Tesis sobre el tema "Stochastic Fokker-Planck"
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Adesina, Owolabi Abiona. "Statistical Modelling and the Fokker-Planck Equation". Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-1177.
Texto completoGuillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.
Texto completoNoble, Patrick. "Stochastic processes in Astrophysics". Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/10013.
Texto completoLi, Wuchen. "A study of stochastic differential equations and Fokker-Planck equations with applications". Diss., Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/54999.
Texto completoMiserocchi, Andrea. "The Fokker-Planck equation as model for the stochastic gradient descent in deep learning". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18290/.
Texto completoЮщенко, Ольга Володимирівна, Ольга Владимировна Ющенко, Olha Volodymyrivna Yushchenko, Тетяна Іванівна Жиленко, Татьяна Ивановна Жиленко y Tetiana Ivanivna Zhylenko. "Description of the Stochastic Condensation Process under Quasi-Equilibrium Conditions". Thesis, Sumy State University, 2012. http://essuir.sumdu.edu.ua/handle/123456789/34910.
Texto completoДенисов, Станіслав Іванович, Станислав Иванович Денисов, Stanislav Ivanovych Denysov, V. V. Reva y O. O. Bondar. "Generalized Fokker-Planck Equation for the Nanoparticle Magnetic Moment Driven by Poisson White Noise". Thesis, Sumy State University, 2012. http://essuir.sumdu.edu.ua/handle/123456789/35373.
Texto completoLi, Yao. "Stochastic perturbation theory and its application to complex biological networks -- a quantification of systematic features of biological networks". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/49013.
Texto completoVellmer, Sebastian. "Applications of the Fokker-Planck Equation in Computational and Cognitive Neuroscience". Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21597.
Texto completoThis thesis is concerned with the calculation of statistics, in particular the power spectra, of point processes generated by stochastic multidimensional integrate-and-fire (IF) neurons, networks of IF neurons and decision-making models from the corresponding Fokker-Planck equations. In the brain, information is encoded by sequences of action potentials. In studies that focus on spike timing, IF neurons that drastically simplify the spike generation have become the standard model. One-dimensional IF neurons do not suffice to accurately model neural dynamics, however, the extension towards multiple dimensions yields realistic behavior at the price of growing complexity. The first part of this work develops a theory of spike-train power spectra for stochastic, multidimensional IF neurons. From the Fokker-Planck equation, a set of partial differential equations is derived that describes the stationary probability density, the firing rate and the spike-train power spectrum. In the second part of this work, a mean-field theory of large and sparsely connected homogeneous networks of spiking neurons is developed that takes into account the self-consistent temporal correlations of spike trains. Neural input is approximated by colored Gaussian noise generated by a multidimensional Ornstein-Uhlenbeck process of which the coefficients are initially unknown but determined by the self-consistency condition and define the solution of the theory. To explore heterogeneous networks, an iterative scheme is extended to determine the distribution of spectra. In the third part, the Fokker-Planck equation is applied to calculate the statistics of sequences of binary decisions from diffusion-decision models (DDM). For the analytically tractable DDM, the statistics are calculated from the corresponding Fokker-Planck equation. To determine the statistics for nonlinear models, the threshold-integration method is generalized.
Sjöberg, Paul. "Numerical Methods for Stochastic Modeling of Genes and Proteins". Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8293.
Texto completoGerritsma, Eric. "Continuous and discrete stochastic models of the F1-ATPase molecular motor". Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210110.
Texto completodoctorat est d’étudier et de décrire les propriétés chimiques et mé-
caniques du moteur moléculaire F1 -ATPase. Le moteur F1 -ATPase
est un moteur rotatif, d’aspect sphérique et d’environ 10 nanomètre
de rayon, qui utilise l’énergie de l’hydrolyse de l’ATP comme car-
burant moléculaire.
Des questions fondamentales se posent sur le fonctionnement de
ce moteurs et sur la quantité de travail qu’il peut fournir. Il s’agit
de questions qui concernent principalement la thermodynamique
des processus irréversibles. De plus, comme ce moteur est de
taille nanométrique, il est fortement influencé par les fluctuations
moléculaires, ce qui nécessite une approche stochastique.
C’est en créant deux modéles stochastiques complémentaires de
ce moteur que nous avons contribué à répondre à ces questions
fondamentales.
