Dissertations / Theses on the topic 'Tabulated Models of Transition state'

Les biocarburants sont une alternative pour réduire les émissions de gaz à effet de serre. Ils ont une composition différente des carburants fossiles, ce qui peut modifier leurs caractéristiques de combustion (ou de pyrolyse), ainsi que leur résistance à l’autoxydation en phase liquide. Les modèles cinétiques détaillés constituent un outil important pour comprendre et prédire la combustion de ces carburants. Leur précision dépend en grande partie de la fiabilité des données cinétiques affectées aux différentes réactions. Dans cette thèse, une nouvelle approche basée sur les modèles tabulés d’état de transition (TMTS) est développée pour estimer les constantes de vitesse en s’appuyant sur des calculs de structures électroniques, couplés aux théories cinétiques (théorie de l’état de transition conventionnelle et variationelle, équation maîtresse). L’approche TMTS consiste à identifier précisément la zone réactionnelle de l’état de transition avec les substituants clés, puis à générer ces structures afin de pouvoir réaliser les calculs de constantes de vitesse. Cette approche a été testée pour l’isomérisation des radicaux alkyles. Les résultats ont montré un impact notable des ramifications de la chaîne sur les coefficients de vitesse, de sorte qu’un tableau de modè les tabulés d’état de transition contenant 51 modèles avec les paramètres cinétiques correspondants, a été proposé pour couvrir les réactions d’isomérisation à 3 et 4 centres. Pour le traitement des isomérisations à 5 centres, un total de 72 modèles a dû être construit, mettant en jeu un grand nombre de diastéréoisomères pour les réactifs et de configurations cycliques pour les TS. Un code en Python, capable de construire et de filtrer toutes les combinaisons y compris les configurations multiples de réactifs et d’états de transition, a été créé. Ce code prépare toutes les entrées du calcul ab initio et traite les sorties pour le code de calcul des constantes de vitesse, en incorporant la détermination de la symétrie ainsi que les différentes voies de réactions pour les structures ramifiées impliquant plusieurs configurations de réactifs et de TS. Les tables de TMTS ont été automatiquement créées pour les réactions d’isomérisations à 6 centres. Les réactions de β-scission des radicaux alkyles, qui représentent une source importante de formation de produits primaires insaturés (alcènes), ont aussi été prises en compte dans ce travail. Le code a été adapté à cette famille de réactions et des tables de TMTS ont également été proposées pour les β-scissions des liaisons C-C et C-H, avec un total de 45 modèles. Les métathèses sur les alcanes, par des radicaux hydrogène et alkyles, ont également été traitées par le code, avec un total de 20 modèles de réaction proposés. Finalement, les réactions de recombinaisons de radicaux alkyles ont également été étudiées mais ont nécessité un traitement variationnel pour évaluer les constantes de vitesse. Pour cette famille de réactions, les constantes de vitesse ont été obtenues en fonction de la température et de la pression pour différentes tailles de chaînes alkyles. Les résultats ont permis de constater qu’une règle simple appelée "règle de la moyenne géométrique" (GMR) était utilisable pour étendre les constantes cinétiques dépendant de la pression à des systèmes moléculaires de grande taille. Cette règle a donc été prise en compte pour finaliser la table des TMTS pour cette famille de réactions. A l’issue de la thèse, les familles de réactions couvertes par les tableaux TMTS englobent la grande majorité des réactions de pyrolyse des alcanes et leur implémentation dans les mécanismes cinétiquesdoit permettre d’améliorer la précision des modèles, notamment pour les alcanes linéaires et ramifiés<br>Bio-sourced fuels are a potential alternative to reduce emissions of greenhouse gases. These fuels present a composition different than the usual fossil fuels, which impacts their combustion and pyrolysis characteristics, as well as their resistance to liquid phase oxidation processes. Detailed kinetic models are an important tool for understanding and predicting the combustion of such fuels. The accuracy of these models mainly depends on the reliability of the kinetic data available for the reactions. In this thesis, a new theoretical approach named "the tabulated models of transition state" (TMTS), to estimate rate constants for reaction mechanisms, is developed. The rate coefficients were obtained based on theoretical methods, via ab initio calculations, coupled with kinetic rate theories (Transition State Theory, Variational TST, and Master Equation). The TMTS approach consists in identifying the key aspects of the reaction moiety that are important when defining the rate constants, and then creating models of reactions covering all the identified aspects. This approach was first tested for the isomerization of alkyl radicals, a reaction family that changes the radical positions in alkyl chains and impacts the final products distribution. The results indicated an important effect of alkyl chain branches on the final rate coefficients, so a table of transition state models with the corresponding parameters was proposed to cover 1,3 and 1,4-H-shift isomerization reactions, representing a total of 51 models of transition states. For the treatment of branching cases of 1,5-H-shift reactions, a total of 72 models had to be built, representing a myriad of reactant diastereoisomers and cyclic transition state configurations. A code in Python capable of building and filtering all the necessary combinations of models, including multiple reactant and TS configurations, was created. This code prepared all the electronic structure calculation inputs and treated the outputs for kinetic calculation code, incorporating features for symmetry determination, as well as classification of reaction pathways for branched structures with multiple configurations of reactant and TS. The results obtained from the code were compared to the ones produced by hand and the code was found to overcome the human results, as it avoided symmetries and optical isomers errors, and the TMTS tables were automatically created to the 1,5-H-shift reactions. The β-scission of alkyl radicals represent another important class of reactions, as they lead to the formation of unsaturated primary products (alkenes), so the same approach was applied for this reaction family, and tables containing the models of transition state were also proposed for C-C and C-H bond scissions, resulting in a total of 45 reaction models. The H-abstraction reactions by hydrogen atom and alkyl radicals were also treated by the code, representinga total of 20 reaction models. Finally, the alkyl recombinations were also investigated, a reaction family with loose TS that required a refined variational treatment. For this reaction family, rate constants were obtained theoretically in function of temperature and pressure for different alkyl chain sizes. From the results, a simple rule called "the geometric mean rule" (GMR) was useful for expanding pressure-dependent rate coefficients from small to large systems. Therefore, this rule was combined with the results calculated theoretically to propose tabulated values for the kinetic data of alkyl recombination reactions. The reaction families covered by the TMTS tables include the majority of the alkane pyrolysis process and their implementation on reaction mechanisms should improve the accuracy of branched and linear alkane models

