Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presente

Localization analysis under dynamic loading

A finite element method proposed by Ortiz et al. (1987) is used to study shear band formation in rate dependent and rate independent pressure sensitive solids under dynamic loading. Under these conditions, shear bands are observed to propagate in an irregular fashion in time and space. In particular, the development of multiple shear bands appears to be a prevalent mechanism of deformation at sufficiently high impact velocities

Solid-fluid phase transformation within grain boundaries during compaction by pressure solution

The overall compaction of porous rocks due to intergranular pressure solution (IPS) results from the dissolution of minerals within contact regions and the diffusive transport through the grain boundary of the dissolved species towards the fluid-filled pore space. The grain boundary structure can be imagined to be composed of dry contact zones, thin fluid films and fluid-filled cavities. The connectiveness and tortuosity of this structure determine the effective diffusivity of grain contacts and thus the potential of porous rock to compact by the action of IPS. The evolution in time of the grain-boundary structure, and thus of the effective diffusivity, is discussed here with the help of two 2D initial- and boundary-value problems which are solved by analytical and numerical means. The evolution of the solid–fluid interfaces within the grain boundary is governed by a phase transformation between the non-hydrostatically stressed elastic solid and the trapped fluid assumed in mechanical equilibrium. The characteristic time is provided by a linear kinetic law. The evolution of the structure away from a state of thermodynamic equilibrium during a loading normal to the grain boundary is found to occur in two steps. The first one consists of a diffuse morphology evolution in time and results in an enhancement of any initial stress concentration. The second step is characterized by a rapid and localized dissolution in the region of stress concentration. The latency period prior to localization is governed by the magnitude of the non-hydrostatic remote stress as well as the microstructural geometric factor responsible for the initial stress concentration at the solid–fluid interface. The localized dissolution is shown to provide a mechanism for the fluid to penetrate a previously dry contact region by marginal dissolution and thus to create a fluid film. However, the newly formed thin fluid layer is found to be unstable pointing to a possible repeated reorganization or dynamic evolution of the grain boundary internal structure during the action of IPS

High-Spatial-Resolution Monitoring of Strong Magnetic Field using Rb vapor Nanometric-Thin Cell

We have implemented the so-called $\lambda$-Zeeman technique (LZT) to investigate individual hyperfine transitions between Zeeman sublevels of the Rb atoms in a strong external magnetic field $B$ in the range of $2500 - 5000$ G (recently it was established that LZT is very convenient for the range of $10 - 2500$ G). Atoms are confined in a nanometric thin cell (NTC) with the thickness $L = \lambda$, where $\lambda$ is the resonant wavelength 794 nm for Rb $D_1$ line. Narrow velocity selective optical pumping (VSOP) resonances in the transmission spectrum of the NTC are split into several components in a magnetic field with the frequency positions and transition probabilities depending on the $B$-field. Possible applications are described, such as magnetometers with nanometric local spatial resolution and tunable atomic frequency references.Comment: 12 page

Full particle simulation of a perpendicular collisionless shock: A shock-rest-frame model

The full kinetic dynamics of a perpendicular collisionless shock is studied by means of a one-dimensional electromagnetic full particle simulation. The present simulation domain is taken in the shock rest frame in contrast to the previous full particle simulations of shocks. Preliminary results show that the downstream state falls into a unique cyclic reformation state for a given set of upstream parameters through the self-consistent kinetic processes.Comment: 4 pages, 2 figures, published in "Earth, Planets and Space" (EPS), the paper with full resolution images is http://theo.phys.sci.hiroshima-u.ac.jp/~ryo/papers/shock_rest.pd

Localization analysis under dynamic loading

A finite element method proposed by Ortiz et al. (1987) is used to study shear band formation in rate dependent and rate independent pressure sensitive solids under dynamic loading. Under these conditions, shear bands are observed to propagate in an irregular fashion in time and space. In particular, the development of multiple shear bands appears to be a prevalent mechanism of deformation at sufficiently high impact velocities

Rotational cooling of molecules using lamps

We investigate theoretically the application of tailored incoherent far-infrared fields in combination with laser excitation of a single rovibrational transition for rotational cooling of translationally cold polar diatomic molecules. The cooling schemes are effective on a timescale shorter than typical unperturbed trapping times in ion traps and comparable to obtainable confinement times of neutral molecules.Comment: 5 pages, 2 figure

Principal modes of variability of Martian atmospheric surface pressure

An analysis of daily-to-interannual variability in the surface pressure field of the Martian northern hemisphere as given by a Martian climate model is presented. In an empirical orthogonal function (EOF) decomposition, the dominant first two modes of variability comprise a zonal wavenumber 1 feature centered at 70 N latitude moving eastward with a period of 6 to 8 sols. This feature is a baroclinic wave and accounts for 53% of the northern hemisphere non-stationary surface pressure variability, and, when active, has an amplitude of up to 2% of local surface pressure. The third mode of the EOF decomposition is annular about the Martian north pole, is null southward of 70 N, and accounts for 7% of the northern hemisphere non-stationary surface pressure variability. The baroclinic wave (EOFs 1 & 2) is active during northern hemisphere winter and spring, consistent with models of the Martian atmospheric circulation, and the annular mode (EOF 3) is active only at the onset and demise of the baroclinic feature. When active, it is not uncommon for the annular mode to reside in either its positive or negative state stably for 20 to 30 sols. It is postulated that baroclinic waves with longitudinal wavenumber 2, 3, and 4 act as a pump for the annular mode. The annular mode should not be present in MGS TES data