arXiv subjects

Francisco J. Solis

Publications and source records attributed to Francisco J. Solis.

At least 19 recordsLinked to original sources

arXiv2026

Electric field effects on electrolytes near rough dielectric surfaces by GPU-accelerated code

Dielectric interfaces are ubiquitous in manufactured and natural systems, such as iontronic devices, supercapacitors, and living cells. These, often rough, dielectric surfaces host ionic charge distributions that depend on the surface geometry and the electric fields present. In this work, we study the effect of electric fields on such ionic charge distributions. We demonstrate, by molecular dynamics (MD) and perturbative analytic calculations, that the pattern of alternating regions of ionic charge density created by a sinusoidal interface can be modified and reversed by applying an electric field. We determine the strength of the critical electric field required to cancel the effect of dielectric interface-driven modulation in ion density and develop an analytic expression for that field for small amplitude sinusoidal variations in surface height. We show that ion concentrations near a surface with height given by a sum of Fourier modes can be found by adding the contributions from the concentration modulation due to each mode, allowing the possibility to predict ion distributions near rough surfaces. We updated and validated a LAMMPS package for MD simulation of polarizable surfaces, the DIELECTRIC package, by implementing a new version that achieves a 2.4-24 times speed increase by GPU parallelization on our test system and adds the capability to simulate an applied electric field on simple and complex electrolytes near dielectric interfaces with arbitrary roughness.

cond-mat.soft↗

arXiv2026

Surface Variables Description of Axion Topological Materials

We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.

cond-mat.mtrl-sci↗

arXiv2021

Pimples reduce and dimples enhance flat dielectric surface image repulsion

Near 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 interaction 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. This article provides analytical results, valid to first order in perturbation theory, for the self-energy of particles near a deformed near-flat interface. Explicit formulas are provided for the case of a sinusoidal deformation; generic deformations can then be treated by superposition. In addition to results for the self-energy, the surface polarization charge due to a single ion 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 curvature of the surface. Solid walls with a lower dielectric constant than the liquid repel all ions. We show here, however, that the repulsion is reduced by local convexity and enhanced by concavity; dimples are more repulsive than pimples.

cond-mat.soft↗

arXiv2020

Ionic Structure and Decay Length in Highly-Concentrated Confined Electrolytes

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 concentration, interfacial separation, surface charge density, and ion size. The investigations are inspired by recent experiments that have directly measured the increase in the decay length for highly-concentrated electrolytes with 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, screening factors, and decay length associated with the screening of the charged interface. Results show the presence of two distinct regimes of screening behavior as the concentration is changed from 0.1 M to 2.5 M for a wide range of electrolyte systems generated by tuning the interfacial separation, surface charge density, and ionic size. For low concentrations, the screening factor exhibits a monotonic decay to 0 with a decay length that decreases sharply with increasing concentration. For high concentrations ($\gtrsim 1$ M), the screening factor 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, exhibiting a power-law behavior. 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.

cond-mat.soft↗

arXiv2018

Asymmetric electrolytes near structured dielectric interfaces

The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, nonuniform local curvature. Using a recently developed, highly efficient computational method, we investigate the effect of surface geometry on ion distribution and interface polarization. We consider an asymmetric 2:1 electrolyte bounded by a sinusoidally deformed solid surface. We demonstrate that even when the surface is neutral, the electrolyte acquires a nonuniform ion density profile near the surface. This profile is asymmetric and leads to an effective charging of the surface. We furthermore show that the induced charge is modulated by the local curvature. The effective charge is opposite in sign to the multivalent ions and is larger in concave regions of the surface.

cond-mat.soft↗

arXiv2017

Chance-Constrained Day-Ahead Hourly Scheduling in Distribution System Operation

This paper aims to propose a two-step approach for day-ahead hourly scheduling in a distribution system operation, which contains two operation costs, the operation cost at substation level and feeder level. In the first step, the objective is to minimize the electric power purchase from the day-ahead market with the stochastic optimization. The historical data of day-ahead hourly electric power consumption is used to provide the forecast results with the forecasting error, which is presented by a chance constraint and formulated into a deterministic form by Gaussian mixture model (GMM). In the second step, the objective is to minimize the system loss. Considering the nonconvexity of the three-phase balanced AC optimal power flow problem in distribution systems, the second-order cone program (SOCP) is used to relax the problem. Then, a distributed optimization approach is built based on the alternating direction method of multiplier (ADMM). The results shows that the validity and effectiveness method.