Rangelands are a major type of land found on all continents. Though they comprise around 70% of the world's land area, knowledge of rangelands is limited and immature. Rangelands supply humans with food and fiber at very low energy costs compared to cultivated lands. They are inherently heterogeneous, highly variable in time and space. Rangeland management needs to consider the impacts of long-term vegetation transition. It needs a conceptual framework defining potential vegetation communities, describing the management induced transition of one vegetation community to another, and documenting the expected benefits provided by the various potential vegetation communities. The most widely used conceptual unit in the rangeland discipline is the "ecological site". Ecological sites can be an effective unit that should respond to management consistently and can help managers understand the site's potential to meet human needs. A state and transition model (STM) brings ecological sites and their potential vegetative states together to build a conceptual framework showing the major causes of transitions between states of an ecological site and thus helping make adaptive management decisions. Within the STM there is a need for an indicator of ecosystem health. Ecosystem services can be important to evaluate alternative states. Ecosystem services do not pass through a market for valuation, though often the cost would be very high if, through mismanagement, the ecosystem is no longer capable of providing those services. Vegetation communities are constantly facing reversible or irreversible transitions triggered by natural events and/or management actions. The framework generated in this study is significant in using remote sensing to generate state and transition models for a large area and in using ecosystem services to evaluate natural and/or management induced transitions as described in the STM. This dissertation addresses the improvement of public rangelands management in the West. It applies geospatial technologies to map ecological sites and states on those sites, characterizes transitions between states and selects a desired state to manage towards based on a systematic assessment of the value of flows of environmental services. The results from this study are an evaluation of improved draft ecological site maps for a larger area using remote sensing images, a simplified state-and-transition model adapted to remote sensing capabilities to study transitions due to climatic events and management practices, and a constrained optimization model that incorporates ecosystem services and the simplified STM to evaluate management costs and conservation benefits. The study showed that brush treatment is the most effective management practice to cause state transitions. The highest increase in the high cover state was by 24%. Areas under grazing and drought show slow transitions from brush to grass and also after prescribed fire vegetation take at least two years to recover.

