Joaquin Delgado

• Phd
• Head of Department at Metropolitan Autonomous University

Using finite element simulation, we study the main features of rotating wave solutions of the cubic complex Ginzburg–Landau equation. To focus on the characteristics of the waves themselves, we have used a circular domain to avoid the effects of irregular boundaries; we have inhibited the formation of defects using an Archimedean wave centered at t...

The study aimed to identify students with mathematical talent in Elementary and High School, with regard to the Mayan and Babylonian numerical system for Elementary School and computational thinking, with the use of Scratch for High School; to design and implement an out-of-school enrichment program with Elementary and High School students; to stud...

In this article we investigate the second order differentiability of a functional associated to a Monge’s optimal transportation problem, namely the case of the quadratic cost, in its dual formulation. The application problem that motivates the present research is an algorithm for warping of images that uses the first derivative of this functional...

In this paper we study the stability of homogeneous states in a continuous one spatial variable of conservation equations in Lagrangian coordinates, including terms of dissipation and relaxation. Local existence is proved applying Kawashima’s theorem for hyperbolic-parabolic systems [7]. We establish that when the subcharactertistic condition is sa...

In this work we assume that the ribosome propels itself during the translocation step of the translation process of protein synthesis by running a cycle of stochastically generated conformational changes involving its two subunits. This cycle includes only two experimentally found ribosome shape changes. The main result is an analytic expression fo...

In the last decade, Acapulco City, Mexico, has faced serious problems related to increasing criminal violence, despite the city’s outstanding tourism and economic importance. We propose a hedonic regression model to quantitatively determine the effect of criminal violence on housing prices in the 2015–2016 period in Acapulco City. In addition to st...

A study on the identification and development of mathematical talent in elementary and secondary school students is presented and based on the Renzulli's School Enrichment Model. The methodology used was mixed type with concurrent embedded design of dominant model. The two stages of the study consisted of: (a) detecting students with mathematical t...

Este artículo de investigación es el resultado de un proyecto de investigación sobre el pensamiento algebraico temprano en entornos tecnológicos de aprendizaje y se reportan resultados sobre el razonamiento proporcional como una ruta de acceso al pensamiento algebraico temprano. El estudio fue realizado con 109 estudiantes de educación básica de es...

In this paper, we conducted a study on the effect of insecurity on housing prices in Acapulco de Juárez using an econometric model of hedonic prices. To do this, the distance of the most unsafe neighborhood in the city from the housing is considered as the variable that will measure such impact. As in the existing literature, in this model we consi...

One of the simplest model of immune surveillance and neoplasia was proposed by Delisi and Resigno. Later Liu et al proved the existence of non-degenerate Takens-Bogdanov bifurcations defining a surface in the whole set of five positive parameters. In this paper we prove the existence of Bautin bifurcations completing the scenario of possible codime...

Se reportan resultados de un estudio sobre los procesos de generalización como una vía de acceso a la introducción temprana al pensamiento algebraico, con 109 estudiantes de educación básica de escuelas públicas, México. El trabajo experimental consistió de tres etapas: 1. Evaluación inicial sobre procesos de generalización, 2. Validación de un ins...

We study the spatially homogeneous time-dependent solutions and their bifurcations in the Gray–Scott model. We find the global map of bifurcations by a combination of rigorous verification of the existence of Takens–Bogdanov and a Bautin bifurcation, in the space of two parameters k–F. With the aid of numerical continuation of local bifurcation cur...

La idea central de la obra es exponer en forma a la vez rigurosa y amena, temas de diversas ramas de las matemáticas y de la física-matemática, en los que el pensamiento científico de Poincaré y Hilbert persiste. Los capítulos presentan los conceptos en forma panorámica y didáctica, con abundantes ejemplos y aplicaciones, manteniendo siempre la cal...

The elliptic isosceles restricted three-body problem (EIR3BP) with collision is defined as follows: Two point masses m 1 = m 2 move along a degenerate elliptic collision orbit under their gravitational attraction, then describe the motion of a third massless particle moving on a plane perpendicular to their line of motion and passing through the ce...

We study traveling wave solutions of the Kerner–Konhäuser PDE for traffic flow. By a standard change of variables, the problem is reduced to a dynamical system in the plane with three parameters. In a previous paper [Carrillo et al., 2010] it was shown that under general hypotheses on the fundamental diagram, the dynamical system has a surface of c...

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-...

We consider the macroscopic, second order model of Kerner–Konhäuser for traffic flow given by a system of PDE. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We prove that under generic conditions on the so-called fundamental diagram, the surface of critical points has a fold or cu...

The motion of the ribosome is modeled here, assuming that its two subunits are subject to stochastic rearrangements, thus producing different conformations constituting its deformation cycle, or swimming stroke. Using a general statistical mechanical formulation, the mean propulsion velocity of the ribosome is obtained as a function of the transiti...

