A 3D non-linear k–ε turbulent model for prediction of flow and mass transport in channel with vegetation

The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.     

Computational study of decaying annular vortex flow using the Rε/k − ε turbulence model

In this article, we present three dimensional CFD study of turbulent vortex flow in an annular passage using OpenFOAM 1.6. The vortex flow is generated by introducing the flow through a tangential entry to the passage. For the analysis presented in this article, turbulence was modeled using the R_ε/k − ε model, in addition, a comparison between such model with the standard k − ε model was conducted and discussed. The main characteristics of the flow such as vortex structure and recirculation zone were investigated. It was found that flow is subjected to Rankine vortex structure with three forced vortex regimes and a free vortex region near to the outer wall. The phenomenon of vortex decay was investigated by depicting the swirl number trend along the axial direction of the flow domain. It was found that the vortex decay is subjected to an exponential decay behavior. New coefficients for the exponential decay correlation were derived based on local values of velocity components in different radial planes.     

Development of boundary transfer method in simulation of gas–solid turbulent flow of a riser

Computational fluid dynamics (CFD) is used to simulate the behavior of two phase gas solid in a fluid catalytic cracking (FCC) riser. Gas and particle phases are considered as separate fully interpenetrating continuous media within each control volume. Each phase described in terms of its own separate mass and momentum conservation equations. Simple k–epsilon (k_g–?_g) turbulence model is used for the gas phase and the solid phase is handled with the kinetic theory of granular flows. Source terms are used to account for the influence of hydrodynamic drag on the production, dissipation and exchange of turbulent kinetic energy between the phases. For the particles partial slip condition is considered at the wall.     

Boundary ε-regularity in optimal transportation

We develop an ε  -regularity theory at the boundary for a general class of Monge–Ampère type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between Hölder densities supported on C²$C^2$ uniformly convex domains are C^1,α$C^{1,\alpha }$ up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost −x⋅y$-x\cdot y$.     

Duality in ε-variational inequality problems

In this paper a general analysis of duality for an extended ε-variational inequality problem based on the notions of ε-convexity and ε-conjugacy is performed. Optimal solutions of both the primal and dual problems are also related to the saddle point of an associated Lagrangian. Gap functions for these problems are proposed. An existence theorem for the extended ε-variational inequality is also established by means of the KKM lemma.     

Semiconductor final test scheduling with Sarsa(λ, k) algorithm

Semiconductor test scheduling problem is a variation of reentrant unrelated parallel machine problems considering multiple resource constraints, intricate {product, tester, kit, enabler assembly} eligibility constraints, sequence-dependant setup times, etc. A multi-step reinforcement learning (RL) algorithm called Sarsa(λ, k) is proposed and applied to deal with the scheduling problem with throughput related objective. Allowing enabler reconfiguration, the production capacity of the test facility is expanded and scheduling optimization is performed at the bottom level. Two forms of Sarsa(λ, k), i.e. forward view Sarsa(λ, k) and backward view Sarsa(λ, k), are constructed and proved equivalent in off-line updating. The upper bound of the error of the action-value function in tabular Sarsa(λ, k) is provided when solving deterministic problems. In order to apply Sarsa(λ, k), the scheduling problem is transformed into an RL problem by representing states, constructing actions, the reward function and the function approximator. Sarsa(λ, k) achieves smaller mean scheduling objective value than the Industrial Method (IM) by 68.59% and 76.89%, respectively for real industrial problems and randomly generated test problems. Computational experiments show that Sarsa(λ, k) outperforms IM and any individual action constructed with the heuristics derived from the existing heuristics or scheduling rules.     

η-series and a Boolean Bercovici-Pata bijection for bounded k-tuples

Let Dc(k) be the space of (non-commutative) distributions of k-tuples of selfadjoint elements in a C^∗-probability space. On Dc(k) one has an operation ? of free additive convolution, and one can consider the subspace of distributions which are infinitely divisible with respect to this operation. The linearizing transform for ? is the R-transform (one has Rμ?ν=Rμ+Rν, ∀μ,ν∈Dc(k)). We prove that the set of R-transforms can also be described as {ημ|μ∈Dc(k)}, where for μ∈Dc(k) we denote ημ=Mμ/(1+Mμ), with Mμ the moment series of μ. (The series ημ is the counterpart of Rμ in the theory of Boolean convolution.) As a consequence, one can define a bijection via the formula

(I)     

Direct numerical simulation of laminar–turbulent flow over a flat plate at hypersonic flow speeds

A method for direct numerical simulation of a laminar–turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier–Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton–Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of M = 5.37. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar–turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer.     

