Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space

In an ambient space with rotational symmetry around an axis (which include the Hyperbolic and Euclidean spaces), we study the evolution under the volume-preserving mean curvature flow of a revolution hypersurface M generated by a graph over the axis of revolution and with boundary in two totally geodesic hypersurfaces (tgh for short). Requiring that, for each time t ≥ 0, the evolving hypersurface M _t meets such tgh orthogonally, we prove that: (a) the flow exists while M _t does not touch the axis of rotation; (b) throughout the time interval of existence, (b1) the generating curve of M _t remains a graph, and (b2) the averaged mean curvature is double side bounded by positive constants; (c) the singularity set (if non-empty) is finite and lies on the axis; (d) under a suitable hypothesis relating the enclosed volume to the n-volume of M, we achieve long time existence and convergence to a revolution hypersurface of constant mean curvature.     

Ill-posedness in three-dimensional plastic flow

This paper examines partial differential equations for frictional materials flowing via plastic yield, including the equations given by the Critical State Theory of Soil Mechanics. In particular, the material density is considered as a dependent variable. In previous work we demonstrated that two-dimensional plastic flow may be ill posed due to an instability along two rays in Fourier transform space. In this paper, we show that in three dimensions the equations are linearly well posed provided all three strain rates are nonzero.     

Rotationally invariant hyperbolic waves

We use weakly nonlinear asymptotics to derive a canonical asymptotic equation for rotationally invariant hyperbolic waves. The equation can include weak dissipative, dispersive, or diffractive effects. We give applications to equations from magnetohydrodynamics, elasticity, and viscoelasticity.     

Rotationally symmetric symphonic maps

Annals of Global Analysis and Geometry - We consider a functional of pullbacks of metrics on the space of maps f between Riemannian manifolds. Harmonic maps are stationary points of the energy...     

Rotationally symmetric viscous gas flows

The Dirichlet boundary value problem for the Navier–Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.     

Mathematical modeling of contact problems of plastic flow

The nonstationary space contact problems of plastic flow in the comparatively thin layer between surfaces of external bodies have been analysed in the present paper. Earlier encountered in mathematical modeling peculiarities characterized for considered processes (as the slipping of layer material along contact, high - comparatively with shears - contact pressures, normal elastic movements commensurable with thickness of the layer, the formation of hardened layers near contact) are noted. Other characterized peculiarities, such as the property of anisotropy of friction forces on contact, the possibility of preserving the intermediate lubricant volumes on contact and contact friction faces control, the influence of initial nonhomogeneity on the formation of plastic flow are also considered. In each caw the induced qualitative effects by them are represented.     

Rotationally symmetric translating soliton of H~k-flow

This paper mainly considers the translating soliton of H k-flow for k > 0.We give the asymptotic expression of the entire rotationally symmetric translating soliton,and obtain non-convex Wing-like solution as well as two barrier solutions.Moreover,we show that the solution with polynomial growth keeps its growth rate when evolution.     

Rotationally Invariant Rank 1 Convex Functions

Let f be a function on the set M ⁿ xn of all n by n real matrices. If f is rotationally invariant with respect to the proper orthogonal group, it has a representation \tilde f through the signed singular values of the matrix argument ?∈ M^nxn. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of \tilde f . Accepted 20 December 2000. Online Publication 18 May, 2001.     

Graphical solution of axially symmetric problems of plastic flow

Résumé Une méthode graphique de solution des problèmes dans le cas de symétrie axiale a été proposée pour des corps rigides, parfaitement plastiques, obéissants au critère d'écoulement de Coulomb-Tresca et à l'hypothèse du potentiel plastique. Deux cas ont été considérés: d'une part des régimes de Haar-Kármán pour lesquels la contrainte circonférencielle est égale à l'une des contraintes principales contenues dans le plan axial, et d'autre part des régimes duor lesquels l'une des vitesses de déformation principales dans le plan axial est nulle.     

Anisotropy in the flow processes of a thin plastic layer

The theory of the flow of a thin layer of plastic material over surfaces developed by Il’yushin is extended to the case of an anisotropic ideally plastic material and anisotropic flow on the surface. Particular attention is given to determining the contact pressure. Two methods are proposed for solving this problem: a variational method and reduction to a Cauchy problem. The effect of anisotropy is revealed using specific examples.     

From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity

We show how Beckner's montonicity result on Hamming cube easily implies the monotonicity of a flow introduced by Janson in Hausdorff–Young inequality     

On the breakdown of a continuous multi-dimensional gasdynamic flow

Summary Starting with the theory of weak discontinuities, an expression for the point at which the solution itself becomes discontinuous is derived. The formula is readily applicable to multidimensional hyperbolic systems, with arbitrary initial data.Detailed application to gasdynamics is given, with explicit results for an atmosphere with exponentially decaying density.

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Résumé Considérant la propagation des discontinuités faibles dans une solution continue d'un système hyperbolique quasilinéaire, on déduit une formule décrivant l'apparition des discontinuités dans la solution même.On présente une application détaillée à l'aérodynamique, avec un exemple concernant une atmosphère à densité décroissant exponentiellement.

     

Forecasting urban traffic flow by SVR with continuous ACO

Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. Because the information of inter-urban traffic presents a challenging situation, the traffic flow forecasting involves a rather complex nonlinear data pattern. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a short-term traffic forecasting model which combines the support vector regression model with continuous ant colony optimization algorithms (SVRCACO) to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed SVRCACO model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA) time series model. Therefore, the SVRCACO model is a promising alternative for forecasting traffic flow.     

Rotationally Symmetric Stress and Strain in Shells of Revolution

In generalization of existing results of the linear theory of symmetrical bending and torsion of thin elastic shells of revolution and of the theory of pure bending and twisting of ring sector shells, this paper considers the differential equations of the theory of shells of revolution under the supposition of rotationally symmetric stress and strain, allowing for transverse shear deformation and for moments turning about the normals to the middle surface. In this way, making use of the simplified static-geometric analogy which is associated with the introduction of the two mentioned effects, known results are rederived in a new way and some new results are obtained, in particular for the dislocation-theory-type problems of pure bending and twisting.     

The Inverse Mean Curvature Flow in Rotationally Symmetric Spaces

In this paper, the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied. It is proved that the flow converges to a unique geodesic sphere, i.e., every principle curvature of the hypersurfaces converges to a same constant under the flow.