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Nucleation in complex systems
Kulveit, Jan ; Demo, Pavel (advisor) ; Slanina, František (referee) ; Vlček, Jaroslav (referee)
Title: Nucleation in complex systems Author: Jan Kulveit Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: prof. Pavel Demo, Institute of Physics of the Czech Academy ofSciences, Department of Optical Materials Abstract: We studied nucleation in progressively more abstract contexts and systems, starting from classical nucleation theory and ending with nucleation in complex networks. The cases studied include impurity nucleation in a solid matrix on several alkali halide crystals, where we determined formation energies for clusters, treated as defects, starting from single impurity-vacancy dipole and small aggregates to possible configurations of larger clusters. In the next part, we turn to the study of heterogeneous nucleation. While in the usual treatment of heterogeneous nucleation the surface energy is assumed to be homogenous, we ask the question what happens if we consider the surface energy to be heteroge- neous.Utilizing umbrella sampling computer simulations we find the nucleation barrier can be significantly lowered in the presence of surface heterogeneity, even if the average surface energy is kept constant. In the last part we study influence of clustering coefficient on phase transitions in scale-free networks, using forward flux sampling (FFS). Keywords: nucleation,...
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Ising Model Boundary States from String Field Theory
Rapčák, Miroslav ; Schnabl, Martin (advisor) ; Novotný, Jiří (referee)
The Ising model is widely studied model in statistical physics. In this thesis, we review methods used to solve it and we concentrate on the state at the critical temperature, where the system exhibits phase transition and can be described by means of conformal field theory (CFT). This description comes with a new insight into the problem and enables to study boundary effects. Critical behavior for systems with boundaries is often described by conformally invariant boundary conditions. Classification of all boundary CFTs still remains an open problem. We discuss methods developed recently in string field theory (SFT) proposing a new approach and we illustrate it on the Ising model. Knowing a solution to the SFT equations of motion, one can construct corresponding boundary state describing consistent conformally invariant boundary condition. We have formulated SFT for the Ising model, found new solutions numerically, and constructed corresponding boundary states. This procedure avoids solving difficult sewing constraints and results agree with exact values. Unlike the renormalization group approach, where we are limited by the g-theorem, we can construct also states with higher energy. Conformal defects and correspondence with free boson on S^1/Z_2 orbifold is also discussed. This thesis is based on...
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Ising model in finance: from microscopic rules to macroscopic phenomena
Dvořák, Pavel ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of this thesis is to inspect the abilities of the Ising model to exhibit selected statistical properties, or stylized facts, that are common to a wide range of financial assets. The investigated properties are heteroskedasticity of returns, rapidly decaying linear autocorrelation, volatility clustering, heavy tails, negative skewness and non-Gaussianity of the return distribution. In the first part of the thesis, we test the presence of these stylized facts in S&P 500 daily returns over the last 30 years. The main part of the thesis is dedicated to the Ising model-based simulations and to discussion of the results. New features such as Poisson process governed lag or magnetisation dependent trading activity are incorporated in the model. We conclude that the Ising model is able to convincingly replicate most of the examined statistical properties while even more satisfactory results can be obtained with appropriate tuning. 1
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Nucleation in complex systems
Kulveit, Jan ; Demo, Pavel (advisor) ; Slanina, František (referee) ; Vlček, Jaroslav (referee)
Title: Nucleation in complex systems Author: Jan Kulveit Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: prof. Pavel Demo, Institute of Physics of the Czech Academy ofSciences, Department of Optical Materials Abstract: We studied nucleation in progressively more abstract contexts and systems, starting from classical nucleation theory and ending with nucleation in complex networks. The cases studied include impurity nucleation in a solid matrix on several alkali halide crystals, where we determined formation energies for clusters, treated as defects, starting from single impurity-vacancy dipole and small aggregates to possible configurations of larger clusters. In the next part, we turn to the study of heterogeneous nucleation. While in the usual treatment of heterogeneous nucleation the surface energy is assumed to be homogenous, we ask the question what happens if we consider the surface energy to be heteroge- neous.Utilizing umbrella sampling computer simulations we find the nucleation barrier can be significantly lowered in the presence of surface heterogeneity, even if the average surface energy is kept constant. In the last part we study influence of clustering coefficient on phase transitions in scale-free networks, using forward flux sampling (FFS). Keywords: nucleation,...
