In the process of translation, ribosomes, a type of macromolecules, read the genetic code on a messenger RNA template (mRNA) and assemble amino acids into a polypeptide chain which folds into a functioning protein product. The ribosomes perform discrete directed motion that is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. We incorporate the essential components of the translation process: Ribosomes, cognate tRNA concentrations, and mRNA templates correspond to particles (covering ell > 1 sites), hopping rates, and the underlying lattice, respectively. As the hopping rates in an mRNA are given by its sequence (in the unit of codons), we are especially interested in the effects of a finite number of slow codons to the overall stationary current. To study this matter systematically, we first explore the effects of local inhomogeneities, i.e., one or two slow sites of hopping rate q<1 in TASEP for particles of size ell > 1(in the unit of lattice site) using Monte Carlo simulation. We compare the results of ell =1 and ell >1 and notice that the existence of local defects has qualitatively similar effects to the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both ell =1 and ell >1 cases. In particular, we notice a novel "edge" effect, i.e., the interaction of a single slow codon with the system boundary. When two slow sites are introduced, more intriguing phenomena such as dramatic decreases in the current when the two are close together emerge. We analyze the simulation results using several different levels of mean-field theory. A finite-segment mean-field approximation is especially successful in understanding the "edge effect." If we consider the systems with finite defects as "contrived mRNA's", the real mRNA's are of more biological significance. Inspired by the previous results, we study several mRNA sequences from Escherichia coli. We argue that an effective translation rate including the context of each codon needs to be taken into consideration when seeking an efficient strategy to optimize the protein production. / Ph. D.

In many situations in the world, the amount of resources available for use is limited. This statement is especially true in the cells of living organisms. During the translation process in protein synthesis, ribosomes move along the mRNA strand constructing proteins based on the sequence of codons that form a gene. The totally asymmetric simple exclusion process (TASEP) models well the translation process. However, these genes are constantly competing for ribosomes and other resources in the cell. To see how finite resources and competition affects such a system, we must construct a simple model to account for the limited resources. We consider coupling multiple TASEPs to a finite reservoir of particles where the entry rate of particles into the TASEPs depends on the number of particles left in the reservoir. Starting with a single TASEP connected to the reservoir, we study the system using both Monte Carlo simulations and theoretical approaches. We explore how the average overall density, density profile, and current change as a function of the number of particles initially in the reservoir for various parameters. New features arise not seen in the ordinary TASEP model, even for a single TASEP connected to the pool of particles. These features include a localized shock in the density profile. To explain what is seen in the simulations, we use an appropriately generalized version of a domain wall theory. The dynamics of the TASEPs with finite resources are also studied through the power spectra associated with the total particle occupancy of each TASEP and the reservoir. Again, we find new phenomena not seen in the power spectrum of the ordinary TASEP. For a single constrained TASEP, we find a suppression at low frequencies when compared to the power spectrum of the ordinary TASEP. The severity of this suppression is found to depend on how the entry rate changes with respect to the number of particles in the pool. For two TASEPs of different lengths, we find an enhancement of the power spectrum of the smaller TASEP when compared to the ordinary TASEP's power spectrum. We explain these findings using a linearized Langevin equation. Finally, we model competition between ten genes found in Escherichia coli using a modified version of the TASEP. This modified version includes extended objects and inhomogeneous internal hopping rates. We use the insight gained from the previous studies of finite resources and competition as well as other studies to gain some insight into how competition affects protein production. / Ph. D.

The objective of this study was to develop a 3-D model for The Pontchartrain Estuary that was capable of long-term mass conservative simulation of salinities. This was accomplished in a multi-stage approach involving: a physical model of salinity exchange through a pass; a 3-D FVCOM model of the physical experiment; the development and testing of an FVCOM model for an idealized Pontchartrain Basin; and for the entire estuary. The data from the physical model tests were used to validate the performance of the FVCOM model with density-driven flows. These results showed that hydrostatic FVCOM captured the primary internal wave movement. The idealized basin simulations were used to evaluate several issues related to salinity transport, namely the relative importance of baroclinic forcing, tidal forcing and hydrology. The idealized domain also permitted the testing of sigma-gradients, spatial distribution of friction coefficients, wind stress and various boundary treatments. The results showed that the density-driven exchange of saltwater at the open boundary required a baroclinic boundary condition for salinity as well as a lateral filter at the boundary on each sigma layer. A new radiative baroclinic open boundary condition was developed for FVCOM. When tides and hydrology were included, the FVCOM model was shown to reproduce the seasonal salinity that has been observed for long-term periods. It was also found that the simulation of tides and salinity in FVCOM is very sensitive to the spatial distribution of the friction coefficient; relatively low friction was required in the open water regions and high friction was needed in the passes and waterways to reproduce the tides and salinity distribution. A variable friction coefficient option was coded on FVCOM. The findings from the idealized model were utilized to setup two models for the actual estuary. Both models extend from Lake Maurepas, one to the Chandeleurs Islands and the other to Mobile Bay. The baroclinic open boundary and variable friction were implemented in these models. They were calibrated for tides and salinity. The 2008 Bonnet Carré Spillway Opening was applied to the first model. A tidal pumping effect in Lake Pontchartrain was observed and captured by the model.