The interaction of land-use and climate can cause non-linear “state” changes in ecosystems, characterized by persistent differences in structure and function. Changes in land-use and climate on the Colorado Plateau may be driving many ecosystems toward undesired states where energy-intensive measures are required to return to previous states. Landscape classification systems based on “ecological potential” offer a robust framework to evaluate ecological conditions. Ecological sites are a popular landscape classification system based on long-term ecological potential and are widely used throughout the western US. Ecological sites have been described extensively for rangelands and woodlands on DOI Bureau of Land Management lands; however, they have yet to be described on USDA Forest Service (USFS) lands. In this thesis, I describe a statistical approach to ecological site delineation and the development of state-and-transition models, diagrams that illustrate ecosystem dynamics and responses to disturbances. In Chapter 2, I used a large inventory dataset and multivariate statistical procedures to classify plots based on life zone, soils, and potential vegetation, effectively delineating statistical ecological site-like groups. Most of the statistical ecological sites matched ecological sites already described by the USDA Natural Resources Conservation Service (NRCS). Additionally, I described one new ecological site that has not been described by the NRCS in the Colorado Plateau region. In Chapter 3, I examined empirical evidence for alternative states in mountain ponderosa pine (Pinus ponderosa Lawson & C. Lawson) and upland piñon-juniper ecosystems. Using multivariate statistical procedures, I found that plots cluster into groups consistent with generalized alternative states identified in a priori conceptual models. Additionally, I showed that ponderosa pine clusters were true alternative states and piñon-juniper clusters were not true alternative states because they were confounded by similarities in climate. Ponderosa pine clusters were differentiated by overstory ponderosa pine density and corresponded to three states: current potential, high fuel load, and reduced overstory. These results illustrate the range of ecosystem variability that is present throughout the study area and present evidence for alternatives states caused by historical land-use. This project is the first to propose ecological sites and state-and-transition models on USFS lands in this region. These techniques could be applied to areas that do not have formally described ecological sites and state-and-transition models and could help identify ecological sites that may have been overlooked using other means of delineation. Additionally, these methods can be used to evaluate the range of ecological variability throughout an area of interest and to improved understanding of ecosystem dynamics.

Broad-scale forest die-off associated with drought and heat has now been reported from every forested continent, posing a global-scale challenge to forest management. Climate-driven die-off is frequently compounded with other drivers of tree mortality, such as altered land use, wildfire, and invasive species, making forest management increasingly complex. Facing similar challenges, rangeland managers have widely adopted the approach of developing conceptual models that identify key ecosystem states and major types of transitions between those states, known as "state-and-transition models" (S&T models). Using expert opinion and available research, the development of such conceptual S&T models has proven useful in anticipating ecosystem changes and identifying management actions to undertake or to avoid. In cases where detailed data are available, S&T models can be developed into probabilistic predictions, but even where data are insufficient to predict transition probabilities, conceptual S&T models can provide valuable insights for managing a given ecosystem and for comparing and contrasting different ecosystem dynamics. We assembled a synthesis of 14 forest die-off case studies from around the globe, each with sufficient information to infer impacts on forest dynamics and to inform management options following a forest die-off event. For each, we developed a conceptual S&T model to identify alternative ecosystem states, pathways of ecosystem change, and points where management interventions have been, or may be, successful in arresting or reversing undesirable changes. We found that our diverse set of mortality case studies fit into three broad classes of ecosystem trajectories: (1) single-state transition shifts, (2) ecological cascading responses and feedbacks, and (3) complex dynamics where multiple interactions, mortality drivers, and impacts create a range of possible state transition responses. We integrate monitoring and management goals in a framework aimed to facilitate development of conceptual S&T models for other forest die-off events. Our results highlight that although forest die-off events across the globe encompass many different underlying drivers and pathways of ecosystem change, there are commonalities in opportunities for successful management intervention.

Studying nuclei beyond the proton dripline can provide valuable information on the structure of nuclei at the limits of stability, where the strong nuclear force starts to be overcome by Coulomb repulsion between protons. Simple experimental observables, such as excitation energies and lifetimes of excited states in these proton-unbound nuclei can provide information on the nuclear wave function. Experimental data, such as that presented in this work, can then be used to improve models of nuclear structure at the proton dripline. This thesis presents data from a recoil-decay tagged differential plunger experiment undertaken at the University of Jyvaskyla in 2014. A fusion-evaporation reaction was used to populate excited states in the deformed ground-state proton emitter 113Cs. The JUROGAM-RITU-GREAT experimental setup was used to correlate gamma rays emitted from these excited states with protons emitted from 113Cs and the differential plunger for unbound nuclear states (DPUNS) was placed at the target position to measure the excited state lifetimes. The lifetime of the (11/2+) state in the most intense rotational band of 113Cs was measured to be tau = 24(6) ps, while a limit of tau is less than or equal to 5 ps was found for the lifetime of the higher energy (15/2+) state. The lifetime of proton emission was measured to be tau = 24.2(2) microseconds. The experimental data were used to test the predictions of a non adiabatic quasi-particle model for proton-emitting nuclei, which was employed to deduce the deformation of the states in 113Cs. Wave functions from the non adiabatic quasi-particle model were used to independently calculate proton-emission rates, gamma-ray transition rates and excited state energies as functions of deformation. The deformation of 113Cs could then be extracted from the intersection of the different theoretical values and experimental observables. A deformation of beta2 = 0.22(6)was extracted from the (11/2+) excitation energy and lifetime. The deformation values taken from the proton-emission rate and the lifetime limit of the (15/2+) state were also consistent with this value. The consistency of the different deformations calculated shows the effectiveness of the non adiabatic quasi-particle method when used to calculate the properties of deformed ground-state proton-emitters.

