Relating single-scenario facets to the convex hull of the extensive form of a stochastic single-node flow polytope

We study when a facet-defining inequality for a deterministic, single-scenario subproblem is also facet-defining for the extensive form of a two-stage stochastic mixed-integer linear program (SMIP). To answer this question, we introduce a novel stochastic variant of the well-known single-node flow (SNF) polytope, and present necessary and sufficient conditions for single-scenario facet-defining inequalities to be facet-defining for the extensive form. We further demonstrate that our stochastic SNF polytope is a relaxation of a broad subclass of SMIPs, illustrating its generality.     

On pulsatile flow of a viscous fluid in a rotating channel

A study is made on the pulsatile flow superposed on a steady laminar flow of a viscous fluid in a parallel plate channel rotating with an angular velocity Ω about an axis perpendicular to the plates. An exact solution of the governing equations of motion is obtained. The solution in dimensionless form contain two parametersK ²=ΩL ²/v which is reciprocal of Ekmann Number and frequency parameter σ=αL ²/v. The effects of these parameters on the principal flow characters such as mean sectional velocity and shear stresses at the plates have been examined. For large σ andK ² the flow near the plates has a multiple boundary layer character.     

On the flow of a cosserat fluid through a curved pipe

Summary A theoretical analysis is made of the flow of a Cosserat fluid in a curved pipe under a pressure gradient. It is assumed that the curvature of the pipe is small, that is the radius of the circle in which the central line of the pipe is coiled is large in comparison with the radius of the cross-section. Following Dean [2] a solution is developed by the method of successive approximation. The paths of the particles in the central plane and the projection of the streamlines on the cross-section of the pipe are compared with those of a Newtonian fluid. It is observed that in the theory of Cosserat fluids the curvature of the streamlines in the central plane increases and the motion is slower in the cross-section of the pipe. It is also shown that the rate of flow of a Cosserat fluid through a curved pipe is decreased due to the curvature of the pipe.

---

Résumé On fait une analyse théorique de l'écoulement d'un fluide de Cosserat dans un tube sous un gradient de pression. On suppose que la courbature du tube est faible, c'est-à-dire que le radius du cercle qui fait la ligne du centre du tube est fort par rapport au radius de la coupe transversale.D'après Dean [2], on développe une résolution par approximations successives. On fait la comparaison des trajectoires des particules dans le plan central et la projection des lignes d'écoulement sur la coupe transversale du tube avec celles d'un fluide de Newton.On note que dans la théorie des fluides de Cosserat, la courbature des lignes d'écoulement dans le plan central augmente, et que la motion est ralentie dans la coupe transversale du tube. On démontre ensuite que le taux d'écoulement d'un fluide de Cosserat dans un tube courbe se diminue à raison de la courbature.

     

On the plane couette flow of a variable viscosity fluid

In the present paper the Plane Couette flow for three cases, (i) Walls at unequal temperatures, (ii) Walls at equal temperatures and (iii) One of the walls is insulated, has been studied by taking a non-linear relation between viscosity and temperature. Exact solutions of the conpled momentum and energy equations have been obtained. A modified law for the transfer of heat at the upper wall is found in the case of unequal wall temperatures.     

On the steady viscous flow of a nonhomogeneous asymmetric fluid

We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a C ² boundary. We use a stream-function formulation after the manner of Frolov (Math Notes 53(5–6):650–656, 1993) in which the fluid density depends on the stream-function by means of another function determined by the boundary conditions. This allows for dropping some of the equations, most notably the continuity equation. We show existence to the resulting system using Galerkin method.     

On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

On the flow of a generalized Burgers fluid in an orthogonal rheometer

We derive an exact solution of a problem which models the stationary flow of an incompressible viscoelastic fluid in an orthogonal rheometer subject to Navier slip boundary conditions, and investigate the effect of the slip coefficient and the material parameters on the solution. The fluid model is a frame-invariant three-dimensional generalization by J. Murali Krishnan and K.R. Rajagopal of a one-dimensional model due to J.M. Burgers.     

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract

In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.     

