14,321 research outputs found
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
-effect, i.e. of the existence of planetary vorticity gradients, is
discussed. In particular, it is shown that increasing increases the
tendency toward barotropization through turbulent stirring. The effectiveness
of barotropisation may be partly parameterized using the Rhines scale . 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 versus load are performed under compression by
imaging the light transmitted at the microcontacts. 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 relationship. Our discrete model also clearly shows
that the adhesion-induced effect on 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
Energetics of a driven Brownian harmonic oscillator
We provide insights into energetics of a Brownian oscillator in contact with
a heat bath and driven by an external unbiased time-periodic force that takes
the system out of thermodynamic equilibrium. Solving the corresponding Langevin
equation, we compute average kinetic and potential energies in the long-time
stationary state. We also derive the energy balance equation and study the
energy flow in the system. In particular, we identify the energy delivered by
the external force, the energy dissipated by a thermal bath and the energy
provided by thermal equilibrium fluctuations. Next, we illustrate Jarzynski
work-fluctuation relation and consider the stationary state fluctuation theorem
for the total work done on the system by the external force. Finally, by
determining time scales in the system, we analyze the strong damping regime and
discuss the problem of overdamped dynamics when inertial effects can be
neglected.Comment: in press: J. Stat. Mech. 201
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
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