Search results for "boundary"

Non-self-adjoint graphs

2013

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way how to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

The Proton Spin in the Chiral Bag Model : Casimir Contribution and Cheshire Cat Principle

1998

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so called {\it Proton Spin Problem}. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated $U_A(1)$ anomaly. This anomaly is intimately associated with the $\eta^\prime$ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the $U_A(1)$ anomaly is known to induce color anomaly leading to "leakage" of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This ``color bounda…

Solution to the Flavor Problem of Warped Extra-Dimension Models

2011

A minimal solution to the flavor problem of warped extra-dimension models, i.e. the excessive mixed-chirality contribution to CP violation in K-Kbar mixing arising from Kaluza-Klein (KK) gluon exchange, is proposed. Extending the strong-interaction gauge group in the bulk by an additional SU(3), and breaking this symmetry to QCD via boundary conditions, the constraints arising from the epsilon_K parameter are significantly relaxed. As a result, KK scales M_KK ~ 2 TeV are consistent with all flavor observables without significant fine-tuning. The model predicts the existence of an extended Higgs sector featuring massive color-octet scalars and a tower of KK pseudo-axial gluon resonances, who…

When Casimir meets Kibble–Zurek

2012

Verification of the dynamical Casimir effect (DCE) in optical systems is still elusive due to the very demanding requirements for its experimental implementation. This typically requires very fast changes in the boundary conditions of the problem. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way for an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system an…

Flavour geometry and effective Yukawa couplings in the MSSM

2010

We present a new geometric approach to the flavour decomposition of an arbitrary soft supersymmetry-breaking sector in the MSSM. Our approach is based on the geometry that results from the quark and lepton Yukawa couplings, and enables us to derive the necessary and sufficient conditions for a linearly-independent basis of matrices related to the completeness of the internal [SU(3) circle times U(1)](5) flavour space. In a second step, we calculate the effective Yukawa couplings that are enhanced at large values of tan beta for general soft supersymmetry-breaking mass parameters. We highlight the contributions due to non-universal terms in the flavour decompositions of the sfermion mass mat…

Boundary Hölder Continuity and Quasiconformal Mappings

1991

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

2001

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.

Diffusion of Oxygen in Thermally Grown Oxide Scales

2009

High temperature reactivity of materials under oxidizing atmospheres is based on the formation of protective oxide scales. The protectiveness is obtained when the thermally grown oxide scales are dense, continuous and adherent to the metallic substrates (even during thermal shocks); as a matter of fact, the growth of the scale has to be governed by diffusion of species across the growing scale. The diffusing species are coming from the substrate (metallic ions) and/or from the oxidizing atmosphere (oxygen ions). The understanding of growth mechanisms can be reached by making two stage oxidation experiments, using oxygen isotopes. The experiment consists in oxidizing first the metallic subst…

Numerical Determination of Intrinsic Diffusion in Fe-Cr-Al Systems

2010

The intrinsic diffusion coefficients in diffusion aluminide coatings based on Fe-30Cr were determined at 1000oC. The diffusion fluxes were given by the Nernst Planck formulae and the Darken method for multicomponent systems was applied. This paper summarizes some numerical results to determine the composition dependent diffusivities in Fe-Cr-Al systems. The method presented in this study to obtain average intrinsic diffusion coefficients is as an alternative to the Dayananda method. Our method based on empirical parameters allowed us to predict the concentration profile during the interdiffusion process.

Numerical Determination of Intrinsic Diffusion Coefficient of Aluminide Coatings on Metals

2009

This paper presents a numerical method to determine the composition dependent diffusivities and to predict the concentration profile during the interdiffusion process. The intrinsic diffusion coefficients in diffusion aluminide coatings (Fe-Al) were determined at 1000oC. The obtained diffusion coefficient for iron in Fe3Al or FeAl is in the range 10-10 to 10-9 cm2.s-1. The aluminum diffusion coefficient varies from 10-11 to 10-7 cm2.s-1 in the same phases.The present approach also permits to model the reactive diffusion in the Fe-Al systems.