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Relating forced climate change to natural variability and emergent dynamics of the climate-economy systemKellie-Smith, Owen January 2010 (has links)
This thesis is in two parts. The first part considers a theoretical relationship between the natural variability of a stochastic model and its response to a small change in forcing. Over a large enough scale, both the real climate and a climate model are characterised as stochastic dynamical systems. The dynamics of the systems are encoded in the probabilities that the systems move from one state into another. When the systems’ states are discretised and listed, then transition matrices of all these transition probabilities may be formed. The responses of the systems to a small change in forcing are expanded in terms of the eigenfunctions and eigenvalues of the Fokker-Planck equations governing the systems’ transition densities, which may be estimated from the eigenvalues and eigenvectors of the transition matrices. Smoothing the data with a Gaussian kernel improves the estimate of the eigenfunctions, but not the eigenvalues. The significance of differences in two systems’ eigenvalues and eigenfunctions is considered. Three time series from HadCM3 are compared with corresponding series from ERA-40 and the eigenvalues derived from the three pairs of series differ significantly. The second part analyses a model of the coupled climate-economic system, which suggests that the pace of economic growth needs to be reduced and the resilience to climate change needs to be increased in order to avoid a collapse of the human economy. The model condenses the climate-economic system into just three variables: a measure of human wealth, the associated accumulation of greenhouse gases, and the consequent level of global warming. Global warming is assumed to dictate the pace of economic growth. Depending on the sensitivity of economic growth to global warming, the model climate-economy system either reaches an equilibrium or oscillates in century-scale booms and busts.
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Stochastická dynamika bublin v DNA / Stochastická dynamika bublin v DNAKaiser, Vojtěch January 2011 (has links)
Název práce: Stochastická dynamika bublin v DNA Autor: Bc. Vojtěch Kaiser Katedra: Katedra fyziky kondenzovaných látek Vedoucí diplomové práce: RNDr. Tomáš Novotný, Ph.D., Katedra fyziky kondenzovaných látek Abstrakt: Bubliny v DNA jsou místa, kde se vlivem tepelných či torsních vlivů otevírá dvojšroubovice DNA. Tyto bubliny jsou považovány za důležité pro termodynamiku DNA [56] a biologické procesy s DNA spojené [23,40,43,49]. V článcích [38, 39] byla řešena stochastická dynamika bublin v DNA na zá- kladě Polandova-Scheragova modelu a získány analytické výsledky při tep- lotě denaturace DNA a pro asymptotiku dlouhých časů, zvláště pro hustotu pravděpodobnosti času setkání konců bubliny. V této práci navazujeme na tyto výsledky a počítáme celkový tvar této hustoty pravděpodobností s vy- užitím numerické inverse analytických vztahů v Laplacově obraze. Dále po- čítáme hustotu pravděpodobnosti místa setkání konců bubliny. Odpovídající výsledky jsou numericky spočteny v případě molekul DNA konečné délky. Zachycování bubliny v oblastech bohatých na AT páry je modelováno jako subdifusivní systém dle článku [42] a jsou počítány stejné veličiny jako pro difusivní model. V závěru diskutujeme tyto výsledky a možnost jejich experi- mentálního ověření. Klíčová slova: bubliny v DNA,...
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Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck EquationKumar, Mrinal 2009 December 1900 (has links)
This dissertation addresses design and analysis aspects of stochastic dynamical
systems using Fokker-Planck equation (FPE). A new numerical methodology based
on the partition of unity meshless paradigm is developed to tackle the greatest hurdle
in successful numerical solution of FPE, namely the curse of dimensionality. A local
variational form of the Fokker-Planck operator is developed with provision for h-
and p- refinement. The resulting high dimensional weak form integrals are evaluated
using quasi Monte-Carlo techniques. Spectral analysis of the discretized Fokker-
Planck operator, followed by spurious mode rejection is employed to construct a
new semi-analytical algorithm to obtain near real-time approximations of transient
FPE response of high dimensional nonlinear dynamical systems in terms of a reduced
subset of admissible modes. Numerical evidence is provided showing that the curse
of dimensionality associated with FPE is broken by the proposed technique, while
providing problem size reduction of several orders of magnitude.
In addition, a simple modification of norm in the variational formulation is shown
to improve quality of approximation significantly while keeping the problem size fixed.
Norm modification is also employed as part of a recursive methodology for tracking
the optimal finite domain to solve FPE numerically.