Made available in DSpace on 2016-06-02T20:15:31Z (GMT). No. of bitstreams: 1 5872.pdf: 509530 bytes, checksum: 496d8919c2fd01cb49ba79b80563de69 (MD5) Previous issue date: 2014-05-26 / Universidade Federal de Minas Gerais / In this work we study vertex models with non-diagonal boundaries, characterized by reection matrices with an upper triangular form. By means of an extension of the algebraic Bethe ansatz, we construct generalized Bethe states as well as the respective eigenvalues for two classes of models: six and nineteen vertex models. As usual, in both cases the exact solution is given in terms of the Bethe equations. / Neste trabalho estudamos modelos de vértices com fronteiras não-diagonais, caracterizadas por matrizes de reflexão com estrutura triangular. Por meio de uma extensão do ansatz de Bethe algébrico usual, construímos estados de Bethe generalizados e os respectivos autovalores para duas classes de modelos: seis e dezenove vértices. Como usual, em ambos os casos a solução exata é dada em termos das equações de Bethe.

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L'objectif de cette thèse consiste à étudier la méthode de pénalité-projection vectorielle notée VPP (Vector Penalty-Projection method), qui est une méthode à pas fractionnaire pour la résolution des équations de Navier-Stokes incompressible avec conditions aux limites ouvertes. Nous présentons une revue bibliographique des méthodes de projection traitant le couplage de vitesse et de pression. Nous nous intéressons dans un premier temps aux conditions de Dirichlet sur toute la frontière. Les tests numériques montrent une convergence d'ordre deux en temps pour la vitesse et la pression et prouvent que la méthode est rapide et peu coûteuse en terme de nombre d'itérations par pas de temps. En outre, nous établissons des estimations d'erreurs de la vitesse et de la pression et les essais numériques révèlent une parfaite concordance avec les résultats théoriques. En revanche, la contrainte d'incompressibilité n'est pas exactement nulle et converge avec un ordre de O(varepsilondelta t) où varepsilon est un paramètre de pénalité choisi assez petit et delta t le pas temps. Dans un second temps, la thèse traite les conditions aux limites ouvertes naturelles. Trois types de conditions de sortie sont étudiés et testés numériquement pour l'étape de projection. Nous effectuons des comparaisons quantitatives des résultats avec d'autres méthodes de projection. Les essais numériques sont en concordance avec les estimations théoriques également établies. Le dernier chapitre est consacré à l'étude numérique du schéma VPP en présence d'une condition aux limites ouvertes non-linéaire sur une frontière artificielle modélisant une charge singulière pour le problème de Navier-Stokes. / Motivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem.

Alle dimensionsbehafteten Gitter-QCD-Observablen muessen in Einheiten einer Referenzskala ausgedrueckt werden und die Bestimmung dieser ist haeufig der erste Schritt in der Berechnung anderer Observablen. In dieser Arbeit beschreiben wir eine scale setting-Strategie fuer eine neue Satz an Ensembles mit großem Volumen, die von CLS generiert worden sind. Die Simulationen enthalten up, down und strange O(a)-verbesserte Wilson-Fermionenfelder. Die Eichfeld-dynamik ist mit Luescher-Weisz-Wirkung implementiert. Um das freezing der Topologie bei kleinen Gitterabstaenden zu ueberwinden, wurden offene Randbedingungen in Zeitrichtung verwendet. Außerdem wurde twisted mass reweighting eingesetzt, eine Technik, um die Fermionbeitraege in der Infrarotregion zu stabilisieren und zu regularisieren. In dieser Arbeit diskutieren wir deren Auswirkungen auf mesonische Spektralgroeßen. Wir berechnen die Gitterabstaende fuer unsere vier β Werte unter Verwendung der pseudoskalaren Zerfallskonstanten, die wir aus den Simulationen mit offenen Randbedingungen extrahieren. Außerdem bestimmen wir die Observable t0 und extrapolieren sie zum Kontinuum. / In lattice computations all dimensionful observables have to be expressed in units of a reference scale and its determination is often the first step before proceeding to other quantities. In this thesis we describe the scale setting strategy for a new set of large-volume ensembles generated within the CLS effort. The simulations have been carried out including up, down and strange quark fields, discretized a là Wilson and following the O(a)-improvement program. The gauge field dynamics is implemented with the improved Luescher-Weisz action. To overcome the freezing of topology in simulations at small lattice spacings, open boundary conditions in the time direction have been adopted, together with twisted-mass reweighting, a technique to regularize and stabilize the fermionic contributions in the infrared region. In this thesis we discuss their implications on mesonic spectral quantities. We compute the lattice spacings, for our four values of β, using the pseudo-scalar decay constants, extracted in the presence of open boundary conditions. In addition to that, we determine the observable t0 and extrapolate it to the continuum.