Le premier modèle discuté au chapitre 5 de la thèse, est un mod-
èle continu dans le temps et l’espace, décrit par des équations de
Fokker-Planck, est construit sur des résultats expérimentaux.
Ce modèle tient compte d’une description explicite des fluctua-
tions affectant le degré de liberté mécanique et décrit les tran-
sitions entre les différents états chimiques discrets du moteur,
par un processus de sauts aléatoires entre premiers voisins. Nous
avons obtenus des résultats précis concernant la chimie d’hydrolyse
et de synthèse de l’ATP, et pour les dépendences du moteur en les
différentes variables mécaniques, à savoir, la friction et le couple
de force extérieur, ainsi que la dépendence en la température.
Les résultats que nous avons obtenus avec ce modèle sont en ex-
cellent accord avec les observations expérimentales.
Le second modèle est discret dans l’espace et continu dans le
temps et est décrit dans le chapitre 6. L’analyse des résultats
obtenus par simulations numériques montre que le modèle est
en accord avec les observations expérimentales et il permet en
outre de dériver des grandeurs thermodynamiques analytique-
ment, décrites au chapitre 4, ce que le modèle continu ne permet
pas.
La comparaison des deux modèles révele la nature du fonction-
nement du moteur, ainsi que son régime de fonctionnement loin
de l’équilibre. Le second modèle a éte soumis récemment pour
publication.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
Wibowo, D. H. "An economic analysis of deforestation mechanisms in Indonesia : empirics and theory based on stochastic differential and fokker-planck equations /". [St. Lucia, Qld.], 1999. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe16272.pdf.
Texto completoMazzarisi, Onofrio. "Diffusion in Hamiltonian systems under stochastic perturbations and LHC dynamic aperture issues". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13862/.
Texto completoMelo, Andrea Barroso. "Análise Crítica da Dinâmica de uma Cavidade Pendular Quântica". Universidade Federal Fluminense, 2004. http://www.bdtd.ndc.uff.br/tde_busca/arquivo.php?codArquivo=268.
Texto completoDesenvolvemos uma análise quântica de uma cavidade pendular, utilizando a representação P positiva, mostrando que o estado quântico do movimento de um espelho,um objeto macroscópico, tem efeitos notáveis na dinâmica deste sistema. Este foi proposto anteriormente como um candidato para medidas quanticamente limitadas de pequenos deslocamentos do espelho devido à pressão de radiação, para a produção de estados com emaranhamento entre espelho e o campo e também para estados de superposição do espelho. Contudo, quando tratamos o espelho oscilante como um oscilador quântico encontramos que este sistema sempre oscila, não possui estados estacionários e exibe incertezas na posição e no momento que são tipicamente maiores que os valores médios. Isto significa que a análise linearizada das flutuações realizadas predominantemente para prever estes estados quânticos são de uso limitado. Achamos que a acuracidade alcançável na realização das medidas é muito pior do que o limite quântico padrão, devido ao ruído térmico, que para parâmteros experimentais típicos é enorme mesmo em 2mK.
We perform a quantum mechanical analysis of a pendular cavity, using the positive-P representation, showing that the quantum state of the moving mirror, a microscopic object, has noticeable eects on the dynamics. This system was previously been proposed as a candidate for the quantum-limited measurement of small displacements os the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady-state, and exhibits uncertainties in position and momentum wich are typically large than the mean values. This means that previous linearised fluctuation analyses wich have been used to predict these highly quantum states are of limited use. We find that achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at 2mK.
Alves, Claudia Marins. "Stochastic models for the treatment of dispersion in the atmosphere". Laboratório Nacional de Computação Científica, 2006. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=135.
Texto completoModelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.
Roper, Peter. "Noise induced processes in neural systems". Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/10882.
Texto completoAmro, Rami M. A. "Nonlinear Stochastic Dynamics and Signal Amplifications in Sensory Hair Cells". Ohio University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1438694373.
Texto completoSchubert, Sven. "Stochastic and temperature-related aspects of the Preisach model of hysteresis". Doctoral thesis, Universitätsbibliothek Chemnitz, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-70798.
Texto completoThe aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales
Yilmaz, Bulent. "Stochastic Approach To Fusion Dynamics". Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608517/index.pdf.
Texto completoBruna, Maria. "Excluded-volume effects in stochastic models of diffusion". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:020c2d3e-5fef-478c-9861-553cd310daf5.