Located just east of Missoula, Montana, Milltown Dam stood from 1908 to 2008 immediately downstream of the Clark Fork River’s confluence with the Blackfoot River. After the discovery of arsenic-contaminated groundwater in the nearby community of Milltown, as well as extensive deposits of contaminated sediment in the dam’s upstream reservoir, in 1981, the area was designated a Superfund site – along with much of the Upper Clark Fork Watershed. This motivated the eventual decision to remove the dam, perform environmental remediation, and reconstruct approximately five kilometers of the Clark Fork River and its floodplain. This study is part conceptual and part empirical. It describes a state-and-transition framework equipped to investigate channel evolution as well as the adjustment trajectories of other socio-biophysical landscapes. This framework is then applied to understand the post-restoration channel evolution of the Clark Fork River’s mainstem, secondary channels, and floodplain. Adopting a state-and-transition framework to conceptualize landscape evolution lets environmental managers more effectively anticipate river response under multiple disturbence scenarios and therefore use more improvisational and adaptive management techniques that do not attempt to guide the landscape toward a single and permanent end state. State-and-transition models can also be used to highlight the spatially explicit patterns of complex biophysical response. The state-and-transition models developed for the Clark Fork River demonstrate the possibility of multiple evolutionary trajectories. Neither the secondary channels nor the main channel have responded in a linear, monotonic fashion, and future responses will be contingent upon hydrogeomorphic and climatic variability and chance disturbances. The biogeomorphic adjustments observed so far suggest divergent evolutionary trajectories and that in some instances the long-term fates of the mainstem, floodplain, and secondary channels are inescapably enmeshed with one another.

The extended finite state machine (EFSM) is a powerful modelling approach that has been applied to represent a wide range of systems. Despite its popularity, testing from an EFSM is a substantial problem for two main reasons: path feasibility and path test case generation. The path feasibility problem concerns generating transition paths through an EFSM that are feasible and satisfy a given test criterion. In an EFSM, guards and assignments in a path‟s transitions may cause some selected paths to be infeasible. The problem of path test case generation is to find a sequence of inputs that can exercise the transitions in a given feasible path. However, the transitions‟ guards and assignments in a given path can impose difficulties when producing such data making the range of acceptable inputs narrowed down to a possibly tiny range. While search-based approaches have proven efficient in automating aspects of testing, these have received little attention when testing from EFSMs. This thesis proposes an integrated search-based approach to automatically test from an EFSM. The proposed approach generates paths through an EFSM that are potentially feasible and satisfy a test criterion. Then, it generates test cases that can exercise the generated feasible paths. The approach is evaluated by being used to test from five EFSM cases studies. The achieved experimental results demonstrate the value of the proposed approach.

Gene transcription in individual living cells is inevitably a stochastic and dynamic process. Little is known about how cells and organisms learn to balance the fidelity of transcriptional control and the stochasticity of transcription dynamics. In an effort to elucidate the contribution of environmental signals to this intricate balance, a Three State Model was recently proposed, and the transcription system was assumed to transit among three different functional states randomly. In this work, we employ this model to demonstrate how the stochastic dynamics of gene transcription can be characterized by the three transition parameters. We compute the probability distribution of a zero transcript event and its conjugate, the distribution of the time durations in gene on or gene off periods, the transition frequency between system states, and the transcriptional bursting frequency. We also exemplify the mathematical results by the experimental data on prokaryotic and eukaryotic transcription. The analysis reveals that no promoters will be definitely turned on to transcribe within a finite time period, no matter how strong the induction signals are applied, and how abundant the activators are available. Although stronger extrinsic signals could enhance promoter activation rate, the promoter creates an intrinsic ceiling that no signals could cross over in a finite time. Consequently, among a large population of isogenic cells, only a portion of the cells, but not the whole population, could be induced by environmental signals to express a particular gene within a finite time period. We prove that the gene on duration follows an exponential distribution, and the gene off intervals show a local maximum that is best described by assuming two sequential exponential process. The transition frequencies are determined by a system of stochastic differential equations, or equivalently, an iterative scheme of integral operators. We prove that for each positive integer n , there associates a unique time, called the peak instant, at which the nth transcript synthesis cycle since time zero proceeds most likely. These moments constitute a time series preserving the nature order of n.

