Gerardo Aragón-González

• Professor (Full)
• Metropolitan Autonomous University

This work provides a comprehensive characterization of coincidence site lattices that arise from the compositions of the reflections of cubic lattices. For this purpose, we apply Cartan's theorem and use reflections as basic isometries, which allows the use of Clifford algebra as a powerful tool to handle reflections and products of reflections, le...

Coincidence site lattices of oblique planar lattices are algebraically characterized using as basic tool the Cartan-Dieudonn\'e theorem, that is, the decomposition of an orthogonal transformation as a product of reflections. The case of rectangular lattices is worked out in detail. We use the rectangular lattices for obtain the characterization of...

An electronic system based on an open source programmable board was designed and tested, for remote control and monitoring of a fluid power machine. To satisfy the requirements for remote two-way communication between the machine and the user interface, a connection must be established via the Internet. The Arduino Uno Wi-Fi Rev 2 board is designed...

Small wind turbines with fixed blades present a significant disadvantage when operating at low wind speeds. Wind speed increase proportionally with the height to the ground and such wind turbines are installed at most on rooftops, so they face low wind speeds < 10 m/s. This work shows the experimental characterization of a wind turbine prototype wi...

The effect of two sources of irreversibilities (limited rate of heat transfers and heat leak) on a stationary irreversible regenerative Stirling cycle model is investigated. The goal of this research is to obtain the partial optimization criterion described in [1]. Since with this criterion, the optimal relations for the allocation and effectivenes...

A Mexican manufacturing plant, whose main product is bottled Pox (a traditional Mexican alcoholic beverage), requested the design and construction of an automatic bottling machine able to fill six bottles of 750 milliliters per minute and satisfy the exigencies of the Mexican regulation NOM-002-SCFI-2011. To develop this machine it was necessary, a...

A stationary irreversible regenerative Stirling cycle model, with two sources of irreversibilities (finite rate of heat transfers and heat leak), is analyzed. The aim of this work is to obtain the criterion of partial optimization presented in [3]. Since with this criterion, the optimal relations for the allocation and effectiveness of the heat exc...

stationary power plant with n Carnot-like cycles is optimized. Each cycle has the following irreversibilities: finite rate heat transfers between the working fluid and the external heat sources, internal dissipation of the working fluid, and heat leak between reservoirs. In a previous work, a plant with two cycles of this type was optimized, with r...

A Mexican manufacturing plant, whose main product is deodorant tablets for domestic and commercial use, requested the design, construction, and start up of an automatic machine to make 3 600 deodorant tablets per hour of Paradichlorobenzene (PDB). The tablets should have a density no less than 1 400 [kg/m3] with a weight variation of 5% maximum. To...

This article presents a methodology to guide and assess the academic work in institutions that carry out research on engineering. It lies in materializing, by means of academic criteria, the generality of the National Development and Normativity Program of the National Science and Technology Council (Consejo Nacional de Ciencia y Tecnología, conacy...

This article presents a methodology to guide and assess the academic work in institutions that carry out research on engineering. It lies in materializing, by means of academic criteria, the generality of the National Development and Normativity Program of the National Science and Technology Council (Consejo Nacional de Ciencia y Tecnología, CONACy...

A model of irreversible Carnot-like power plant with n Carnot-like cycles is optimized. The irreversibilities of each cycle are: finite rate heat transfer between the working fluid and the external heat sources, internal dissipation of the working fluid, and heat leak between reservoirs; is extended to two or more of this combined model. Applying t...

A stationary power plant with two Carnot-like cycles is optimized. Each cycle has the following irreversibilities: finite rate heat transfer between the working fluid and the external heat sources, internal dissipation of the working fluid, and heat leak between reservoirs; is extended to two or more of this combined model. Using the Bellman' Princ...

A stationary power plant with two Carnot-like cycles is optimized. Each cycle has the following irreversibilities: finite rate heat transfer between the working fluid and the external heat sources, internal dissipation of the working fluid, and heat leak between reservoirs. The optimal allocation or effectiveness of the heat exchangers for this pow...

A method for generating all rational generalized matrices on indefinite real inner product spaces isomorphic to $R^{p,q}$ is presented. The proposed method is based on the proof of a weak version of the Cartan–Dieudonné theorem, handled using Clifford algebras. It is shown that all rational B-orthogonal matrices in an indefinite inner product space...

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the com...

The last step in the industrial leather gloves manufacturing is to turn the inside out so that the sewing be in the inside of the glove. This work presents the design and testing of a machine for that purpose. In order to quantify the relevant variables, testing was performed with a prototype glove. The employed devices and the testing proceeding w...

In this work a Stirling regenerative cycle with some irreversibilities is analyzed. The analyzed irreversibilities are located at the heat exchangers. They receive a finite amount of heat and heat leakage occurs between both reservoirs. Using this model, power and the efficiency at maximum power are obtained. Some optimal design parameters for the...

