Zero-preserving iso-spectral flows based on parallel sums

Driessel [K.R. Driessel, Computing canonical forms using flows, Linear Algebra Appl 379 (2004) 353-379] introduced the notion of quasi-projection onto the range of a linear transformation from one inner product space into another inner product space. Here we introduce the notion of quasi-projection onto the intersection of the ranges of two linear transformations from two inner product spaces into a third inner product space. As an application, we design a new family of iso-spectral flows on the space of symmetric matrices that preserves zero patterns. We discuss the equilibrium points of these flows. We conjecture that these flows generically converge to diagonal matrices. We perform some numerical experiments with these flows which support this conjecture. We also compare our zero-preserving flows with the Toda flow.     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

Isospectral Flows for the Inhomogeneous String Density Problem

We derive isospectral flows of the mass density in the string boundary value problem corresponding to general boundary conditions. In particular, we show that certain class of rational flows produces in a suitable limit all flows generated by polynomials in negative powers of the spectral parameter. We illustrate the theory with concrete examples of isospectral flows of discrete mass densities which we prove to be Hamiltonian and for which we provide explicit solutions of equations of motion in terms of Stieltjes continued fractions and Hankel determinants.     

Exponential mixing for smooth hyperbolic suspension flows

We present some simple examples of exponentially mixing hyperbolic suspension flows. We include some speculations indicating possible applications to suspension flows of algebraic Anosov systems. We conclude with some remarks about generalizations of our methods.     

A metric study involving independent sequences

We investigate the distribution of sequences in compact metric spaces, involving spectra of flows and notions of statistical independences. We pay attention to sequences closely related to group extensions of flows.     

Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data

Several nonlinear constitutive equations have been proposed to overcome the limitations of the linear eddy-viscosity models to describe complex turbulent flows. These nonlinear equations have often been compared to experimental data through the outputs of numerical models. Here we perform a priori analysis of nonlinear eddy-viscosity models using direct numerical simulation (DNS) of simple shear flows. In this paper, the constitutive equation is directly checked using a tensor projection which involves several invariants of the flow. This provides a 3 terms development which is exact for 2D flows, and a best approximation for 3D flows. We provide the quadratic nonlinear constitutive equation for the near-wall region of simple shear flows using DNS data, and estimate their coefficients. We show that these coefficients have several common properties for the different simple shear flow databases considered. We also show that in the central region of pipe flows, where the shear rate is very small, the coefficients of the constitutive equation diverge, indicating the failure of this representation for vanishing shears.     

Heavy-traffic limits for stationary network flows

This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck queue is especially tractable because it yields limit processes involving one-dimensional reflected Brownian motion. That limit plays an important role in our new nonparametric decomposition approximation of the steady-state performance using indices of dispersion and robust optimization.

     

Extended Toda Lattice

We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.     

Invariant hypersurface flows in centro-affne geometry

In this paper, the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows. Based on these fundamental evolution equations, we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations, which can be solved explicitly. Finally, the centro-affine invariant normal flows for hypersurfaces are investigated, and two specific flows are provided to illustrate the behaviour of the flows.     

Expansive measures for flows

We extend the concept of expansive measure [2] from homeomorphism to flows. We prove for continuous flows on compact spaces that every expansive measure has no singularities in the support, is aperiodic, is expansive with respect to time-T maps (but not conversely), remains expansive under topological equivalence, vanishes along the orbits and is natural under suspensions. We apply these properties to prove that there are no expansive flows (in the sense of [26]) of any closed surface.     

Geometric aspects of transversal Killing spinors on Riemannian flows

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those flows carrying non-trivial solutions.      

Short-Time Existence for Some Higher-Order Geometric Flows

We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. We apply this theorem to flows by powers of the Laplacian of the Ricci tensor, and to flows generated by the ambient obstruction tensor. As a special case, we prove short-time existence for a type of Bach flow.     

On the mixing property for hyperbolic systems

We describe an elementary argument from abstract ergodic theory that can be used to prove mixing of hyperbolic flows. We use this argument to prove the mixing property of product measures for geodesic flows on (not necessarily compact) negatively curved manifolds. We also show the mixing property for the measure of maximal entropy of a compact rank-one manifold.     

Variational inequalities in magneto-hydrodynamics

We study subdifferential initial boundary-value problems for the magneto-hydrodynamics (MHD) equations of a viscous incompressible liquid. We construct a solvability theory for an abstract evolution inequality in Hilbert space for operators with quadratic nonlinearity. The results obtained are applied to the study of MHD flows. For three-dimensional flows, we prove the existence of weak solutions of variational inequalities “globally” with respect to time, while, for two-dimensional flows, we establish the existence and uniqueness of strong solutions.     

On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems

Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.     

最大利润流问题及算法

最大利润流是以运输利润最大为目标的网络优化问题 .一个利润可行流可分解为若干个路流和圈流 ,相应地该可行流的利润也等于这些路流和圈流的利润之和 .本文证明了一个可行流为最大利润流的充要条件是不存在利润增广路 ,并据此提出了求解算法 .文章最后给出了一个计算实例 .     

Unidirectional flows of viscoelastic fluids and their gasdynamic counterparts

We have shown that unidirectional flows of viscoelastic fluids are mathematically equivalent to plane potential flows of a fictitious gas. The classification of type and some exact solutions of the equations describing fictitious gas flows are presented. The Prandtl-Mayer flow and its viscoelastic counterpart is discussed in more details in connection with the Sternberg-Koiter paradox.     

Topological robustness of non-saddle sets

We study in this paper preservation of dynamical and shape theoretical properties under continuation for parametrized families of flows. We show that, although attractors continue, the same does not hold for non-saddle sets. However, when they continue, their shape is preserved in quite general settings, which include differentiable families of flows and regular non-saddle sets for general flows, not necessarily differentiable.We also study how the continuation of a non-saddle set influences that of its dual non-saddle set.     

Vector equilibrium flows with nonconvex ordering relations

In this note we introduce the concept of vector network equilibrium flows when the ordering cone is the union of finitely many closed and convex cones. We show that the set of vector network equilibrium flows is equal to the intersection of finitely many sets, where each set is a collection of vector equilibrium flows with respect to a closed and convex cone. Sufficient and necessary conditions for a vector equilibrium flow are presented in terms of scalar equilibrium flows.     

On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane

We consider the Navier‐Stokes equations for viscous incompressible flows in the half‐plane under the no‐slip boundary condition. By using the vorticity formulation we prove the local‐in‐time convergence of the Navier‐Stokes flows to the Euler flows outside a boundary layer and to the Prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary. © 2014 Wiley Periodicals, Inc.