Searching the (really) real general solution of 2D Laplace differential equation

This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific literature and, if present, often it is justified with the assertion that an arbitrary analytic complex function is a solution of Laplace equation, so introducing the condition of complex-differentiability which is not really necessary for the existence of a real solution. The question of the knowledge of real exact solutions to Laplace equation is of great importance in science and engineering.Comment: None new, but re-vie

Modeling and ecodesigning crossflow ventilation fans with Mathematica

The efficiency of a simple model of crossflow fan is maximized when the geometry depends on a design parameter. The flow field is numerically computed using a Galerkin method for solving a Poisson partial differential equation.Comment: 7 pages, 6 figure

Fast computing of velocity field for flows in industrial burners and pumps

In this work we present a technique of fast numerical computation for solutions of Navier-Stokes equations in the case of flows of industrial interest. At first the partial differential equations are translated into a set of nonlinear ordinary differential equations using the geometrical shape of the domain where the flow is developing, then these ODEs are numerically resolved using a set of computations distributed among the available processors. We present some results from simulations on a parallel hardware architecture using native multithreads software and simulating a shared-memory or a distributed-memory environment.Comment: 14 pages, 5 figures; paper accepted for Special Issue "Application of distributed and grid computing", Future Generation Computer Systems journal, 200

Costruction of classic exact solutions for Tricomi equation

A formula to construct classic exact solutions to Tricomi partial differential equation. The steps to obtain this formula require only elementary resolution of a simple system of first order PDEs

On local symbolic approximation and resolution of ODEs using Implicit Function Theorem

In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a fluid, are developed. These examples seem to show that local approximation of non linear differential equations can give useful informations about symbolic form of possible solutions, and in the case a global solution is known, locally the accuracy of approximation can be good.Comment: 12 pages, 2 figures; keywords: ordinary differential equations, implicit function theorem, local solutions, symbolic solutions, cavitatio

Poster on MPI application in Computational Fluid Dynamics

Poster-presentation of the paper "Message Passing Fluids: molecules as processes in parallel computational fluids" held at "EURO PVMMPI 2003" Congress; the paper is on the proceedings "Recent Advances in Parallel Virtual Machine and Message Passing Interface", 10th European PVM/MPI User's Group Meeting, LNCS 2840, Springer-Verlag, Dongarra-Laforenza-Orlando editors, pp. 550-554.Comment: 1 page, PDF version of a poster-session presentation during "EuroPVM/MPI 2003", Sep. 29 - Oct. 2, Venice (Italy), please visit http://www.dsi.unive.it/pvmmpi0

Adaptive grids as parametrized scale-free networks

In this paper we present a possible model of adaptive grids for numerical resolution of differential problems, using physical or geometrical properties, as viscosity or velocity gradient of a moving fluid. The relation between the values of grid step and these entities is based on the mathematical scheme offered by the model of scale-free networks, due to Barabasi, so that the step can be connected to the other variables by a constitutive relation. Some examples and an application are discussed, showing that this approach can be further developed for treatment of more complex situations.Comment: 10 pages, 3 figure

Computational Aspects of a Numerical Model for Combustion Flow

A computational method for numeric resolution of a PDEs system, based on a Finite Differences schema integrated by interpolations of partial results, and an estimate of the error of its solution respect to the normal FD solution.Comment: 9 pages, 4 figures; Talk at Workshop 2004 on Science and Applications of Advanced Computing Paradigms, Centre of Excellence MIUR (prof. Gianfranco Bilardi), Universita' di Padova, Department of Information Engineering, October 28-29, 200

An expansion based on Reynolds number powers for the velocity field of elementary analytical flows

The paper describes a possible physical characterization for the definition of elementary fluid flow. As consequence, an analytical expansion based on Reynolds number powers for the velocity field is shown in the weakly turbulent case.Comment: 6 pages, 3 figure

A matrix generalization of Euler identity e^(ix) = cosx + i sinx

In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix.Comment: 5 pages, research work done at R&D Dept. of Company Institutio