Exterior complex scaling as a perfect absorber in time-dependent problems

It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schr\"odinger equation with strong infrared fields. This is demonstrated by computing high harmonic spectra and wave-function overlaps with the exact solution for a one-dimensional model system and by three-dimensional calculations for the H atom and a Ne atom model. We lay out the key ingredients for correct implementation and identify criteria for efficient discretization

How to centralize and normalize quandle extensions

We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments coming from categorical Galois theory and by constructing concretely a centralization congruence. Moreover, we show that a similar result holds for normal quandle extensions.Comment: 17 page

The catalytic role of beta effect in barotropization processes

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the $\beta$-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing $\beta$ increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropisation may be partly parameterized using the Rhines scale $2\pi E_{0}^{1/4}/\beta^{1/2}$. As this parameter decreases (beta increases) then barotropization can progress further, because the beta term provides enstrophy to each layer

Adhesive contact of model randomly rough rubber surfaces

We study experimentally and theoretically the equilibrium adhesive contact between a smooth glass lens and a rough rubber surface textured with spherical microasperities with controlled height and spatial distributions. Measurements of the real contact area $A$ versus load $P$ are performed under compression by imaging the light transmitted at the microcontacts. $A(P)$ is found to be non-linear and to strongly depend on the standard deviation of the asperity height distribution. Experimental results are discussed in the light of a discrete version of Fuller and Tabor's (FT) original model (\textit{Proceedings of the Royal Society A} \textbf{345} (1975) 327), which allows to take into account the elastic coupling arising from both microasperities interactions and curvature of the glass lens. Our experimental data on microcontact size distributions are well captured by our discrete extended model. We show that the elastic coupling arising from the lens curvature has a significant contribution to the $A(P)$ relationship. Our discrete model also clearly shows that the adhesion-induced effect on $A$ remains significant even for vanishingly small pull-off forces. Last, at the local asperity length scale, our measurements show that the pressure dependence of the microcontacts density can be simply described by the original FT model

Extended MacMahon-Schwinger's Master Theorem and Conformal Wavelets in Complex Minkowski Space

We construct the Continuous Wavelet Transform (CWT) on the homogeneous space (Cartan domain) D_4=SO(4,2)/(SO(4)\times SO(2)) of the conformal group SO(4,2) (locally isomorphic to SU(2,2)) in 1+3 dimensions. The manifold D_4 can be mapped one-to-one onto the future tube domain C^4_+ of the complex Minkowski space through a Cayley transformation, where other kind of (electromagnetic) wavelets have already been proposed in the literature. We study the unitary irreducible representations of the conformal group on the Hilbert spaces L^2_h(D_4,d\nu_\lambda) and L^2_h(C^4_+,d\tilde\nu_\lambda) of square integrable holomorphic functions with scale dimension \lambda and continuous mass spectrum, prove the isomorphism (equivariance) between both Hilbert spaces, admissibility and tight-frame conditions, provide reconstruction formulas and orthonormal basis of homogeneous polynomials and discuss symmetry properties and the Euclidean limit of the proposed conformal wavelets. For that purpose, we firstly state and prove a \lambda-extension of Schwinger's Master Theorem (SMT), which turns out to be a useful mathematical tool for us, particularly as a generating function for the unitary-representation functions of the conformal group and for the derivation of the reproducing (Bergman) kernel of L^2_h(D_4,d\nu_\lambda). SMT is related to MacMahon's Master Theorem (MMT) and an extension of both in terms of Louck's SU(N) solid harmonics is also provided for completeness. Convergence conditions are also studied.Comment: LaTeX, 40 pages, three new Sections and six new references added. To appear in ACH

The Zero discounting and maximin optimal paths in a simple model of global warming

Following Stollery [1998], we extend the Solow, Dasgupta-Heal model to analyze the effects of global warning. The rise of temperature is caused by the use of fossil resources so that the temperature level can be linked to the remaining stock of these resources. The rise of temperature affects both productivity and utility. We characterize optimal solutions for the maximin and zero-discounting cases and present closed form solutions for the case where the production function and utility function are Cobb-Douglas, and the temperature level is an exponential function of the remaining stock of resources. We show that a greater weight of temperature in the preferences or a larger intertemporal elasticity of substitution both lead to postpone resource use.Maximin ; zero discounting ; global warming