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Title: The study of the association behaviour of the amphiphilic copolymers in solutions containing low molar compounds by means of computer simulations. Author: Mgr. Karel Šindelka Department: Faculty of Science, Charles University Supervisor: Doc. Ing. Zuzana Limpouchová, Csc. Abstract This doctoral thesis focuses on the study of electrostatic self- and co-assembly in complex polymer solutions containing polyelectrolyte (PE) block copolymers together with surfactants, neutral homopolymers, or oppositely charged PEs using the dissipative particle dynamics (DPD). It was shown that the electro- static self-assembly depends not only on the cooperative interactions of oppo- sitely charged PE chains, but also on the amphiphilicity of PE species or on the polymer block compatibility, among other properties. PEs with incompatible blocks create well-defined core-shell structures, while large ill-defined crew-cut aggregates form from PEs with compatible blocks In non-stoichiometric mixtures of PEs with incompatible blocks, co-assembled nanoparticles are smaller than in stoichiometric mixtures and are charged. The destabilization of larger aggregates depends on how the PE charge surplus is introduced: the effect is strongest when the density of the surplus PE charge on the PE chains is increased and weakest when the...

In der vorliegenden Arbeit werden Untersuchungen vorgestellt, die sich mit drei verschiedenen Aspekten der Dynamik offener Quantensysteme beschäftigen. Zwei Themenkreise haben dabei mehr grundsätzliche Probleme der Theorie dissipativer Molekularsysteme zum Gegenstand. Dementsprechend müssen die Betrachtungen dazu auf einem allgemeineren Niveau verbleiben. In dem dritten Themenkreis jedoch, der sich mit Zwei-Teilchen-Effekten in der dissipativen Dynamik befaßt, können die Untersuchungen bis hin zu Berechnung von Meßgrößen geführt werden. Im ersten Teil der Arbeit gelingt eine Verallgemeinerung der vielbenutzten Standardform der Quanten-Master-Gleichung hin zur Nichtlinearen Quanten-Master-Gleichung. Mit der Anwendung der dazugehörigen zeitabhängigen Projektionsoperator-Technik kann ein Formalismus reaktiviert werden, der in der Literatur bisher eine nur sehr eingeschränkte Verbreitung findet. Der zweite Teil der Arbeit widmet sich Untersuchungen zur Monte-Carlo-Wellenfunktions-Methode mit dem Ergebnis, eine konsistente Verallgemeinerung auf ein Reservoir mit endlicher Temperatur anzugeben. Den Ausgangspunkt dazu bildet ein mikroskopisches Modell zur System-Reservoir-Kopplung, welches im Rahmen der Bewegungsgleichung für den reduzierten statistischen Operator in die sogenannte Lindblad-Form der Dissipation überführt wird. Nach der Betrachtung von Ein-Teilchen-Transferprozessen beschäftigt sich der dritte Teil der Arbeit mit der korrelierten Bewegung von zwei Quantenteilchen in einer dissipativen Umgebung mit der Hinwendung zum Zwei-Wasserstoff-System (Dihydrid-System) an Übergangsmetall-Verbindungen. Zunächst werden Modellrechnungen zur dissipationfreien Zwei-Teilchen-Dynamik in einem Potentialmodell durchzuführt. Der Einfluß, den die Teilchen-Teilchen-Korrelationen auf das Durchtunneln eines Potentialwalles besitzt, können durch verschiedene numerische Rechnungen aufgezeigt werden. Wie sich diese Effekte in Neutronenstreuexperimenten an dem Zwei-Teilchen-System der Übergangsmetall-Hydrid-Komplexe äußern, wird basierend auf Simulationsrechnungen untersucht. Kernstück dieser Betrachtungen bildet eine neuartige Formel für die Neutronenstreuung, die auf der dissipativen Dynamik des betrachteten Zwei-Teilchen-Systems aufbaut. / In the report at hand studies are presented dealing with three differentaspects of the dynamics of open quantum systems. Two topics are about the fundamental problems of the theory of dissipative molecular systems. Accordingly these investigations must remain on a more general level. In the third subject, however, which is about the two-particle effects in the dissipative dynamics the analyses can be extended to the computation of measurements. In the first part of the report a generalization of the well known standard quantum master equation to the nonlinear quantum master equation is developed. With the help of the projection operator technique belonging to it a formalism, that has not been popular in literature so far, can be reactivated. The second part of the report concentrates on examinations of the Monte-Carlo wave-function method, and results in the consistent generalization for a reservoir of finite temperature. The starting point for this is a microscopic model of the system-reservoir coupling, which is expanded to the so called Lindblad form of the dissipation in the line of the equation of motion for the reduced statistical operator. After the analysis of one-particle transfer processes the third part of the report is about the correlated motion of two quantum particles in a dissipative environment with main emphasis on the two-hydrogen system (dihydrid system) in transition metal complexes. First of all model computations for the dissipationless two-particle dynamics in a potential model are made. By different numerical computations the influence, which the particle-particle correlations exert on the tunneling through a potential barrier, can be shown.Based on simulations it is examined how these effects can be seen in neutron scattering experiments on two-particle systems of transition metal complexes. Main item of these investigations is a new formula for the neutron scattering which is based on the dissipative dynamics of the examined two-particle system.