The basic tools developed to solve FPE are applied to solving problems in nonlinear stochastic optimal control and nonlinear filtering. A policy iteration algorithm for
stochastic dynamical systems is implemented in which successive approximations of
a forced backward Kolmogorov equation (BKE) is shown to converge to the solution
of the corresponding Hamilton Jacobi Bellman (HJB) equation. Several examples,
including a four-state missile autopilot design for pitch control, are considered.
Application of the FPE solver to nonlinear filtering is considered with special emphasis
on situations involving long durations of propagation in between measurement
updates, which is implemented as a weak form of the Bayes rule. A nonlinear filter
is formulated that provides complete probabilistic state information conditioned on
measurements. Examples with long propagation times are considered to demonstrate
benefits of using the FPE based approach to filtering.
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Application of optimal prediction to molecular dynamicsBarber IV, John Letherman January 2004 (has links)
Thesis (Ph.D.); Submitted to the University of California at Berkeley, Berkeley, CA 94720 (US); 1 Dec 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56842" Barber IV, John Letherman. USDOE Director. Office of Science. Advanced Scientific Computing Research (US) 12/01/2004. Report is also available in paper and microfiche from NTIS.
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Numerical methods and stochastic simulation algorithms for reaction-drift-diffusion systemsMauro, Ava J. 12 March 2016 (has links)
In recent years, there has been increased awareness that stochasticity in chemical reactions and diffusion of molecules can have significant effects on the outcomes of intracellular processes, particularly given the low copy numbers of many proteins and mRNAs present in a cell. For such molecular species, the number and locations of molecules can provide a more accurate and detailed description than local concentration. In addition to diffusion, drift in the movements of molecules can play a key role in the dynamics of intracellular processes, and can often be modeled as arising from potential fields. Examples of sources of drift include active transport, variations in chemical potential, material heterogeneities in the cytoplasm, and local interactions with subcellular structures.
This dissertation presents a new numerical method for simulating the stochastically varying numbers and locations of molecular species undergoing chemical reactions and drift-diffusion. The method combines elements of the First-Passage Kinetic Monte Carlo (FPKMC) method for reaction-diffusion systems and the Wang—Peskin—Elston lattice discretization of the Fokker—Planck equation that describes drift-diffusion processes in which the drift arises from potential fields. In the FPKMC method, each molecule is enclosed within a "protective domain," either by itself or with a small number of other molecules. To sample when a molecule leaves its protective domain or a reaction occurs, the original FPKMC method relies on analytic solutions of one- and two-body diffusion equations within the protective domains, and therefore cannot be used in situations with non-constant drift. To allow for such drift in our new method (hereafter Dynamic Lattice FPKMC or DL-FPKMC), each molecule undergoes a continuous-time random walk on a lattice within its protective domain, and the lattices change adaptively over time.
One of the most commonly used spatial models for stochastic reaction-diffusion systems is the Smoluchowski diffusion-limited reaction (SDLR) model. The DL-FPKMC method generates convergent realizations of an extension of the SDLR model that includes drift from potentials. We present detailed numerical results demonstrating the convergence and accuracy of our method for various types of potentials (smooth, discontinuous, and constant). We also present several illustrative applications of DL-FPKMC, including examples motivated by cell biology.
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Evolução de estruturas via função de distribuição de partículasCalister, Ricardo January 2015 (has links)
Orientador: Prof. Dr. Maximiliano Ujevic Tonino / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015. / Neste trabalho, estudamos uma série de estruturas bidimensionais como discos
finos e varios tipos de anéis finos, que possam representar objetos astrofísicos,
usando a func¸ão de distribuição de partículas. Como primeiro passo, resolvemos
a equação de Fokker-Planck estacionária, ajustando os parâmetros de modo que
a função de distribuição satisfação, simultaneamente, a equação de Fokker-Planck
e a equação de Poisson para um determinado potencial gravitacional conhecido
dos modelos. A seguir fazemos uma análise da evolução temporal da função de
distribuição de partículas, de alguns destes sistemas, após as estruturas sofrerem
uma perturbação em seu campo gravitacional. As soluções e evoluções da equação
de Fokker-Planck são encontradas usando diretamente m'etodos numéricos, primeiramente
fazemos uma discretização da equação de Fokker-Planck usando o método das diferenc¸as finitas, e resolvendo o sistema de equações lineares resultante através de métodos que possam reduzir o tempo de processamento computacional e que resultem em soluções robustas quanto a convergência do sistema de equaçõess lineares, como o método GMRES (método do resíduo mínimo generalizado) e LCD (método das direções conjugadas a esquerda), que tornam viávell o estudo das evoluções temporais de estruturas bidimensionais que estamos interessados. / In this work we study, using the particle distribution function, several thin
structures like thin disks and thin rings that may represent astropysical objects.
