Discrete Self-Similarity in Type-II Strong Explosions

We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\omega}$, where $\omega>3$ (Type-II solutions). The perturbations we consider are spherically symmetric and log-periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log-periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e. the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition

Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.Comment: 12 pages, 3 figure

Energy Loss from Reconnection with a Vortex Mesh

Experiments in superfluid 4He show that at low temperatures, energy dissipation from moving vortices is many orders of magnitude larger than expected from mutual friction. Here we investigate other mechanisms for energy loss by a computational study of a vortex that moves through and reconnects with a mesh of small vortices pinned to the container wall. We find that such reconnections enhance energy loss from the moving vortex by a factor of up to 100 beyond that with no mesh. The enhancement occurs through two different mechanisms, both involving the Kelvin oscillations generated along the vortex by the reconnections. At relatively high temperatures the Kelvin waves increase the vortex motion, leading to more energy loss through mutual friction. As the temperature decreases, the vortex oscillations generate additional reconnection events between the moving vortex and the wall, which decrease the energy of the moving vortex by transfering portions of its length to the pinned mesh on the wall.Comment: 9 pages, 10 figure

How to detect level crossings without looking at the spectrum

We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians representable by matrices. This approach provides a pedagogical introduction to (avoided) crossings, is capable of handling realistic Hamiltonians analytically, and offers a way to visualize crossings which is sometimes superior to that provided by the spectrum. We illustrate the method using the Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground state hydrogen atom in a uniform magnetic field.Comment: Accepted for publication in the American Journal of Physic

ROTATIONAL-DYNAMICS OF SOLID C-70 - A NEUTRON-SCATTERING STUDY

PMID: 10011126PMID: 10011126 This work at the University of Sussex at supported by the Science and Engineering Research Council, U.K.PMID: 10011126 This work at the University of Sussex at supported by the Science and Engineering Research Council, U.K.PMID: 10011126 This work at the University of Sussex at supported by the Science and Engineering Research Council, U.K.We report the results of neutron-diffraction and low-energy neutron-inelastic-scattering experiments on high-purity solid C-70 between 10 and 640 K. Thermal hysteresis effects are found to accompany structural changes both on cooling and on heating. The observed diffuse scattering intensity does not change with temperature. At 10 K broad librational peaks are observed at 1.82(16) meV [full width at half maximum=1.8(5) meV]. The peaks soften and broaden further with increasing temperature. At and above room temperature, they collapse into a single quasielastic line. At 300 K, the diffusive reorientational motion appears to be somewhat anisotropic, becoming less so with increasing temperature. An isotropic rotational diffusion model, in which the motions of adjacent molecules are uncorrelated, describes well the results at 525 K. The temperature dependence of the rotational diffusion constants is consistent with a thermally activated process having an activation energy of 32(7) meV.This work at the University of Sussex at supported by the Science and Engineering Research Council, U.K

Aggression and Anxiety: Social Context and Neurobiological Links

Psychopathologies such as anxiety- and depression-related disorders are often characterized by impaired social behaviours including excessive aggression and violence. Excessive aggression and violence likely develop as a consequence of generally disturbed emotional regulation, such as abnormally high or low levels of anxiety. This suggests an overlap between brain circuitries and neurochemical systems regulating aggression and anxiety. In this review, we will discuss different forms of male aggression, rodent models of excessive aggression, and neurobiological mechanisms underlying male aggression in the context of anxiety. We will summarize our attempts to establish an animal model of high and abnormal aggression using rats selected for high (HAB) vs. low (LAB) anxiety-related behaviour. Briefly, male LAB rats and, to a lesser extent, male HAB rats show high and abnormal forms of aggression compared with non-selected (NAB) rats, making them a suitable animal model for studying excessive aggression in the context of extremes in innate anxiety. In addition, we will discuss differences in the activity of the hypothalamic–pituitary–adrenal axis, brain arginine vasopressin, and the serotonin systems, among others, which contribute to the distinct behavioural phenotypes related to aggression and anxiety. Further investigation of the neurobiological systems in animals with distinct anxiety phenotypes might provide valuable information about the link between excessive aggression and disturbed emotional regulation, which is essential for understanding the social and emotional deficits that are characteristic of many human psychiatric disorders

Entanglement production in quantum decision making

The quantum decision theory introduced recently is formulated as a quantum theory of measurement. It describes prospect states represented by complex vectors of a Hilbert space over a prospect lattice. The prospect operators, acting in this space, form an involutive bijective algebra. A measure is defined for quantifying the entanglement produced by the action of prospect operators. This measure characterizes the level of complexity of prospects involved in decision making. An explicit expression is found for the maximal entanglement produced by the operators of multimode prospects.Comment: Latex file, 7 page

Band Crossing and Novel Low-Energy Behaviour in a Mean Field Theory of a Three-Band Model on a Cu--O lattice

We study correlation effects in a three-band extended Hubbard model of Cu -- O planes within the 1/N mean field approach, in the infinite U limit. We investigate the emerging phase diagram and discuss the low energy scales associated with each region. With increasing direct overlap between oxygen orbitals, $t_{pp} >0$, the solution displays a band crossing which, for an extended range of parameters, lies close to the Fermi level. In turn this leads to the nearly nested character of the Fermi surface and the resulting linear temperature dependence of the quasi-particle relaxation rate for sufficiently large T. We also discuss the effect of band crossing on the optical conductivity and comment on the possible experimental relevance of our findings.Comment: 12 pages, Latex-Revtex, 6 PostScript figures. Submitted to Phys. Rev.

Reexamination of the galaxy formation-regulated gas evolution model in groups and clusters

As an alternative explanation of the entropy excess and the steepening of the X-ray luminosity-temperature relation in groups and clusters, the galaxy formation-regulated gas evolution (GG) model proposed recently by Bryan makes an attempt to incorporate the formation of galaxies into the evolution of gas without additional heating by nongravitational processes. This seems to provide a unified scheme for our understanding of the structures and evolution of both galaxies and gas in groups and clusters. In this paper, we present an extensive comparison of the X-ray properties of groups and clusters predicted by the GG model and those revealed by current X-ray observations, using various large data sources in the literature and also taking the observational selection effects into account. These include an independent check of the fundamental working hypothesis of the GG model, i.e., galaxy formation was less efficient in rich clusters than in groups, a new test of the radial gas distributions revealed by both the gas mass fraction and the X-ray surface brightness profiles, and an reexamination of the X-ray luminosity-temperature and entropy-temperature relations. In particular, it shows that the overall X-ray surface brightness profiles predicted by the GG model are very similar in shape, insensitive to the X-ray temperature, and the shallower X-ray surface brightness profiles seen at low-temperature systems may arise from the current observational selection effect. This can be used as the simplest approach to distinguishing between the GG model and the preheating scenario. The latter yields an intrinsically shallower gas distribution in groups than in rich clusters.Comment: 30 pages, 10 figures, accepted for publication in Ap