eess.SY↗

arXiv2017

Load Forecasting Based Distribution System Network Reconfiguration-A Distributed Data-Driven Approach

In this paper, a short-term load forecasting approach based network reconfiguration is proposed in a parallel manner. Specifically, a support vector regression (SVR) based short-term load forecasting approach is designed to provide an accurate load prediction and benefit the network reconfiguration. Because of the nonconvexity of the three-phase balanced optimal power flow, a second-order cone program (SOCP) based approach is used to relax the optimal power flow problem. Then, the alternating direction method of multipliers (ADMM) is used to compute the optimal power flow in distributed manner. Considering the limited number of the switches and the increasing computation capability, the proposed network reconfiguration is solved in a parallel way. The numerical results demonstrate the feasible and effectiveness of the proposed approach.

eess.SY↗

arXiv2015

Stability of real parametric polynomial discrete dynamical systems

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $λ$, and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real $m$-th degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept of Canonical Polynomial Maps which are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates, and even when chaos arises, as it passes through what we have termed stability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.

nlin.CD↗

arXiv2014

Free-energy functional of the electronic potential for Schrödinger-Poisson theory

In the study of model electronic device systems where electrons are typically under confinement, a key obstacle is the need to iteratively solve the coupled Schrödinger-Poisson (SP) equation. It is possible to bypass this obstacle by adopting a variational approach and obtaining the solution of the SP equation by minimizing a functional. Further, using molecular dynamics methods that treat the electronic potential as a dynamical variable, the functional can be minimized on the fly in conjunction with the update of other dynamical degrees of freedom leading to considerable reduction in computational costs. But such approaches require access to a true free-energy functional, one that evaluates to the equilibrium free energy at its minimum. In this paper, we present a variational formulation of the Schrödinger-Poisson (SP) theory with the needed free-energy functional of the electronic potential. We apply our formulation to semiconducting nanostructures and provide the expression of the free-energy functional for narrow channel quantum wells where the local density approximation yields accurate physics and for the case of wider channels where Thomas-Fermi approximation is valid.

cond-mat.mes-hall↗

arXiv2013

A variational formulation of electrostatics in a medium with spatially varying dielectric permittivity

In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it is important to take into account the spatial dependence of the permittivity of the medium. However, due to the ensuing theoretical and computational challenges, this inhomogeneous dielectric response of the medium is often ignored or excessively simplified. We develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response. Our formulation is based on a true energy functional of the polarization charge density. The defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy; this is a feature not found in many commonly used electrostatic functionals. We explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity, and we show that for this case our functional reduces to a functional of only the surface polarization charge density. We apply this reduced functional to study model problems for which analytical solutions are well known. We demonstrate, in addition, that the functional has many properties that make it ideal for use in molecular dynamics simulations.

cond-mat.soft↗

arXiv2013

Free-energy functionals of the electrostatic potential for Poisson-Boltzmann theory

In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional; a functional that not only provides the correct solution of the PB equation upon extremization, it also evaluates to the true free energy of the system at its minimum. Moreover, the numerical efficiency of such procedures is further enhanced if the free-energy functional is local and is expressed in terms of the electrostatic potential. Existing PB functionals of the electrostatic potential, while possessing the local structure, are not free-energy functionals. We present a variational formulation with a local free-energy functional of the potential. In addition, we also construct a nonlocal free-energy functional of the electrostatic potential. These functionals are suited for employment in simulation schemes based on the ideas of dynamical optimization.

cond-mat.soft↗

arXiv2013

Generating true minima in constrained variational formulations via modified Lagrange multipliers

Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as dynamical optimization methods. Systems with charged objects in dielectric media and systems with magnetically active particles are important examples. In these examples and other important cases, the variational principles describing the system are required to obey a number of constraints. These constraints are implemented within the variational formulation by means of Lagrange multipliers. Such constrained variational formulations are in general not unique. For the application of efficient simulation methods, one must find specific formulations that satisfy a number of important conditions. An often required condition is that the functional be positive-definite, in other words, its extrema be actual minima. In this article, we present a general approach to attack the problem of finding, among equivalent variational functionals, those that generate true minima. The method is based on the modification of the Lagrange multiplier which allows us to generate large families of effective variational formulations associated with a single original constrained variational principle. We demonstrate its application to different examples and, in particular, to the important cases of Poisson and Poisson-Boltzmann equations. We show how to obtain variational formulations for these systems with extrema that are always minima.

