arXiv subjects
Publications and source records attributed to Gianluca Argentini.
About global and local algebraic integrability of ovals. A contribution to clarify Newton results and relative comments on his work done by Arnol'd and Pourciau. A possibile application to air damper sections computation is offered, as example of unexpected link between pure mathematics and industrial technology.
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.
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.
In this work a result of existence and uniqueness for a plane cavity driven steady flow is deduced using an analytical method for the resolution of a linear partial differential problem on a triangular domain. The solution admits a symbolic expression based on integration over the domain. Some examples of flow are computed and graphed. In particular, it is shown a realistic example of a shear-forced flow with two eddies, usually computed only by numerical methods. The mathematical techniques used for the demonstration of the main result are elementary.
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.
Where a 2D problem of optimal profile in variable speed flow is resolved in a class of convex Bezier curves, using symbolic and numerical computations.
In this work a simple problem on 2D optimal shape for body immersed in a viscous flow is analyzed. The body has geometrical constraints and its profile would be found in the class of cubics which satisfy those conditions. The optimal profile depends on the leading coefficient of these cubics and its relation with the Reynolds number of the system is found. The solution to the problem uses a method based on a suitable transformation rule for the cartesian reference.
The paper describes a mathematical model on the physical principles of the Pitot device for acquiring flows speed. The relation between speed and static pressures is derived from simple integration of the fluid dynamics equations for an inviscid flow. In this way, the treatment is general and is not based on the Bernoulli theorem on energy conservation, as usually done in scientific and technical literature. The application to Formula 1 cars is discussed.
A nonlinear differential equation about optimal shapes for blades of a fan. A boundary value differential problem from engineering, geometrical or physical bonds. A relation between linear profiles and constant speed along the side under flow.
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.
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.
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.
An elementary analytical fluid flow is composed by a geometric domain, a list of analytical constraints and by the function which depends on the physical properties, as Reynolds number, of the considered fluid. For this object, notions of laminar or weakly turbulent behavior are described using a simple mathematical model.
Treating a boundary value problem in analytical fluid dynamics, translation of 2D steady Navier-Stokes equations to ordinary differential form leads to a second order equation of Riccati type. In the case of a compressible fluid with constant kinematic viscosity along streamlines, it is possible to find an exact solution of the differential problem by rational combination of Airy's functions and their derivatives.
In this paper we present a mathematical model for estimate the collapse time of a gas bubble in a vane of a oil gerotor pump. This amount of time cannot be greater of the total time spent by the pump for filling and then emptying out a vane in a single revolution, otherwise there is a loss of lubrication between internal and external gears. We assume that oil is incompressible and viscous, the bubble has a spherical shape and it is not translating into the external fluid. The analytical treatment of the model shows that the Navier-Stokes equations for the velocity field of the oil can be reduced to a single non linear ordinary differential equation for the variation in time of the bubble radius. The collapse time estimated by a numerical resolution of this equation and the collapse time calculated from an analytical resolution of the linearized equation are substantially equal.
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.
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite differences, or particular techniques, such as finite elements. Also, the method doesn't require the use of matrices, as in resolution of linear algebraic systems, nor the use of like-Newton algorithms, as in resolution of non linear sets of equations. An initial equation is resolved only once, then the method is based on iterated evaluations of appropriate polynomials.
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.