arXiv subjects

Eduardo Piña

Publications and source records attributed to Eduardo Piña.

3 recordsLinked to original sources

arXiv2011

Geometry of the Vapor Liquid Coexistence in the Gibbs Space

The phase coexistence is illuminated with geometric views of the thermodynamic variables, according to Gibbs' choices. Quantities and relations between them are obtained. The existence of the edge of regression with tangents coincident with the straight lines connecting the coexistence points of phase equilibrium is stressed. A geometric approach to the critical point leads to estimation of the values of the critical exponents for the angles formed by the coexistence curve and the straight lines with the principal direction along the minimal curvature.

math-ph↗

arXiv2010

Algorithm for planar 4-Body Problem central configurations with given masses

An algorithm to compute the six distances between particles of a planar Four-Body central configuration is presented according to the following schema. An orthocentric tetrahedron is computed as a function of given masses. Each mass is placed at the corresponding vertex of the tetrahedron. The center of mass (and orthocenter) of the tetrahedron is at the origin of coordinates. The tetrahedron is orientated in a particular position function of the masses: with one of the particles placed on axis 3. The tetrahedron is rotated by two angles (to be tuned variables) around the center of mass until a direction orthogonal to the plane of configuration coincides with axis 3. The four coordinates of the vertices of the tetrahedron along this direction are identified with the weighted directed areas of the central configuration. The central configuration corresponding to these weighted directed areas is computed giving rise to four masses and corresponding distances. The given masses are compared with the computed ones. The two angles of the rotation are tuned until the given masses coincide with the computed. The corresponding distances of this last computation determine the central configuration. The case with two equal masses also is considered.

math-ph↗

arXiv2009

The Schröder functional equation and its relation to the invariant measures of chaotic maps

The aim of this paper is to show that the invariant measure for a class of one dimensional chaotic maps, $T(x)$, is an extended solution of the Schröder functional equation, $q(T(x))=λq(x)$, induced by them. Hence, we give an unified treatment of a collection of exactly solved examples worked out in the current literature. In particular, we show that these examples belongs to a class of functions introduced by Mira, (see text). Moreover, as a new example, we compute the invariant densities for a class of rational maps having the Weierstrass $\wp$ functions as an invariant one. Also, we study the relation between that equation and the well known Frobenius-Perron and Koopman's operators.

math-ph↗