Abstract:
A numerical method of mode analysis of rapidly rotating relativistic stellar models by the Cowling approximation is applied to rotating neutron stars with realistic equations of state. For selected equations of state, eigenvalues and eigenfunctions of f-modes are numerically solved for stellar models from non-rotating to maximally rotating states. Neutral points of the lower order f-modes are determined as a function of the stellar rotational frequency. As in the polytropic case, we find that the bar mode can have neutral points for models with relatively strong gravity. The rotational frequency at the neutral point increases as the gravitational mass of the model becomes larger. As astrophysical applications of our analysis, we discuss the time scales of gravitational radiation induced instability and the possibility of the resonant excitation of f-modes during inspiraling motion of compact binary systems.

Abstract:
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a new regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an anomalous diffusion exponent in full order of the perturbation series with respect to a nonlinearity.

Abstract:
Adiabatic invariants foliate phase space, and impart a macro-scale hierarchy by separating microscopic variables. On a macroscopic leaf, long-scale ordered structures are created while maximizing entropy. A plasma confined in a magnetosphere is invoked for unveiling the organizing principle ---in the vicinity of a magnetic dipole, the plasma self-organizes to a state with a steep density gradient. The resulting nontrivial structure has maximum entropy in an appropriate, constrained phase space. One could view such a phase space as a leaf foliated in terms of Casimir invariants ---adiabatic invariants measuring the number of quasi-particles (macroscopic representation of periodic motions) are identified as the relevant Casimir invariants. The density clump is created in response to the inhomogeneity of the energy level (frequency) of quasi-particles.

Abstract:
We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length n in the boundary is bounded by \delta n, where \delta < 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on \delta), the spectral gap decreases exponentially in n.

Abstract:
Quantum systems often exhibit fundamental incapability to entertain vortex. The Meissner effect, a complete expulsion of the magnetic field (the electromagnetic vorticity), for instance, is taken to be the defining attribute of the superconducting state. Superfluidity is another, close-parallel example; fluid vorticity can reside only on topological defects with a limited (quantized) amount. Recent developments in the Bose-Einstein condensates produced by particle traps further emphasize this characteristic. We show that the challenge of imparting vorticity to a quantum fluid can be met through a nonlinear mechanism operating in a hot fluid corresponding to a thermally modified Pauli-Schroedinger spinor field. In a simple field-free model, we show that the thermal effect, represented by a nonlinear, non-Hermitian Hamiltonian, in conjunction with spin vorticity, leads to new interesting quantum states; a spiral solution is explicitly worked out.

Abstract:
We construct the phase diagram of a homogeneous two component Fermi gas with population imbalance under a Feshbach resonance. In particular, we study the physics and stability of the Larkin-Ovchinnikov phase. We show that this phase is stable over a much larger parameter range than what has been previously reported by other authors.

Abstract:
By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing functions of the rotational frequency. The eigenfrequency curve of each mode as a function of the rotational frequency has discontinuities, which arise from the avoided crossing with other curves of axisymmetric modes.

Abstract:
For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of it differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By using this new method, we have succeeded in obtaining eigenvalues and eigenfunctions of r-mode oscillations of differentially rotating polytropic stars. Our numerical results show that as the degree of differential rotation is increased, it becomes more difficult to solve r-mode oscillations for slightly deformed configurations from sphere compared to solving r-mode oscillations of considerably deformed stars. One reason for it seems that for slightly deformed stars corotation points appear near the surface region if the degree of differential rotation is strong enough. This is similar to the situation that the perturbational approach of r-mode oscillations for it slowly rotating stars in general relativity results in a singular eigenvalue problem.

Abstract:
Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric Yang-Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) Renormalization Group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N=1 the form of effective actions in terms of massless fields is quite reasonable, while in the case of the N=2 model we appear to have problems related to instantons.

The photo-controlled/living radical polymerization of methacrylic acid (MAA) was performed at room temperature by irradiation with a high-pressure mercury lamp using azoinitiators and 4-methoxy-2,2,6,6-tetramethylpiperidine-1-oxyl as the mediator in the presence of (4-tert-butylphenyl)diphenylsulfonium triflate (^{t}BuS) as the accelerator. Whereas the bulk polymerization yielded polymers with a bimodal molecular weight distribution in both the absence and presence of ^{t}BuS, the solution polymerization in methanol produced unimodal polymers with the molecular weight distribution of 2.0-2.3 in the presence of ^{t}BuS. The molecular weight distribution of the resulting poly(MAA) decreased with an in- crease in ^{t}BuS. The dilution of the monomer concentration also reduced the molecular weight distribution. The use of the initiator with a low 10-h half-life temperature also effectively controlled the molecular weight. The livingness of the polymerization was confirmed by obtaining linear increases in the first-order conversion versus time, the molecular weight versus the conversion, and the molecular weight versus the reciprocal of the initiator concentration.