Search results for "Computational Mathematic"
showing 10 items of 987 documents
Parametric nonlinear singular Dirichlet problems
2019
Abstract We consider a nonlinear parametric Dirichlet problem driven by the p -Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions.
Steady states and nonlinear buckling of cable-suspended beam systems
2018
This paper deals with the equilibria of an elastically-coupled cable-suspended beam system, where the beam is assumed to be extensible and subject to a compressive axial load. When no vertical load is applied, necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the stationary solutions are shown to exhibit at most two non-vanishing Fourier modes and the critical values of the axial-load parameter which produce their pitchfork bifurcation (buckling) are established. Depending on two dimensionless parameters, the complete set of resonant modes is devised. As expected, breakdown of the p…
Effect of electron correlation corrections on phase competition in Ag film on MgO substrate
2002
Abstract The effect of electron correlation corrections in the novel theory predicting the growth mode of a thin metallic film on an insulating substrate has been studied. We discuss the influence of the substrate slab thickness on the energies of formation for several two-dimensional phases, which, in principle, may form in Ag layer on (0 0 1) MgO substrate. We analyze also the sensitivity of the key energy parameter––Fourier transform of the mixing potential V (0) to the choice of correlation functionals.
Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions
2020
The authors acknowledge the assistance of the University Computer Center of Saint-Petersburg State University in the accomplishment of high-performance computations. A.K. is grateful to the Latvian Council of Science project no. lzp-2018/2-0353 for financial support. Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.
Molecular dynamics study of high-pressure alumina polymorphs with a tight-binding variable-charge model
2016
Abstract A tight-binding variable-charge model aimed at performing large-scale realistic simulations of bulk, surfaces and interfaces of aluminum oxides have been developed. This model is based on the charge equilibration (QEq) method and explicitly takes into account the mixed iono–covalent character of the metal–oxygen bond by means of a tight-binding analytical approach in the second-moment approximation of the electronic structure. The parameters of the model were optimized to reproduce structural and energetic properties of the α-Al2O3 corundum structure at room temperature and pressure. The model exhibits a good transferability between five alumina polymorphs: corundum, Rh2O3(II)-type…
The smectic phase in semiflexible polymer materials: A large scale Molecular Dynamics study
2019
Abstract Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the monomeric units for several contour lengths that are taken smaller than the chain persistence length. The difficulties concerning the equilibration of such systems and the choice of appropriate ensemble (constant volume versus constant pressure, where all three linear dimensions of the simulation box can fluctuate independently) are carefully discussed. Using HOOMD-blue on graphics processing units, systems containing more than a million monomeri…
Backbone of credit relationships in the Japanese credit market
2016
We detect the backbone of the weighted bipartite network of the Japanese credit market relationships. The backbone is detected by adapting a general method used in the investigation of weighted networks. With this approach we detect a backbone that is statistically validated against a null hypothesis of uniform diversification of loans for banks and firms. Our investigation is done year by year and it covers more than thirty years during the period from 1980 to 2011. We relate some of our findings with economic events that have characterized the Japanese credit market during the last years. The study of the time evolution of the backbone allows us to detect changes occurred in network size,…
On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method
2017
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
2012
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.