arXiv subjects

I. C. Charret

Publications and source records attributed to I. C. Charret.

6 recordsLinked to original sources

arXiv2006

Individual-based model for coevolving competing populations

Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the same resources \textit{without} niche partition. Motivated by this experimental challenge to classical competition theory, we propose an individual-based stochastic competition model, which is essentially a modification of a deterministic Lotka-Volterra type model. The proposed model of competition dynamics incorporates the effects of a discrete genotype, which determines the individual's adaptation to the environment, as well as its interaction with the other species.

q-bio.PE↗

arXiv2006

Spontaneous emergence of spatial patterns ina a predator-prey model

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays travelling waves solutions, clustering and uniform distributions, all related to the parameters values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plants, regulated the presence of predators, as well as the type of spatial configuration.

q-bio.PE↗

arXiv2000

Analytical Results of the One-Dimensional Hubbard Model in the High Temperature Limit

We investigate the grand potential of the one-dimensional Hubbard model in the high temperature limit, calculating the coefficients of the high temperature expansion ($β$-expansion) of this function up to order $β^4$ by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the one-dimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni {\it et al.} and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by Jüttner {\it et al}. is applied to the determination of the range of validity of our expansion in $β$ in the half-filled case, for several different values of $U$.

cond-mat↗

arXiv1998

Grassmann Algebra and Fermions at Finite Temperature

For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai-Kohmoto model, reobtaining well-known results.

cond-mat.stat-mech↗

arXiv1997

Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order $β^5$

We calculate the exact analytical coefficients of the $β$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order $β^5$, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.

cond-mat.str-el↗

arXiv1996

Grand Canonical Partition Function for Unidimensional Systems: Application to Hubbard Model up to Order beta^3

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.

cond-mat↗