Un système embarqué est un système électronique et informatique autonome dédié à une tâche précise. Dans le secteur de l’automobile, le nombre de systèmes embarqués dans les voitures a considérablement augmenté au cours de ces dernières années et va certainement continuer à augmenter. Ces systèmes sont dédiés entre autres, à la sécurité, au confort de conduite,et à l’assistance à la conduite. Cette croissance des systèmes est associée avec une croissance en taille des logiciels qui les contrôlent. En conséquence, leur gestion(système et logiciel) devient de plus en plus complexe et problématique. Par ailleurs, la concurrence dans le secteur automobile est très féroce et les temps de mise sur le marché sont de plus en plus courts. Ainsi, pour garantir le bon fonctionnement des systèmes en général et du logiciel en particulier, étant donné leur complexité,et aussi les délais courts de mise sur le marché des produits automobiles, de nouvelles méthodes de développement doivent être considérées. Ainsi, de nombreuses méthodes de développement, incluant de nouveaux standards (de développement) et approches automatiques ont émergé au cours de ces dernières années. Dans le cas particulier de la vérification et validation de logiciel, une des activités critiques qui a connu une avancée significative est la génération de cas de test, avec l’avènement d’approches automatiques.Malgré cela, ces approches peinent souvent à s’imposer en milieu industriel. Une des raisons est que celles ci sont souvent peu adaptées ou peu utilisées dans un contexte industriel.Dans ce contexte, cette thèse vise à proposer une approche de vérification et de validation de logiciels embarqués, basée sur la génération automatique de cas de test. Pour cela, nous avons mis en place une approche permettant de représenter sous forme de modèles abstraits les spécifications d’un logiciel, puis de générer à partir de ces modèles un ensemble de cas de test en considérant en particulier le critère de couverture MC/DC<br>An embedded system is a system that performs a specific task and has a computer embedded inside. In the automotive sector, the amount of embedded systems in the vehicle has risen dramatically in recent years and is set to increase. They deal essentially with safety, comfort, and driving assistance. Furthermore, the increase in number and complexity of the systems is associated with a growth in software. As a consequence, their management (system and software) have become more and more complex and problematic. Also, the competition and time-to-market in the automotive industry are very tough. Thus, to guarantee the efficiency and reliability of the embedded systems in the vehicle in general and the software in particular, in view of the complexity as well as the competition and time-to-market law, new development methods should be considered. Therefore, new development methods including new standards, and automatic approaches have emerged over the last years. In the particular case of embedded software verification and validation, one of the most critical activities that has experienced a significant progress is test case generation with the advent of automatic approaches. Despite this, these approaches are not widely used or are not well adapted in industrial context. In that context, our goal in this PhD. thesis is to propose a new verification and validation approach, based on automatic test case generation of embedded embedded. Thus, we have set up an approach that automatically generates test cases, with respect to the MC/DC criterion, from abstract models of the software specifications expressed in the form of state-transition models

This study tested the performance of classification, regression, and ordination techniques to evaluate the spatiotemporal dynamics of threats to big sagebrush ecological sites. The research was focused on invasion by annual exotic grasses and encroachment by woodlands. We sought to identify those areas that have had a persistent coverage of cheatgrass (Bromus tectorum) in big sagebrush ecological sites. We took advantage of the contrast in greenness between multi-temporal (within one year) remotely sensed vegetation indices captured in the spring and summer to find a distinct phenological signature that allowed mapping cheatgrass. We utilized support vector machines (SVM) to classify three temporal scenarios for which field data sets were available. SVM performed very well with accuracies of 70% (producer's) and 95% (user's) for the class of interest (presence of cheatgrass). This was the focus of chapter 2. In chapter 3 we report the development of vegetation continuous fields (VCF) for three years of interest 1996, 2001, and 2007 in order to detect active woodland encroachment. We prepared VCF for shrubs, trees, herbaceous vegetation, and bare ground using a suite of remotely sensed spectral reflectance, vegetation indices, and transformations. We compared the performance of multivariate regression trees (MRT) and random forests (RF) to develop the VCF multi-temporal series. RF outperformed MRT in both accuracy and ability to appropriately map the continuum of percent cover across large landscapes. We estimate that 17,570 hectares of big sagebrush lands showed encroachment by woodlands. Our goal in chapter 4 was to develop a similarity index for large rangeland landscapes. Trend assessments field sites and a long-term annual series (1984 - 2008) of remotely sensed imagery were used in conjunction with multidimensional scaling (MDS) to measure ecological distance to undesired states such as invasion by exotic annuals and encroachment by woodlands. In this chapter our units of analysis were soil-mapping units, which were predominantly composed of one ecological site (>60%). Our MDS results show that different ecological sites can be identified in the reduced MDS statistical space. The observed transitions and trajectories of mountain, Wyoming, and basin big sagebrush sites correlated well with the ecological expectation in semiarid lands. We anticipate that managers can use our protocols to update ecological site descriptions and state and transition models from a remotely sensed perspective.

