Lack of energy equipartition in homogeneous heated binary granular mixtures

 We consider the problem of determining the granular temperatures of the components of a homogeneous binary heated mixture of inelastic hard spheres, in the framework of Enskog kinetic theory. Equations are derived for the temperatures of each species and their ratio, which is different from unity, as may be expected since the system is out of equilibrium. We focus on the particular heating mechanism where the inelastic energy loss is compensated by an injection through a random external force (“stochastic thermostat”). The influence of various parameters and their possible experimental relevance is discussed. Received: 18 February 2002     

Dynamics of a gas bubble rising through a thin immersed layer of granular material: an experimental study

 Packings of non-cohesive grains, immersed in a fluid, differ significantly from classical porous media as the grains, subjected to stresses and flows, can move within the sample, changing then the local properties of the material. We study experimentally the conditions for a gas to pass through a layer of immersed granular material. Above a threshold pressure, which depends mainly on the grains size and on the surface free energy of the liquid-gas interface, the gas creates a channel within the whole thickness of the layer. Received: 23 January 2002     

Monte Carlo simulation of the homogeneous cooling state for a granular mixture

 The Direct Simulation Monte Carlo (DSMC) method is used to numerically solve the Enskog equation for a granular binary mixture in the homogeneous cooling state (HCS). The fourth velocity moments, the temperature ratio, and also the velocity distribution functions are obtained and compared with approximate analytical results derived recently from a Sonine polynomial expansion [V. Garzó and J. W. Dufty, Phys. Rev. E 60, 5706 (1999)]. The comparison shows an excellent agreement between both approaches, even for strong dissipation or disparate values of the mechanical parameters of the mixture. In contrast to previous studies, the partial temperatures of each species are clearly different, so that the total energy is not equally distributed between both species. Finally, in the same way as in the one-component case, the simulation as well as the theory show a high energy tail of the distribution functions. Received: 9 May 2001     

Hydrodynamics of rapid granular flow of inelastic particles into vacuum

The problem of expansion of a dilute granular gas consisting of smooth, inelastic hard spheres into vacuum was investigated by three different methods: both (1) analytical and (2) computational (CFD) treatments of a hydrodynamic model, and (3) by Discrete Element Method (DEM) simulation. Furthermore, the systems were followed for long times, over which the granular kinetic energy decreases by several hundredfold. The hydrodynamic model assumes that the particles are uniformly distributed in space, yet, in the DEM simulations, the particles are free to cluster. Thus the comparison allows us to evaluate the effects of cluster formation on the system. All three methods give quantitatively similar results for the escape momentum, energy evolution, and for the hydrodynamic velocity distribution, even for restitution coefficients as small as e=0.8. The maximum deviation between the escape momentum computed from the hydrodynamic model and from DEM is shown to be no more than 4%. This means that cluster formation exerts only a relatively minor effect on the hydrodynamic quantities, suggesting to us that the hydrodynamic model in combination with the CFD algorithm may provide an efficient tool in other related problems. In addition, it is one of few cases where hydrodynamic theory and DEM agree quantitatively. Received: 17 June 2002     

Piston-driven laminar flow and heat transfer in a plane channel with a sudden expansion

 This paper presents a numerical study of piston-driven heat transfer and fluid flow in a plane channel containing a sudden expansion. The numerical method employed is based on a control-volume-based finite element method for incompressible flow with a staggered and moving grid and SIMPLER algorithm for pressure-velocity coupling. The numerical results show a good agreement with the experimental data reported in the literature. Results concerning time and space evolution of the thermal and flow fields are presented for different values of the expansion ratio, the initial clearance volume, and the piston velocity. Received: 20 April 2002 / Accepted: 23 January 2003     

Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and the blood as a Newtonian fluid, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method. The governing evolution equation is obtained as the dissipative nonlinear Schrödinger equation with variable coefficients. It is shown that this type of equations admit solitary wave solutions with variable wave amplitude and speed. It is observed that, the wave speed increases with distance for tubes of descending radius while it decreases for tubes of ascending radius. The dissipative effects cause a decay in wave amplitude and wave speed.     

