Direct discretizations of bi-variate population balance systems with finite difference schemes of different order

The accurate and efficient simulation of bi-variate population balance systems is nowadays a great challenge since the domain spanned by the external and internal coordinates is five-dimensional. This report considers direct discretizations of this equation in tensor-product domains. In this situation, finite difference methods can be applied. The studied model includes the transport of dissolved potassium dihydrogen phosphate (KDP) and of energy (temperature) in a laminar flow field as well as the nucleation and growth of KDP particles. Two discretizations of the coupled model will be considered which differ only in the discretization of the population balance equation: a first order monotone upwind scheme and a third order essentially non-oscillatory (ENO) scheme. The Dirac term on the right-hand side of this equation is discretized with a finite volume method. The numerical results show that much different results are obtained even in the class of direct discretizations

Hyperplane Neural Codes and the Polar Complex

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a stable hyperplane code is shellable and show that most currently known properties of the hyperplane codes follow from the shellability of the appropriate polar complex.Comment: 23 pages, 5 figures. To appear in Proceedings of the Abel Symposiu

Finite element LES and VMS methods on tetrahedral meshes

AbstractFinite element methods for problems given in complex domains are often based on tetrahedral meshes. This paper demonstrates that the so-called rational Large Eddy Simulation model and a projection-based Variational Multiscale method can be extended in a straightforward way to tetrahedral meshes. Numerical studies are performed with an inf–sup stable second order pair of finite elements with discontinuous pressure approximation

A numerical method for the simulation of an aggregation-driven population balance system

A population balance system which models the synthesis of urea is studied in this paper. The equations for the flow field, the mass and the energy balances are given in a three-dimensional domain and the equation for the particle size distribution (PSD) in a four-dimensional domain. This problem is convection-dominated and aggregation-driven. Both features require the application of appropriate numerical methods. This paper presents a numerical approach for simulating the population balance system which is based on finite element schemes, a finite difference method and a modern method to evaluate convolution integrals that appear in the aggregation term. Two experiments are considered and the numerical results are compared with experimental data. Unknown parameters in the aggregation kernel have to be calibrated. For appropriately chosen parameters, good agreements are achieved of the experimental data and the numerical results computed with the proposed method. A detailed study of the computational results reveals the influence of different parts of the aggregation kernel

A numerical method for the simulation of an aggregation-driven population balance system

A population balance system which models the synthesis of urea is studied in this paper. The equations for the flow field, the mass and the energy balances are given in a three-dimensional domain and the equation for the particle size distribution (PSD) in a four-dimensional domain. This problem is convection-dominated and aggregation-driven. Both features require the application of appropriate numerical methods. This paper presents a numerical approach for simulating the population balance system which is based on finite element schemes, a finite difference method and a modern method to evaluate convolution integrals that appear in the aggregation term. Two experiments are considered and the numerical results are compared with experimental data. Unknown parameters in the aggregation kernel have to be calibrated. For appropriately chosen parameters, good agreements are achieved of the experimental data and the numerical results computed with the proposed method. A detailed study of the computational results reveals the influence of different parts of the aggregation kernel

2012-2013 Master of Music Recital - Carina Mayumi Inoue (Collaborative Piano)

El curso proporciona fundamentos de la ingeniería industrial y su actuación en la empresa. Desarrolla los conceptos básicos de las variables externas que afectan las estrategias de negocios de la empresa las características de una empresa competitiva y las funciones que requiere para el logro de sus objetivos.El curso desarrolla la visión futura del ingeniero industrial y su rol en la empresa

Tarapacol 15-Acetate, a New Diterpenoid from Grindelia tarapacana Phil.

In the title compound, 15-acetoxy-14(S)-hydroxy-13-epi-manoyl oxide {IUPAC systematic name: 2-(dodecahydro-3,4a,7,7,10a-pentamethyl-1H-naphtho[2,1-b]pyran-3-yl)-2-hydroxyethyl acetate}, C22H38N4, rings A and B have chair conformations. Ring C adopts a boat conformation with the 16-methyl group in an axial position and the bulky glycol monoacetate group in an equatorial position. Ring systems A/B and B/C (conventional IUPAC labdane diterpenoid nomenclature) are trans fused about the C(5)-C(10) and C(8)-C(9) bonds, respectively. The present study establishes the relative stereochemistry at the C(14) position.This work was supported by a grant to the American Association for the Advancement of Science from the John D. and Catherine T. MacArthur Foundation, awarded to BNT. The structure was determined in the Molecular Structure Laboratory of the Department of Chemistry as a special class project in Chemistry 517