Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlations functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions

Two-dimensional two-component plasma with adsorbing impurities

We study the behavior of the two-dimensional two-component plasma in the presence of some adsorbing impurities. Using a solvable model, we find analytic expressions for the thermodynamic properties of the plasma such as the $n$-body densities, the grand potential, and the pressure. We specialize in the case where there are one or two adsorbing point impurities in the plasma, and in the case where there are one or two parallel adsorbing lines. In the former case we study the effective interaction between the impurities, due to the charge redistribution around them. The latter case is a model for electrodes with adsorbing sticky sites on their surface

Injuries in epilepsy: a review of its prevalence, risk factors, type of injuries and prevention

Currently, there is intense clinical research into various aspects of the medical risks relating to epilepsy, including total and cause-specific mortality, accidents and injuries in patients with epilepsy and mortality related with seizures. Seizures occurring in precarious situations and resulting in injuries are still an important concern for patients with epilepsy, their employers and their care-givers. Submersion injuries, motor vehicle accidents, burns, and head injuries are among the most feared epilepsy-related injuries. These concerns seem valid because the hallmark of epilepsy, episodic impairment of consciousness and motor control, may occur during interictal EEG epileptiform discharges, even in the absence of a clinical seizure. In addition, psychomotor comorbidity and side effects of antiepileptic drugs may contribute to the risk of injuries in patients with epilepsy. Published risk factors for injuries include the number of antiepileptic drugs, history of generalized seizures, and seizure frequency. In general, epidemiological information about incidence of injuries has been conflicting and sparse. In general, studies focusing on populations with more severe forms of epilepsy tend to report substantially higher risks of injuries than those involving less selected populations. On the other hand, studies based on non-selected populations of people with epilepsy have not shown an increased frequency of injuries in people with epilepsy compared with the general population. Some studies have shown that patients with epilepsy are more frequently admitted to the hospital following an injury. Possible explanations include: more cautious attitude of clinicians toward injuries occurring in the setting of seizures; hospitalization required because of seizures and not to the injuries themselves; and hospitalization driven by other issues, such as comorbidities, which are highly prevalent in patients with epilepsy. Potentially the high rate of hospitalizations could be related with the severity of the injury. This article reviews the best available epidemiological information about injuries, including incidence and risk factors. Also this article reviews information about specific types of injuries such as fractures, burns, concussions, dislocations, etc. Information about accidents in people with epilepsy is also discussed

Onsager-Manning-Oosawa condensation phenomenon and the effect of salt

Making use of results pertaining to Painleve III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density, and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limit. In addition, we obtain explicit expressions for the condensate thickness and the electric potential. The case of asymmetric electrolytes is also briefly addressed.Comment: to appear in Phys. Rev. Let

Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances

Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile

We complement a recent exact study by L. Samaj on the properties of a guest charge $Q$ immersed in a two-dimensional electrolyte with charges $+1/-1$. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Samaj's previous work, exact results for arbitrary coulombic coupling $\beta$ were obtained for a system where all the charges are points, provided $\beta Q<2$ and $\beta < 2$. Here, we first focus on the mean field situation which we believe describes correctly the limit $\beta\to 0$ but $\beta Q$ large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value $\beta Q>2$. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Samaj for the renormalized charge are not valid for $\beta Q>2$, contrary to a hypothesis put forward by Samaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough ($\beta Q\geq 2-\beta$). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning--Oosawa threshold $\beta Q=2$

Identifying clusters of anomalous payments in the salvadorian payment system

We develop an unsupervised methodology to group payments and identify possible anomalies. With our methodology, we identify clusters based on a set of network features, using transactional (unlabeled) information from a systemically important payment system of El Salvador. We first preprocess network features, such as degree and strength, through a principal components analysis we reduce the dimensionality of the newly defined data, then we place the main variables into clustering algorithms (k-means and DBSCAN) to analyze anomalous payments. We then analyze, these clusters using random forest to obtain the main network feature. Our results suggest that the proposed methodology works very well to detect anomalous payments, and it is very important to study the case of El Salvador, because of the recent restructuring of the Massive Payment System in El Salvador (promoted by the Transfer365 project), because the authorities want to increase financial inclusion. This change will make the SPM available to the public, to diversify services and incorporate more participants because, historically, it has operated with only three active participants. We expected that Transfer365 will interconnect the LBTR participants' systems with their banking core, the systems of the Ministry of Finance, and other authorized participants to channel large payment flows. Then, identifying possible anomalies through methodology will enhance risk monitoring and management by payment systems overseers

The Ideal Conductor Limit

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge