Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

水斗非定常自由水膜流三维贴体数值模拟

本研究采用水斗三维非正交贴体坐标系进行了非定常自由水膜流动的数值解析。对不规则水斗内表面采用三维非正交贴体坐标系下离散点进行拟合,推导了曲面离散点的法向矢量和曲面微元面高斯曲率、平均曲率等几何特征量的计算公式,进而导出流体粒子在运动方向上曲率计算式。在水斗三维贴体坐标系中,还推导了流体粒子在水斗曲面上的运动控制方程。最后对某水轮机水斗内表面非定常自由水膜流进行了数值模拟,得到其非定常水膜流态分布。     

FAST ACCURATE PREDICTION OF BLANK SHAPE IN SHEET METAL FORMING

By using the Finite Element Inverse Approach based on the Hill quadratic anisotrop-ically yield criterion and the quadrilateral element, a fast analyzing software-FASTAMP for the sheet metal forming is developed. The blank shapes of three typical stampings are simulated and compared with numerical results given by the AUTOFORM software and experimental results, respectively. The comparison shows that the FASTAMP can predict blank shape and strain distribution of the stamping more precisely and quickly than those given by the traditional methods and the AUTOFORM.     

Poly(L‐lysine) and clay nanocomposite with desired matrix secondary structure: Effects of polypeptide molecular weight

Nanocomposites (NC) were formed using cationic poly(L ‐lysine) (PLL), a semicrystalline polypeptide, that was reinforced by sodium montmorillonite (MMT) clay via solution intercalation technique. By varying solution conditions such as pH, temperature, and polypeptide concentration in the presence of clay platelets, the secondary structure of PLL was controllably altered into α‐helical, β‐sheet, and random coil. The high molecular weight polypeptide shows a strong propensity to fold into the β‐sheet structure when cast as films, irrespective of the initial secondary structure in solution. Nanocomposite local morphology confirms intercalated MMT platelets with PLL over a wide range of compositions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 239–252, 2007.     

Effect of a Shock Pulse on a Floating Ice Sheet

The vibrations of a viscoelastic plate lying on an elastic liquid base subjected to pulse loading have been studied theoretically and experimentally. The effect of the variable depth of the reservoir, plate thickness, and strain relaxation time on the value of the plate vibration amplitude and the length and curvature of the flexural gravity wave profile are analyzed. Good agreement of theoretical and experimental results is obtained.     

Almost-sure path properties of fractional Brownian sheet

The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions.     

Some path properties of generalized Lévy sheet

Let X(t) be an N parameter generalized Lévy sheet taking values in ℝ^d with a lower index α, ℜ = {(s, t] = ∏ _i=1 ^N (s _i, t _i], s _i < t _i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established.     

On the evolution of two-dimensional patterns in an inviscid liquid sheet

We perform an analysis of the pattern formation for a moving sheet of inviscid fluid. The sheet, which is assumed to have an infinite horizontal extent, moves at some prescribed velocity into a passive surrounding gas. The sheet’s thickness is assumed much smaller than the horizontal scale of the fluid motion. By considering a system that is symmetric with respect to the horizontal planes, long scale asymptotics are used to reduce the full governing equations in three dimensions to a set of three coupled nonlinear partial differential equations for the horizontal components of the velocity field and the height of the interface profile. The interfacial conditions consisting of the kinematic and normal stress balance are incorporated into these evolution equations. Investigations are carried out as function of the sole dimensionless parameter, namely the Weber number. A small amplitude stability analysis around the planar gas–liquid interface reveals that wave patterns in the form of traveling plane waves occur subcritically, and are therefore unstable. The reduced evolution equations are solved numerically for fixed values of the Weber number. Since the reduced system of equations is homogeneous, the wave motion is generated by initial conditions. Five initial conditions have been imposed: one-dimensional rolls, two-dimensional squares, two-dimensional hexagons, two-dimensional ridges, and smooth peaks. The ensuing evolution of the liquid sheet’s shape and corresponding flow fields are described by illustrations of the changes in the sheet’s morphology with time.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.