Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

Universal computation with limited resources: Belousov-Zhabotinsky and Physarum computers

Using the examples of an excitable chemical system (Belousov-Zhabotinsky medium) and plasmodium of Physarum polycephalum we show that universal computation in a geometrically unconstrained medium is only possible when resources (excitability or concentration of nutrients) are limited. In situations of limited resources the systems studied develop travelling localizations. The localizations are elementary units of dynamical logical circuits in collision-based computing architectures.Comment: Int. J. Bifurcation and Chaos (2008), accepte

Coherent addition of two dimensional array of fiber lasers

Configurations for efficient free space coherent addition of four separate fiber lasers arranged in two dimensional array are presented. They include compact and robust interferometric combiners that can be inserted either inside or outside the cavity of the combined lasers system. The results reveal that over 85% combining efficiency can be obtained.Comment: To be published in Optics Communicatio

Physarum boats: If plasmodium sailed it would never leave a port

Plasmodium of \emph{Physarum polycephalum} is a single huge (visible by naked eye) cell with myriad of nuclei. The plasmodium is a promising substrate for non-classical, nature-inspired, computing devices. It is capable for approximation of shortest path, computation of planar proximity graphs and plane tessellations, primitive memory and decision-making. The unique properties of the plasmodium make it an ideal candidate for a role of amorphous biological robots with massive parallel information processing and distributed inputs and outputs. We show that when adhered to light-weight object resting on a water surface the plasmodium can propel the object by oscillating its protoplasmic pseudopodia. In experimental laboratory conditions and computational experiments we study phenomenology of the plasmodium-floater system, and possible mechanisms of controlling motion of objects propelled by on board plasmodium

Spin and density excitations in the triangular-lattice tt-JJ model with multiple-spin exchange interactions: 3^3He on graphite

Using an exact diagonalization technique on small clusters, we study spin and density excitations of the triangular-lattice $t$-$J$ model with multiple-spin exchange interactions, whereby we consider anomalous properties observed in the doped Mott region of the two-dimensional liquid $^3$He adsorbed on a graphite surface. We find that the double-peak structure consistent with experiment appears in the calculated temperature dependence of the specific heat; the low-temperature sharp peak comes from the spin excitations reflecting the frustrated nature of the spin degrees of freedom and high-temperature broad peak comes from the density excitations extending over the entire band width. The clear separation in their energy scales is evident in the calculated spin and density excitation spectra. The calculated single-particle excitation spectra suggest the presence of fermionic quasiparticles dressed by the spin excitations, with an enhanced effective mass consistent with experiment.Comment: 9 pages, 9 figure

Uniaxial-Pressure induced Ferromagnetism of Enhanced Paramagnetic Sr3Ru2O7

We report a uniaxial pressure-dependence of magnetism in layered perovskite strontium ruthenate Sr3Ru2O7. By applying a relatively small uniaxial pressure, greater than 0.1 GPa normal to the RuO2 layer, ferromagnetic ordering manifests below 80 K from the enhanced-paramagnet. Magnetization at 1 kOe and 2 K becomes 100 times larger than that under ambient condition. Uniaxial pressure dependence of Curie temperature T_C suggests the first order magnetic transition. Origin of this uniaxial-pressure induced ferromagnetism is discussed in terms of the rotation of RuO6 octahedra within the RuO2 plane.Comment: 8 pages, 3 figures. to be published in Journal of the Physical Society of Japan, vol.73, No.5 (2004

Composite Yb : YAG/Cr4+: YAG ceramics picosecond microchip lasers

Efficient laser-diode pumped picosecond self-Q-switched all-ceramic composite Yb: YAG/ Cr4+: YAG microchip lasers with 0.72 MW peak power has been developed. Lasers with nearly diffraction-limited beam quality (M-2 < 1.09), oscillate at stable single- and multi- longitudinal-modes due to the combined etalon effects in the Yb:YAG and Cr4(+:) YAG parts of its binary structure. (C) 2007 Optical Society of America

Linear Field Dependence of the Normal-State In-Plane Magnetoresistance of Sr2RuO4

The transverse and longitudinal in-plane magnetoresistances in the normal state of superconducting Sr2RuO4 single crystals have been measured. At low temperatures, both of them were found to be positive with a linear magnetic-field dependence above a threshold field, a result not expected from electronic band theory. We argue that such behavior is a manifestation of a novel coherent state characterized by a spin pseudo gap in the quasi-particle excitation spectrum in Sr2RuO4.Comment: 4 pages + 5 figure