Texto completoArenas, Zochil González. "Formulação supersimétrica de processos estocásticos com ruído multiplicativo". Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4684.
Texto completoOs processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi.
Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.
Zhao, Lin. "Aggregate Modeling of Large-Scale Cyber-Physical Systems". The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549.
Texto completoDolgov, Sergey. "Tensor product methods in numerical simulation of high-dimensional dynamical problems". Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-151129.
Texto completoMaillet, Raphaël. "Analyse statistique et probabiliste de systèmes diffusifs en présence de bruit". Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD025.
Texto completoThis thesis deals with the long-time behavior of stochastic Fokker-Planck equations with additive common noise and presents statistical methods for estimating the invariant measure of multidimensional ergodic diffusion processes from noisy data. In the first part, we analyze stochastic Fokker-Planck Partial Differential Equations (SPDEs), obtained as the mean-field limit of interacting particle systems influenced by both idiosyncratic and common Brownian noises. We establish conditions under which the addition of common noise restores uniqueness if the invariant measure. The main challenge arises from the finite-dimensional nature of the common noise, while the state variable — interpreted as the conditional marginal law of the system given the common noise — operates within an infinite-dimensional space. We demonstrate that uniqueness is restored if the mean field interaction term attracts the system towards its conditional mean given the common noise, particularly when the intensity of the idiosyncratic noise is small. In the second part, we develop a new statistical methodology using kernel density estimation to effectively approximate the invariant measure from noisy observations, highlighting the crucial role of the underlying Markov structure in the denoising process. This method involves a pre-averaging technique that proficiently reduces the intensity of the noise while maintaining the analytical characteristics and asymptotic properties of the underlying signal. We investigate the convergence rate of our estimator, which depends on the anisotropic regularity of the density and the intensity of the noise. We establish noise intensity conditions that allow for convergence rates comparable to those in noise-free environments. Additionally, we demonstrate a Bernstein concentration inequality for our estimator, leading to an adaptive procedure for selecting the kernel bandwidth
Montanari, Carlo Emilio. "Diffusive approach for non-linear beam dynamics in a circular accelerator". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19289/.
Texto completoCohen, Jack Andrew. "Active colloids and polymer translocation". Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e8fd2e5d-f96f-4f75-8be8-fc506155aa0f.
Texto completoDe, Moor Sylvain. "Limites diffusives pour des équations cinétiques stochastiques". Electronic Thesis or Diss., Rennes, École normale supérieure, 2014. http://www.theses.fr/2014ENSR0001.
Texto completoThis thesis presents several results about stochastic partial differential equations. The main subject is the study of diffusive limits of kinetic models perturbed with a random term. We also present a result about the regularity of a class of stochastic partial differential equations and a result of existence and uniqueness of invariant measures for a stochastic Fokker-Planck equation.First, we give three results of approximation-diffusion in a stochastic context. The first one deals with the case of a kinetic equation with a linear operator of relaxation whose velocity equilibrium has a power tail distribution at ininity. The equation is perturbed with a Markovian process. This gives rise to a stochastic fluid fractional limit. The two remaining results consider the case of the radiative transfer equation which is a non-linear kinetic equation. The equation is perturbed successively with a cylindrical Wiener process and with a Markovian process. In both cases, we are led to a stochastic Rosseland fluid limit.Then, we introduce a result of regularity for a class of quasilinear stochastic partial differential equations of parabolic type whose random term is driven by a cylindrical Wiener process.Finally, we study a Fokker-Planck equation with a noisy force governed by a cylindrical Wiener process. We prove existence and uniqueness of solutions to the problem and then existence and uniqueness of invariant measures to the equation
Mukhtar, Qaisar. "On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal Plasmas". Doctoral thesis, KTH, Fusionsplasmafysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-120590.
Texto completoQC 20130415
Izydorczyk, Lucas. "Probabilistic backward McKean numerical methods for PDEs and one application to energy management". Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE008.