cond-mat.soft↗

arXiv2013

Simulation of Charged Systems in Heterogeneous Dielectric Media via a True Energy Functional

For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional; one that evaluates to the equilibrium electrostatic energy at its minimum. In this letter, we derive the needed functional. As an application, we develop a Car-Parrinello MD method for the simulation of free charges present near a spherical emulsion droplet separating two immiscible liquids with different dielectric constants. Our results show the presence of non-monotonic ionic profiles in the dielectric with lower dielectric constant.

cond-mat.soft↗

arXiv2007

Thermodynamics of Ion Solvation and Differential Adsorption at Liquid-Liquid Interfaces and Membranes

We construct a mean-field formulation of the thermodynamics of ion solvation in immiscible polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of different constant dielectric medium, we study the electrostatic phenomenon of differential adsorption of ions at the interface. Using general thermodynamic considerations, we construct the mean-field $Ω$-potential and demonstrate the spontaneous formation of an electric double-layer around the interface necessarily follow. In our framework, we can also relate both the bulk ion densities in the two phases and the distribution potential across the interface to the fundamental Born free energy of ion polarization. We further illustrate this selective ion adsorption phenomenon in respective examples of fully permeable membranes that are neutral, negative, or positive in charge polarity.

cond-mat.soft↗

arXiv2007

Ion condensation on charged patterned surfaces

We study ion condensation onto a patterned surface of alternating charges. The competition between self-energy and ion-surface interactions leads to the formation of ionic crystalline structures at low temperatures. We consider different arrangements of underlying ionic crystals, including single ion adsorption, as well as the formation of dipoles at the interface between charged domains. Molecular dynamic simulation illustrates existence of single and mixed phases. Our results contribute to understanding pattern recognition, and molecular separation and synthesis near patterned surfaces.

cond-mat.stat-mech↗

arXiv2005

Instabilities of micro-phase separated Coulombic systems in constant electric fields

Mixtures of near-symmetric oppositely charged components with strong attractive short range interactions exhibit ordered lamellar phases at low temperatures. In the strong segregation limit the state of these systems can be described by the location of the interfaces between the components. It has previously been shown that these systems are stable against small deformations of the interfaces. We examine their stability in the presence of a uniform electric field. When the field is perpendicular to the lamellae, the system is unstable against long wavelength deformations for all non-zero values of the external field. A field parallel to the lamellae produces deformed but persistent interfaces. In a finite thickness system, onset of an external perpendicular field modifies the ground state. Flow between the old and new ground states requires the destruction of the original interfaces; this destruction proceeds through the instabilities identified in the bulk case. We examine the possibility of dynamical stabilization of structures by means of oscillating fields.

cond-mat.soft↗

arXiv2002

Phase diagram of dilute polyelectrolytes: Collapse and redissolution by association of counterions and coions

Dilute solutions of strongly charged polymer electrolytes undergo, upon addition of multivaltent salt to the solutions, a phase transition from extended conformations to collapsed or bundled ones. Upon further addition of salt they experience a second transition, a redissolution back into extended conformations. This paper presents a theoretical study of the structure and properties of the phase diagram of these solutions. On the basis of simple phenomenological observations a schematic phase diagram is constructed that allows a simple and explicit determination of the direction of the tie lines within the coexistence region. The actual shape of the coexistence boundary is determined by means of a model mean free energy functional that explicitly includes the possibility of association of both counterions and coions to the electrolyte. It is found that it is possible to redissolve the electrolytes into conformations where the bare charge of the electrolyte is overcompensated by the counterions but, due to the associated coions, can have either sign of total effective charge. When coion association is possible, the redissolution approximately coincides with the reassociation of the coions and counterions in the bulk of the solution.

cond-mat.soft↗

arXiv2000

Attractions between charged colloidal spheres mediated by correlated absorbed ions

We describe arrangements of ions capable of producing short-range attractive interactions between pairs of charged colloidal spheres in the low temperature strongly correlated limit. For particles of radius $R$ with bare charge $Z$ and comparable absorbed charge $-N$ ($N \sim Z$), the correlations contribution to the spheres self-energy scales as $N^{3/2}/R$, and as $N/R$ for the interaction energy between two touching spheres. We show that the re-arrangement of charges due to polarization plays an insignificant role in the nature and magnitude of the interaction.

cond-mat.str-el↗