Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions.

"Complete range" The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed.

"Complete methods" Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods.

"Complete solutions" A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed - which is an important problem of current research.

The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .

The simulation of turbulent reacting flows, connected with environmental protection and the design of chemical and mechanical processes, is increasingly important. Statistical Mechanics of Turbulent Flows presents a modern overview of basic ways to calculate such flows. It discusses the fundamental problems related to the use of basic equations and their modifications. Special emphasis is placed on the discussion of very promising statistical methods which provide solutions to these problems by models for the underlying stochastic physics of turbulent reacting flows. Their foundations and important new developments up through current challenges are systematically explained. Students and researchers in atmospheric sciences and oceanography, mechanical and chemical engineering and applied mathematics and physics may use Statistical Mechanics of Turbulent Flows as a guide to solve many problems related, e.g. to the assessment of complex atmospheric chemistry, chemical reactor processes, turbulent combustion, and multi-phase flows.

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed - which is an important problem of current research.

Wissenschaftlicher Aufsatz aus dem Jahr 2009 im Fachbereich Politik - Internationale Politik - Region: Mittel- und Sudamerika, Note: 3.0, Friedrich-Schiller-Universitat Jena (Politikwissenschaft), Veranstaltung: Prasidentialismus in Amerika, Sprache: Deutsch, Abstract: Betrachtet der Forscher die Verfassung an sich, bleibt ihm auch im Vergleich zu anderen prasidentiellen Regierungssystemen Lateinamerikas nur die Fest-stellung, dass es sich um ein relativ schwach ausgestattetes Prasidentenamt in Venezuela handelt. Auch die beiden Neuschopfungen von Burgerlicher- und Wahlgewalt sind aus demokratischer Sicht Zugewinne an Transparenz, Legiti-mation und Kontrolle der offentlichen Institutionen sowie der Verfassung, im Ruckschluss auf den politischen Einfluss des Prasidenten behindern sie ihn eher. Zusatzliche Kontrollen und Gewaltenverschrankung limitieren seine Handlungsfahigkeit und die Durchsetzung seiner politischen Agenda. Soweit die Theorie. In der Praxis hat Chavez eine Bewegung der Armen, gesellschaftlich Benach-teiligten und Minderheiten mit politischer Langzeitvision gegrundet: Die Alli-anz fur den Sozialismus des 21. Jahrhundert." Er stellt als eine Art revolutio-narer Vorkampfer sowohl innenpolitisch als auch international seine propagan-distischen Forderungen auf. Er will mit den Volkern des Subkontinents Latein-amerika einen Systemwechsel erreichen. Populistische Programmpunkte von Umverteilung und Verstaatlichung fehlen dabei nicht. Im Zuge dieser Vision schreckt er vor Verfassungsanderungen nicht zuruck. Im Gegenteil, notfalls setzt Chavez sie ohne Parlament per Referendum durch. Der Prasident und andere offentliche Amtstrager des Staates konnen mit Inkraftreten der Ande-rung uneingeschrankt wiedergewahlt werden. Diese Entwicklung ist in hochs-tem Masse Ausdruck tatsachlicher prasidentieller Macht. Allein die Amtszeit-verlangerung per Referendum 2004 und die spatere tatsachliche Verfassungs-anderung, waren zuvor in keiner der alten Verfassungen vorgeseh