Texto completoThis thesis concerns McKean Stochastic Differential Equations (SDEs) to representpossibly non-linear Partial Differential Equations (PDEs). Those depend not onlyon the time and position of a given particle, but also on its probability law. In particular, we treat the unusual case of Fokker-Planck type PDEs with prescribed final data. We discuss existence and uniqueness for those equations and provide a probabilistic representation in the form of McKean type equation, whose unique solution corresponds to the time-reversal dynamics of a diffusion process.We introduce the notion of fully backward representation of a semilinear PDE: thatconsists in fact in the coupling of a classical Backward SDE with an underlying processevolving backwardly in time. We also discuss an application to the representationof Hamilton-Jacobi-Bellman Equation (HJB) in stochastic control. Based on this, we propose a Monte-Carlo algorithm to solve some control problems which has advantages in terms of computational efficiency and memory whencompared to traditional forward-backward approaches. We apply this method in the context of demand side management problems occurring in power systems. Finally, we survey the use of generalized McKean SDEs to represent non-linear and non-conservative extensions of Fokker-Planck type PDEs
Alves, Claudia Marins. "Modelos estocásticos para tratamento da dispersão de material particulado na atmosfera". Laboratório Nacional de Computação Científica, 2006. https://tede.lncc.br/handle/tede/62.
Texto completoLagrangian stochastic models are a largely used tool in the study of passive substances dispersion inside the Atmospheric Boundary Layer. Its application is related to the trajectory computation of thousands of particles, that numerically simulate the dispersion of suspense substances in the atmosphere. In this study, the basic concepts related to the Lagrangian stochastic modelling are presented and discussed together with its main characteristics and its computational implementation, to the study of particles dispersion in the atmosphere. In a computational experiment, the obtained results are compared with observational data from the TRACT experiment, that took place in Europe in 1992. The input data needed for the dispersion model are extracted from simulations with the numerical weather forecast model RAMS. Dispersion over Rio de Janeiro region is also tested in a second experiment.
Modelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.
Adhikari, Shishir Raj. "STATISTICAL PHYSICS OF CELL ADHESION COMPLEXES AND MACHINE LEARNING". Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1562167640484477.
Texto completoCeccato, Alessandro. "Approaches to dimensionality reduction and model simplification of dynamics in the chemical context". Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3426709.
Texto completoNelle moderne scienze fisiche e chimiche, uno sforzo considerevole è dedicato allo studio di fenomeni dinamici complessi. Tale studio è spesso ostacolato dalla considerevole complessità (dovuta all'elevata dimensionalità) dei sistemi di interesse. In questo progetto di ricerca, di carattere teorico e metodologico, esploriamo alcuni aspetti riguardanti la riduzione della dimensionalità e la semplificazione di dinamiche complesse, sia deterministiche che stocastiche. In particolare, la prima parte del lavoro (capitoli 2-5), si concentra su sistemi deterministici. Nel capitolo 2, partendo dai risultati ottenuti in due precedenti lavori [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101 (2013) and P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)] introduciamo il concetto di "forma canonica" della legge di evoluzione per cinetiche chimiche basate sulla legge di azione di massa, e mostriamo che lo studio di tali forme può condurre alla scoperta di nuove interessanti proprietà e alla razionalizzazione di altre già note. Specificamente, mostriamo l'esistenza di "sottospazi attrattivi" in una rappresentazione astratta (ipersferica) della dinamica del sistema reagente. Nel capitolo 3, basandoci sulla teoria formulata nel capitolo 2, sviluppiamo un algoritmo (implementato nel software DRIMAK, acronimo di Dimensional Reduction for Isothermal Mass-Action Kinetics) finalizzato alla localizzazione di punti prossimi allo Slow Manifold, ossia all’ipersuperficie, nello spazio delle concentrazioni, in prossimità della quale ha luogo la parte lenta dell'evoluzione. L'individuazione dello Slow Manifold per un sistema reagente è potenzialmente un passaggio chiave per elaborare strategie di riduzione di dimensionalità. Nel capitolo 4 estendiamo la teoria a network aperti di reazioni chimiche, ossia a casi in cui uno o più reagenti sono continuamente immessi nell'ambiente di reazione. Infine, nel capitolo 5 generalizziamo ulteriormente la teoria a dinamiche (anche smorzate) nello spazio delle fasi. La seconda parte del lavoro (capitoli 6-8) è dedicata ai sistemi stocastici. Nel capitolo 6 muoviamo i primi passi verso la riduzione di dimensionalità di cinetiche chimiche stocastiche. Specificamente, mostriamo l'esistenza di strutture geometriche (nello spazio dei numeri di molecole per ogni specie) analoghe agli Slow Manifold nella controparte macroscopica. Ancora nel contesto delle cinetiche chimiche stocastiche, nel capitolo 7 mostriamo i risultati di uno studio critico di due comuni approssimazioni continue della ‘chemical master equation’ e dell'algoritmo di simulazione di Gillespie, ossia, le cosiddette equazioni di Fokker-Planck e di Langevin “chimiche”. In particolare, dimostriamo che entrambe le approssimazioni soffrono di una inconsistenza fisica che si manifesta nella presenza di correnti di probabilità spurie all'equilibrio, anche per network di reazioni chimiche completamente reversibili e verificanti il bilancio dettagliato. Infine, nel capitolo 8 ci concentriamo su sistemi fluttuanti sovrasmorzati di tipo generale, i quali, a parte casi molto semplici e a bassa dimensionalità, sono spesso matematicamente intrattabili. In questo contesto miriamo ad ottenere solo un'informazione parziale, ma con basso costo computazionale, sullo stato futuro del sistema. In particolare, otteniamo una serie di disuguaglianze che consentono di vincolare alcune quantità rilevanti del sistema.