Dynamic and scalar turbulent fluctuation in a diffusion flame of an-axisymmetric methane jet into air

 A study of turbulence/combustion interactions in a relatively large turbulent diffusion flame of an axisymmetric methane jet into air is presented. A first order k–ɛ turbulence closure model is used along with two different models (equal scales and non-equal scales) for the submodel describing the scalar dissipation rate. The flamelet concept is used to model the turbulent combustion along with a joint mixture fraction/strain rate probability density function (PDF) for the prediction of the average parameters of the turbulent diffusion flame. The numerical approach is that of Patankar and Spalding, while the flamelet simulations are obtained from the RUN-1DL code of Rogg and co-workers based on a 17 species detailed reaction mechanism. The chosen configuration is that of the experimentally studied turbulent diffusion flame of Streb [1]. A comparison between these experimental results and the obtained numerical ones is thus presented. Relatively good agreements are obtained which show the usefulness of the two-scale model compared to the classical one-scale model for predicting turbulent diffusion flames. Nonetheless some discrepancies are obtained in the outer and downstream regions of the jet, especially in comparison with the experimental data. These are attributed to short coming of the considered turbulence model and soot radiation which is not accounted for. Received: 2 May 2002 / Accepted: 31 January 2003     

Detection and stimulation of impulse electromagnetic radiation (IEMR) of radio-frequency (rf) range (∼200 khz) by sensitive element based on a resonant circuit with HTSC element

 The abnormally high sensitivity to low power impulse electromagnetic radiation (IEMR) systems that include a sensing element consisting of a resonant circuit with secondary coil and high-temperature superconductor (HTSC) core was experimentally investigated. The core was produced using epoxied composites containing HTSC powders [YBa₂Cu₃O_x and Bi(Pb)₂Sr₂Ca₂Cu₃O_x composition]. Received: 22 July 1998 / Reviewed and accepted: 28 August 1998     

A multi-agent system for chemical supply chain simulation and management support

Modern chemical production is customer-driven and the desired delivery time for the products is often shorter than their campaign length. In addition, the raw materials supplying time is often long. These features make it desirable to provide tools to support collaborative supply chain decision making, preferably over the Internet, and where there are conflicts, compromise decisions can be quickly reached and the effects of the decisions can be quantitatively simulated. This paper des cribes such a multi-agent system (MAS) that can be used to simulate the dynamic behaviour and support the management of chemical supply chains over the Internet. Geographically distributed retailers, logistics, warehouses, plants and raw material suppliers are modelled as an open and re-configurable network of co-operative agents, each performing one or more supply chain functions. Communication between agents is made through the common agent communication language KQML (knowledge query message language). A t the simulation layer, the MAS allows distributed simulation of the chain behaviour dynamically, so that compromise decisions can be rapidly and quantitatively evaluated. Because in a chemical supply chain the scheduling of the plant often dominates the chain performance, an optimum scheduling system for batch plants is integrated into the MAS. The functions of the system are illustrated by reference to a case study for the supply and manufacture using a multi-purpose batch plant of paints and coatings.     

Mathematical Model and Experimental Validation of Free Surface Size Segregation for Polydisperse Granular Materials

 A mathematical model of free surface size segregation of granular matter is proposed. The material is assumed to be dry, cohesionless and to consist of several populations with distinct diameter ranges. It is not necessary that one population is predominant. The extent of segregation depends mainly on the relative amount of small and large particles and on the diameter ratios but not on their absolute values. The model predicts how the fractions of these populations change from the position where the material is fed onto a heap to its bottom. It is based on ideas of L. Prigozhin} to treat binary mixtures. Introducing a new scheme to interpolate the local deposition rates from situations with one predominant population it becomes possible to handle mixtures with three and more diameters. The model may be applied to storage systems of any kind, such as bunkers, hoppers, silos or mixing beds, provided the source is sufficiently weak and concentrated. Numerical simulations are discussed for conical and ramp-like geometries and for ternary mixtures. In order to validate the model a few experiments were conducted. As measured by the natural variability of the problem and the simplicity of the model, which is sufficiently easy to be used in an industrial controller, good agreement between theory and experiment is found. Received: 2 August 2001     

