arXiv subjects

Gabriel Tellez

Publications and source records attributed to Gabriel Tellez.

At least 19 recordsLinked to original sources

arXiv2024

Self Organized Critical Dynamic on the Sierpinski Carpet

Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power-law with a non-integer exponent, i.e. a fractal. To achieve this, we proposed an Ising-BCP (bond-correlated percolation) model as the foundation for investigating critical dynamics. Within this framework, we outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice. This efficiency was attributed to the iterative construction of the lattice and the distribution of spins within it. The key outcome of our findings is a novel dependence of self-organized criticality on topology for this particular model, which may have several applications in fields regarding information transmission.

cond-mat.stat-mech↗

arXiv2023

Like-charge attraction in one- and two-dimensional Coulomb systems

The bare Coulomb interaction between two like-charges is repulsive. When these charges are immersed in an electrolyte, the thermal fluctuations of the ions turn the bare Coulomb interaction into an effective interaction between the two charges. An interesting question arises: is it possible that the effective interaction becomes attractive for like-charges? We will show how this like-charge attraction phenomenon is indeed predicted in some one- and two-dimensional models of Coulomb systems. Exact analytical results can be obtained for these Coulomb systems models due to some connections that they have with integrable field theories. We will explain the techniques that allow obtaining exact results for the correlation functions between like-charge particles and how, under certain circumstances, the natural repulsion interaction shifts to being attractive. Although the technical details differ for 1d or 2d systems, the physical cause of this phenomenon is rooted in a three-body interaction between the two like-charges and an ion of the electrolyte with an opposite charge.

cond-mat.stat-mech↗

arXiv2021

One-dimensional colloidal model with dielectric inhomogeneity

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to recover the mean-field prediction in the limit $N\to \infty$.

cond-mat.soft↗

arXiv2019

Annihilation of single-species charged particles based on the Dyson gas dynamics

We analyze the annihilation of equally-charged particles based on the Brownian motion model built by F. Dyson for $N$ particles with charge $q$ interacting via the log-Coulomb potential on the unitary circle at a reduced inverse temperature $β$, defined as $β=q^2/(k_B T)$. We derive an analytical approach in order to describe the large-$t$ asymptotic behaviour for the number density decay, which can be described as a power law, i.e., $n\sim t^{-ν}$. For a sufficiently large $β$, the power law exponent $ν$ behaves as $(β+1)^{-1}$, which was corroborated through several computational simulations. For small $β$, in the diffusive regime, we recover the exponent of 1/2 as predicted by single-species uncharged annihilation.

cond-mat.stat-mech↗

arXiv2019

Free energy of cylindrical polyions: analytical results

Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.

cond-mat.soft↗

arXiv2016

Configurational and energy landscape in one-dimensional Coulomb systems

We study a one dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. Temperature being given, two situations are addressed: the colloids are either kept at fixed positions (canonical ensemble), or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal: how many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left/right symmetry breakdown? We evidence a cascade of transitions, as system size is varied in the canonical treatment, or as pressure is increased in the isobaric formulation.

cond-mat.stat-mech↗

arXiv2015

Screening like-charges in one-dimensional Coulomb systems: Exact results

The possibility that like-charges can attract each other under the mediation of mobile counterions is by now well documented experimentally, numerically, and analytically. Yet, obtaining exact results is in general impossible, or restricted to some limiting cases. We work out here in detail a one dimensional model that retains the essence of the phenomena present in higher dimensional systems. The partition function is obtained explicitly, from which a wealth of relevant quantities follow, such as the effective force between the charges or the counterion profile in their vicinity. Isobaric and canonical ensembles are distinguished. The case of two equal charges screened by an arbitrary number $N$ of counterions is first studied, before the more general asymmetric situation is addressed. It is shown that the parity of $N$ plays a key role in the long range physics.

cond-mat.stat-mech↗

arXiv2015

Counter-ion density profile around a charged disk: from the weak to the strong association regime

We present a comprehensive study of the two dimensional one component plasma in the cell model with charged boundaries. Departing from weak couplings through a convenient approximation of the interacting potential we were able to obtain an analytic formulation to the problem deriving the partition function, density profile, contact densities and integrated profiles that compared well with the numerical data from Monte-Carlo simulations. Additionally, we derived the exact solution for the special cases of $Ξ= 1, 2, 3, ...$ finding a correspondence between the results from weak couplings and exact results. Furthermore, we investigated the strong coupling regime taking into consideration the Wigner formulation. Departing from this, we procured the profile to leading order, computed the contact density values as compared to those derived in a work on the contact theorem. We formulated adequately the strong coupling regime for this system that differed from previous formulations. Ultimately, we computed the first order corrections and compared those results against numerical results from our simulations obtaining very good agreement; this results compared equally well in the planar limit, whose results are known.

cond-mat.stat-mech↗

arXiv2015

Relations Among Two Methods for Computing the Partition Function of the Two-Dimensional One-Component Plasma

