Search results for "Computational Mathematic"
showing 10 items of 987 documents
GEPOL: An improved description of molecular surfaces II. Computing the molecular area and volume
1991
The algorithm used by the program GEPOL for a finer description of molecular surface (for a fast calculation of molecular area and volume and for an efficient selection of sampling points) is presented in detail. Different types of surfaces such as van der Waals and Richard's molecular surfaces can be computed. As we described in the first article (J.L. Pascual-Ahuir and E. Silla, J. Comp. Chem., 11, 1047(1990)), GEPOL begins by building a set of spherical surfaces which fill the space which is not solvent accessible. In this second article, a triangular tessellation approach to select the parts of these spherical surfaces which form the molecular surface is described. By using a data coded…
Electrostatic interaction of a solute with a continuum. Improved description of the cavity and of the surface cavity bound charge distribution.
1987
Algorithms for a finer description of cavities in continuous media and for a more efficient selection of sampling points on the cavity surface are described. Applications to the evaluation of solute surface and volume and to the calculation of the solute-solvent electrostatic interaction energy, as well as of the cavitation energy are shown as examples.
GEPOL: An improved description of molecular surfaces. I. Building the spherical surface set
1990
The algorithm used by the program GEPOL to compute the Molecular Surface (MS), as defined by Richards, is presented in detail. GEPOL starts like other algorithms from a set of spheres with van der Waals radii, centered on the atoms or group of atoms of the molecule. GEPOL computes the MS by first searching the spaces inaccessible to the solvent and consequently filling them with a new set of spheres. Here we study the behavior of the method with its parameters, presenting several examples of application.
INITIAL PARAMETRIC REPRESENTATION OF BLOBS
2009
Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on …
Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points
2021
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…
On the Neron-Severi group of surfaces with many lines
2008
For a binary quartic form $\phi$ without multiple factors, we classify the quartic K3 surfaces $\phi(x,y)=\phi(z,t)$ whose Neron-Severi group is (rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of prime degree without multiple factors, we prove that the Neron-Severi group of the surface $\phi(x,y)=\psi(z,t)$ is rationally generated by lines.
A surface hopping algorithm for nonadiabatic minimum energy path calculations
2015
The article introduces a robust algorithm for the computation of minimum energy paths transiting along regions of near-to or degeneracy of adiabatic states. The method facilitates studies of excited state reactivity involving weakly avoided crossings and conical intersections. Based on the analysis of the change in the multiconfigurational wave function the algorithm takes the decision whether the optimization should continue following the same electronic state or switch to a different state. This algorithm helps to overcome convergence difficulties near degeneracies. The implementation in the MOLCAS quantum chemistry package is discussed. To demonstrate the utility of the proposed procedur…
Electronic structure trends of Möbius graphene nanoribbons from minimal-cell simulations
2014
Investigating topological effects in materials requires often the modeling of material systems as a whole. Such modeling restricts system sizes, and makes it hard to extract systematic trends. Here, we investigate the effect of M\"obius topology in the electronic structures of armchair graphene nanoribbons. Using density-functional tight-binding method and minimum-cell simulations through revised periodic boundary conditions, we extract electronic trends merely by changing cells' symmetry operations and respective quantum number samplings. It turns out that for a minimum cell calculation, once geometric and magnetic contributions are ignored, the effect of the global topology is unexpectedl…
A contribution to the mathematical modeling of immune-cancer competition
2018
Abstract This paper deals with the modeling of interactions between the immune system and cancer cells, in the framework of the mathematical kinetic theory for active particles. The work deepens a previous paper of Belloquid et al. that assumes spatial homogeneity and discrete values of the activity of cancer and immune cells. A number of simulations are made with the aim to investigate how the state of the various cell populations evolves in time depending on the choice of the free parameters.
Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson
2011
We present a discontinuous Galerkin scheme for the numerical approximation of the one-dimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases. Une méthode de Galerkin discontinu est proposée pour l’approximation numérique de l’équation de Vlasov-Poisson 1D. L’approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, …