Master Operators Govern Multifractality in Percolation

Using renormalization group methods we study multifractality in percolation at the instance of noisy random resistor networks. We introduce the concept of master operators. The multifractal moments of the current distribution (which are proportional to the noise cumulants $C_R^{(l)} (x, x^\prime)$ of the resistance between two sites x and $x^\prime$ located on the same cluster) are related to such master operators. The scaling behavior of the multifractal moments is governed exclusively by the master operators, even though a myriad of servant operators is involved in the renormalization procedure. We calculate the family of multifractal exponents ${\psi_l}$ for the scaling behavior of the noise cumulants, $C_R^{(l)} (x, x^\prime) \sim | x - x^\prime |^{\psi_l /\nu}$, where $\nu$ is the correlation length exponent for percolation, to two-loop order.Comment: 6 page

Double layer for hard spheres with an off-center charge

Simulations for the density and potential profiles of the ions in the planar electrical double layer of a model electrolyte or an ionic liquid are reported. The ions of a real electrolyte or an ionic liquid are usually not spheres; in ionic liquids, the cations are molecular ions. In the past, this asymmetry has been modelled by considering spheres that are asymmetric in size and/or valence (viz., the primitive model) or by dimer cations that are formed by tangentially touching spheres. In this paper we consider spherical ions that are asymmetric in size and mimic the asymmetrical shape through an off-center charge that is located away from the center of the cation spheres, while the anion charge is at the center of anion spheres. The various singlet density and potential profiles are compared to (i) the dimer situation, that is, the constituent spheres of the dimer cation are tangentially tethered, and (ii) the standard primitive model. The results reveal the double layer structure to be substantially impacted especially when the cation is the counterion. As well as being of intrinsic interest, this off-center charge model may be useful for theories that consider spherical models and introduce the off-center charge as a perturbation.Comment: 11 pages, 7 figure

Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer

Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and asymmetric valencies. The cations consist of two tangentially tethered hard spheres of the same diameter, $d$. One sphere is charged while the other is neutral. Spherical anions are charged hard spheres of diameter $d$. The ion valency asymmetry 1:2 and 2:1 is considered, with the ions being immersed in a solvent mimicked by a continuum dielectric medium at standard temperature. The simulations are carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M. Profiles of the electrode-ion, electrode-neutral sphere singlet distributions, the average orientation of dimers, and the mean electrostatic potential are calculated for a given electrode surface charge, $\sigma$, while the contact electrode potential and the differential capacitance are presented for varying electrode charge. With an increasing electrolyte concentration, the shape of differential capacitance curve changes from that with a minimum surrounded by maxima into that of a distorted single maximum. For a 2:1 electrolyte, the maximum is located at a small negative $\sigma$ value while for 1:2, at a small positive value.Comment: 10 pages, 6 figure

Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions

We study analytically the logarithmic corrections to the critical exponents of the critical behavior of correlation length, susceptibility and specific heat for the temperature and the finite-size scaling behavior, for a generic $\phi^3$ theory at its upper critical dimension (six). We have also computed the leading correction to scaling as a function of the lattice size. We distinguish the obtained formulas to the following special cases: percolation, Lee-Yang (LY) singularities and $m$-component spin glasses. We have compared our results for the Ising spin glass case with numerical simulations finding a very good agreement. Finally, and using the results obtained for the Lee-Yang singularities in six dimensions, we have computed the logarithmic corrections to the singular part of the free energy for lattice animals in eight dimensions.Comment: 18 pages. We have extended the computation to lattice animals in eight dimensions. To be published in Journal of Physics

Human cachexia induces changes in mitochondria, autophagy and apoptosis in the skeletal muscle

Cachexia is a wasting syndrome characterized by the continuous loss of skeletal muscle mass due to imbalance between protein synthesis and degradation, which is related with poor prognosis and compromised quality of life. Dysfunctional mitochondria are associated with lower muscle strength and muscle atrophy in cancer patients, yet poorly described in human cachexia. We herein investigated mitochondrial morphology, autophagy and apoptosis in the skeletal muscle of patients with gastrointestinal cancer-associated cachexia (CC), as compared with a weight-stable cancer group (WSC). CC showed prominent weight loss and increased circulating levels of serum C-reactive protein, lower body mass index and decreased circulating hemoglobin, when compared to WSC. Electron microscopy analysis revealed an increase in intermyofibrillar mitochondrial area in CC, as compared to WSC. Relative gene expression of Fission 1, a protein related to mitochondrial fission, was increased in CC, as compared to WSC. LC3 II, autophagy-related (ATG) 5 and 7 essential proteins for autophagosome formation, presented higher content in the cachectic group. Protein levels of phosphorylated p53 (Ser46), activated caspase 8 (Asp384) and 9 (Asp315) were also increased in the skeletal muscle of CC. Overall, our results demonstrate that human cancer-associated cachexia leads to exacerbated muscle-stress response that may culminate in muscle loss, which is in part due to disruption of mitochondrial morphology, dysfunctional autophagy and increased apoptosis. To the best of our knowledge, this is the first report showing quantitative morphological alterations in skeletal muscle mitochondria in cachectic patients

Anti-ganglioside antibodies in patients with Zika virus infection-associated Guillain-Barré Syndrome in Brazil.

Zika virus infection is associated with the development of Guillain-Barré syndrome (GBS), a neurological autoimmune disorder caused by immune recognition of gangliosides and other components at nerve membranes. Using a high-throughput ELISA, we have analyzed the anti-glycolipid antibody profile, including gangliosides, of plasma samples from patients with Zika infections associated or not with GBS in Salvador, Brazil. We have observed that Zika patients that develop GBS present higher levels of anti-ganglioside antibodies when compared to Zika patients without GBS. We also observed that a broad repertoire of gangliosides was targeted by both IgM and IgG anti-self antibodies in these patients. Since Zika virus infects neurons, which contain membrane gangliosides, antigen presentation of these infected cells may trigger the observed autoimmune anti-ganglioside antibodies suggesting direct infection-induced autoantibodies as a cause leading to GBS development. Collectively, our results establish a link between anti-ganglioside antibodies and Zika-associated GBS in patients

Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

Logarithmic Corrections in Dynamic Isotropic Percolation

Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin we calculate the number of active sites, the survival probability as well as the radius of gyration.Comment: 9 pages, 3 figures, version to appear in Phys. Rev.

Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions

We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of $s^\theta$ bytes where $\theta$ ranges from 0.4 for 2-dimensional lattices to 0.5 for 6- (or higher)-dimensional lattices. We use this method to estimate $d_{\scriptsize min}$, the exponent relating the minimum path $\ell$ to the Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site and bond percolation, we find $d_{\scriptsize min}=1.607\pm 0.005$ (4D) and $d_{\scriptsize min}=1.812\pm 0.006$ (5D). In order to determine $d_{\scriptsize min}$ to high precision, and without bias, it was necessary to first find precise values for the percolation threshold, $p_c$: $p_c=0.196889\pm 0.000003$ (4D) and $p_c=0.14081\pm 0.00001$ (5D) for site and $p_c=0.160130\pm 0.000003$ (4D) and $p_c=0.118174\pm 0.000004$ (5D) for bond percolation. We also calculate the Fisher exponent, $\tau$, determined in the course of calculating the values of $p_c$: $\tau=2.313\pm 0.003$ (4D) and $\tau=2.412\pm 0.004$ (5D)