Stability of Banach spaces via nonlinear ε-isometries

In this paper, we prove that the existence of an ε-isometry from a separable Banach space X into Y (the James space or a reflexive space) implies the existence of a linear isometry from X into Y. Then we present a set valued mapping version lemma on non-surjective ε-isometries of Banach spaces. Using the above results, we also discuss the rotundity and smoothness of Banach spaces under the perturbation by ε-isometries.     

Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems

As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a posteriori methods convey much more information to the decision maker. Especially, the a posteriori (or generation) methods give the whole picture (i.e. the Pareto set) to the decision maker, before his/her final choice, reinforcing thus, his/her confidence to the final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The present work is an effort to effectively implement the ε-constraint method for producing the Pareto optimal solutions in a MOMP. We propose a novel version of the method (augmented ε-constraint method - AUGMECON) that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations. The method AUGMECON has been implemented in GAMS, a widely used modelling language, and has already been used in some applications. Finally, an interactive approach that is based on AUGMECON and eventually results in the most preferred Pareto optimal solution is also proposed in the paper.     

Homogenization of a conductive suspension in a Stokes–Boussinesq flow

Radiant spherical suspensions have an ε-periodic distribution in a tridimensional incompressible viscous fluid governed by the Stokes–Boussinesq system. We perform the homogenization procedure when the radius of the solid spheres is of order ε³ (the critical size of perforations for the Navier-Stokes system) and when the ratio of the fluid/solid conductivities is of order ε⁶, the order of the total volume of suspensions. Adapting the methods used in the study of small inclusions, we prove that the macroscopic behavior is described by a Brinkman–Boussinesq type law and two coupled heat equations, where certain capacities of the suspensions and of the radiant sources appear.     

π and the hypergeometric functions of complex argument

Text

In this article we derive some new identities concerning π, algebraic radicals and some special occurrences of the Gauss hypergeometric function ₂F₁ in the analytic continuation. All of them have been derived by tackling some elliptic or hyperelliptic known integral, and looking for another representation of it by means of hypergeometric functions like those of Gauss, Appell or Lauricella. In any case we have focused on integrand functions having at least one couple of complex-conjugate roots. Founding upon a special hyperelliptic reduction formula due to Hermite (1876) [6], π is obtained as a ratio of a complete elliptic integral and the four-variable Lauricella function. Furthermore, starting with a certain binomial integral, we succeed in providing as a ratio of a linear combination of complete elliptic integrals of the first and second kinds to the Appell hypergeometric function of two complex-conjugate arguments. Each of the formulae we found theoretically has been satisfactorily tested by means of Mathematica^®.

Video

For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=rQqtVtAf-RQ.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

On a σ-ideal of compact sets

We recall from [T. Mátrai, Kenilworth, Proc. Amer. Math. Soc. 137 (3) (2009) 1115-1125] a Gδσ-ideal of compact subsets of ω² and prove that it is not Tukey reducible to the ideal . This result answers a question of S. Solecki and S. Todor?evi? in the negative.     

The γ-vector of a barycentric subdivision

We prove that the γ-vector of the barycentric subdivision of a simplicial sphere is the f-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the h-vector of the barycentric subdivision of a boolean complex.     

On the nonexistence of a relation between σ-left-porosity and σ-right-porosity

Given an arbitrarily weak notion of left-〈f〉$〈f〉$-porosity and an arbitrarily strong notion of right-〈g〉$〈g〉$-porosity, we construct an example of closed subset of R$\mathbb{R}$ which is not σ  -left-〈f〉$〈f〉$-porous and is right-〈g〉$〈g〉$-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity.     

Direct numerical simulation of the laminar–turbulent transition at hypersonic flow speeds on a supercomputer

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar–turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier–Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton–Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar–turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar–turbulent transition.     

On homotopy rigidity of the functor ΣΩ on co-H-spaces

In this paper we study the homotopy rigidity property of the functors ΣΩ and Ω. Our main result is that both functors are homotopy rigid on simply-connected p-local finite co-H-spaces. The result is obtain by a subtle interplay of homotopy decomposition techniques, modular representation theory and the counting principle.     

The ω-limit set of a graph map

Let G be a graph and be continuous. Denote by P(f), , ω(f) and Ω(f) the set of periodic points, the closure of the set of periodic points, ω-limit set and non-wandering set of f, respectively. In this paper we show that: (1) v∈ω(f) if and only if v∈P(f) or there exists an open arc L=(v,w) contained in some edge of G such that every open arc U=(v,c)⊂L contains at least 2 points of some trajectory; (2) v∈ω(f) if and only if every open neighborhood of v contains at least r+1 points of some trajectory, where r is the valence of v; (3) ; (4) if , then x has an infinite orbit.