An algorithm for modeling two species plasmas, which evolves the number density, flow velocity, and temperature equations coupled to Maxwell's electric and magnetic field equations, is discussed. Charge separation effects and the displacement current are retained. Mathematical derivations of normal modes in cold and hot plasmas, as represented by dispersion relations resulting from a linear analysis of the two fluid equations, are presented. In addition, numerical theory in relation to the ideas of geometry, temporal and spatial discretization, linearization of the fluid equations, and an expansion using finite elements is given. Numerical results generated by this algorithm compare favorably to analytical results and other published work. Specifically, we present numerical results, which agree with electrostatics, plasma oscillations at zero pressure, finite temperature acoustic waves, electromagnetic waves, whistler waves, and magnetohydrodynamics (MHD) waves, as well as a Fourier analysis showing fidelity to multiple dispersion relations in a single simulation. Final consideration is given to two species plasma stability calculations with a focus on the force balance of the initial conditions for a resistive MHD tearing mode benchmark and a static minimum energy plasma state.

An algorithm for modeling two species plasmas, which evolves the number density, flow velocity, and temperature equations coupled to Maxwell's electric and magnetic field equations, is discussed. Charge separation effects and the displacement current are retained. Mathematical derivations of normal modes in cold and hot plasmas, as represented by dispersion relations resulting from a linear analysis of the two fluid equations, are presented. In addition, numerical theory in relation to the ideas of geometry, temporal and spatial discretization, linearization of the fluid equations, and an expansion using finite elements is given. Numerical results generated by this algorithm compare favorably to analytical results and other published work. Specifically, we present numerical results, which agree with electrostatics, plasma oscillations at zero pressure, finite temperature acoustic waves, electromagnetic waves, whistler waves, and magnetohydrodynamics (MHD) waves, as well as a Fourier analysis showing fidelity to multiple dispersion relations in a single simulation. Final consideration is given to two species plasma stability calculations with a focus on the force balance of the initial conditions for a resistive MHD tearing mode benchmark and a static minimum energy plasma state.

Cette thèse s'intéresse à la migration cellulaire d'une population composée de deux espèces qui interagissent par le biais de signaux chimiques. Ces signaux chimiques auxquels sont soumis les deux espèces sont de nature différente. Ils sont soit intérieur (produit par les deux espèces) ou bien extérieur (apporté par le milieu et consommé par les deux espèces). On observe le phénomène de synchronisation et de désynchronisation lors de la migration d'une population composée de deux espèces différentes d'E.Coli. Séparément, les bactéries rouges d'E.Coli se déplacent deux fois plus vite que les bactéries vertes. Cependant dans le cas d'une population mixte composée de rouges et de vertes, les bactéries rouges et vertes se déplacent ensemble ou séparément en fonction de la proportion de la bactérie la plus rapide rouge dans la population.Cette observation expérimentale est interprétée par un modèle macroscopique parabolique de chimiotactisme à deux espèces pour lequel l'existence et la non-existence des ondes de concentration sont prouvées. Ce modèle macroscopique parabolique à deux espèces est construit à partir des modèles microscopiques qui traduisent le mouvement individuel des cellules.Ce phénomène de synchronisation et de désynchronisation est aussi présent dans la dynamique des masses de dirac des deux espèces après l'explosion des solutions classiques dans un modèle d'agrégation à deux espèces avec une seule substance chimique.Nous proposons aussi dans cette thèse une méthode pour obtenir des schémas numériques préservant à la fois l'équilibre et l'asymptotique. Cette méthode est testée aux modèles cinétiques de chimiotactisme et de transfert radiatif. / This thesis is concerned about cellular motion of a population composed of two species in interaction through chemical cues. The chemical cues to which the two species are subject are of different kind.They can be internal (produced by the two species) or external (present in the meduim and consommed by the two species). Synchronising and non-synchronising effects are observed during the migration of the population formed by two different strains of E.Coli.Although separately, red bacteria E.Coli travel twice as fast as green bacteria E.Coli, put together, they travel or split depending on the percentage of the faster bacteria in the population. This experimental result is explained by a two-species parabolic macroscopic chemotaxis model for which the existence and non-existence of traveling pulses are showed. The parabolic macroscopic model is derived from microscopic models which describe the individual motion of cells. The synchronising and non-synchronising effect is also encountered in dynamics of the two-species dirac masses after blow-up of classical solutions in a two-species model for aggregation. A method to design both well-balanced and asymptotic preserving schemes is proposed. This method is tested to chemotaxis and radiative transport kinetic models.