碩士<br>國立交通大學<br>資訊科學與工程研究所<br>106<br>Nowadays, more and more people concern the energy and environmental issues and would like to manage the use of electric power from a small-scale area such as a house, a building, or community. One of the most important tasks is to forecast the power consumption in next several minutes and/or hours so that people may cooperatively use their appliances in an asynchronous manner to alleviate the peak power consumption of an area. Different from conventional large-scale power consumption forecast schemes which are mainly based on artificial intelligence methods such as artificial neural network, this paper proposes a new approach to predict the energy consumption of a house and building based on appliance state transition models which can be gathered from a nonintrusive load monitoring (NILM) meter. First, the appliance usage patterns of a house or a building are obtained from the NILM meter. Then, appliance state transition models can be established and they can be used to predict the energy consumption of a house or building efficiently. Simulation results indicate that only 3% to 5% prediction error is introduced for a typical house environment.

The problem of relative spacecraft motion estimation is considered with application to various reference and relative orbits. Mean circular and elliptic orbits are analyzed, with relative orbits ranging in size from 1 km to 10 km. Estimators are built for three propagation models: (i) Gim-Alfriend State Transition Matrix, (ii) the J2-Linearized Equations of Motion for Circular Orbits, and (iii) the Clohessy-Wiltshire Equations of Motion. Two alternative models were developed in an attempt to ac- count for unmodeled nonlinearities: (i) Biased Clohessy-Whiltshire Equations, and (ii) J2 -Linearized State Transition Matrix. Two estimation techniques are presented in an attempt to explore and determine which propagation model minimizes the error residual: the linear Kalman filter is presented under the assumption of vector based, GPS-type measurements; the extended Kalman filter is analyzed assuming angle-range, optical-type measurements. Sampling time is varied to look at the effect of measurement frequency. It is assumed that the orbit of one of the satellites, the chief, is known reasonably well. This work showed that the error residuals from the state estimates were minimized when the propagation technique utilized was the Gim-Alfriend State Transition Matrix. This supports conclusions that are obtained outside of the estimation problem. Additionally, the error residuals obtained when the propagation technique was the Clohessy-Wiltshire Equations is comparable to the more complicated models. Unmodeled nonlinearities affect the magnitude of the error residuals. As expected, the Gim-Alfriend STM comes closest to the truth; for smaller eccentricities (0.005), the Clohessy-Wiltshire EOM show minor deviations from the truth. As the eccentricity increases, the linear models begin to diverge greatly from the true response. The additional two models (the biased CW equations, and the linear STM) show decent performance under specific conditions. The former accounts for some of the unaccounted for nonlinearities. The latter exhibits comparable performance to the Gim-Alfrien STM for circular reference orbits. However, in each case, as the nonlinearity of the problem increases, the accuracy of the model decreases.

In the thesis work we investigate four problems connected with dynamical processes in condensed medium, using different techniques of equilibrium and non-equilibrium statistical mechanics. Biology is rich in dynamical events ranging from processes involving single molecule [1] to collective phenomena [2]. In cell biology, translocation and transport processes of biological molecules constitute an important class of dynamical phenomena occurring in condensed phase. Examples include protein transport through membrane channels, gene transfer between bacteria, injection of DNA from virus head to the host cell, protein transport thorough the nuclear pores etc. We present a theoretical description of the problem of protein transport across the nuclear pore complex [3]. These nuclear pore complexes (NPCs) [4] are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. In the thesis, we propose a model for the transport of a protein through the plug, which is treated as elastic continuum, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein is referred to as the bubble. The relevant coordinate describing the transport is the center of the bubble. We write down an expression for the energy of the system, which is used to analyze the motion. It shows that the bubble executes a random walk, within the gel. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. Further, on adopting the same kind of free energy for the brush too, one finds that though the energy cost for the entry of the particle is small but the diffusion coefficient is much lower and hence, explanation of the rapid diffusion of the particle across the nuclear pore complex is easier within the gel model. In chemical physics, processes occurring in condensed phases like liquid or solid often involve barrier crossing. Simplest possible description of rate for such barrier crossing phenomena is given by the transition state theory [5]. One can go one step further by introducing the effect of the environment by incorporating phenomenological friction as is done in Kramer’s theory [6]. The “method of reactive flux” [7, 8] in chemical physics allows one to calculate the time dependent rate constant for a process involving large barrier by expressing the rate as an ensemble average of an infinite number of trajectories starting at the barrier top and ending on the product side at a specified later time. We compute the time dependent transmission coefficient using this method for a structureless particle surmounting a one dimensional inverted parabolic barrier. The work shows an elegant way of combining the traditional system plus reservoir model [9] and the method of reactive flux [7] and the normal mode analysis approach by Pollak [10] to calculate the time dependent transmission coefficient [11]. As expected our formula for the time dependent rate constant becomes equal to the transition state rate constant when one takes the zero time limit. Similarly Kramers rate constant is obtained by taking infinite time limit. Finally we conclude by noting that the method of analyzing the coupled Hamiltonian, introduced by Pollak is very powerful and it enables us to obtain analytical expressions for the time dependent reaction rate in case of Ohmic dissipation, even in underdamped case. The theory of first passage time [12] is one of the most important topics of research in chemical physics. As a model problem we consider a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space we derive a very general expression of the survival probability and the first passage time distribution, irrespective of the statistical nature of the dynamics. Also using the prescription adopted elsewhere [13] we define a bound to the actual survival probability and an approximate first passage time distribution which are expressed in terms of the position-position, velocity-velocity and position-velocity variances. Knowledge of these variances enables one to compute the survival probability and consequently the first passage distribution function. We compute both the quantities for gaussian Markovian process and also for non-Markovian dynamics. Our analysis shows that the survival probability decays exponentially at the long time, irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant [14]. Although the field of equilibrium thermodynamics and equilibrium statistical mechanics are well explored, there existed almost no theory for systems arbitrarily far from equilibrium until the advent of fluctuation theorems (FTs)[15] in mid 90�s. In general, these fluctuation theorems have provided a general prescription on energy exchanges that take place between a system and its surroundings under general nonequilibrium conditions and explain how macroscopic irreversibility appears naturally in systems that obey time reversible microscopic dynamics. Based on a Hamiltonian description we present a rigorous derivation [16] of the transient state work fluctuation theorem and the Jarzynski equality [17] for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is valid for a general non-Ohmic bath.