A motion control system with four and 1/2 degrees of freedom, designed to move small objects within a 0.25 m3 space, parallel to a horizontal table, with high speed and performance similar to a robotic manipulator arm was built. The machine employs several actuators and control devices. Its main characteristic is to incorporate a servomotor, steepe...

A PEM electrolyser for hydrogen production was evaluated. It was fed with water and a 400 mA, 3.5 V cc electrical power source. The electrolyser was built with two acrylic plates to form the anode and the cathode, two meshes to distribute the current, two seals, two gas diffusers and an assembly membrane-electrode. A small commercial neoprene sheet...

The problem of characterizing the coincidence site lattices obtained by superimposing a planar hexagonal lattice with its rotated version is solved using simple reflections handled with Clifford algebras. For any possible coincidence rotation, analytical expressions for the coincidence index and for a basis of the coincidence site lattices are deduce...

In this work a didactic approach to some fundamental thermodynamic concepts as reversibility, possible and impossible processes and entropy is proposed. The approach is obtained through the concepts of heat transfer flows and reduced heat. A broad essay with undergraduate engineering students taking their first and second formal course on classic T...

The construction of miniature LTD Stirling engine prototypes, developed with low-cost materials and simple technologies is described. The protypes follow the Ringbom motor array, without mechanical linkages to actuate the displacer piston. Different designs, sizes, materials and mechanisms components have been tested. The power piston has been repl...

A Brayton cycle with internal irreversibilities due to isentropic efficiencies of the turbine and compressor, is analyzed using two criterions. One was developed by the authors [1] to obtain the maximum efficiency with respect to the isentropic temperature ratio. Another was obtained in [2] and gives the conditions to obtain a better cycle if a hea...

A Brayton cycle with, external and internal irreversibilities, is analyzed. Optimization of the dimensionless work with respect to two parameters: the isentropic temperatures ratio and the allocation ratio of the heat exchangers, is performed. The qualitative and asymptotic behaviour of the coupled optimal analytic expressions obtained are presente...

We have shown that the expression theta=2tan-1/ derived by Ranganathan to calculate the angles at which there exists a CSL for rotational interfaces in the cubic system can also be applied to general (oblique) two-dimensional lattices provided that the quantities 2 and /cos() are rational numbers, with =|b|/|a| and is the angle between the basis ve...

This paper presents a methodology of optimisation that analyses a stationary Carnot-like power plant model with three sources of irreversibilities. The methodology is based on expressing several objective functions (operation regimes) that can be applied to any objective function expressed as algebraic combinations of power and/or efficiency. The o...

In this work simple reflections or rotations of canonical vectors are used to generate all Pythagorean vectors, i.e. vectors in \mathbbQn{\mathbb{Q}^{n}} that satisfy the Pythagoras generalized equation. By using Clifford algebra we develop a constructive method that explicitly provides an algorithm to generate generalized Pythagorean numbers. M...

In this work, the equivalence class representatives of integer solutions of the Diophantine equation of the type \({{a_1x_1^2+ .\,.\,. + a_px_p^2 = a_{p+1}x^2_{p+1} + .\,.\,. +a_{p+q}x^2_{p+q} +a_1x^2_{n+1} (a_i > 0,i=1, .\,.\,.\,,p+q,x_{n+1}\neq0)}}\) are found using simple reflections of orthogonal vectors, manipulated using the Clifford algebra...

The problem of coincidences of lattices in the space , with p + q = 2, is analyzed using Clifford algebra. We show that, as in , any coincidence isometry can be decomposed as a product of at most two reflections by vectors of the lattice. Bases and coincidence indices are constructed explicitly for several interesting lattices. Our procedure is met...

We present an algorithmic proof of the Cartan-Dieudonn\'e theorem on generalized real scalar product spaces with arbitrary signature. We use Clifford algebras to compute the factorization of a given orthogonal transformation as a product of reflections with respect to hyperplanes. The relationship with the Cartan-Dieudonn\'e-Scherk theorem is also...

A stationary Carnot-like power plant model, with three sources of irreversibilities (the finite rate of heat transfers, heat leak and internal dissipations of the working fluid), is analyzed by a criterion of partial optimization for five objective functions (power, efficiency, ecological function, efficient power and criterion). A remarkable resul...

In this article, simple reflections, rotations and the Cartan theorem are handled using Clifford algebras. With this tool we provide a constructive proof of the Cartan theorem and the relationship with Pythagorean numbers is discussed.

A test bench was conceived in order to determine experimentally the flow coefficient [CV] for process control valves, operating with compressible fluids, under established regulations by the standards ANSI/ISA-75.02-1996 and ANSI/ISA- 75.01.01-2002. This test bench is used to verify the calibration of valves with continually variable opening, after...

