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

Anisotropic magnetic properties of CeAg2_2Ge2_2 single crystal

In order to investigate the anisotropic magnetic properties of CeAg$_2$Ge$_2$, we have successfully grown the single crystals, for the first time, by high temperature solution growth (flux) method. We have performed a detailed study of the grown single crystals by measuring their electrical resistivity, magnetic susceptibility, magnetization, specific heat and magnetoresistance. A clear anisotropy and an antiferromagnetic transition at $T_{\rm N}$ = 4.6 K have been observed in the magnetic properties. The magnetic entropy reaches $R$ ln 4 at 20 K indicating that the ground state and the first excited state are very closely spaced (a quasi-quartet state). From the specific heat measurements and crystalline electric field (CEF) analysis of the magnetic susceptibility, we have found the level splitting energies as 5 K and 130 K. The magnetization measurements reveal that the a-axis is the easy axis of magnetization and the saturation moment is $\mu_{\rm s}$ = 1.6 $\mu_{\rm B}$/Ce, corroborating the previous neutron diffraction measurements on a polycrystalline sample.Comment: Submitted to Phys. Rev.