Manca, Luigi. "Kolmogorov operators in spaces of continuous functions and equations for measures". Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85697.
Texto completoDans la première partie, la théorie de la convergence faibles des fonctions est mis au point afin de donner des résultats généraux sur les semi-groupes des Markov et leur générateur.
Dans la deuxième partie, des modèles de semi-groups de Markov associés à des équations aux dérivées partielles stochastiques sont étudiés. En particulier, Ornstein-Uhlenbeck, réaction-diffusion et équations de Burgers ont été envisagées. Pour chaque cas, le semi-groupe de transition et son générateur infinitésimal ont été étudiées dans un espace de fonctions continues.
Les résultats principaux montrent que l'ensemble des fonctions exponentielles fournit un Core pour l'opérateur de Kolmogorov. En conséquence, on prouve l'unicité de l'équation de Kolmogorov de mesures (autrement dit de Fokker-Planck).
Heidernätsch, Mario. "On the diffusion in inhomogeneous systems". Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-169979.
Texto completoThe aim of this thesis is to investigate the influence of the stochastic interpretation of the Langevin equation with state-dependent diffusion coefficient on the propagator of the related stochastic process, or its averages, respectively. This helps to obtain a deeper understanding and to interpret measurement data of diffusion in inhomogeneous systems and is accompanied with the question of the proper form of the diffusion equation in such systems. To simplify the question, in this thesis only systems are considered which can be fully described by a spatially dependent diffusion coefficient and a given stochastic interpretation. Therefore, for several experimentally relevant one-dimensional systems, the respective general propagator is determined, which is valid for any possible stochastic interpretation. Then, the propagator for two exemplary stochastic interpretations, here the Itô and Klimontovich-Hänggi interpretation, are compared and the differences are identified. For mean and variance of the processes three major interpretations are compared, namely the Itô, the Stratonovich and the Klimontovich-Hänggi interpretation. This systematic research on inhomogeneous diffusion process may help in future to identify these kind of, in exactly one stochastic interpretation, drift-free systems more easily. Another important part of this thesis extends this question to multidimensional inhomogeneous anisotropic systems. This is of high relevance, for instance, for the research of diffusion in liquid crystalline systems with an inhomogeneous director field. Although, in contrast to one-dimensional systems, the propagator may not be calculated generally, the influence of the inhomogeneity on measurement data like the mean squared displacement or the distribution of diffusivities is determined. Based on one example, also the influence of the stochastic interpretation on these quantities is demonstrated
Friedrich, Benjamin M. "Nonlinear dynamics and fluctuations in biological systems". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-234307.
Texto completoDas Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten
Kumar, Mrinal. "Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation". 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500.
Texto completo"Linear response and stochastic resonance of subdiffusive bistable fractional Fokker-Planck systems and the effects of colored noises on bistable systems". 2006. http://library.cuhk.edu.hk/record=b5893039.
Texto completoThesis (M.Phil.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (leaves 85-89).
Text in English; abstracts in English and Chinese.