On a free piston problem for potential ideal fluid flow

Our goal was to model and analyze a stationary and evolutionary potential ideal fluid flow through the junction of two pipes in the gravity field. Inside the ‘vertical’ pipe, there is a heavy piston that can freely move along the pipe. In the stationary case, we are interested in the equilibrium position of the piston in dependence on the geometry of junction, and in the evolutionary case, we study motion of the piston also in dependence on geometry. We formulate corresponding initial and boundary value problems and prove the existence results. The problem is nonlinear because the domain is unknown. Furthermore, we study some qualitative properties of the solutions and compare them with the qualitative properties of a free piston problem for Newtonian fluid flow. All theoretical results are illustrated with numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

The vibrations of a conical shell filled with a variable volume of fluid

We consider the vibrations of a conical shell filled with a fluid. We obtain a system of differential equations that describes the interaction of a variable volume of fluid with the shell. We solve the problem of determining the natural frequencies for a completely full shell. We obtain a formula for computing the fundamental frequency as a function of the geometric parameters of the shell. One figure. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 85–88, 1991.     

The steady axisymmetric flow of ideally plastic materials in a conical channel

The problem of the asymmetric flow of an ideally plastic medium is formulated within the framework of the von Mises model and the total plasticity condition, using the invariant condition of compatibility for the deviator component of the stress tensor. Flow in a converging conical channel, on the boundary of which the shear stresses are specified, is considered. First-order differential equations are obtained, describing the shear-stress distribution in the moving medium, one of which corresponds to the von Mises model, and the other to the total plasticity condition. It is established from an analysis of the solution in the neighbourhood of singular points, that the minus sign in front of the radical in these equations corresponds to positive shear stresses and vice versa. The problem of the shear stresses reaching a maximum value on the specified boundary surface of the channel is investigated. The aperture angle of the channel, beginning from which this value is reached, is determined. It is established that the value of the angle, following from the total plasticity condition, somewhat exceeds its value obtained within the framework of the von Mises model.     

On mass transfer in three‐dimensional flow of a viscoelastic fluid

This attempt theoratically examines the mass transfer analysis of the boundary layer flow caused by a stretching surface. Analytic solutions are derived with the Homptopy analysis method (HAM). Numerical values of skin friction coefficients and the surface mass transfer are reported. The effectiveness of this method is explicitly illustrated by discussing the convergence of the obtained series solutions. Velocity and gradient of mass transfer are shown graphically and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 915–936, 2011     

Heat transfer due to the flow through a conical tube

Résumé On étudie la distribution de la température dans un fluide visqueux incompressible s'écoulant dans un tube conique. On fait également la comparaison de la distribution de température entre deux parois inclinées non-parallèles à celle du tube conique précédemment étudiée.     

On matrices that admit unitary reduction to band form

It is proved in the paper that any low rank perturbation of a Hermitian matrix is unitarily reducible to band form. Moreover, if a normal matrix is unitarily reducible to band form, then any of its rank one perturbations is unitarily reducible as well.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 871–880, December, 1998.     

On the global convergence of an SLP–filter algorithm that takes EQP steps

 A global convergence proof is presented for a class of trust region filter–type methods for nonlinear programming. Such methods are characterized by their use of the dominance concept of multiobjective optimization, instead of a penalty parameter whose adjustment can be problematic. The methods are based on successively solving linear programming subproblems for which effective software is readily available. The methods also permit the use of steps calculated on the basis of an equality constrained quadratic programming model, which enables rapid convergence to take place for problems in which second order information is important. The proof technique is presented in a fairly general context, allowing a range of specific algorithm choices associated with choosing the quadratic model, updating the trust region radius and with feasibility restoration. Received: July 4, 2001 / Accepted: December 19, 2002 Published online: March 21, 2003 Mathematics Subject Classification (2000): 20E28, 20G40, 20C20     

On MHD flow of an incompressible viscous fluid

In this paper, we apply Homotopy Perturbation Method (HPM) to find the analytical solutions of nonlinear MHD flow of an incompressible viscous fluid through convergent or divergent channels in presence of a high magnetic field. The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. The graphs are presented to reveal the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.