About

Francisco J. Solis is an Associate Professor at CIMAT (Centro de Investigacion en Mathematicas) in Mexico. He completed his PhD under the supervision of Hermann Flaschka, with a dissertation titled "Geometric Aspects of Local Adaptive Galerkin Bases." He held the position of Associate Professor at CIMAT from 1988 to 1993 and continues to serve there. His research focuses on applied mathematics, with particular interest in geometric aspects related to Galerkin bases and adaptive methods.

Research topics

• Materials science
• Chemical physics
• Chemistry
• Biology
• Microbiology

Selected publications

• Synthesis and characterization of the graphene-reinforced Al–Ni system by means of high and low energy mechanical alloying

  MRS Advances · 2025-02-26

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• Conduction in heterogeneous systems in the low-frequency regime: variational principles and boundary integral equations

  The European Physical Journal E · 2024-09-01

  article1st authorCorresponding
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• Electrical properties of tissues from a microscopic model of confined electrolytes

  Physics in Medicine and Biology · 2023-04-21 · 1 citations

  articleOpen access1st authorCorresponding

  Abstract Objective . In the presence of oscillatory electric fields, the motion of electrolyte ions in biological tissues is often limited by the confinement created by cell and organelle walls. This confinement induces the organization of the ions into dynamic double layers. This work determines the contribution of these double layers to the bulk conductivity and permittivity of tissues. Approach . Tissues are modeled as repeated units of electrolyte regions separated by dielectric walls. Within the electrolyte regions, a coarse-grained model is used to describe the associated ionic charge distribution. The model emphasizes the role of the displacement current in addition to the ionic current and enables the evaluation of macroscopic conductivities and permittivities. Main results . We obtain analytical expressions for the bulk conductivity and permittivity as a function of the frequency of the oscillatory electric field. These expressions explicitly include the geometric information of the repeated structure and the contribution of the dynamic double layers. The low-frequency limit of the conductivity expression yields a result predicted by the Debye permittivity form. The model also provides a microscopic interpretation of the Maxwell–Wagner effect. Significance . The results obtained contribute to the interpretation of the macroscopic measurements of electrical properties of tissues in terms of their microscopic structure. The model enables a critical assessment of the justification for the use of macroscopic models to analyze the transmission of electrical signals through tissues.

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• Luminometric Studies of Yeast Response to Complex Environmental Calcium Variations Demonstrate Sensing of External Calcium Ion Changes

  Advances in Microbiology · 2022-01-01 · 1 citations

  articleOpen access

  The response of yeast to sharp environmental increases in calcium concentration has been extensively studied. However, systematic studies of the response under more general changes are still lacking. Only limited exploration of cellular responses has been conducted where calcium concentration is decreased. This article describes a set of luminometric experiments that monitor the cytosolic calcium concentration under changing external concentration conditions. As a decrease in external calcium concentrations requires the use of large sample volumes, the experiments require the use of equipment adapted for this purpose. We describe the modification of commercial luminometric equipment to make the exploration possible. We explore the yeast cellular behavior when an increase in external calcium concentration is followed by a decrease in external calcium concentration. We compare these results with those from the case of a double pulse of concentration increase. Results from the experiment show that the first, concentration increasing pulse produces the well-known sharp increase in cytosolic calcium followed by calcium sequestration to return to a cytosolic concentration near its initial condition. Surprisingly, the calcium decrease step shows similar results with a cytosolic increase followed by a return to lower levels. The results suggest the presence of a calcium sensing mechanism regulating calcium influx from external sources. This mechanism would produce channel opening as a response to any changes in external concentration, be it an enhancement or a depletion.

  PublisherOA PDFDOI

• Pimples reduce and dimples enhance flat dielectric surface image repulsion

  The Journal of Chemical Physics · 2021-09-14 · 1 citations

  preprintOpen access1st authorCorresponding

  In solid-liquid, or liquid-liquid, interfaces with dielectric contrast, charged particles interact with the induced polarization charge of the interface. These interactions contribute to an effective self-energy of the bulk ions and mediate ion-ion interactions. For flat interfaces, the self-energy and the mediated interactions are neatly constructed by the image charge method. For other geometries, explicit results are scarce and the problem must be treated via approximations or direct computation. The case of interfaces with roughness is of great practical importance. This article provides analytical results, valid to first-order in perturbation theory, for the self-energy of particles near rough substrates. Explicit formulas are provided for the case of a sinusoidal deformation of a flat surface. Generic deformations can be treated by superposition. In addition to results for the self-energy, the surface polarization charge is presented as a quadrature. The interaction between an ion and the deformed surface is modified by the change in relative distance as well as by the local curvature of the surface. Solid walls, with a lower dielectric constant than the liquid, repel all ions. We show that the repulsion is reduced by local convexity and enhanced by concavity; dimples are more repulsive than pimples.

