584 research outputs found
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
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