Two-beam dynamical approach to multiple successive diffractors in X-ray crystal optics

To devise and optimise new monolithic components for X-ray diffraction optics more and more refined theoretical procedures are required. In addition to the simple geometrical approach utilising the vector Bragg equation, the two-beam dynamical approach including the asymmetric and tilted cases has been worked out for multiple successive diffractors. Based on the conditions derived and on the refined imaging equations for beam tracing, several types of monolithic X-ray magnifiers and beam conditioners have been devised, constructed, and tested. High spatial resolution of the X-ray magnifier when applied to synchrotron radiation and relatively low intensity of the X-rays passed from sealed off X-ray tube through the monolithic X-ray magnifier and through the near-coplanar beam conditioner are discussed.We would like to thank Prof. B.K. Tanner from Durham University, Prof. D.K. Bowen from Warwick University, Dr. G. Clark from Daresbury Laboratory and Dr. J. Brádler from Institute of Physics, Czech Acad. Sci., for their help with synchrotron radiation experiments and Mr. Pastorok from CMK arnovica and Dr. Sekáová and Mr. tefanec for their help with cutting and polishing the devices.     

A dynamical approach to the cosmological constant

This Letter presents an exact analytic solution of a simple cosmological model in presence of both nonrelativistic matter and scalar field where Einstein's cosmological constant Λ appears as an integration constant. Unlike Einstein's cosmological constant ascribed to vacuum energy, the dark energy density and the energy density of the ordinary matter decrease at the same rate during the expansion of the universe. Therefore the model is free of the coincidence problem. Comparing the predictions using this model with the current cosmological observations shows that the results are consistent.     

A dynamical systems approach to spiral wave dynamics

A simple system of five nonlinear ordinary differential equations is shown to reproduce many dynamical features of spiral waves in two-dimensional excitable media.     

A cellular dynamical mean field theory approach to Mottness

We investigate the properties of a strongly correlated electron system in the proximity of a Mott insulating phase within the Hubbard model, using a cluster generalization of the dynamical mean field theory. We find that Mottness is intimately connected with the existence in momentum space of a surface of zeros of the single particle Green’s function. The opening of a Mott-Hubbard gap at half filling and the opening of a pseudogap at finite doping are necessary elements for the existence of this surface. At the same time, the Fermi surface may change topology or even disappear. Within this framework, we provide a simple picture for the appearance of Fermi arcs. We identify the strong short-range correlations as the source of these phenomena and we identify the cumulant as the natural irreducible quantity capable of describing this short-range physics. We develop a new version of the cellular dynamical mean field theory based on cumulants that provides the tools for a unified treatment of general lattice Hamiltonians.     

Cumulant approach to dynamical correlation functions

A new theoretical approach, based on the introduction of cumulants, to calculate time dependent correlation functions at zero temperature is presented. In contrast to usual diagrammatic treatments of Green functions, the present method can be applied to operators which do not satisfy standard fermion or boson commutation relations. The introduction of cumulants is equivalent to applying the linked-cluster theorem. Thus, only connected expectation values have to be evaluated, even in cases for which Wick's theorem does not apply. The method expresses correlation functions in a form accessible to projection technique approaches. However, it circumvents a conceptual difficulty inherent in standard projection technique. There static expectation values, which are defined within the exact ground state, have to be evaluated independently. Our technique is a generalization, to dynamical aspects, of a recently introduced cumulant approach, which was restricted to the calculation of static ground-state properties. It seems to be an appropriate theoretical tool to treat the influence of strong electronic correlations like, e.g., in the new high-T _c superconducting materials. Two applications of the formalism have been given recently.     

A dynamical approach to symplectic and spectral invariants for billiards

The Lazutkin parameter for curves which are invariant under the billiard ball map is viewed symplectically in a way which makes it analogous to the sum of the values of a generating function over a closed orbit. This leads to relations among lengths of closed geodesics, lengths of invariant curves for the billiard map, rotation numbers, and the Lazutkin parameter. These relations establish the Birkhoff invariant and the expansion for the lengths of invariant curves in terms of the Lazutkin parameter as symplectic and spectral invariants (for the Dirichlet spectrum) and provide invariants which characterize a family of ellipses among smooth curves with positive curvature. Geodesic flow on a bounded planar region gives rise to several geometric objects among which are closed reflected geodesics and invariant curves-closed curves whose tangents are invariant under reflection at the boundary. On a bounded domain, the map that assigns to each geodesic segment its successor after reflection at the boundary is called the billiard ball map and its dual (in the cotangent bundle for the boundary) is called the boundary map.     

A variational approach to connecting orbits in nonlinear dynamical systems

We propose a variational method for determining homoclinic and heteroclinic orbits including spiral-shaped ones in nonlinear dynamical systems. Starting from a suitable initial curve, a homotopy evolution equation is used to approach a true connecting orbit. The procedure is an extension of a variational method that has been used previously for locating cycles, and avoids the need for linearization in search of simple connecting orbits. Examples of homoclinic and heteroclinic orbits for typical dynamical systems are presented. In particular, several heteroclinic orbits of the steady-state Kuramoto–Sivashinsky equation are found, which display interesting topological structures, closely related to those of the corresponding periodic orbits.     

A dynamical system approach to SOC models of Zhang's type

We discuss Zhang's model of SOC in the framework of hyperbolic dynamical systems with singularities. The fractal structure of the invariant energy distribution, correlation decay-like phenomena, and symbolic coding are discussed.     

A Hamiltonian approach for skew-product dynamical systems

The problem on the existence of Hamiltonian structures for (nonlinear) skew-product dynamical systems is studied via coupling Poisson structures. This research was partially supported by CONACYT under grant no. 55463.     

Quantum dynamical semigroups and approach to equilibrium

For a quantum dynamical semigroup possessing a faithful normal stationary state, some conditions are discussed, which ensure the uniqueness of the equilibrium state and/or the approach to equilibrium for arbitrary initial condition.A fellowship from the Italian Ministry of Public Education is acknowledged.     

A dynamical approach to the information content of collinear inelastic scattering

The information content of collinear inelastic scattering is discussed in terms of (a) the nature of the classical transformation in internal angle-action space induced by the collision, (b) the number of parameters required to characterize the transformation, and (c) the number and choice of trajectories required to determine the parameters. The constraints of time reversal symmetry, energy and flux conservation are embodied in the transformation equations. In a model application the full S matrix is successfully estimated in terms of a single information parameter deduced from knowledge of the purely elastic scattering trajectories.     

A new approach for controlling chaotic dynamical systems

The chaos control method proposed by Ott and his coworkers and now called the OGY method has attracted much attention. However, in some applications this technique requires a very long time until the control applies and it is not so effective. In this Letter, we present a new chaos control method in which this problem is improved. The main difference from the OGY method is the use of nonlinear approximations for chaotic dynamical systems and stable manifolds of the target points. We give an example for the Hénon map to demonstrate the effectiveness of the present method. Our method is also shown to be robust to modeling errors like the OGY method.     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.