Representation of classifier distributions in terms of hypergeometric functions

This paper derives alternative analytical expressions for classifier product distributions in terms of Gauss hypergeometric function, 2F1, by considering feed distribution defined in terms of Gates-Gaudin-Schumann function and efficiency curve defined in terms of a logistic function. It is shown that classifier distributions under dispersed conditions of classification pivot at a common size and the distributions are difference similar. The paper also addresses an inverse problem of classifier distributions wherein the feed distribution and efficiency curve are identified from the measured product distributions without needing to know the solid flow split of particles to any of the product streams.     

Gas–Dynamic Structures in Supersonic Combustion of Hydrogen in a System of Plane Jets in a Supersonic Flow

Results of numerical and theoretical studies of supersonic diffusive combustion of a system of plane hydrogen jets in a supersonic air flow are described. It is shown that large–scale vortex structures appear in the mixing zone of the system of hydrogen jets and the cocurrent flow. These vortex structures affect the mechanism of turbulent exchange between the fuel and the oxidizer.     

Unified Theory of Variation Principles in Non-linear Theory of Elasticity

The purpose of this paper is to introduce and to discuss several main variation principles in non-linear theory of elasticity——namely the classic potential energy principle,complementary energyprinciple,and other two complementary energy principles(Levinson principle and Fraeijs de Veu-beke principle)which are widely discussed in recent literatures.At the same time,the generalizedvariational principles are given also for all these principles.In this paper,systematic derivation andrigorous proof are given to these variational principles on the unified bases of principle of virtualwork,and the intrinsic relations between these principles are also indicated.It is shown that,theseprinciples have unified bases,and their differences are solely due to the adoption of different varia-bles and Legendre tarnsformation.Thus,various variational principles constitute an organized totalityin an unified frame.For those variational principles not discussed in this paper,the same frame canalso be used,a diagram is giv     

Numerical modeling of gas-phase kinetics in formation of secondary aerosol

Three basic modules of gas-phase photochemical reactions involved in the formation of secondary aerosol are developed for modeling the concentration variation of precursors of aerosol, including ketone （RCOx）, aldehyde （ALD）, peroxyacetylnitrate （PAN）, NO2, and SO2, followed by numerical solution for each of the modules. Reasonable trends of concentration variation of the precursors can be obtained from the proposed modules.     

Large-scale distribution of elements in Chinese aerosol

In spite of increasing attention on Chinese aerosol, there has never been a country-wide survey of its general characteristics. This paper presents elemental data for aerosol at 23 sites in and around China, mostly drawn from the literature, and shows some of the large-scale patterns. Al, Na, and Se are used to represent the crustal, marine, and pollution components, respectively. Most of the patterns are aligned in SW-NE. Al and Na are highest to the NW and the SE, respectively, and their ratio changes rapidly near the coast. Se has a broad maximum over Central China, and the Se/Al ratio （an indicator of pollution vs. crustal aerosol） increases progressively from the NW to the SE. A simple index for simulating pollution aerosol, which uses population density, annual precipitation, and mean wind speed, adequately reproduces the large-scale pattern of pollution aerosol and shows how crustal Al in the NW gradually gives way to flyash Al toward the SE.     

Adjoint problems of mechanics of continuous media in gas‐laser cutting of metals

A mathematical model of gaslaser cutting of metal plates in an inert gas is proposed. The formation and flow of the liquid metal melt film at the cutting front is considered within the framework of incompressible boundarylayer equations. Based on the resultant analytical solution, a local law of energy conservation on the cutting surface is derived, which takes into account the meltfilm thickness and the temperature dependence of thermophysical parameters of the metal. The problem of the cutting shape and depth is solved in the twodimensional formulation. A comparison with experimental data is made in terms of the cutting depth and maximum cutting velocity for carbon and alloy steel.     

The role of texture in tension–compression asymmetry in polycrystalline NiTi

The purpose of the present study is to thoroughly understand the stress–strain behavior of polycrystalline NiTi deformed under tension versus compression. To do this, a micro-mechanical model is used which incorporates single crystal constitutive relationships and experimentally measured polycrystalline texture into the self-consistent formulation. For the first time it is quantitatively demonstrated that texture measurements coupled with a micro-mechanical model can accurately predict tension/compression asymmetry in NiTi shape memory alloys. The predicted critical transformation stress levels and transformation stress–strain slopes under both tensile and compressive loading are consistent with experimental results. For textured polycrystalline NiTi deformed under tension it is demonstrated that the martensite evolution is very abrupt, consistent with the Luders type deformation experimentally observed. The abrupt transformation under tension is attributed to the fact that the majority of the grains are oriented along the [111] crystallographic direction, which is soft under tensile loading. Since single crystals of the [111] orientation are hard under compression it is also demonstrated that under compression the martensite in textured polycrystalline NiTi evolves relatively slower.     