As a first step, we solve the stationary Fokker-Planck equation adjusting the parameters
of the system so that the particles distribution function satisfies simultaneously
the Fokker-Planck and Poisson equations for a determined gravitational
potential model. Then, we make an analysis of the temporal evolution of the particle
distribution function for some of these systems under a perturbation on the
gravitational field. The solutions and evolutions of the Fokker-Planck equation are
found using direct numerical methods, first we use a finite difference scheme discretization
method for a Fokker-Planck equation, and then we solve the resulting
linear system through robust numerical methods that reduce the computational
processing time, as the GMRES method (generalized minimum residual method)
and the LCD method (left conjugated direction method).
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Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck / Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equationAlarcon LLacctarimay, Cesar Juan, 1982- 05 March 2012 (has links)
Orientadores: Maximiliano Ujevic Tonino, Javier Fernando Ramos Caro, Carola Dobrigkeit Chinellato / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-20T00:26:31Z (GMT). No. of bitstreams: 1
AlarconLLacctarimay_CesarJuan_D.pdf: 2806949 bytes, checksum: 588125c56d514dbfd77030a564888461 (MD5)
Previous issue date: 2012 / Resumo: Nesta tese pretendemos modelar a distribuição de matéria em um Anel estelar fino imerso no campo gravitacional de um e dois Satélites Shepherds (Satélites Pastores) usando a equação de Fokker-Planck. Em particular, estudamos a evolução de um anel fino ao redor de um monopolo central. Os coeficientes de difusão são aqui calculados e escritos em termos de um ¿potencial¿ semelhante aos usuais potencias de Rosenbluth. Neste caso, consideramos que as partículas campo obedecem uma distribuição Gaussiana. Resolvemos a equação de Fokker-Planck 1-dimensional para a função de distribuição das partículas teste que conformam o anel usando o método das diferenças finitas (versão Euler implícita). Demonstramos que o anel é uma configuração estável para uma evolução de longo tempo, tanto na ausência como na presença de shepherds. Estudamos também a variação da densidade de massa do anel para diferentes configurações. Em todos os casos é observada uma variação máxima e negativa da densidade perto da localização do shepherd devido a efeitos dinâmicos / Abstract: In this thesis we intend to model the distribution of matter in a thin stellar ring immersed in the gravitational field of one and two shepherd satellites using the Fokker-Planck equation. In particular, we study the evolution of a thin ring around a central monopole. The diffusion coefficients are calculated and written in terms of a ¿potential¿ similar to the usual Rosenbluth potentials. In this case, we consider that the particles follow a Gaussian distribution. We solve the 1-dimensional Fokker-Planck equation for the ring particles distribution function using the finite difference method (implicit Euler version). We show that the ring is a stable configuration for long time evolutions in the absence or in the presence of shepherds. We also studied the change in the mass density of the ring for different configurations. In all of the cases, it is observed a maximum negative variation of the density near the location of the shepherd due to dynamical effects / Doutorado / Física / Doutor em Ciências
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Aggregate Modeling of Large-Scale Cyber-Physical SystemsZhao, Lin January 2017 (has links)
No description available.
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Nonlinear Stochastic Dynamics and Signal Amplifications in Sensory Hair CellsAmro, Rami M. A. 17 September 2015 (has links)
No description available.
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Parameter estimation in interest rate models using Gaussian radial basis functionsvon Sydow, Gustaf January 2024 (has links)
When modeling interest rates, using strong formulations of underlying differential equations is prone to bad numerical approximations and high computational costs, due to close to non-smoothness in the probability density function of the interest rate. To circumvent these problems, a weak formulation of the Fokker–Planck equation using Gaussian radial basis functions is suggested. This approach is used in a parameter estimation process for two interest rate models: the Vasicek model and the Cox–Ingersoll–Ross model. In this thesis, such an approach is shown to yield good numerical approximations at low computational costs.
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