Thin boundary layers of chiral smectics

We consider a reduced Landau–de Gennes energy functional which describes a chiral smectic liquid crystal with large elastic coefficients. We prove that, according to this model, chiral smectics exhibit behavior which is similar to surface superconductivity: a thin layer of smectics near the boundary, and cholesterics in the bulk of the material. We obtain this behavior for a wide region in the parameter space. We show that in a certain limit case this boundary layer can determine the direction of the helical axis of the cholesterics.     

On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations

In this paper we improve the regularity in time of the gradient of the pressure field arising in Brenier’s variational weak solutions (Comm Pure Appl Math 52:411–452, 1999) to incompressible Euler equations. This improvement is necessary to obtain that the pressure field is not only a measure, but a function in . In turn, this is a fundamental ingredient in the analysis made by Ambrosio and Figalli (2007, preprint) of the necessary and sufficient optimality conditions for the variational problem by Brenier (J Am Mat Soc 2:225–255, 1989; Comm Pure Appl Math 52:411–452, 1999).     

Some problems in metric fixed point theory

Three papers, published coincidentally and independently by Felix Browder, Dietrich G?hde, and W. A. Kirk in 1965, triggered a branch of mathematical research now called metric fixed point theory. This is a survey of some of the highlights of that theory, with a special emphasis on some of the problems that remain open. Dedicated to Felix Browder on the occasion of his 80th birthday     

Symmetry analysis of the charged squashed Kaluza–Klein black hole metric

In this research article, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza–Klein black hole space‐time in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space‐time metric using Lie point symmetries is presented, and then the n‐dimensional optimal system of this space‐time metric, for n = 1,…,4, are computed. It is shown that there is no any n‐dimensional optimal system of Lie symmetry subalgebra associated to the system of geodesic for n≥5. Then the point symmetries of the one‐parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian that means Noether symmetries are found, and then the conservation laws associated to the system of geodesic equations are calculated via Noether's theorem. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonexistence of asymptotically self-similar singularities in the Euler and the Navier–Stokes equations

In this paper we rule out the possibility of asymptotically self-similar singularities for both of the 3D Euler and the 3D Navier–Stokes equations. The notion means that the local in time classical solutions of the equations develop self-similar profiles as t goes to the possible time of singularity T. For the Euler equations we consider the case where the vorticity converges to the corresponding self-similar voriticity profile in the sense of the critical Besov space norm, . For the Navier–Stokes equations the convergence of the velocity to the self-similar singularity is in L ^q (B(z,r)) for some , where the ball of radius r is shrinking toward a possible singularity point z at the order of as t approaches to T. In the convergence case with we present a simple alternative proof of the similar result in Hou and Li in arXiv-preprint, math.AP/0603126. This work was supported partially by KRF Grant(MOEHRD, Basic Research Promotion Fund) and the KOSEF Grant no. R01-2005-000-10077-0.     

A RANS 3D model with unbounded eddy viscosities

We consider the Reynolds Averaged Navier–Stokes (RANS) model of order one (u,p,k)$(\mathbf{u},p,k)$ set in R³${\mathbb{R}}^3$ which couples the Stokes Problem to the equation for the turbulent kinetic energy by k-dependent eddy viscosities in both equations and a quadratic term in the k  -equation. We study the case where the velocity and the pressure satisfy periodic boundary conditions while the turbulent kinetic energy is defined on a cell with Dirichlet boundary conditions. The corresponding eddy viscosity in the fluid equation is extended to R³${\mathbb{R}}^3$ by periodicity. Our contribution is to prove that this system has a solution when the eddy viscosities are nondecreasing, smooth, unbounded functions of k, and the eddy viscosity in the fluid equation is a concave function.     

C 1,α-regularity for electrorheological fluids in two dimensions

We prove the existence of -solutions to a system of nonlinear partial differential equations describing steady planar motions of electrorheological fluids with Dirichlet boundary conditions for inf .     

Local regularity criteria of a suitable weak solution to MHD equations

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1).     

76Sr核yrast带结构演化的微观研究

对于发生在同一个原子核中的、从一种高有序激发模式向着另一种低有序激发模式演化的机理和物理图像,提出了一种新的理解：被布居到高角动量态的高有序激发核,以E₂跃迁方式先行退耦到yrast带,再退耦到共存区时释放了结构能,诱发价核子对耦合强度改变,重新组合出低有序的激发模式基准态,实现了基准态结构的过渡.从微观上看,这是一种既温和而又平稳的转变.并以⁷⁶Sr核为例作了深入阐述. 关键词： 量子相变 yrast带结构演化 微观sdIBM-2方案 76Sr核')" href="#">⁷⁶Sr核