In this paper we analyze the non-integrability of the Wilbeforce spring-pendulum by means of J. J. Morales-Ruiz and P. Ramis’ theory [Methods Appl. Anal. 8, No. 1, 33–95 (2001; Zbl 1140.37352), ibid. 8, No. 1, 97–111 (2001; Zbl 1140.37354)], in which it is enough to prove that the Galois group of the variational equation is not virtually abelian. W...

An n-dimensional nonlinear control system is considered, whose nominal vector field has a double-zero eigenvalue and no other eigenvalue on the imaginary axis, and then the idea is to find under which conditions there exists a scalar control law such that it is possible to establish a priori, that the closed loop system undergoes the controllable T...

The restricted three-body problem (R3BP) possesses the property that some classes of doubly asymptotic (i.e., homoclinic or heteroclinic) orbits are limit members of families of periodic orbits, this phenomenon has been known as the “blue sky catastrophe” termination principle. A similar case occurs in the restricted four body problem for the colli...

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral triangle in a rotating coordinate system. A massless fourth body moves under the Newtonian gravitational law due to t...

We consider the continuous model of Kerner–Konäuser for traffic flow given by a second order PDE for the velocity and density. Assuming conservation of cars, traveling waves solution of the PDE are reduced to a dynamical system in the plane. We describe the bifurcations set of critical points and show that there is a curve in the set of parameters...

A collective phenomenon appearing in the simulation of bidirectional pedestrian flow in corridors is dynamic multi-lane (DML) flow. We present a cellular automata model that reproduces this behavior. We propose to incorporate a social distance emulating a territorial effect through a social field, similar to the dynamic floor field of Burstedde et...

In this paper we prove the existence of central configurations of the pn-body problem where the masses are at the vertices of p nested regular n-gons with a common center for all p ≥ 2 and n≥ 2. In such configurations all the masses on the same n-gon are equal, but masses on different n-gons could be different. KeywordsPlanar central configuration...

Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional cen...

The basic theory of Differential Galois and in particular Morales--Ramis theory is reviewed with focus in analyzing the non--integrability of various problems of few bodies in Celestial Mechanics. The main theoretical tools are: Morales--Ramis theorem, the algebrization me\-thod of Acosta--Bl\'azquez and Kovacic's algorithm. Morales--Ramis states t...

Central configurations provide special solutions of the general n- body problem. Using the mutual distances between the n bodies as coordinates we study the bifurcations of the spatial central configurations of the 5-body problem going from the problem with equals masses to the 1+4- body problem which has one large mass and four infinitesimal equal...

En el espíritu de rendir un modesto homenaje al gran Euler a los trescientos años de su nacimiento, se publica el presente libro, en el cual se exponen en forma concisa y amena, temas de diversas ramas de la matemática pura y aplicada en la cual la influencia de Leonhard Euler persiste. Los autores de los capítulos son investigadores que cultivan a...

In this paper, we compare the translation efficiencies of a deformable circle that swims by means of low amplitude periodic tangential surface waves versus a rigid circle, moving in a bounded fluid domain. The swimmer is found to be much more efficient than the rigid body. We believe that this result gives some support to the active hypothesis of s...

In this paper, we prove the existence of special type of motions in the restricted planar parabolic three-body problem, of the type exchange, emission–capture, and emission–escape with close passages to collinear and equilateral triangle configuration, among others. The proof is based on a gradient-like property of the Jacobian function when equati...

Ten years ago, Dixon et al. [1993] studied the behavior of a continuous-time system displaying erratic, apparently chaotic, dynamics. This is a paradoxical case since the system is two-dimensional, which is seemingly a violation of the Poincare–Bendixon theorem. Using numerical studies, Dixon et al. explained such a behavior from the presence of an...

In the n n –body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 n=3 and for n > 4 n>4 that if n − 1 n-1 masses are located at fixed points in the plane, then there are only a finite number of way...

An extremal principle for obtaining the variational equations of a Lagrangian system is reviewed and formalized. Formalization is accomplished by relating the new Lagrangian function γ needed in such scheme to a prolongation of the original Lagrangian L. This formalization may be regarded as a necessary step before using the approach for stablishin...

We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any $n$-parameter continuous symmetry group of the Lagrangian there exist 1) the usual $n$ constants of motion and 2) $n$...

In this paper we introduce the tetrahedral four body problem where the particles form a tetrahedral configuration of variable size without rotation. In order for this configuration to be feasible, masses are equal pairwise with a parameter µ measuring their ratio. We first perform the blow up of total collision leading to an invariant four-dimensio...

Two attracting bodies m 1,m 2 move in parabolic orbits and a third massless body mo = 0 moves in the plane under the attraction of the primaries. We obtain the equations of motion of the massless particle in a rotating-pulsating coordinate system where the primaries remain fixed. Introducing an appropriate time scaling we obtain two invariant subsy...

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of p...

We consider the symmetric planar (3 + 1)-body problem with finite masses m 1 = m 2 = 1, m 3 = and one small mass m 4 = . We count the number of central configurations of the restricted case = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with as the parameter. The diagram shows a fol...

