Documents published in Scipedia

• A mathematical model of the formation of urine

  F. Domínguez Pérez, J. LOPEZ

  SMCCA (2024). 4

  
  

  Abstract

  In this work, a mathematical model of renal hemodynamics involved in urine production is studied. The model is formed by three sub-models: one corresponds to the glomerular filtration stage, which gives input to the blood that is processed in the kidney; another one is the corresponding to the renal autoregulation process which defines the blood flow that must enter the kidney, to maintain its correct functioning, even in the face of blood pressure variations; and the last sub-model corresponding to the reabsorption and secretion stages, the former corresponds to the process by which the kidneys recover useful substances from the glomerular filtrate and return them to the blood and in the latter the kidneys eliminate unwanted substances from the blood into the peritubular capillaries.

  Abstract
  In this work, a mathematical model of renal hemodynamics involved in urine production is studied. The model is formed by three sub-models: one corresponds to the glomerular [...]

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• A Mathematical Model to Estimate the COVID-19 Pandemic in Red Lights of México

  A. Peregrino, D. Gonzalez, J. LOPEZ

  SMCCA (2023). 5

  
  

  Abstract

  The goal of this work is a dynamic and numerical study of a compartmental mathematical model in order to know the evolution of state variables of the pandemic caused by COVID-19 on red spotlights in México. The model include 7 compartments and the results were compared with the classic SIR model, resulting that our predictions adjusted better the official data. A parameter sensitivity analysis is included.

  Abstract
  The goal of this work is a dynamic and numerical study of a compartmental mathematical model in order to know the evolution of state variables of the pandemic caused by COVID-19 [...]

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• Stabilizing a Josephson Junction Array Memory around an unstable equilibrium: A control approach using a first order state model

  J. LOPEZ, L. Juárez Valencia, R. Glowinski

  SMCCA (2022). 1

  
  

  Abstract

  In this paper we consider a system of three nonlinear ordinary differential equations that model a three Josephson Junctions Array (JJA). Our goal is to stabilize the system around an unstable equilibrium employing an optimal control approach. We first define the cost functional and calculate its differential by using perturbation analysis and variational calculus. For the computational solution of the optimality system we consider a conjugate gradient algorithm for quadratic functionals in Hilbert spaces,  combined with a finite difference discretization of the involucrated differential equations.

  Abstract
  In this paper we consider a system of three nonlinear ordinary differential equations that model a three Josephson Junctions Array (JJA). Our goal is to stabilize the system [...]

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• Método de Newton para búsquedas en Línea en el espacio de Hilbert (L^2)^3.

  J. LOPEZ

  SMCCA (2021). 1

  
  

  Abstract

  Este trabajo trata sobre la aplicación del método de Newton para resolver un problema de búsqueda en línea asociado con la minimización de un funcional definido en el espacio de Hilbert (L^{2}(0,T))^3, con T un tiempo final dado. El funcional es parte de un problema de control de un circuito de 3 juntas de Josephson modelado por un sistema de tres ecuaciones diferenciales ordinarias no lineales dependientes del tiempo. El problema de control se puede resolver con el método de gradiente conjugado, dentro del cual se deben resolver problemas de búsqueda en línea como el descrito en este trabajo. Se describe tanto el caso continuo como su versión discreta para lo cual, las funciones en (L^{2}(0,T)) se aproximan por funciones lineales por pedazos y los sistemas diferenciales ordinarios se resuelven con el método de Euler Explícito.

  Abstract
  Este trabajo trata sobre la aplicación del método de Newton para resolver un problema de búsqueda en línea asociado con la minimización [...]

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