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

Um estudo das taxas de perda de átomos ocorrendo numa armadilha magneto-óptica mista foi realizado aqui. Observamos experimentalmente, pela primeira vez, a ocorrência de processos colisionais inelásticos envolvendo duas espécies atômicas distintas. Identificamos o escape radiativo como o processo dominante nas taxas de perda de átomos da armadilha de sódio, devidas às colisões desses com os átomos de rubídio aprisionados, para as dadas condições experimentais. Realizamos estudos semelhantes com uma mistura K-Rb, onde as taxas de perda de átomos da armadilha de potássio foram observadas. Procurou-se interpretar os resultados através um modelo semiclássico que teve de ser modificado por nós. Esses estudos foram importantes porque revelaram a grande influência do processo de escape radiativo nas taxas de perda. Também verificou-se que outros canais podem manifestar a sua influência e suspeitamos que isso se deva às diferenças estruturais das \"quasimoléculas\" formadas na colisão. A compreensão de processos colisionais em armadilhas magneto-ópticas mistas é importante para a obtenção e estudo de amostras distintas de condensados bosônicos coexistindo numa mesma região. / We report the results of the trap-Ioss collisional rates observed in a mixed species magneto-optical trapo These are the first systematic studies about the collisionalloss channels due to heteronuclear interactions between two cold atomic sampIes in aMOr. We have used two different combinations: Na-Rb and K -Rb. lt was observed that the rates are strongly affected by the radiative escape Ioss channel, especially in the Na-Rb system. We also observed that some other Ioss channels may ruIe the rates behavior depending on the combination or the experimento To understand the results a semiclassical approach was used: the Gallagher-Prichard theory. We beIieve that these studies will soon be helpful to control the interatomic collisional rates for the achievement of heteronuclear sampIes of Bose-Einstein condensates.

Neste trabalho, abordamos dois assuntos independentes e interessantes que permeiam o cotidiano dos pesquisadores da área de resfriamento e confinamento de átomos neutros. O primeiro está relacionado aos processos de perda de átomos ocorrendo em armadilhas magneto-ópticas, a partir das quais o fenômeno é observado. Mostramos que a conjunção de dois modelos tradicionais da literatura é capaz de gerar um modelo semiclássico e semi-analítico básico e robusto, capaz de reproduzir as características fundamentais dos resultados experimentais já obtidos, incluindo os mais recentes. Isto demonstra que os aspectos essenciais dos mecanismos de perda em armadilhas são, agora, bem compreendidos. O segundo assunto abordado aqui está relacionado à observação de moléculas diatômicas formadas em armadilhas magneto-ópticas. Nesse sentido, uma série de experimentos básicos foi realizada, gerando resultados e discussões que constituem uma rica fonte de informação inspirando a continuação e conclusão do trabalho iniciado aqui, cujo objetivo final é a caracterização precisa e o desenvolvimento técnicas de resfriamento e aprisionamento de moléculas diatômicas heteronucleares. / We report the results concerning to two main subjects of laser cooling and trapping community. We begin by presenting the results of modeling two-body trap loss rates as a function of the trap laser intensity. We show that one can merge two simple theories to obtain a semiclassical and semi-analytical model which is able to provide the fundamental properties observed in the experimental results found in the literature. Hence, we concluded that the essential features of the two-body trap loss rates taking place in MOTs are now well understood. On the other hand, we run a set of experiments trying to produce and detect heteronuclear diatomic ultracold molecules. Although this has not been accomplished yet, we have acquired a wide and rich amount of data that will certainly be very helpful for continuing and concluding the work here started. In the near future the photoassociation spectroscopy of ultracold heteronuclear diatomic molecules will provide valuable information to help in its manipulation.

