Orientador: Elso Drigo Filho / Banca: Sergio Henrique Monari Soares / Banca: José Roberto Ruggiero / Resumo: Neste trabalho são apresentadas as solu cões da equação de movimento clássica para uma partícula sujeita ao potencial de Morse Generalizado. Nesse potencial, utilizando parâmetros adequados recupera-se o potencial de Morse na sua forma conhecida. Essa mesma resolução também em foi feita para potenciais sim etricos de Morse. Este estudo foi realizado pensando no modelo mecânico do Acido Desoxirribonucléico (DNA), mais especi camente, na simulação das pontes de hidrogênio entre os pares de base. As equações de movimento s~ao tratadas como clássicas, pois algumas propriedades do DNA permitem a essa mol ecula um tratamento deste tipo. Manipulando-se classicamente, a resolução da equação de movimento e bastante simples e, através de t écnicas de integração, encontra-se uma solução exata para o potencial em questão. Poucos trabalhos são vistos na literatura com o potencial de Morse num estudo clássico, o que foi mais um incentivo para o desenvolvimento desse resultado. / Abstract: This study presents the solutions of classical motion equation for a particle subject to a Generalized Morse Potential. With this potential are using appropriate parameters one can recover the Morse potential as it is usually known. The same work had been done for symmetric Morse potentials. The main motivation for this work are the mechanical models for Deoxiribonucleic Acid (DNA), more speci cally, the H-bonds simulation between base pairs. The motion equations are discussed in a classical level, because some DNA properties allow these treatment. In Classical way, the resolution of motion equation is very simpler. Applying integration tecniques meets an exact solution when the Morse Potential is employed in this equation. There are few Classical Morse Potential studies founded in the literature. Due to this fact, it was an impulse to develop this result. / Mestre

Made available in DSpace on 2014-06-11T19:22:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-20Bitstream added on 2014-06-13T18:49:53Z : No. of bitstreams: 1 barboza_flm_me_sjrp.pdf: 572549 bytes, checksum: b0271e32ce51fab4b9ce169d0c28118b (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho são apresentadas as solu cões da equação de movimento clássica para uma partícula sujeita ao potencial de Morse Generalizado. Nesse potencial, utilizando parâmetros adequados recupera-se o potencial de Morse na sua forma conhecida. Essa mesma resolução também em foi feita para potenciais sim etricos de Morse. Este estudo foi realizado pensando no modelo mecânico do Acido Desoxirribonucléico (DNA), mais especi camente, na simulação das pontes de hidrogênio entre os pares de base. As equações de movimento s~ao tratadas como clássicas, pois algumas propriedades do DNA permitem a essa mol ecula um tratamento deste tipo. Manipulando-se classicamente, a resolução da equação de movimento e bastante simples e, através de t écnicas de integração, encontra-se uma solução exata para o potencial em questão. Poucos trabalhos são vistos na literatura com o potencial de Morse num estudo clássico, o que foi mais um incentivo para o desenvolvimento desse resultado. / This study presents the solutions of classical motion equation for a particle subject to a Generalized Morse Potential. With this potential are using appropriate parameters one can recover the Morse potential as it is usually known. The same work had been done for symmetric Morse potentials. The main motivation for this work are the mechanical models for Deoxiribonucleic Acid (DNA), more speci cally, the H-bonds simulation between base pairs. The motion equations are discussed in a classical level, because some DNA properties allow these treatment. In Classical way, the resolution of motion equation is very simpler. Applying integration tecniques meets an exact solution when the Morse Potential is employed in this equation. There are few Classical Morse Potential studies founded in the literature. Due to this fact, it was an impulse to develop this result.

No description available.

A carbon atom diffusion jump in iron austenite was considered as a subsequence of transformations between the cementite structure and the regular FCC packing. A model of this transformation was based on a 2D model of the elemental act of a polymorph transformation in metals. The energy threshold of this transformation has been calculated using the Morse pair potential. It occurs that the estimated enthalpy of the transformation is equal to 149±20 kJ/mole which is in satisfactory agreement with experimental data.

Swarms are groups of agents, which we model as point particles, whose collective behavior emerges from individual interactions. We study a first-order swarming model in a periodic coordinate system with pairwise social forces, investigating its stable configurations for differing numbers of agents relative to the periodic width. Two states emerge from numerical simulations in one dimension: even spacing throughout the period, or clumping within a certain portion of the period. A mathematical analysis of the energy of the system allows us to determine stability of these configurations. We also perform numerical simulations for evolution to equilibrium over time, and find results in agreement with our mathematical analysis. For certain values of the periodic width relative to the number of agents, our numerical simulations show that either clumping or even spacing can be stable equilibria, and which equilibrium is reached depends on on starting conditions, indicating hysteresis.

