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We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics
It is shown that the ff effect of mean-field magnetohydrodynamics, which consists in the generation of a mean electromotive force along the mean magnetic field by turbulently fluctuating parts of velocity and magnetic field, is equivalent to the simultaneous generation of both turbulent and mean-field magnetic helicities, the generation rates being equal in magnitude and opposite in sign. In the particular case of statistically stationary and homogeneous fluctuations this implies that the ff effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there.
We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.
The present paper is related to the problem of approximating the exact solution to the magnetohydrodynamic equations (MHD). The behaviour of a viscous, incompressible and resistive fluid is exemined for a long period of time. Contents: 1 The magnetohydrodynamic equations 2 Notations and precise functional setting of the problem 3 Existence, uniqueness and regularity results 4 Statement and Proof of the main theorem 5 The approximate inertial manifold 6 Summary
We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.
The failure of politics is closely connected with deeply rooted misconceptions about the term politics. The author argues that a re-reading of Immanuel Kant's work "The Perpetual Peace" written 200 years ago offers a challenging possibility for a new conceptualization of politics, morality and peace. Morality is seen by Kant as an essential dimension of politics and the implementation and acknowledgement of laws by moral demands is defined as a precondition for a community of free citizens. In its public discourse politics does require law and morality. Deriving future rights from existing laws is one of the most favored argumentation used by politicians in the public. If the needs of law and justice are interpretated by politicians in their own interest, i.e. above all guarantees for the realization of political selfdetermination, then a real chance will exist for improving peace in the future.
The article argues that the concept of statehood is not functioning any longer. It exists a crisis for the international legal order which is represented by the failure of state to maintain order within its borders. The problem of violence in international relations are connected to the implosion of a considerable number of the state entities in the contemporary international society. The federalist institutional approach in international law and international theory could not contribute in an appropriate way to the solution of the "problem of violence", because it supposes a willingness on the part of states to do so. Only the concept of "national interest", in a sociological sense, connected to the development of a discource of solidarity and mutual responsibility between the "West" and the "rest of the world" offers the possibility to create a common consciousness which could make it easier to overcome the contemporary crises for the international legal order.
The Chinese coastal cities play an increasing economic role in the Yellow Sea region. The inclusion of these cities into the intra Asian economic cooperation is accomplished not only in the conventional sphere of trade but also by a growing involvement in telecommunication networks, technological exchange and the circulation of human resources. That is why these cities emerge as autonomous actors in the East Asian integration process. In this context national states face deep structural change, especially in the field of sovereignty and territory. Concerning the internal situation of China, this change could also cause a turn over of the relationship between the central government and the regions.
There is sufficient evidence of integration processes in the Asia-Pacific rim. But these processes differ profoundly from the European case. On the other hand integration theory up to the present day has been based mainly on the European evidence. Does this mean, that conventional integration theory is irrelevant in the case of the Asia-Pacific development? This contributuion tries to re-examine the theoretical capacity of various approaches (institionalism, functionalism, regionalism, flying geese pattern, regime-theory) when applied to the realities of transnational interaction and international organization in the Asia-Pacific rim.
Based on the discussion on Germany´s new 'central location', the author tries to sketch Germany´s geopolitical position in view of the constellation of powers in Europe from a national point of view. This favourable position offers a great chance for the country to play an active role in Europe’s integration. However, German historical heritage as well as the delicate relationship of Germany´s political elite to the use of power are reasons for the country´s hesitation to fulfill her neighbours’ and her allies’ expectations. Anyhow, Summaries 192 rooted in the West-European and transatlantic integration is Germany the natural dooropener for its Eastern, South-Eastern and Baltic neighbours to become 'members of the club'. )</a> Jahresabo: 40,00 € (ermäßigt: 25,00 €)
The existence of the Soviet Union was a remarkable anomalie in the history of the 20th century, which was also characterized by the collapse of multinational and colonial empires. Starting with the structural definitions of empires, the author describes the particularities of the Soviet empire. He analyzes the order, ideology and culture of the Soviet Empire. Looking for the reasons of its collapse, he presents a genesis of the longterm and short-term reasons. He is focusing on the breakdown of the post-totalitarian Leviathan, the cultural decline, the renaissance of nationalism and of the imperial overstretching. Finally he asseses the role of the policy of Perestroika in the breakdown of the Soviet Empire in the beginning of the 1990s.
Modelle der Sozialstruktur
(1995)
Inhalt:
1) Klassische Modelle gesellschaftlicher Handlungsressourcen 2) Drei Typen von industriellen Dienstleistungsgesellschaften - Die Bundesrepublik im internationalen Vergleich 3) Überprüfung eines Berufsstrukturmodells - als Bündelung gesellschaftlicher Handlungsressourcen - in der alten Bundesrepublik (d.h. vor 1989/90) 4) Entwicklungstendenzen in der Sozialstruktur der Bundesrepublik nach dem Umbruch von 1989/90 5) Berufsstrukturmodell für die alten und neuen Bundesländer - Ungleichheit und Angleichung
Inhalt: Wettbewerb der Regionen Marketing-Konzept für Regionen -Die Region als Produkt und Unternehmung -Regionales Management -Phasen zur Entwicklung eines Regionen-Marketing-Konzepts Eine empirische Studie zur Region Brandenburg -Theorien zur Standortwahl privater Unternehmen -Design und Ergebnisse der empirischen Studie: Standorteignung und Standortanforderungen, Unternehmenstypologie nach marketingrelevanten Kriterien, Imageanalyse, Resümee
Inhalt: Umweltschutz als gesellschaftlicher Anspruch -Sustainable Development -Umweltorientierte Anspruchsgruppen einer Unternehmung -Die Betroffenheit der Unternehmen -Bedeutung von Anspruchsgruppen -Lebenszyklen von gesellschaftlichen Anliegen Umweltschutz als Unternehmensziel -Duales Zielkonzept -Priorität des Umweltschutzes -Konfliktfelder zwischen ökonomischen und ökologischen Zielen -Umweltschutz als Chance -Umweltschutz als ethischer Anspruch -Umweltaktive Verbände und Unternehmen Rahmenbedingungen umweltorientierter Unternehmensführung -Übersicht -Ökologie-Pull: das Umweltbewußtsein von Konsumenten, Ökologieorientierung im Handel -Ökologie-Push: Die EU-Umwelt-Auditing Verordnung Umweltmanagement -Das Umweltmanagement-Konzept -Übersicht: Strategien im Umweltmanagement -Ökologische Basisstrategien -Risikostrategien Instrumente des Umweltmanagements -Öko-Bilanzen -Umwelt- und Risikodialog
Inhalt: Begriffsklärung -Ökologisches Marketing -Dialog -Chancen -Umweltmanagement Verankerung einer Dialogorientierung im Normativen Umweltmanagement: Das dialogische Verantwortungskonzept Dialogchancen im Strategischen Umweltmanagement -Anspruchsgruppenmanagement -Risiko- und Krisenmanagement -Konflikt- und Konsensusmanagement -Issue-Management Dialogische Verfahren und Techniken der ökologischen Kommunikationspolitik
Basismodelle des Unterrichts
(1995)