Observations on the Role of Vorticity in the Stability Theory of Wall Bounded Flows

The linearized equations for the evolution of disturbances to four wall bounded flows are treated. The flows are plane Couette flow and plane Poiseuille flow, Hagen-Poiseuille pipe flow, and the asymptotic suction profile. By looking at the vorticity it is proved simply that plane Couette flow and Hagen-Poiseuille flow are linearly stable. Further study is made of the structure of the disturbance equation by the introduction of a special vorticity adjoint.     

Geometric evolution equations in critical dimensions

We make a qualitative comparison of phenomena occurring in two different geometric flows: the harmonic map heat flow in two space dimensions and the Yang–Mills heat flow in four space dimensions. Our results are a regularity result for the degree-2 equivariant harmonic map flow, and a blow-up result for an equivariant Yang–Mills-like flow. The results show that qualitatively differing behaviours observed in the two flows can be attributed to the degree of the equivariance.     

An interior-point approach for primal block-angular problems

Multicommodity flows belong to the class of primal block-angular problems. An efficient interior-point method has already been developed for linear and quadratic network optimization problems. It solved normal equations, using sparse Cholesky factorizations for diagonal blocks, and a preconditioned conjugate gradient for linking constraints. In this work we extend this procedure, showing that the preconditioner initially developed for multicommodity flows applies to any primal block-angular problem, although its efficiency depends on each particular linking constraints structure. We discuss the conditions under which the preconditioner is effective. The procedure is implemented in a user-friendly package in the MATLAB environment. Computational results are reported for four primal block-angular problems: multicommodity flows, nonoriented multicommodity flows, minimum-distance controlled tabular adjustment for statistical data protection, and the minimum congestion problem. The results show that this procedure holds great potential for solving large primal-block angular problems efficiently.     

Modeling of three dimensional thermocapillary flows with evaporation at the interface based on the solutions of a special type of the convection equations

Theoretical and numerical study of the convection processes, which are accompanied by evaporation/condensation, in the framework of new non-standard problem is largely motivated by new physical experiments. One of the principal questions is to understand the character and to evaluate the degree of influence of particular factors or their combined action on the structure of the joint flows of liquid and gas-vapor mixture. The flow topology is determined by four main mechanisms: natural and thermocapillary convection, tangential stresses and mass transfer due to evaporation at the interface. The mathematical modeling of the fluid flows in an infinite channel with a rectangular cross section is carried out on the basis of the solution of a special type of the convection equations. The effects of thermodiffusion and diffusive thermal conductivity in the gas phase and evaporation at the thermocapillary interface are taken into consideration. Numerical investigations are performed for the liquid – gas (ethanol – nitrogen) system under normal and low gravity. The fluid flows are characterized as translational and progressively rotational motions and can be realized in various forms.     

Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation

The effect of thermal radiation with a regular three-parameter perturbation analysis has been studied for the effects in some free convection flows of Newtonian fluid-saturated porous medium. The effects of the thermal radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface, uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source, and, a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge–Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and a heat transfer and total heat and mass convected downstream are presented in a tabular form with the parameters characterizing the radiation, permeability of the porous medium, pressure stress work and viscous dissipation. The obtained results are compared and a representative set is displayed graphically to illustrate the influences of the radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles.     

Modelling confined multi-material heat and mass flows using SPH

Many applications in mineral and metal processing involve complex flows of multiple liquids and gases coupled with heat transfer. The motion of the surfaces of the liquids can involve sloshing, splashing and fragmentation. Substantially differing material properties are common. The flows are frequently complicated by other physical effects. Smoothed particle hydrodynamics (SPH) is a computational modelling technique that is ideally suited to such difficult flows. The Lagrangian framework means that momentum dominated flows and flows with complicated material interface behaviours are handled easily and naturally. To be able to model complex multi-physics flows, many aspects of SPH need to be explored. In this paper we describe developments that allow conductive and convective heat transfer to be modelled accurately for a sequence of idealised test problems.     

一个高维loop代数及其应用

本文构造了一个7维loop代数,由此获得两个已知的Liouville可积族．利用屠格式和可积耦合定义得到了相应的四个扩展可积模型．另外,利用马格式求得了上面已知可积系之一的非等谱流．     

Experiments on the transition to time‐dependence in highly strained vortex flow inside a rectangular cavity

The flows in a two‐sided lid‐driven cavity with a cross‐sectional aspect ratio Γ = 1.96 is experimentally investigated by laser‐Doppler anemometry and by hot‐film measurements. When the two facing walls move in opposite directions, a robust three‐dimensional flow consisting of four cells arises for Reynolds numbers Re ≥ 275 as a result of the elliptic instability. The flow within these steady cells is measured to high precision. For Re > 825 the four cell flow becomes oscillatory. The oscillations are due to a standing wave with the same wavelength as the underlying cellular flow.     

A pair of stream functions for three-dimensional vortex flows

Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method.     

