purpose of this investi- gation is to re-derive...

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work. / Graduate