Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves

A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Henon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.Comment: 11 pages, 7 figures, LaTeX. To appear in Phys. Lett.

Continuous coordinates for all impulsive pp - waves

We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.Comment: 4 pages, LaTeX, no figures, to be published in Phys. Lett.

Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.Comment: 9 RevTeX pages, 11 figures, submitted to Physical Review

Actual changes in system of urban planning in post-socialist city: the case of Prague

After the change of political system in Czechoslovakia (1989) came also a lot of social, economical and cultural changes. Today, all the Czech cities stay in front of the biggest change of city planning philosophy in last two decades. Prague, the capital city of Czech Republic, decided for a big institutional transition in 2012. The municipality, in cooperation with Faculty of Architecture CTU in Prague, is preparing completely pioneering methodology for quality commissioning of land use plans and, in cooperation with the new Institute of Planning and Development, is preparing innovative system of city planning. There are new ordinances, laws, regulations, tourist trade strategies and many other documents. Prague, as one of the strongest regions in East-Central Europe, can be seen like a laboratory of current development of post-socialist city. The new methodology of Metropolitan Plan could be a key to success

The role of the tissue microenvironment in the regulation of cancer cell motility and invasion

During malignant neoplastic progression the cells undergo genetic and epigenetic cancer-specific alterations that finally lead to a loss of tissue homeostasis and restructuring of the microenvironment. The invasion of cancer cells through connective tissue is a crucial prerequisite for metastasis formation. Although cell invasion is foremost a mechanical process, cancer research has focused largely on gene regulation and signaling that underlie uncontrolled cell growth. More recently, the genes and signals involved in the invasion and transendothelial migration of cancer cells, such as the role of adhesion molecules and matrix degrading enzymes, have become the focus of research. In this review we discuss how the structural and biomechanical properties of extracellular matrix and surrounding cells such as endothelial cells influence cancer cell motility and invasion. We conclude that the microenvironment is a critical determinant of the migration strategy and the efficiency of cancer cell invasion