We consider the isosceles 3–body problem with the third particle having a small mass which eventually tend to zero. Classical McGehee’s blow up is not defined because the matrix of masses becomes degenerate. Following Elbialy [3] we perform the blow up using the Euclidean norm in the planar 3–body problem. We then complete the phase portrait of the...

In the n-body problem a central conguration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n =3 and for n> 4t hat ifn 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remainin...

Noether's theorem relating continuous symmetries of a Lagrangian system to the existence of conserved quantities is shown to be valid at the level of the variational equations of the system. This result can be helpful in the study of perturbations and of integrability in various areas of current interest. As examples, we derive conserved quatities...

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. O...

Swimming spherical shapes at low Reynolds number have been used as a model to describe locomotion of several microorganisms such as cyanobacteria. Other examples of biological interest include the motion of vesicles within eucaryotic cells which persists even in the absence of microtubules [Eur. J. Cell. Biol. 60 (1993) 217]. The role of tangential...

We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new Lagrangian in an extended configuration space ---which we call D'Alambert's--- comprising both the original coor...

A geometrical approach for low Reynolds number swimming was introduced by Shapere and Wilczek1. Here we pursue some developments for the two dimensional theory. The outer membrane or the ciliary envelope of the planar organism is represented by the conformal image of the unit circle. Power expenditures and velocities can be computed using complex v...

Consider 4 bodies of equal unit masses in space at the vertices of a regular tetrahedron with variable height, interacting under gravitational forces. A topological and dynamical description of the total collision manifold, parabolic orbits of escape, and homoclinic and heteroclinic orbits asymptotic to total collision and infinity arc given. This...

Consider 4 bodies of equal unit masses in space at the vertices of a regular tetrahedron with variable height, interacting under gravitational forces. A topological and dynamical description of the total collision manifold, parabolic orbits of escape, and homoclinic and heteroclinic orbits asymptotic to total collision and infinity arc given. This...

We compare two notions of efficiency for locomotion processes modelled by linear variational problems with nonholonomic constraints. We revisit Lighthill's work on squirming motions of a sphere inside a viscous fluid, also studied by Blake and by Shapere and Wilczek. Our approach uses the spectral basis of the propulsion operator (sending velocity...

According to a modern formulation of the classic result of H. Lorentz (1907), the propulsion operator P Σ (U →)=F →, which maps the velocity U → along a C 2 surface Σ to the surface force field F →, is selfadjoint and positive. Using the boundary integral representation, we show that P has a discrete set of eigenvalues tending to infinity, and that...

A theory of reduction of stability properties of a not necessarily compact invariant set to a subsystem defined on a subspace of lower dimension is presented in the context of a dynamical or semidynamical system on a metric space.

The Manev problem (a two-body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinate...

Accidents have their origin in human failures or unsafe conditions. Both factors are management's responsibility. In the Mexican petrochemical industry, most of the published data confirms a decrease of personal accidents in the decade from 1980 to 1991. Despite this particular index, the frequency of deaths in the same period has not presented the...

According to a classic result of H.Lorentz, the propulsion opera- tor P�( ~ U) = ~ F, which maps the velocity boundary condition along a C 2 surfaceto the surface force field, is self-adjoint and positive. Using the boundary integral representation, we show that P has a dis- crete set of eigenvalues tending to infinity, and that the eigenbasis is L...

It is shown that Hill’s problem in celestial mechanics has invariant tori for large values of the Jacobian constant, and also that Hill’s periodic orbits are orbitally stable. Levi-Civita regularization and a scaling of coordinates transform the problem into a perturbation of two harmonic oscillators in the plane with equal frequencies. Normalizati...

There exists an extensive literature on changes of variables which transform the equations of motion of interesting problems in Celestial Mechanics into polynomial form (see [Heg]). In most cases this is achieved by regularizing double collisions or introducing redundant variables, or both. In previous works [DLLP1,2] we have exploited this idea to...

The vector field of the n-body problem can always be written as a polynomial vector field. The idea is to regularize binary collisions in such a way that collisions involving more than two bodies become critical points of the new vector field, [Heg]. For three or more bodies, this procedure introduces redundant variables.

In this work, we have considered a particular case of the planar four-body problem, obtained when the masses form a rhomboidal configuration. If we take the ratio of the masses α as a parameter, this problem is a one parameter family of non-integrable Hamiltonian systems with two degrees of freedom. We use the blow up method introduced by McGhee to...

In a recent paper [3], Lacomba and Llibre showed numerically the existence of two transversal ejection-collision orbits in Hill's problem for a valueC=5 of the Jacobian constant. This result can be used to prove the non-existence ofC 1-extendable regular integrals for Hill's problem. Here we give an analytic proof of the existence of four ejection-...

A. Shapere and F. Wilczek theory of microswimming [J. Fluid Mech. 198, 557–585 (1989; Zbl 0674.76114)] is revisited and formalized as an infinite fiber bundle with a mechanical connection where the horizontal spaces are given by the kernel of the momentum map associated to a Riemannian metric which is invariant under the Euclidean group. Stokes par...