The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica is introduced through a presentation of the main ideas of Clif...

A test bench was conceived in order to determine experimentally the flow coefficient [C_V] for process control valves, operating with compressible fluids, under established regulations by the standards ANSI/ISA-75.02-1996 and ANSI/ISA-75.01.01-2002. This test bench is used to verify the calibration of valves with continually variable open...

The design and assembly of a mechanism to bend schedule 80 stainless steel pipe up to 1 1/2 in nominal diameter is presented. The use of a relatively small hydraulic actuator, coupled with a toothed wheel to produce the bending torque, is a novel approach to the process. The bending method uses two arms and a radius block in order to accomplish the...

In this work we include, for the Carnot cycle, irreversibilities of linear finite rate of heat transferences between the heat engine and its reservoirs, heat leak between the reservoirs and internal dissipations of the working fluid. A first optimization of the power output, the efficiency and ecological function of an irreversible Carnot cycle, wi...

In this work, we consider the class of irreversible Carnot engines that results from combining the characteristics of two models found in the literature: the model in finite time and the model in finite size. The performance of the resulting model, including three irreversibilities, was doubly-optimized in finite time and finite size. The first opt...

The scaling limit of the energy correlations in non-integrable Ising models In this work, an algorithm to decompose a given orthogonal transformation as a product of reflections through hyperplanes is presented. This in fact constitutes a constructive proof of a Cartan theorem, valid over any field K = Q, R or C. Clifford algebras are used to expli...

We show some suggestions to develop the topic about vapor tables for a basic thermodynamics course for engineers. It is based on a methodology designed by the authors. This methodology shows the need of reinforce the subject with experimental work and historical aspects, in order to get a feed-back of the teaching-learning process. It is also sugge...

A gravimetric automatic dosing machine has been designed. To start working it needs pneumatic and electrical power. The compressed air consumption required is 17 SCFM at 90 PSI, and its need electrical requirements are 60 W at 110 VAC, @60 Hz. This machine may give 10 doses of grains per minute, weighing 0.5 or 1 kg, with +/- 15 g of maximum error....

In this work is discussed the numerical, mathematical and experimental modelling of a sump, for a centrifugal pumps testing facility. The testing rig is suitable for conducting tests on centrifugal and vertical turbine type pumps, up to 75 kW power input, 0.20 m3/s flow capacity and 365 m of head, according to the Hydraulic Institute tests standard...

In this paper we analyze a Brayton cycle with external and internal irreversibilities. The external ones come from heat transfer with counterflow heat exchangers in the cold and hot sides; the internal irreversibilities are given by the isentropic efficiencies of the compressor and turbine. Optimization is carried out with respect to the pressure r...

The purpose of this work is to obtain a more precise calculation of the effective limits to the efficiency, of several cyclic heat engines. This calculation is based, first, on the equations describing the irreversible efficiency, and second, on a method which results from a general criterion to maximize this efficiency, applicable to several heat...

The aim of mathematical crystallography is the classification of periodic structures by means of different equivalence relationships, yielding the well known crystallographic classes and Bravais lattices [1]. Periodicity (crys-tallinity) has been the paradigm of classical crystallography. Recently, more systematical attention has been paid to struc...

In teaching thermodynamics for engineers, on a basis of a curricular design methodology, we analyze the how and why internal combustion engines perform. We introduce the concept irreversibility to analyse the themodynamic cycles of power, then we consider some irreversibilities by mean of the compresion and expansion processes efficiency. In partic...

In teaching thermodynamics for engineers, on a basis of a curricular design methodology, we analyze the how and why internal combustion engines perform. We introduce the concept irreversibility to analyse the themodynamic cycles of power, then we consider some irreversibilities by mean of the compresion and expansion processes efficiency. In partic...

The concept of the efficiency of a process is used to analyse various thermodynamic power cycles with ideal gases. The Otto cycle is treated by considering irreversibilities coming exclusively from expansion and compression processes. For this cycle, the maximum irreversible work and the maximum efficiency are obtained in terms of the isentropic ef...

In most of the introductory works on the finite element method, either physical aspects or mathematical foundations are stressed. The main objective of this work is to present a unified view of this method which considers both physical and mathematical points of view. This work can also serve as an introduction to more advanced topics.

In most of the introductory works on the finite element method, either physical aspects or mathematical foundations are stressed. The main objective of this work is to present a unified view of this method which considers both physical and mathematical points of view. This work can also serve as an introduction to more advanced topics.

The geometric algebra as defined by D. Hestenes is compared with a constructive definition of Clifford algebras. Both approaches are discussed and the equivalence between a finite geometric algebra and the universal Clifford algebra R p, q is shown. Also an intermediate way to construct Clifford algebras is sketched. This attempt to conciliate two...