Anisotropic bending-torsion coupling for warping in a non-linear beam

 MEMS devices made from single crystal silicon often contain rod-like structures that are operated in bending and/or torsion. The design of these devices usually relies upon simple mechanical theories that ignore the coupling between these two modes of operation. In this paper, we develop a theory that is capable of accounting for the material coupling in the bending and twisting of single crystal beams which arises from anisotropic elastic properties and apply it in selected examples to the case of silicon. The generalized Saint–Venant torsion theory, which is valid for isotropic materials, is extended to arbitrary anisotropic linear elastic materials. The anisotropic material behavior couples the bending and torsion behavior. Thus, for the geometrically linear case, we find two warping functions associated with the bending moments and one warping function which is associated with the torsion moment. These warping patterns or functions are then taken as inputs to a geometrically non-linear formulation. Due to the presence of the additional warping functions, we find the existence of non-standard bi-moment and bi-shears which play an important role under certain conditions of extreme deformations. The final complexity of the non-linear formulation dictates the usage of a numerical solution procedure for practical computations. Here we employ a finite element scheme to solve the governing equations. Example computations elucidate the importance of the coupling effects by examining beams cut from (1 0 0) type silicon wafers. RID="⋆" ⋆ Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and co-operation as a colleague and friend over many years. S.Klinkel gratefully acknowledges the financial support of the Deutsche Forschungsgemeinschaft (DFG) for a research fellowship at the University of California at Berkeley.     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

Solitary wave trains in granular chains: experiments,theory and simulations

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.     

Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure

 Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H ₂ controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural and control design variables equally within the same framework, a nested solving approach is adopted in which the controller syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes, while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples show that the approach used in this paper can produce systems with clear structural topology and high control performance. Received 16 November 2001 / Accepted 26 February 2002     

Multi-objective optimization of tire carcass contours using a systematic aspiration-level adjustment procedure

 While forming a basic tire configuration and supporting most static and dynamic loads of automobiles, tire carcass influences major tire performances according to its contour. Among significant tire performances, we in this study intend to improve the automobile maneuverability and the tire durability by optimizing the sidewall carcass contour. In order to effectively maximize these multi-objectives, we refine the conventional satisficing trade-off methods (STOM) which were proposed originally for the multi-objective structural optimization, by introducing a systematic aspiration-level adjustment procedure. According to the systematic procedure, we perform the sidewall contour optimization that ideally distributes the sidewall carcass tension and minimizes strain-energy density at the belt edge. Since the tire analysis is highly nonlinear problem we employ an incremental analysis scheme, together with the finite-difference sensitivity scheme. Through the numerical experiment, we confirmed that the refined multi-objective optimization technique systematically leads to a final optimum sidewall contour, together with the stable and rapid convergence. Received: 20 August 2001 / Accepted: 29 July 2002 This work was supported by Kumho Industries Co., Ltd in Korea and by the Ministry of Science and Technology under the NRL program (M10203000017-02J0000-00910).     

Electrophoretic motion of two solid particles embedded in an unbounded and viscous electrolyte

 This work determines the electrophoretic motion of two colloidal particles embedded in a viscous and unbounded electrolyte. Contrary to other works in the field, the advocated method does not calculate the perturbation electric potential and the electrolyte Stokes flow in the whole fluid domain and its range of applications is not restricted to the case of uniformly charged particles embedded in a uniform electric field E _∞. The idea consists in establishing and solving thirteen Fredholm boundary integral equations (one of the second kind plus twelve of the first kind). The numerical implementation is briefly reported. Numerical benchmarks and new results are both presented and discussed with a special attention to the interactions between the particles. Received 26 February 2001     

Swept and curved wings: a numerical approach based on generalized lifting-line theory

 Whenever the lifting-line is used for curved and swept wings with high aspect ratios, available software shows weaknesses. Actually, when considering sweep and curvature, most of these programs use the normal component of the incident flow in an empirical extension of Prandtl's model, which is theoretically founded only in the case of straight unswept wings. Recent theory based on the matched asymptotic expansions technique shows that, in addition to this 2D-type correction, extra terms have to be considered in order to express the three-dimensional induced velocity, when computing the spanwise variation of the circulation. These terms require finite parts in Hadamard's sense integrals computation. On these theoretical foundations, the computational approach presented in this paper improves on the empirical approach for swept, curved lifting-lines, including all the necessary corrections. The validity of the approach is examined in a simple application compared with available analytical and numerical results. Considering these results, it can be said that the model described here offers real improvements over the usual empirical numerical computations for arbitrarily shaped lifting-lines. Received: 26 February 2001 / Accepted: 14 June 2002     

On the method of finite spheres in applications: towards the use with ADINA and in a surgical simulator

 In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present the development of a preprocessor for the generation of nodal points on two-dimensional computational domains. Then, the development of a specialized version of the method of finite spheres using point collocation and moving least squares approximation functions and singular weight functions is reported for rapid computations in virtual environments involving multi-sensory (visual and touch) interactions. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.