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Capital market efficiency in the Ising model environment: Local and global effects
Krištoufek, Ladislav ; Vošvrda, Miloslav
Financial Ising model is one of the simplest agent-based models (building on a parallel between capital markets and the Ising model of ferromag- netism) mimicking the most important stylized facts of financial returns such as no serial correlation, fat tails, volatility clustering and volatility persistence on the verge of non-stationarity. We present results of Monte Carlo simulation study investigating the relationship between parameters of the model (related to herding and minority game behaviors) and crucial characteristics of capital market e ciency (with respect to the e cient market hypothesis). We find a strongly non-linear relationship between these which opens possibilities for further research. Specifically, the existence of both herding and minority game behavior of market participants are necessary for attaining the e cient market in the sense of the e cient market hypothesis.
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Dissection of Bornholdt's model: examination of inner dynamics and effect of parameter change
Chrz, Štěpán ; Krištoufek, Ladislav (advisor) ; Vácha, Lukáš (referee)
Dissection of Bornholdt's model - Analysis of Inner Dynamics and Effect of Parameter Change Mgr. Štěpán Chrz Abstract In this work we thoroughly analyze Bornholdt's version of Ising model of ferro- magnetism, with emphasis on its ability to mimic some basic stylized facts of financial series. Initially, we provide a breakdown of model definition and anal- ysis of underlying dynamics. Subsequently, we examine and confirm model's ability to mimic stylized facts of financial series. To examine robustness of this ability to parameter change, we conduct simulations over a set of parameter combinations. We conclude that there is a wide set of combinations that yields acceptable simulation results. We also note that the seemingly best results are obtained at parameter values close to border of this set. 1
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Ising Model Boundary States from String Field Theory
Rapčák, Miroslav ; Schnabl, Martin (advisor) ; Novotný, Jiří (referee)
The Ising model is widely studied model in statistical physics. In this thesis, we review methods used to solve it and we concentrate on the state at the critical temperature, where the system exhibits phase transition and can be described by means of conformal field theory (CFT). This description comes with a new insight into the problem and enables to study boundary effects. Critical behavior for systems with boundaries is often described by conformally invariant boundary conditions. Classification of all boundary CFTs still remains an open problem. We discuss methods developed recently in string field theory (SFT) proposing a new approach and we illustrate it on the Ising model. Knowing a solution to the SFT equations of motion, one can construct corresponding boundary state describing consistent conformally invariant boundary condition. We have formulated SFT for the Ising model, found new solutions numerically, and constructed corresponding boundary states. This procedure avoids solving difficult sewing constraints and results agree with exact values. Unlike the renormalization group approach, where we are limited by the g-theorem, we can construct also states with higher energy. Conformal defects and correspondence with free boson on S^1/Z_2 orbifold is also discussed. This thesis is based on...
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Ising model in finance: from microscopic rules to macroscopic phenomena
Dvořák, Pavel ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of this thesis is to inspect the abilities of the Ising model to exhibit selected statistical properties, or stylized facts, that are common to a wide range of financial assets. The investigated properties are heteroskedasticity of returns, rapidly decaying linear autocorrelation, volatility clustering, heavy tails, negative skewness and non-Gaussianity of the return distribution. In the first part of the thesis, we test the presence of these stylized facts in S&P 500 daily returns over the last 30 years. The main part of the thesis is dedicated to the Ising model-based simulations and to discussion of the results. New features such as Poisson process governed lag or magnetisation dependent trading activity are incorporated in the model. We conclude that the Ising model is able to convincingly replicate most of the examined statistical properties while even more satisfactory results can be obtained with appropriate tuning. 1
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