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• Electroencephalographic Signal Source Estimation Using Power Dissipation and Interface Surface Charge

  2020-01-01

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• Ionic Structure and Decay Length in Highly-Concentrated Confined\n Electrolytes

  arXiv (Cornell University) · 2020-09-05

  preprintOpen access

  We use molecular dynamics simulations of the primitive model of electrolytes\nto study the ionic structure in aqueous monovalent electrolyte solutions\nconfined by charged planar interfaces over a wide range of electrolyte\nconcentration, interfacial separation, surface charge density, and ion size.\nThe investigations are inspired by recent experiments that have directly\nmeasured the increase in the decay length for highly-concentrated electrolytes\nwith increase in concentration. The behavior of ions in the nanoconfinement\ncreated by the interfaces is probed by evaluating the ionic density profiles,\nnet charge densities, screening factors, and decay length associated with the\nscreening of the charged interface. Results show the presence of two distinct\nregimes of screening behavior as the concentration is changed from 0.1 M to 2.5\nM for a wide range of electrolyte systems generated by tuning the interfacial\nseparation, surface charge density, and ionic size. For low concentrations, the\nscreening factor exhibits a monotonic decay to 0 with a decay length that\ndecreases sharply with increasing concentration. For high concentrations\n($\\gtrsim 1$ M), the screening factor has a non-monotonic behavior signaling\ncharge inversion and formation of structured layers of ions near the\ninterfaces. The decay length under these conditions rises with increasing\nconcentration, exhibiting a power-law behavior. To complement the simulation\nresults, a variational approach is developed that produces charge densities\nwith characteristics consistent with those observed in simulations. The results\ndemonstrate the relation between the rise in the strength of steric\ncorrelations and the changes in the screening behavior.\n

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• Ionic structure and decay length in highly concentrated confined electrolytes

  AIP Advances · 2020-12-01 · 1 citations

  preprintOpen access

  We use molecular dynamics simulations of the primitive model of electrolytes to study the ionic structure in aqueous monovalent electrolyte solutions confined by charged planar interfaces over a wide range of electrolyte concentrations, interfacial separations, surface charge densities, and ion sizes. The investigations are inspired by recent experiments that have directly measured the increase in the decay length for highly concentrated electrolytes with an increase in concentration. The behavior of ions in the nanoconfinement created by the interfaces is probed by evaluating the ionic density profiles, net charge densities, integrated charges, and decay lengths associated with the screening of the charged interface. The results show the presence of two distinct regimes of screening behavior as the concentration is changed from 0.1M to 2.5M for a wide range of electrolyte systems generated by tuning the interfacial separation, surface charge density, and ionic size. For low concentrations, the integrated charge exhibits a monotonic decay to 0 with a decay length that decreases sharply with increasing concentration. For high concentrations (≳1M), the integrated charge has a non-monotonic behavior signaling charge inversion and formation of structured layers of ions near the interfaces. The decay length under these conditions rises with increasing concentration. To complement the simulation results, a variational approach is developed that produces charge densities with characteristics consistent with those observed in simulations. The results demonstrate the relation between the rise in the strength of steric correlations and the changes in the screening behavior.

  PublisherOA PDFDOI

• Power Dissipation and Surface Charge in EEG: Application to Eigenvalue Structure of Integral Operators

  IEEE Transactions on Biomedical Engineering · 2019-08-08 · 4 citations

  article1st authorCorresponding

  OBJECTIVE: To demonstrate the role of surface charge and power dissipation in the analysis of EEG measurements. METHODS: The forward EEG problem is formulated in terms of surface charge density. Using bounds based on power dissipation, the integral equations for forward solutions are shown to satisfy bounds on their eigenvalue structure. RESULTS: We show that two physical variables, dissipated power and the accumulated charge at interfaces, can be used in formulating the forward problem. We derive the boundary integral equations satisfied by the charge and show their connection to the integral equations for the potential that are known from other approaches. We show how the dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in EEG boundary element methods. Using the eigenvalue structure, we propose a new method for the solution of the forward problem, where the integral kernels are regularized by the exclusion of eigenvectors associated to a finite range of eigenvalues. We demonstrate the method on a head model with realistic shape. CONCLUSION: The eigenvalue analysis of the EEG forward problem is given a clear interpretation in terms of power dissipation and surface charge density. SIGNIFICANCE: The use of these variables enhances our understanding of the structure of EEG, makes connection with other techniques and contributes to the development of new analysis algorithms.

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• Ionic Structure in Highly-Concentrated Confined Electrolytes

  Bulletin of the American Physical Society · 2019-03-06

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Recent grants

• Kinetic Properties of Multicomponent Charged Systems

  NSF · $219k · 2009–2013

Frequent coauthors

• Mónica Olvera de la Cruz

  Northwestern University

  52 shared

• Vikram Jadhao

  Indiana University

  16 shared

• Katsuyo Thornton

  University of Michigan–Ann Arbor

  6 shared

• Chloe M. Funkhouser

  University of Michigan–Ann Arbor

  6 shared

• M. Casal

  Universitat Oberta de Catalunya

  6 shared

• M. Casal

  Hospital Universitario Reina Sofía

  6 shared

• Esther Orozco

  Center for Research and Advanced Studies of the National Polytechnic Institute

  6 shared

• Manuel Casal

  5 shared

Education

• Ph. D. , Physics

  University of Chicago