arXiv subjects

P. A. de Castro

Publications and source records attributed to P. A. de Castro.

3 recordsLinked to original sources

arXiv2004

Micellar shape anisotropy and elastic constants in discotic lyotropic liquid crystals

The elastic constants of a discotic lyotropic nematic liquid crystal are calculated by means of a pseudo-molecular approach as functions of the micellar shape anisotropy. By assuming that the temperature dependence of the ratio of the elastic constants comes from the temperature dependence of the micellar shape anisotropy, the theoretical predictions are connected with experimental measurements for the ratio $K_{33}/K_{11}$. This procedure permits to determine, in a phenomenological way, the temperature dependence for the ratio of elastic constants and for the micellar shape anisotropy near the nematic-isotropic transition in agreement with the experimental data.

cond-mat.stat-mech↗

arXiv2004

Nonlinear Barabási-Albert Network

In recent years there has been considerable interest in the structure and dynamics of complex networks. One of the most studied networks is the linear Barabási-Albert model. Here we investigate the nonlinear Barabási-Albert growing network. In this model, a new node connects to a vertex of degree $k$ with a probability proportional to $k^α$ ($α$ real). Each vertex adds $m$ new edges to the network. We derive an analytic expression for the degree distribution $P(k)$ which is valid for all values of $m$ and $α\le 1$. In the limit $α\to -\infty$ the network is homogeneous. If $α> 1$ there is a gel phase with $m$ super-connected nodes. It is proposed a formula for the clustering coefficient which is in good agreement with numerical simulations. The assortativity coefficient $r$ is determined and it is shown that the nonlinear Barabási-Albert network is assortative (disassortative) if $α< 1$ ($α> 1$) and no assortative only when $α= 1$. In the limit $α\to -\infty$ the assortativity coefficient can be exactly calculated. We find $r=7/13$ when $m=2$. Finally, the minimum average shortest path length $l_{min}$ is numerically evaluated. Increasing the network size, $l_{min}$ diverges for $α\le 1$ and it is equal to 1 when $α> 1$.

cond-mat.stat-mech↗

arXiv2003

Optimization and self-organized criticality in a magnetic system

We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter $τ$, the extremal optimization dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the system's ground state.

cond-mat.stat-mech↗