Global Existence of Large BV Solutions in a Model of Granular Flow

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20 Hadeler , K. P. , Kuttler , C. ( 1999 ). Dynamical models for granular matter . Granular Matter 2 : 9 – 18 . [Google Scholar]], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hyperbolic system of balance laws, which we study in the one-dimensional case. The system is linearly degenerate along two straight lines in the phase plane, and therefore is weakly linearly degenerate at the point of the intersection. The source term is quadratic, consisting of product of two quantities, which are transported with strictly different speeds. Assuming that the initial height of the moving layer is sufficiently small, we prove the global existence of entropy-weak solutions to the Cauchy problem, for a class of initial data with bounded but possibly large total variation.     

A simulated annealing algorithm for transient optimization in gas networks

In this paper we present a simulated annealing approach for the gas network optimization problem. A gas network consists of a set of pipes to transport the gas from the sources to the sinks whereby gas pressure gets lost due to friction. Further on there are compressors, which increase gas pressure, and valves. The aim is to minimize fuel gas consumption of the compressors whereas demands of consumers have to be satisfied. The problem of transient (time-dependent) optimization of gas networks results in a highly complex mixed integer nonlinear program. We relax the equations describing the gas dynamic in pipes by adding these constraints combined with appropriate penalty factors to the objective function. A suitable neighborhood structure is developed for the relaxed problem where time steps as well as pressure and flow of the gas are decoupled. Our approach convinces with flexibility and very good computational results.     

Enzymatic alcoholysis of palm and palm kernel oils

The use of lipases as biocatalysts in ester synthesis has been the object of growing interest, owing to the importance of esters as emulsifiers, intermediates to produce oleochemicals, and fuel alternatives. We consider in this report the application of lipases in the ethanolysis of palm and palm kernel oils to produce fatty-acid esters, using n-hexane assolvent. In order to maximize ester production, wea dopted a Taguchi design and built an empirical model. Using this procedure, we determined the optimal condition for each system and established the influence of process variables in the conversion.     

A Serious Look at Changeable Silly Putty

Changeable Silly Putty is a thermochromic material. It changes color due to a change in temperature. This paper describes advanced experiments designed to find the mechanism of the color change, provides a discussion of proposed mechanisms, and describes three experiments using Changeable Silly Putty that are suitable for young children.     

Global BV Entropy Solutions and Uniqueness for Hyperbolic Systems of Balance Laws

We consider the Cauchy problem for n×n strictly hyperbolic systems of nonresonant balance laws each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that and are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, we give a characterization of the resulting semigroup trajectories in terms of integral estimates.