Yim Man Yi = Ya kuo san shuang wen fen shu Fuke-Pulangke xi tong de xian xing xiang ying ji sui ji gong zhen he you se zao yin dui shuang wen xi tong suo yin qi de xiao ying / Yan Minyi.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Brownian motion and anomalous dynamics --- p.1
Chapter 1.2 --- White and colored noises --- p.3
Chapter 2 --- Linear response theory of sub diffusive Fokker-Planck systems --- p.6
Chapter 2.1 --- Introduction to subdiffusive Fokker-Planck systems --- p.6
Chapter 2.2 --- Spectral density --- p.8
Chapter 2.3 --- Linear response --- p.11
Chapter 2.4 --- Signal-to-noise ratio (SNR) --- p.13
Chapter 2.5 --- Stochastic energy --- p.14
Chapter 3 --- Perturbation due to a sinusoidal signal --- p.16
Chapter 3.1 --- Presence of an external sinusoidal forcing --- p.16
Chapter 3.1.1 --- PDF and linear reponse --- p.16
Chapter 3.1.2 --- Phase lag --- p.19
Chapter 3.1.3 --- SNR --- p.19
Chapter 3.1.4 --- Stochastic energy --- p.23
Chapter 3.2 --- Presence of a sinusoidally time-varying diffusion coefficient --- p.23
Chapter 4 --- Perturbation due to a rectangular signal --- p.26
Chapter 4.1 --- Linear response to a rectangular pulse --- p.26
Chapter 4.2 --- Perturbation due to a periodic rectangular signal --- p.28
Chapter 4.2.1 --- Linear response --- p.29
Chapter 4.2.2 --- SNR --- p.31
Chapter 4.2.3 --- Stochastic energy --- p.33
Chapter 4.3 --- Comparison with the response to a sinusoidal driving force --- p.35
Chapter 5 --- The Effects of Colored Noise on the Stationary Probability Distribution --- p.38
Chapter 5.1 --- Formulation of a general colored noises-driven system --- p.39
Chapter 5.2 --- Approximation schemes for a colored noise --- p.42
Chapter 5.2.1 --- Decoupling approximation --- p.42
Chapter 5.2.2 --- UCNA --- p.45
Chapter 5.2.3 --- Small r approximation . --- p.46
Chapter 5.2.4 --- Presence of an additive noise: g(x) = 1 --- p.47
Chapter 5.2.5 --- Presence of a multiplicative noise: g(x) = x --- p.52
Chapter 5.3 --- Approximation scheme for two colored noises --- p.53
Chapter 5.3.1 --- Presence of two additive noises --- p.55
Chapter 5.3.2 --- Presence of an additive noise and a multiplicative noise --- p.55
Chapter 5.4 --- Unimodal-bimodal transitions --- p.61
Chapter 6 --- A stochastic genetic regulatory transcription model with colored noises --- p.68
Chapter 6.1 --- Biological background --- p.69
Chapter 6.2 --- Effect of a single noise --- p.72
Chapter 6.3 --- Effects of two noises --- p.75
Chapter 6.4 --- Biological implications of colored noises in the model --- p.81
Chapter 7 --- Conclusions --- p.82
Bibliography --- p.85
Chapter A --- Mittag-Leffler function --- p.90
Chapter B --- H-function (Fox function) --- p.92
Chapter C --- Operator algebra --- p.94
Chapter D --- Mean first passage time --- p.97
Poggio, Tomaso y Federico Girosi. "Continuous Stochastic Cellular Automata that Have a Stationary Distribution and No Detailed Balance". 1990. http://hdl.handle.net/1721.1/6012.
Texto completoMauro, Ava J. "Numerical methods and stochastic simulation algorithms for reaction-drift-diffusion systems". Thesis, 2014. https://hdl.handle.net/2144/15259.
Texto completoKaiser, Vojtěch. "Stochastická dynamika bublin v DNA". Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313899.
Texto completoHeidernätsch, Mario. "On the diffusion in inhomogeneous systems". Doctoral thesis, 2014. https://monarch.qucosa.de/id/qucosa%3A20253.