O modelo raise and peel é um modelo estocástico unidimensional com absorção local e desorção não local. O modelo depende de um único parâmetro u que é a razão entre a taxa de absorção pela de dessorção. Em um valor especial deste parâmetro (u = 1) o modelo tem características interessantes. O espectro é descrito por uma teoria de campos conforme (carga central c = 0), sendo que a distribuição de probabilidade estacionária está relacionada a um sistema de equilíbrio em duas dimensões. O diagrama de fases do modelo, como função do parâmetro u, tem uma fase massiva (com lacuna de massa) e uma sem massa (lacuna de massa nula) com expoentes críticos que variam continuamente com o parâmetro u. Nesta dissertação estudamos uma extensão do modelo raise and peel model no ponto u = 1, e que depende de um parâmetro adicional p. Surpreendentemente o novo modelo exibe invariância conforme para todo o domínio do seu parâmetro p, e está na mesma classe de universalidade do modelo raise and peel usual (u = 1). A única diferença entre os dois modelos é o valor da velocidade do som vs(p), que agora é função de p. Os métodos que utilizamos nesta dissertação foram diagonalizações exatas do operador de evolução do modelo (Hamiltoniano) para cadeias pequenas e simulações de Monte Carlo. / The raise and peel model is a one-dimensional nonlocal stochastic model where adsorption happens locally and desorption is nonlocal. The model depends on the single parameter u that is the ratio among the desorption and adsorption rates. At a special value of this parameter (u = 1) the model has interesting features. The spectrum is described by a conformal field theory (central charge c = 0), and its stationary probability density is related to the equilibrium distribution of a two dimensional system. The phase diagram of the model, as a function of the parameter u, has a massive phase (gapped phase) and a massless (gapless phase) whose critical exponents vary continuously with u. In this monography we study a one-parameter extension of the raise and peel model at u = 1, that depends on the additional parameter p. The new model exhibits conformal invariance for the whole range of values of its parameter p, and it is in the same universality class as the usual raise and peel model. The single difference between the models is the value of the sound velocity vs(p) which is a function of p. The methods used in this monography are the exact diagonalization of the evolution operator of the stochastic model (Hamiltonian), for small lattice sizes and Monte Carlo simulations.

O modelo raise and peel é um modelo estocástico unidimensional com absorção local e desorção não local. O modelo depende de um único parâmetro u que é a razão entre a taxa de absorção pela de dessorção. Em um valor especial deste parâmetro (u = 1) o modelo tem características interessantes. O espectro é descrito por uma teoria de campos conforme (carga central c = 0), sendo que a distribuição de probabilidade estacionária está relacionada a um sistema de equilíbrio em duas dimensões. O diagrama de fases do modelo, como função do parâmetro u, tem uma fase massiva (com lacuna de massa) e uma sem massa (lacuna de massa nula) com expoentes críticos que variam continuamente com o parâmetro u. Nesta dissertação estudamos uma extensão do modelo raise and peel model no ponto u = 1, e que depende de um parâmetro adicional p. Surpreendentemente o novo modelo exibe invariância conforme para todo o domínio do seu parâmetro p, e está na mesma classe de universalidade do modelo raise and peel usual (u = 1). A única diferença entre os dois modelos é o valor da velocidade do som vs(p), que agora é função de p. Os métodos que utilizamos nesta dissertação foram diagonalizações exatas do operador de evolução do modelo (Hamiltoniano) para cadeias pequenas e simulações de Monte Carlo. / The raise and peel model is a one-dimensional nonlocal stochastic model where adsorption happens locally and desorption is nonlocal. The model depends on the single parameter u that is the ratio among the desorption and adsorption rates. At a special value of this parameter (u = 1) the model has interesting features. The spectrum is described by a conformal field theory (central charge c = 0), and its stationary probability density is related to the equilibrium distribution of a two dimensional system. The phase diagram of the model, as a function of the parameter u, has a massive phase (gapped phase) and a massless (gapless phase) whose critical exponents vary continuously with u. In this monography we study a one-parameter extension of the raise and peel model at u = 1, that depends on the additional parameter p. The new model exhibits conformal invariance for the whole range of values of its parameter p, and it is in the same universality class as the usual raise and peel model. The single difference between the models is the value of the sound velocity vs(p) which is a function of p. The methods used in this monography are the exact diagonalization of the evolution operator of the stochastic model (Hamiltonian), for small lattice sizes and Monte Carlo simulations.

Die elektromagnetische Wechselwirkung der Teilchen untereinander, wie sie typischerweise in einem Strahl hoher Intensität in den CERN Beschleunigern auftritt, kann in Langzeitsimulationen nicht vernachlässigt werden. Simulationen sind insbesondere notwendig, um diese Beschleuniger zu optimieren und die zugrundeliegende kohärente und inkohärente Dynamik besser zu verstehen. Die Auswirkungen der unumgänglichen Vereinfachungen in der Modellierung der komplizierten Dynamik müssen deshalb untersucht werden. Wir gehen diese Aufgabe an, indem wir sechs verschiedene Strahlführungsmodelle am CERN Proton Synchrotron (PS) und am Super Proton Synchrotron (SPS) untersuchen, die wir dynamisch in der Nähe von horizontalen Integer-Resonanzen operieren. Die sechs Modelle, welche insgesamt in den beiden bewährten Programmpaketen MAD-X und PyOrbit implementiert sind, werden mit den jeweiligen Messungen an beiden Maschinen verglichen, wobei der Schwerpunkt hier auf dem PS liegt. / In long-term tracking simulations of high-intensity beams which are typical in the CERN accelerators, the electromagnetic interaction between the individual particles can not be neglected. Simulations are required to optimize the performance of the accelerators, and to better understand the involved coherent and incoherent dynamics. The impact due to the unavoidable simplifications when modeling the complex dynamics must therefore be studied. We approach this task by examining six different tracking models, applied to the CERN Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS), both of which were dynamically operated near horizontal integer resonances. The six models, which are overall implemented in the well-known program packages MAD-X and PyOrbit, are compared to beam-based measurements on both machines, with the PS as the main emphasis.