In the thesis work we investigate four problems connected with dynamical processes in condensed medium, using different techniques of equilibrium and non-equilibrium statistical mechanics. Biology is rich in dynamical events ranging from processes involving single molecule [1] to collective phenomena [2]. In cell biology, translocation and transport processes of biological molecules constitute an important class of dynamical phenomena occurring in condensed phase. Examples include protein transport through membrane channels, gene transfer between bacteria, injection of DNA from virus head to the host cell, protein transport thorough the nuclear pores etc. We present a theoretical description of the problem of protein transport across the nuclear pore complex [3]. These nuclear pore complexes (NPCs) [4] are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. In the thesis, we propose a model for the transport of a protein through the plug, which is treated as elastic continuum, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein is referred to as the bubble. The relevant coordinate describing the transport is the center of the bubble. We write down an expression for the energy of the system, which is used to analyze the motion. It shows that the bubble executes a random walk, within the gel. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. Further, on adopting the same kind of free energy for the brush too, one finds that though the energy cost for the entry of the particle is small but the diffusion coefficient is much lower and hence, explanation of the rapid diffusion of the particle across the nuclear pore complex is easier within the gel model. In chemical physics, processes occurring in condensed phases like liquid or solid often involve barrier crossing. Simplest possible description of rate for such barrier crossing phenomena is given by the transition state theory [5]. One can go one step further by introducing the effect of the environment by incorporating phenomenological friction as is done in Kramer’s theory [6]. The “method of reactive flux” [7, 8] in chemical physics allows one to calculate the time dependent rate constant for a process involving large barrier by expressing the rate as an ensemble average of an infinite number of trajectories starting at the barrier top and ending on the product side at a specified later time. We compute the time dependent transmission coefficient using this method for a structureless particle surmounting a one dimensional inverted parabolic barrier. The work shows an elegant way of combining the traditional system plus reservoir model [9] and the method of reactive flux [7] and the normal mode analysis approach by Pollak [10] to calculate the time dependent transmission coefficient [11]. As expected our formula for the time dependent rate constant becomes equal to the transition state rate constant when one takes the zero time limit. Similarly Kramers rate constant is obtained by taking infinite time limit. Finally we conclude by noting that the method of analyzing the coupled Hamiltonian, introduced by Pollak is very powerful and it enables us to obtain analytical expressions for the time dependent reaction rate in case of Ohmic dissipation, even in underdamped case. The theory of first passage time [12] is one of the most important topics of research in chemical physics. As a model problem we consider a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space we derive a very general expression of the survival probability and the first passage time distribution, irrespective of the statistical nature of the dynamics. Also using the prescription adopted elsewhere [13] we define a bound to the actual survival probability and an approximate first passage time distribution which are expressed in terms of the position-position, velocity-velocity and position-velocity variances. Knowledge of these variances enables one to compute the survival probability and consequently the first passage distribution function. We compute both the quantities for gaussian Markovian process and also for non-Markovian dynamics. Our analysis shows that the survival probability decays exponentially at the long time, irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant [14]. Although the field of equilibrium thermodynamics and equilibrium statistical mechanics are well explored, there existed almost no theory for systems arbitrarily far from equilibrium until the advent of fluctuation theorems (FTs)[15] in mid 90�s. In general, these fluctuation theorems have provided a general prescription on energy exchanges that take place between a system and its surroundings under general nonequilibrium conditions and explain how macroscopic irreversibility appears naturally in systems that obey time reversible microscopic dynamics. Based on a Hamiltonian description we present a rigorous derivation [16] of the transient state work fluctuation theorem and the Jarzynski equality [17] for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is valid for a general non-Ohmic bath.

