Search results for "Euler"
showing 10 items of 159 documents
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
A new Euler–Mahonian constructive bijection
2011
AbstractUsing generating functions, MacMahon proved in 1916 the remarkable fact that the major index has the same distribution as the inversion number for multiset permutations, and in 1968 Foata gave a constructive bijection proving MacMahon’s result. Since then, many refinements have been derived, consisting of adding new constraints or new statistics.Here we give a new simple constructive bijection between the set of permutations with a given number of inversions and those with a given major index. We introduce a new statistic, mix, related to the Lehmer code, and using our new bijection we show that the bistatistic (mix,INV) is Euler–Mahonian. Finally, we introduce the McMahon code for …
A Vector Approach to Euler's Line of a Triangle
1992
Among the many interesting properties that triangles possess there is one that quickly attracts our curiosity and stays easily in our mind: The centroid, circumcentre and orthocentre all lie in a common line (Euler's Line). An elementary simple proof can be obtained using metric and affine properties of the points involved, [1]. Our aim here is to illustrate a proof using vectors. We identify points in the plane with their position vectors. It is easy to see that the centroid G of the triangle ABC is given by the identity
A new solver for incompressible non-isothermal flows in natural and mixed convection over unstructured grids
2022
Abstract In the present paper we propose a new numerical methodology for the solution of 2D non-isothermal incompressible flows for natural and mixed convection in irregular geometries. The governing equations are the Incompressible Navier-Stokes Equations and the Energy Conservation Equation. Fluid velocity and temperature are coupled in the buoyancy term of the momentum equations according to the Oberbeck–Boussinesq approximation. The governing equations are discretized over unstructured triangular meshes satisfying the Delaunay property. Thanks to the Oberbeck–Boussinesq hypothesis, the flow and energy problems are solved in an uncoupled way, and two fractional time step procedures are s…
ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS
2010
In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.
Un modelo no hidrostático global con coordenada vertical basada en altura
2015
Memoria presentada en la Universitat de València para optar grado de de Doctor Esta tesis documenta la investigación que he realizado en modelización atmosférica: se parte de las ecuaciones físicas de la atmósfera y se aplican métodos numéricos eficientes para encontrar una solución a dichas ecuaciones a partir de unas condiciones iniciales dadas. Para este fin, se ha desarrollado un modelo atmosférico cuyas características principales son: espectral en la representación horizontal de los campos, discretización vertical de alto orden de exactitud, y semi-implícito en la integración temporal. Además, el modelo es no hidrostático y tiene una coordenada vertical basada en altura, en vez de la …
Эмануэль Гринберг - выдающиеся достижения в прикладной математике: радио-фильтры, корпуса танкеров, графы и интегральные схемы Emanuels Grinbergs - i…
2018
The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation of radio filters (1949-1959), hull of tanker calculations (1962-1964), the study of graph theory and the proof of the Grinberg theorem (1968), designing of integrated circuits (1968-1980). Calculations of radio filters are associated with the expansion of the use of continued fractions for the analysis of linear electric circuits (the Kauer model) and the developing of new tools – the Grinberg brackets (as an extension of the Euler brackets)…
CFD simulations of dense sloid-liquid suspensions in baffled stirred tanks: Prediction of suspension curves
2011
Mixing of solid particles into liquids within contactors mechanically agitated by stirrers is a topic of primary importance for several industrial applications. A great research effort has been devoted to the assessment of the minimum impeller speed (Njs) able to guarantee the suspension of all particles. Conversely, only little attention has been paid so far to the evaluation of the amount of solid particles that are suspended at impeller speeds lower than Njs. In some cases the loss in available interfacial area between particles and liquid could be reasonably counterbalanced by a decreased mechanical power, making it of interest to evaluate the percentage of suspended solids at different…
Geometrical analysis of self-compensating suspension systems for railcar engineering
2002
The present analysis addresses several passive tilt systems for railroad cars aiming to compensate for the cart deficiency on curved tracks. To this end, the virtual centre of suspension must be located as close as possible to the longitudinal plane of symmetry of the coach, above the mass centre level for stability reasons. On the one hand, pantograph or Peaucellier's mechanisms may achieve the correct self-compensation. On the other hand, simpler articulated systems yield the desired goal with an excellent approximation. For example, selective algorithms can be applied for designing eight-link mechanisms, to be optimized thereafter by some method of the gradient type, minimizing the mean…
Bending test for capturing the fractional visco-elastic parameters: theoretical and experimental investigation on giant reeds
2014
In this paper attention is devoted on searching a proper model for characterizing the behavior of giant reeds. To aim at this, firstly, meticulous experimental tests have been performed in the Laboratory of structural materials of University of Palermo. Further, the novel aspect of this paper is that of using an advanced Euler-Bernoulli model to fit experimental data of bending tests. Such a model of continuum beam takes into account different constitutive laws of visco-elasticity, being real materials visco-elastic.