No / Nonadiabatic Monte Carlo transition-state theory is used to explore competing C¿Cl and C¿Br bond fission processes in a simple model of 1[n,pi*(CO)] photoexcited bromoacetyl chloride. Morse potentials are used to represent bond stretching coordinates, and the positions and magnitudes of nonadiabatic coupling between excited state potentials are modeled using ab initio data. The main effect of nonadiabaticity is to favor C¿Cl fission over C¿Br, despite a larger barrier to C¿Cl dissociation. The absolute values of the rate constants are smaller than observed experimentally, but the calculated branching ratios are close to the experimental value. For C¿Cl fission, it is shown that the minimum energy crossing point is not sufficient to describe the rate constant, suggesting that care must be taken when using alternative models which make this assumption.

Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single component. We are still examining the local minimizers with multiple components to determine whether the candidate solution is the minimum-energy configuration.

No description available.

In this thesis a reduced dimensionality quantum scattering model is applied to the study of polyatomic reactions of type X + CH4 <--> XH + CH3. Two dimensional quantum scattering of the symmetric hydrogen exchange reaction CH3+CH4 <--> CH4+CH3 is performed on an 18-parameter double-Morse analytical function derived from ab initio calculations at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. Spectator mode motion is approximately treated via inclusion of curvilinear or rectilinear projected zero-point energies in the potential surface. The close-coupled equations are solved using R-matrix propagation. The state-to-state probabilities and integral and differential cross sections show the reaction to be primarily vibrationally adiabatic and backwards scattered. Quantum properties such as heavy-light-heavy oscillating reactivity and resonance features significantly influence the reaction dynamics. Deuterium substitution at the primary site is the dominant kinetic isotope effect. Thermal rate constants are in excellent agreement with experiment. The method is also applied to the study of electronically nonadiabatic transitions in the CH3 + HCl <--> CH4 + Cl(2PJ) reaction. Electrovibrational basis sets are used to construct the close-coupled equations, which are solved via Rmatrix propagation using a system of three potential energy surfaces coupled by spin-orbit interaction. Ground and excited electronic surfaces are developed using a 29-parameter double-Morse function with ab initio data at the CCSD(T)/ccpV( Q+d)Z-dk//MP2/cc-pV(T+d)Z-dk level of theory, and with basis set extrapolated data, both corrected via curvilinear projected spectator zero-point energies. Coupling surfaces are developed by fitting MCSCF/cc-pV(T+d)Z-dk ab initio spin orbit constants to 8-parameter functions. Scattering calculations are performed for the ground adiabatic and coupled surface models, and reaction probabilities, thermal rate constants and integral and differential cross sections are presented. Thermal rate constants on the basis set extrapolated surface are in excellent agreement with experiment. Characterisation of electronically nonadiabatic nonreactive and reactive transitions indicate the close correlation between vibrational excitation and nonadiabatic transition. A model for comparing the nonadiabatic cross section branching ratio to experiment is discussed.

Pour décrire les vibrations à l'intérieur des molécules diatomiques, le potentiel de Morse est une meilleure approximation que le système de l'oscillateur harmonique. Ainsi, en se basant sur la définition des états cohérents et comprimés donnée dans le cadre du problème de l'oscillateur harmonique, la première partie de ce travail suggère une construction des états cohérents et comprimés pour le potentiel de Morse. Deux types d’états seront construits et leurs différentes propriétés seront étudiées en portant une attention particulière aux trajectoires et aux dispersions afin de confirmer la quasi-classicité de ces états. La deuxième partie de ce travail propose d'insérer ces deux types d’états cohérents et comprimés de Morse dans un miroir semi-transparent afin d'introduire un nouveau moyen de créer de l'intrication. Cette intrication sera mesurée à l’aide de l’entropie linéaire et nous étudierons la dépendance par rapport aux paramètres de cohérence et de compression. / In order to describe the vibrations inside a diatomic molecule, the Morse potential is a better approximation than the harmonic oscillator system. Thus, based on the definition of the coherent states given in the context of the harmonic oscillator, the first part of this work suggests a construction for the squeezed coherent states of the Morse potential. Two types of states will be constructed and their diverse properties will be studied with special attention to the trajectories and dispersions in order to confirm their quasi-classicity. The second part of this work proposes to insert those two types of Morse squeezed coherent states in a beam splitter in order to introduce a new way of creating entanglement. This entanglement will be measured by the linear entropy and we will study the dependence with the coherence and squeezing parameters.