Search results for "boundary"
showing 10 items of 1626 documents
Numerical solution of a class of nonlinear boundary value problems for analytic functions
1982
We analyse a numerical method for solving a nonlinear parameter-dependent boundary value problem for an analytic function on an annulus. The analytic function to be determined is expanded into its Laurent series. For the expansion coefficients we obtain an operator equation exhibiting bifurcation from a simple eigenvalue. We introduce a Galerkin approximation and analyse its convergence. A prominent problem falling into the class treated here is the computation of gravity waves of permanent type in a fluid. We present numerical examples for this case.
Pairs of nontrivial smooth solutions for nonlinear Neumann problems
2020
Abstract We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a reaction term that exhibits strong resonance at infinity. Using variational tools based on the critical point theory, we prove the existence of two nontrivial smooth solutions.
Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter
1999
Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
2011
In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a…
Boundaries between law and religion: considerations regarding the use of curses in the documents of Norman Sicily
2022
The word ‘boundary’ does not only indicate a physical division between different worlds. The border often represents a point of contact. This concept of a ‘boundary’ is particularly critical in the field of legal history because often the plurality of iura contributes not only to the fusion of different cultures but also to the creation of new ones. The purpose of this paper is to investigate the relevance and the meaning of expressions of Anathema and curse it’s possible to find in some Latin documents that date back to the Norman period of Sicily. This period is pivotal for the consolidation of the secular and spiritual power of the Church and the use of curses by the lay power highlights…
Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
2011
We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
Ab initio simulations of oxygen interaction with surfaces and interfaces in uranium mononitride
2012
Abstract The results of DFT supercell calculations of oxygen behavior upon the UN (0 0 1) and (1 1 0) surfaces as well as at the tilt grain boundary are presented. Oxygen adsorption, migration, incorporation into the surface N vacancies on (0 0 1) and (1 1 0) surfaces have been modeled using 2D slabs of different thicknesses and supercell sizes. The temperature dependences of the N vacancy formation energies and oxygen incorporation energies are calculated. We demonstrate that O atoms easily penetrate into UN surfaces and grain boundaries containing N vacancies, due to negative incorporation energies and a small energy barrier. The Gibbs free energies of N vacancy formation and O atom incor…
Dynamical analysis of anisotropic inflation
2016
Inflaton coupling to a vector field via the $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation and to circumvent the $\eta$-problem. Here, I perform dynamical analysis of such a system allowing for most general Bianchi I initial conditions. I also confirm the stability of attractor equilibrium points in phase-space directions that had not been investigated before.
Magnetic field effect on the corrosion processes at the Eurofer–Pb–17Li flow interface
2015
Abstract Structural and elemental analyses of the RAFM steel (EUROFER 97) interface with flowing Pb–17Li eutectic (velocity 5 cm/s at 550 °C, 1000 h) under the action of a strong magnetic field (B = 1.7 T) were performed using optical microscopy, SEM, confocal microscopy, precision micro-hardness methods, SIMS and point or line-scan EDX analyses. The results show that the magnetic field induces a faster crushing of martensite into the grains, a deeper dissolution of grain boundaries, an enhancement of the Fe and Cr mass transfer and a fast detachment of corrosion layers due to MHD effects.
Effective diffusion coefficient and diffusion-controlled reactions in insulating solids with defects
1995
Abstract The expressions for effective diffusion coefficient are obtained in the mean field approximation for two-phase system for spatial dimensions of 1, 2 and 3. The existence of potential barrier for diffusion on the phase boundary was taken into account via the boundary conditions. Obtained formulae could be applied in the theory of diffusion-controlled reactions and for interpreting the experimental data on defect diffusion in two-phase media.