The two-dimensional one-component plasma ---2dOCP--- is a system composed by $n$ mobile particles with charge $q$ over a neutralizing background in a two-dimensional surface. The Boltzmann factor of this system, at temperature $T$, takes the form of a Vandermonde determinant to the power $Γ= q^2/(2π\varepsilon k_BT)$, where $Γ$ is the coupling constant of this Coulomb system. The partition function of the model has been computed exactly for the even values of the coupling constant $Γ$, and a finite number of particles $n$, by two means: 1) by recognizing that the Boltzmann factor is the square of a Jack polynomial and expanding it in an appropriate monomial base, and 2) by mapping the system onto a 1-dimensional chain of interacting fermions. In this work the connection among the two methods is derived, and some properties of the expansion coefficients for the power of the Vandermonde determinant are explored.

cond-mat.stat-mech↗

arXiv2014

The contact theorem for charged fluids: from planar to curved geometries

When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the boundaries are curved, and we work out how it generalizes when the fluid is confined between two concentric spheres (or cylinders), in two and in three space dimensions. The analysis is thus performed within the cell model picture. The generalized contact relation opens the possibility to derive new exact expressions, of particular interest in the regime of strong coulombic couplings. Some emphasis is put on cylindrical geometry, for which we discuss in depth the phenomenon of counter-ion evaporation/condensation, and obtain novel results. Good agreement is found with Monte Carlo simulation data.

cond-mat.stat-mech↗

arXiv2013

Slow sedimentation and deformability of charged lipid vesicles

The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended vesicles labelled with a fluorescent probe, which allows visualization using fluorescence microscopy and confers the membrane with a negative surface charge. The electrostatic interaction between the vesicle and the surface was modeled using the linear Derjaguin approximation for a low ionic concentration solution. The sedimentation rate as a function of the distance of the vesicle to the surface was determined both experimentally and from the computer simulations. The gap between the vesicle and the surface, as well as the shape of the vesicle at equilibrium were also studied. It was determined that inclusion of the electrostatic interaction is fundamental to accurately predict the sedimentation rate as the vesicle approaches the surface and the size of the gap at equilibrium, we also observed that the presence of charge in the membrane increases its rigidity.

physics.bio-ph↗

arXiv2012

Counter-ion density profile around charged cylinders: the strong-coupling needle limit

Charged rod-like polymers are not able to bind all their neutralizing counter-ions: a fraction of them evaporates while the others are said to be condensed. We study here counter-ion condensation and its ramifications, both numerically by means of Monte Carlo simulations employing a previously introduced powerful logarithmic sampling of radial coordinates, and analytically, with special emphasis on the strong-coupling regime. We focus on the thin rod, or needle limit, that is naturally reached under strong coulombic couplings, where the typical inter-particle spacing $a'$ along the rod is much larger than its radius R. This regime is complementary and opposite to the simpler thick rod case where $a'\ll R$. We show that due account of counter-ion evaporation, a universal phenomenon in the sense that it occurs in the same clothing for both weakly and strongly coupled systems, allows to obtain excellent agreement between the numerical simulations and the strong-coupling calculations.

cond-mat.stat-mech↗

arXiv2012

Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma

The two-dimensional one-component plasma (2dOCP) is a system of $N$ mobile particles of the same charge $q$ on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature $T$ can be expressed as a Vandermonde determinant to the power $Γ=q^{2}/(k_B T)$. Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for $N$ values up to 14 and $Γ$ equal to 4, 6 and 8. In this work, we explore two applications of this formalism to study the moments of the pair correlation function of the 2dOCP on a sphere, and the distribution of radial linear statistics of the 2dOCP in the plane.

math-ph↗

arXiv2012

Constrained quantum mechanics: chaos in non-planar billiards

We illustrate some of the techniques to identify chaos signatures at the quantum level using as a guiding examples some systems where a particle is constrained to move on a radial symmetric, but non planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or dunce hat billiard and the rectangular billiard with an inner Gaussian surface.

quant-ph↗

arXiv2010

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson--Botzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.

cond-mat.stat-mech↗

arXiv2009

Nonlinear screening of charged macromolecules

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Huckel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear equation give some interesting insight on physical phenomena like the charge renormalization and the Manning counterion condensation.

cond-mat.soft↗

arXiv2008

Two-dimensional one-component plasma on a Flamm's paraboloid

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Gamma=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.

cond-mat.stat-mech↗

arXiv2008

The polydisperse cell model: Non-linear screening and charge renormalization in colloidal mixtures

We propose a model for the calculation of renormalized charges and osmotic properties of mixtures of highly charged colloidal particles. The model is a generalization of the cell model and the notion of charge renormalization as introduced by Alexander and his collaborators (J. Chem. Phys. 80, 5776 (1984)). The total solution is partitioned into as many different cells as components in the mixture. The radii of these cells are determined self-consistently for a given set of parameters from the solution of the non-linear Poisson-Boltzmann equation with appropriate boundary conditions. This generalizes Alexanders's model where the (unique) Wigner-Seitz cell radius is fixed solely by the colloids packing fraction. We illustrate the technique by considering a binary mixture of colloids with the same sign of charge. The present model can be used to calculate thermodynamic properties of highly charged colloidal mixtures at the level of linear theories, while taking the effect of non-linear screening into account.

cond-mat.soft↗