博士<br>東海大學<br>統計學系<br>101<br>Many countries have been facing the challenges of aging population over decades. Depressive symptoms in later life of elderly have serious implications for the health and functioning has caused wide public concern. The purpose of this study is to explore the effect of the covariates related to demographic characteristics, home and environment conditions, and health status, on the changing status of depression of old people in Taiwan. A representative panel sample survey data collected in the six waves of “The Longitudinal Sample Survey of Health and Living Status of the Elderly in Taiwan” conducted from 1989 to 2007 by the predecessor organization of the Bureau of Health Promotion, Department of Health is used for analysis. Since cases of depression status are recurrent events with the characteristics of interval censored data, Cox model with interval-censored approach is applied for investigating the variables related to the changing status of depression among the elderly under the assumption that the observations within a subject are mutually independent. However, a major disadvantage of interval censored model is unable to deal with the situation that two or more different events of interest exist simultaneously, a more general method, multi-state model considered as a Markov chain for event history analysis is used to interpret the changing status of depression. To verify the proportional assumption in the conventional Cox model, Aalen’s additive model taking into account instantaneous covariate effects in time is employed as an alternative on a supplement. Also, the scaled Schoenfeld residuals plots are used for investigating the proportional hazard assumption. Furthermore, the transition probabilities for the changing status of depression obtained from Cox and Aalen models are provided. From the results of this study, age, gender, education, spouse, living with children, economic status, self-rated health, ADL function and physical function are significantly related to the depression. Also, the transition probabilities show the death rate has a greater impact on the elderly with initial depression state.

Anthropogenic utilization of forest and woodland ecosystems can cause declines in flora and fauna species. It is imperative to restore these ecosystems to mitigate further declines. In this thesis, I focused on a highly degraded region, the Box-Ironbark forests and woodlands of Victoria, Australia. Rather than mature stands with large trees, stands are currently dominated by high densities of small stems. This change has resulted in reduced populations of many flora and fauna species dependent on older-growth forests and woodlands. Managers are interested in restoring mature Box-Ironbark forests and woodlands through three alternative management strategies: allocating land to National Parks and allowing stands to develop naturally without harvesting, modifying timber harvesting regimes to retain more medium and large trees, or a new ecological thinning technique that retains target habitat trees and removes competing trees to encourage growth of retained stems.<br>The effects of each management strategy are not easy to predict due to complex interactions between intervention and stochastic natural processes. Forest simulation models are often employed to overcome this problem. I constructed state-and-transition simulation models (STSMs) to predict the effects of alternative management actions and natural disturbances on vegetation structure. Due to a lack of empirical data, I relied on the knowledge of experts in Box-Ironbark ecology and management to construct STSMs. Models predicted that the development of mature woodlands under all strategies was minimal over the next 150 years, and neither current harvesting nor ecological thinning is likely to expedite the development of mature stands relative to growth and natural disturbances. However, differences in experts’ opinions led to widely diverging model predictions.<br>Uncertainty must be acknowledged in model construction because it can affect model predictions. I quantified uncertainty due to four sources – between-expert variation, imperfect expert knowledge, natural stochasticity, and model parameterization – to determine which source caused the most variance in model predictions. I found that models were very uncertain and between-expert uncertainty contributed the majority of variance in model predictions. This brings into question the use of consensus methods in forest management where differences between experts are ignored.<br>Using uncertain model predictions to make management decisions is problematic because any given action can have many plausible outcomes. I applied several decision criteria to uncertain STSM predictions using a formal decision-making framework to determine the optimal management action in Box-Ironbark forests and woodlands. I found that natural development is the most risk-averse option, while ecological thinning is the most risky option because there is a small likelihood that it will greatly expedite the development of mature woodlands. Rather than selecting one option, managers could rely on a risk-spreading approach where the majority of land is allocated to no-cutting National Parks and a small amount of land is allocated to the other two harvesting strategies. This would allow managers to collect monitoring data for all management strategies in order to learn about effects of harvesting and update model predictions through time using adaptive management.