Texto completoThe aim of this thesis is to investigate the influence of the stochastic interpretation of the Langevin equation with state-dependent diffusion coefficient on the propagator of the related stochastic process, or its averages, respectively. This helps to obtain a deeper understanding and to interpret measurement data of diffusion in inhomogeneous systems and is accompanied with the question of the proper form of the diffusion equation in such systems. To simplify the question, in this thesis only systems are considered which can be fully described by a spatially dependent diffusion coefficient and a given stochastic interpretation. Therefore, for several experimentally relevant one-dimensional systems, the respective general propagator is determined, which is valid for any possible stochastic interpretation. Then, the propagator for two exemplary stochastic interpretations, here the Itô and Klimontovich-Hänggi interpretation, are compared and the differences are identified. For mean and variance of the processes three major interpretations are compared, namely the Itô, the Stratonovich and the Klimontovich-Hänggi interpretation. This systematic research on inhomogeneous diffusion process may help in future to identify these kind of, in exactly one stochastic interpretation, drift-free systems more easily. Another important part of this thesis extends this question to multidimensional inhomogeneous anisotropic systems. This is of high relevance, for instance, for the research of diffusion in liquid crystalline systems with an inhomogeneous director field. Although, in contrast to one-dimensional systems, the propagator may not be calculated generally, the influence of the inhomogeneity on measurement data like the mean squared displacement or the distribution of diffusivities is determined. Based on one example, also the influence of the stochastic interpretation on these quantities is demonstrated.
Friedrich, Benjamin M. "Nonlinear dynamics and fluctuations in biological systems". Doctoral thesis, 2016. https://tud.qucosa.de/id/qucosa%3A30879.
Texto completoDas Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten.:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 66
Ferrero, Eduardo Ezequiel. "Dinámica de relajación del modelo de Potts de q estados bidimensional: una contribución a la descripción de propiedades de no-equilibrio en transiciones de fase de primer orden". Doctoral thesis, 2011. http://hdl.handle.net/11086/163.
Texto completoEstudiamos el modelo de Potts de q estados bidimensional, que presenta transiciones de fase magnéticas con temperatura de primer (q > 4) y segundo orden (q = 4). Trabajamos con simulaciones tipo Monte Carlo para las cuales implementamos distintas técnicas algorítmicas, incluyendo una implementación en GPUs. No obstante, presentamos también algunos resultados analíticos. Analizamos la Dinámica de Tiempos Cortos en la aproximación de Campo Medio del modelo de Potts con q=2 resolviendo exactamente la ecuación de Fokker-Planck asociada a la dinámica de Glauber. Confirmamos la validez de la hipótesis de escala de la Dinámica de Tiempos Cortos tanto cerca del punto crítico como de puntos spinodales. Mostramos que es posible definir el punto spinodal a partir del comportamiento dinámico del sistema a tiempos cortos. Estudiamos la metaestabilidad asociada a la transición de fase de primer orden para el modelo de Potts de q estados con q > 4. Realizamos un estudio sistemático de la dinámica del modelo de Potts luego de un enfriamiento brusco a temperaturas subcríticas. Para q > 4 advertimos la existencia de diferentes regímenes dinámicos, de acuerdo al rango de temperaturas. Caracterizamos estos regímenes y los correspondientes estados del sistema.
We analyze the bidimensional q-state Potts model, a paradigmatic model in the study of Statistical Mechanics of Critical Phenomena and Phase Transitions, which presents first (q > 4) and second order (q ≤ 4) temperature driven magnetic phase transitions and has shown a very rich dynamic phenomenology. We mostly work on Monte Carlo numerical simulations, for which we have implemented different algorithm techniques, both traditional and original, including an implementation to run code on graphics cards. Nevertheless, we also present analytic results for some cases where this approach was possible. We study the Short Time Dynamics in the Mean-Field approximation for the 2-states Potts model (the Curie-Weiss model) solving the Fockker-Planck equation associated to the Glauber dynamics for this model. We obtain closed-form expressions for the first moments of the order parameter, near to both the critical and spinodal points, starting from different initial conditions. We confirm the validity of the short-time dynamical scaling hypothesis in both cases. We show that it is possible to define the spinodal point through the short time dynamical behaviour of the system; our definition works both for meanfield and short-range interactions systems. We study the the first order phase transition associated metastability for the q-state Potts model with q >4. We show that the spinodal point is clearly separated from the transition point for all q > 4, delimiting an interval of temperatures capable to hold metastable states. We provide numerical evidence for the existence of metastable states associated to the first order phase transition. We analyze the relaxation mechanism from these states to equilibrium. We perform a systematic study about the nonequilibrium dynamics of the Potts model on the square lattice after a quench from infinite to subcritical temperatures. We analyze the long term behaviour of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q > 4 we found the existence of different dynamical regimes, according to quench temperature range. We characterize those regimes and the system’s corresponding states. We analyze in detail the finite size scaling properties of different relaxation times involved, as well as their temperature dependency.