The European Commission manages fish stocks by applying a fishing mortality based on the maximum sustainable yield concept. So far most Baltic Sea fishing maximum sustainable yieldmodels have focused on one species at a time. The few existing multi-species models have assumed that a species’ maturity and growth is dependent on the availability of food. Our two-species models make it possible to investigate if there is a conflict between fishing maximum sustainable yield for cod and herring in the Baltic Sea. This two-species model of cod, as a predator and herring as prey, takes into account environmental drivers on cod and herring recruitment. Reproductive volume together with year-growth, (a year specific effect on growth of external variables like food availability) and predation by grey seals was included in the cod model. The herring model was dependent on cod spawning stock biomass and year-growth. The result shows that the reproductive volume is the main factor that affects the maximum sustainable yield for cod. The spawning stock biomass at maximum sustainable yield is more sensitive to reproductive volume than year-growth. When predation from seals is added in mortality and high environmental factors occurs the spawning stock biomass would be 50% compared to the spawning stock biomass at high environmental effects without seal predation. Four simulations of high cod spawning stock biomass were devastating for the herring population that was eradicated with high predation pressure. The herring maximum sustainable yield depends on the amount of cod spawning stack biomass i.e. the effect of high or low reproductive volume. Two analyses were made on a current environmental state for both species. The first analysis had a natural mortality of 0.2 for cod, which gave an fishing mortality of 0.20 and maximum sustainable yield of 410 000 tons. The herring had a fishing mortality of 0.03 and maximum sustainable yield of 11 000 tons. The second simulation included seal predation in cod mortality which decreased the cod maximum sustainable yield by 98% at a fishing mortality of 0.02, which gave a fishing mortality of 0.19 and maximum sustainable yield of 275 000 tons for herring. This gives a 25 times increase of herring maximum sustainable yield compared to the result without predation on cod. The cod population dynamics is vulnerable to environmental changes and to secure a healthy and productive cod population the target fishing mortality should be kept in phase with current reproductive volume. / Europeiska kommissionen förvaltar fiskbestånden genom att tillämpa fiskekvoter baserat på konceptet maximalt hållbart uttag. Hittills har de flesta maximalt hållbara fiske-fångst modeller för Östersjön fokuserat på en art i taget. De få befintliga fler-arts-modeller har antagit att en arts mognad och tillväxt är beroende av tillgången på föda. Vår två-arts-modell gör det möjligt att undersöka om det finns en konflikt mellan maximal hållbar fiske-fångst på torsk och sill i Östersjön. Denna två-arts-modell med torsk som ett rovdjur och sill som byte, tar hänsyn till miljön som drivkraft på deras rekrytering. I torskmodellen ingick reproduktiv volym tillsammans med årlig tillväxt (ett års specifika effekt på tillväxten beroende av externa variabler som tillgången till föda) och predation av gråsäl. Sill-modellen var beroende av årlig tillväxt och lekbeståndets biomassa hos torsk. Resultaten visar att den viktigaste faktorn som påverkar maximalt hållbart uttag för torsk är reproduktiv volym. Lekbeståndets biomassa vid maximalt hållbart uttag är mer känsligt för förändringar i reproduktiv volym än årlig tillväxt. När predation från säl tillsätts och höga gynnsamma miljöfaktorer råder är lekbeståndets biomassa 50 % jämfört med lekbeståndets biomassa vid höga gynnsamma miljöeffekter utan säl predation. Fyra simuleringar gav hög lekbestånds biomassa för torsk vilket var förödande för sillpopulationen som utrotades pga. högt predationstryck. Sillens maximala hållbara uttag beror på mängden lekbestånds biomassa hos torsk, d.v.s. effekten av hög eller låg reproduktiv volym. Två analyser gjordes på nuvarande miljömässiga nivåer för båda arterna. Den första analysen hade en naturlig dödlighet på 0,2 för torsk, vilket gav en fiske-mortalitet på 0,20 och maximalt hållbart uttag på 410 000 ton. Sillen hade en fiske-mortalitet på 0,03 och maximalt hållbart uttag på 11 000 ton. I den andra simuleringen ingår sälpredation på torsk vilket minskade torskens maximala hållbara uttag med 98 % vid en fiske-mortalitet på 0,02, vilket gav en fiske-mortalitet på 0,19 och maximalt hållbart uttag på 275 000 ton för sill. Detta ger en ökning av maximalt hållbart uttag för sill 25 gånger jämfört med resultatet utan predation på torsk. Torskens populationsdynamik är sårbar för miljöförändringar och för att säkra ett sunt och produktivt torskbestånd bör fiskemortaliteten hållas i fas med nuvarande reproduktiva volym.