On appearance of “cold” layer in explosive consolidation of powders

Abstract. Numerical modeling of explosive consolidation of powders under two-dimensional conditions has been performed. Various regimes of flow depending on detonation velocity have been considered. The appearance of “cold” layer during explosive consolidation of powders has been studied by calculations. Received 12 July 1999 / Accepted 27 April 2000     

Regularity Criteria of Weak Solutions in terms of the Pressure in Lorentz Spaces to the Navier–Stokes Equations

We consider the incompressible Navier–Stokes equations in Ω ×?(0, T), where Ω is a domain in ${\mathbb{R}^3}$ . We give regularity criteria in terms of the pressure in Lorentz spaces with the corresponding small norm. In particular, our results extend previous ones to the Lorentz space with respect to temporal variable.     

Extended thermodynamics – consistent in order of magnitude

It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a “one-dimensional gas” is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized – or parabolized – in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density. Received April 15, 2002 / Published online November 6, 2002 RID="*" ID="*"Communicated by Kolumban Hutter, Darmstadt     

Dynamics of fine particles in liquid-solid fluidized beds

On the basis of the Local Equilibrium Model （LEM）, fine particles with large Richardson-Zaki exponent n show, under certain conditions during bed expansion and collapse, different dynamic behavior from particles with small n. For an expansion process there may be a concentration discontinuity propagating upward from the distributor, and, on the contrary, for a collapse process there may be a progressively broadening and upward-propagating continuous transition zone instead of discontinuity. The predictions of the bed height variation and the discontinuity trace have been validated experimentally.     

Singularities of Electromagnetic Fields¶in Polyhedral Domains

In this paper, we investigate the singular solutions of time-harmonic Maxwell equations in a domain which has edges and polyhedral corners. It is now well known that in the presence of non-convex edges, the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the Laplace operator [4,-5]. We show how this type of result can be derived from the classical Mellin analysis, and how this analysis leads to sharper results concerning the singular parts which belong to H¹. For the singular functions, we exhibit simple and explicit formulas based on (generalized) Dirichlet and Neumann singularities for the Laplace operator. These formulas are more explicit than the results announced in our note [10].     

Theoretical Formulation of Finite-Element Methods in Linear-Elastic Analysis of General Shells∗

A systematic classification of the variational functional whose stationarity conditions (Euler equations) can be used alternately to solve for the various unknowns in a boundary-value problem in linear-shell theory is made. The application of these alternate variational principles to a finite-element assembly of a shell and thus, the development of the properties of an individual discrete element are studied in detail. A classification of the finite-element methods, formulated from the variational principles by systematically relaxing the continuity requirements at the interelement boundaries of adjoining discrete elements is made.     

Heterogeneous nucleation in CFD simulation of flashing flows in converging–diverging nozzles

Flashing flow is an important phenomenon in many industrial contexts; however simulation of these flows remains difficult. CFD simulations are able to describe the distribution and evolution of 3D structures in the flow but are dependent on good closure relations for interphase transfer. Nucleation during flashing flow is often neglected in CFD simulation where a minimum starting vapour fraction and a constant bubble number density are given. Models that include nucleation have used wall nucleation terms from 1D system code models, averaged over the domain. In this work, three models for wall nucleation are tested and compared with experimental data from a converging–diverging nozzle. Nucleation is applied at the walls of the domain, and various models are investigated. Good agreement with the critical flow rate and axial profiles are found, but agreement with the radial void fraction data is not satisfactory. Methods of addressing this are explored, and it is found that including a small bulk heterogeneous nucleation term gives the best agreement with the radial profiles, with negligible impact on the axial average properties.     

Optimization of regularization parameter of inversion in particle sizing using light extinction method

In particle sizing by light extinction method, the regularization parameter plays an important role in applying regularization to find the solution to ill-posed inverse problems. We combine the generalized cross-validation （GCV） and L-curve criteria with the Twomey-NNLS algorithm in parameter optimization. Numerical simulation and experimental validation show that the resistance of the newly developed algorithms to measurement errors can be improved leading to stable inversion results for unimodal particle size distribution.     

A Physical Model of the Structure and Attenuation of Shock Waves in Metals

In this paper,a physical model of the structure and attenuation of shockwaves in metals is presented.In order to establish the constitutive equa-tions of materials under high velocity deformation and to study the struc-ture of transition zone of shock wave.two independent approaches are in-volved.Firstly,the specific internal energy is decomposed into the elasticcompression energy and elastic deformation energy,and the later is represent-ed by an expansion to third-order terms in elastic strain and entropy.includ-ing the coupling effect of heat and mechanical energy.Secondly,a plasticrelaxation function describing the behaviour of plastic flow under high tem-perature and high pressure is suggested from the viewpoint of dislocationdynamics.In addition.a group of ordinary differential equations has beenbuilt to determine the thermo-mechanical state variables in the transitionzone of a steady shock wave and the thickness of the high pressure shockwave.and an analytical solution of the equations can be foun     

Andronov–Hopf bifurcations in wave models of torsional vibrations of drill strings

A wave model of torsional vibrations of rotating drill strings is set up. The ranges of rotational speed in which self-excited vibrations occur are found. Andronov–Hopf bifurcations occur at the limits of these ranges. The conditions for the occurrence and development of self-excited oscillatory processes are established