Valuation under technological change

This paper presents a valuation model, which includes the possibility of a future change in technology that affects in the short term the level of net cash flows receivable. The user can consider the effects of such a change on the flows, depending on whether the company is an innovator itself, or a follower of the innovations of others. The model is based upon a number of assumptions. The cash flows before the technological breakthrough follow a geometric Brownian motion. The breakthrough is modelled by a Poisson jump. For the innovator, cash flows are boosted, then decline through competition. By contrast, for the technological follower the breakthrough has an immediate depressing effect on cash flows, but subsequent cash flows rise and are modelled by an upward logistic curve.     

两同心旋转球间流动问题分歧解的连续算法

1引言本文数值地考察了两个同心旋转球之间的定常轴对称不可压流动．这种流动被称为球面Couette流（SphericalCouetteFlow），简称SCF．SCF对干天体物理，地球物理和工程应用均具重要意义，虽然过往所做的研究甚少（一方面由于分析研究的难度，另方面，所做的实验也少），目前，对其研究的兴趣有增长的趋势．实验发现，SCF在低雷诺数下既是轴对称的，又是关于赤道成反射对称的（Khlebutin［‘］，ZlereP＆SawatskiL‘）．ZiereP＆Sawatski和Wimmer［’］都发现SCF有临界雷诺数Rec，当Re＞Rec，有泰勒旋涡（TaylorVortices）形成…     

Stability Properties and Nonlinear Mappings of Two and Three-Layer Stratified Flows

Two and three-layer models of stratified flows in hydrostatic balance are studied. For the former, nonlinear transformations are found that map [ baroclinic ] two-layer flows with either rigid top and bottom lids or vertical periodicity, into [ barotropic ] single-layer, shallow water free-surface flows. We have previously shown that two-layer flows with Richardson number greater than one are nonlinearly stable, in the following sense: when the system is well-posed at a given time, it remains well-posed through the nonlinear evolution. Here, we give a general necessary condition for the nonlinear stability of systems of mixed type. For three-layer flows with vertical periodicity, the domains of local stability are determined and the system is shown not to satisfy the necessary condition for nonlinear stability. This means that there are wave-motions that evolve into shear unstable flows.     

On a class of stochastic flows driven by quantum Brownian motion

A class of quantum stochastic flows on^*-algebras is introduced which includes both classical flows on Riemannian manifolds and flows induced by Lie group actions onC ^*-algebras. Criteria are established to determine those flows which are unitarily equivalent to ones driven by classical Brownian motion. It is shown that taking complex combinations of the driving coefficients of such flows gives rise to flows which are not of Evans-Hudson type (i.e., all driving coefficients do not preserve the relevant algebra).     

On the structure of Markov flows

A new infinitesimal characterization of completely positive but not necessarily homomorphic Markov flows from a C^*-algebra to bounded operators on the boson Fock space over L²(R) is given. Contrarily to previous characterizations, based on stochastic differential equations, this characterization is universal, i.e., valid for arbitrary Markov flows. With this result the study of Markov flows is reduced to the study of four C₀-semigroups. This includes the classical case and even in this case it seems to be new. The result is applied to deduce a new existence theorem for Markov flows.     

Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

     

When does a T-junction require a left-turn lane?

A four-state, ergodic Markov chain is used to model a T-junction on a narrow, two-lane, major road. The states are defined more realistically than by previous authors. A formula is obtained for the proportion of traffic configurations in which cars travelling one way are brought to a halt by those turning left onto the minor road. This formula is obtained as a function of four parameters: the mean traffic flows in each direction, the probability that a car on the major road will turn left at the junction and the minimum time gap, in the oncoming flow of traffic, which that manouevre requires. If this proportion is higher than is deemed acceptable, then a left-turn is needed.     

Analytical solutions of channel and duct flows due to general pressure gradients

Pursued herein are the closed-form solutions of the Navier–Stokes equations for both planar channel and circular duct flows, influenced by either periodic or aperiodic pressure gradients, of which the amplitudes are sufficiently low to yield laminar incompressible flows. The analyses conducted for the unsteady flows parallel to the walls lead to the analytical solutions that encompass not only the long-time oscillations by periodic pressure gradients, but also the transient start-up flows commencing from zero velocity due to arbitrary aperiodic pressure gradients. With the standard methods employed, the present solutions generalizing the classic ones are written in the forms rendering the explicit dependence on the pressure gradient, and are numerically validated by the existing solutions of simple sinusoidal oscillations and a flow involving an aperiodic impulsive pressure gradient. By virtue of their functional forms, the present solutions can be applied with any pressure gradients, even if the gradients are not in closed forms.     

Groebner Basis Methods for Stationary Solutions of a Low-Dimensional Model for a Shear Flow

We use Groebner basis methods to extract all stationary solutions for the nine-mode shear flow model described in Moehlis et al. (New J Phys 6:56, 2004). Using rational approximations to irrational wave numbers and algebraic manipulation techniques we reduce the problem of determining all stationary states to finding roots of a polynomial of order 30. The coefficients differ by 30 powers of 10, so that algorithms for extended precision are needed to extract the roots reliably. We find that there are eight stationary solutions consisting of two distinct states, each of which appears in four symmetry-related phases. We discuss extensions of these results for other flows.     

Elementary chaotic snap flows

Hyperjerk systems with 4th-order derivative of the form have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.