Neste trabalho, abordamos dois assuntos independentes e interessantes que permeiam o cotidiano dos pesquisadores da área de resfriamento e confinamento de átomos neutros. O primeiro está relacionado aos processos de perda de átomos ocorrendo em armadilhas magneto-ópticas, a partir das quais o fenômeno é observado. Mostramos que a conjunção de dois modelos tradicionais da literatura é capaz de gerar um modelo semiclássico e semi-analítico básico e robusto, capaz de reproduzir as características fundamentais dos resultados experimentais já obtidos, incluindo os mais recentes. Isto demonstra que os aspectos essenciais dos mecanismos de perda em armadilhas são, agora, bem compreendidos. O segundo assunto abordado aqui está relacionado à observação de moléculas diatômicas formadas em armadilhas magneto-ópticas. Nesse sentido, uma série de experimentos básicos foi realizada, gerando resultados e discussões que constituem uma rica fonte de informação inspirando a continuação e conclusão do trabalho iniciado aqui, cujo objetivo final é a caracterização precisa e o desenvolvimento técnicas de resfriamento e aprisionamento de moléculas diatômicas heteronucleares. / We report the results concerning to two main subjects of laser cooling and trapping community. We begin by presenting the results of modeling two-body trap loss rates as a function of the trap laser intensity. We show that one can merge two simple theories to obtain a semiclassical and semi-analytical model which is able to provide the fundamental properties observed in the experimental results found in the literature. Hence, we concluded that the essential features of the two-body trap loss rates taking place in MOTs are now well understood. On the other hand, we run a set of experiments trying to produce and detect heteronuclear diatomic ultracold molecules. Although this has not been accomplished yet, we have acquired a wide and rich amount of data that will certainly be very helpful for continuing and concluding the work here started. In the near future the photoassociation spectroscopy of ultracold heteronuclear diatomic molecules will provide valuable information to help in its manipulation.

Um estudo das taxas de perda de átomos ocorrendo numa armadilha magneto-óptica mista foi realizado aqui. Observamos experimentalmente, pela primeira vez, a ocorrência de processos colisionais inelásticos envolvendo duas espécies atômicas distintas. Identificamos o escape radiativo como o processo dominante nas taxas de perda de átomos da armadilha de sódio, devidas às colisões desses com os átomos de rubídio aprisionados, para as dadas condições experimentais. Realizamos estudos semelhantes com uma mistura K-Rb, onde as taxas de perda de átomos da armadilha de potássio foram observadas. Procurou-se interpretar os resultados através um modelo semiclássico que teve de ser modificado por nós. Esses estudos foram importantes porque revelaram a grande influência do processo de escape radiativo nas taxas de perda. Também verificou-se que outros canais podem manifestar a sua influência e suspeitamos que isso se deva às diferenças estruturais das \"quasimoléculas\" formadas na colisão. A compreensão de processos colisionais em armadilhas magneto-ópticas mistas é importante para a obtenção e estudo de amostras distintas de condensados bosônicos coexistindo numa mesma região. / We report the results of the trap-Ioss collisional rates observed in a mixed species magneto-optical trapo These are the first systematic studies about the collisionalloss channels due to heteronuclear interactions between two cold atomic sampIes in aMOr. We have used two different combinations: Na-Rb and K -Rb. lt was observed that the rates are strongly affected by the radiative escape Ioss channel, especially in the Na-Rb system. We also observed that some other Ioss channels may ruIe the rates behavior depending on the combination or the experimento To understand the results a semiclassical approach was used: the Gallagher-Prichard theory. We beIieve that these studies will soon be helpful to control the interatomic collisional rates for the achievement of heteronuclear sampIes of Bose-Einstein condensates.

Neste trabalho apresentamos a produção de moléculas frias heteronucleares em uma armadilha magneto-óptica mista de 39K e 85Rb e detectadas no estado fundamental. A técnica de detecção consiste na fotoionização pulsada das moléculas que, após terem sido fotoassociadas, decaem através de emissão espontânea para estados ligados do potencial do estado molecular fundamental. A partir dos resultados da produção de moléculas frias KRb, estudamos-as com relação ao tipo de colisões que as originam, e à temperatura associada ao seu movimento translacional. Experimentos foram também realizados para comprovar que as moléculas detectadas são provenientes do estado fundamental. Finalmente, também estudamos neste trabalho, a taxa segundo a qual são formadas. Concomitantemente à produção de KRb, moléculas frias homonucleares 39K2 e 85Rb2 são também formadas, detectadas e caracterizadas. São apresentados também, os primeiros passos dados em direção à realização de espectroscopia fotoassociativa dos estados ligados das moléculas heteronucleares obtidas. / In this work, cold ground-state KRb molecules were produced by photoassociation in a two species magneto-optical trap (MOT) containing 39K and 85Rb. The KRb molecules are produced through photoassociation and detected in the ground state by multiphoton pulsed ionization. We have characterized their translational temperature and measured their formation rate constant. Homonuclear cold molecules 39K2 and 85Rb2 detected in their ground state were also formed in our trap and characterized as well. It is also reported our first efforts towards the realization of photoassociation spectroscopy of the heteronuclear molecules produced in our trap.