arXiv subjects

G. Torres-Vargas

Publications and source records attributed to G. Torres-Vargas.

4 recordsLinked to original sources

arXiv2022

The role of spontaneous curvature in the formation of cell membrane necks

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous of neck formation in cellular membranes. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution is determined by the equilibrium mechanical equations, and, in order to establish the role played by the inhomogeneity, we focus on the catenoid, a surface of zero mean curvature, which can be described in terms of the catenary curve parameterized by arc length. We show that analytic solutions exist for the spontaneous curvature, as well as for both, the surface tension and the radial elastic force. An analytic expression for the constrictive force at the neck, is obtained. From the energetic analysis, it is found that, if we fix the value of the constrictive force at the neck, the set of solutions lies on two branches separated by an energetic barrier. This barrier corresponds to the energy of the maximum catenoid. If instead we fix the axial force, the solution has access to catenoid of any size

cond-mat.soft↗

arXiv2019

Normal mode analysis of disordered random-matrix ensembles

The statistics of random-matrix spectra can be very sensitive to the unfolding procedure that separates global from local properties. In order to avoid the introduction of possible artifacts, recently it has been applied to ergodic ensembles of Random Matrix Theory (RMT) the singular value decomposition (SVD) method, based on normal mode analysis, which characterizes the long-range correlations of the spectral fluctuations in a direct way without performing any unfolding. However, in the case of more general ensembles, the ergodicity property is often broken leading to ambiguities between spectrum-unfolded and ensemble-unfolded fluctuation statistics. Here, we apply SVD to a disordered random-matrix ensemble with tunable nonergodicity, as a mathematical framework to characterize the nonergodicity. We show that ensemble-averaged and individual-spectrum averaged statistics are calculated consistently using the same normal mode basis, and the nonergodicity is explained as a breakdown of this common basis.

nlin.CD↗

arXiv2019

Normal mode analysis of spectra of random networks

Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires performing an unfolding procedure, which may not be an easy task. In this work, network spectra are interpreted as time series, and we show how their short and long-range correlations can be characterized without implementing any previous unfolding. In particular, we consider three different representations of Erdös-Rényi (ER) random networks: standard ER networks, ER networks with random-weighted self-edges, and fully random-weighted ER networks. In each case, we apply singular value decomposition (SVD) such that the spectra are decomposed in trend and fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear crossover between the Poisson and the Gaussian orthogonal ensemble statistics when increasing the average degree of ER networks. Moreover, by using the trend modes, we perform a data-adaptive unfolding to calculate, for comparison purposes, traditional fluctuation measures such as the nearest neighbor spacing distribution, number variance $Σ$2, as well as $Δ$3 and δn statistics. The thorough comparison of RMT short and long-range correlation measures make us identify the SVD method as a robust tool for characterizing random network spectra.

cond-mat.dis-nn↗

arXiv2018

Induced stresses in quasi-spherical elastic vesicles: local and global Laplace-Young law

On elastic spherical membranes, there is no stress induced by the bending energy and the corresponding Laplace-Young law does not involve the elastic bending stiffness. However, when considering an axially symmetrical perturbation that pinches the sphere, it induces nontrivial stresses on the entire membrane. In this paper we introduce a theoretical framework to examine the stress induced by perturbations of geometry around the sphere. We find the local balance force equations along the normal direction to the vesicle, and along the unit binormal, tangent to the membrane; likewise, the global balance force equation on closed loops is also examined. We analyze the distribution of stresses on the membrane as the budding transition occurs. For closed membranes we obtain the modified Young-Laplace law that appears as a consequence of this perturbation.

cond-mat.soft↗