Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction

Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associated free energy. Furthermore, we prove that this global minimizer is a radially decreasing compactly supported continuous density function which is smooth inside its support, and it is characterized as the unique compactly supported stationary state of the evolution model. This unique profile is the clear candidate to describe the long time asymptotics of the diffusion dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure

AdS_3/CFT_2 Correspondence and Space-Time N=3 Superconformal Algebra

We study a Wess-Zumino-Witten model with target space AdS_3 x (S^3 x S^3 x S^1)/Z_2. This allows us to construct space-time N=3 superconformal theories. By combining left-, and right-moving parts through a GSO and a Z_2 projections, a new asymmetric (N,\bar{N})=(3,1) model is obtained. It has an extra gauge (affine) SU(2) symmetry in the target space of the type IIA string. An associated configuration is realized as slantwise intersecting M5-M2 branes with a Z_2-fixed plane in the M-theory viewpoint.Comment: 27 pages, 1 figure, final versio

Scalability of spin FPGA: A Reconfigurable Architecture based on spin MOSFET

Scalability of Field Programmable Gate Array (FPGA) using spin MOSFET (spin FPGA) with magnetocurrent (MC) ratio in the range of 100% to 1000% is discussed for the first time. Area and speed of million-gate spin FPGA are numerically benchmarked with CMOS FPGA for 22nm, 32nm and 45nm technologies including 20% transistor size variation. We show that area is reduced and speed is increased in spin FPGA owing to the nonvolatile memory function of spin MOSFET.Comment: 3 pages, 7 figure

Systematic limits on sin^2{2theta_{13}} in neutrino oscillation experiments with multi-reactors

Sensitivities to sin^2{2theta_{13}} without statistical errors (``systematic limit'') are investigated in neutrino oscillation experiments with multiple reactors. Using an analytical approach, we show that the systematic limit on sin^2{2theta_{13}} is dominated by the uncorrelated systematic error sigma_u of the detector. Even in an experiment with multi-detectors and multi-reactors, it turns out that most of the systematic errors including the one due to the nature of multiple sources is canceled as in the case with a single reactor plus two detectors, if the near detectors are placed suitably. The case of the KASKA plan (7 reactors and 3 detectors) is investigated in detail, and it is explicitly shown that it does not suffer from the extra uncertainty due to multiple reactors.Comment: 26 pages, 10 eps-files, revtex