47,458 research outputs found
A nonlinear elliptic problem with terms concentrating in the boundary
In this paper we investigate the behavior of a family of steady state
solutions of a nonlinear reaction diffusion equation when some reaction and
potential terms are concentrated in a -neighborhood of a portion
of the boundary. We assume that this -neighborhood shrinks
to as the small parameter goes to zero. Also, we suppose
the upper boundary of this -strip presents a highly oscillatory
behavior. Our main goal here is to show that this family of solutions converges
to the solutions of a limit problem, a nonlinear elliptic equation that
captures the oscillatory behavior. Indeed, the reaction term and concentrating
potential are transformed into a flux condition and a potential on ,
which depends on the oscillating neighborhood
Scalable Population Synthesis with Deep Generative Modeling
Population synthesis is concerned with the generation of synthetic yet
realistic representations of populations. It is a fundamental problem in the
modeling of transport where the synthetic populations of micro-agents represent
a key input to most agent-based models. In this paper, a new methodological
framework for how to 'grow' pools of micro-agents is presented. The model
framework adopts a deep generative modeling approach from machine learning
based on a Variational Autoencoder (VAE). Compared to the previous population
synthesis approaches, including Iterative Proportional Fitting (IPF), Gibbs
sampling and traditional generative models such as Bayesian Networks or Hidden
Markov Models, the proposed method allows fitting the full joint distribution
for high dimensions. The proposed methodology is compared with a conventional
Gibbs sampler and a Bayesian Network by using a large-scale Danish trip diary.
It is shown that, while these two methods outperform the VAE in the
low-dimensional case, they both suffer from scalability issues when the number
of modeled attributes increases. It is also shown that the Gibbs sampler
essentially replicates the agents from the original sample when the required
conditional distributions are estimated as frequency tables. In contrast, the
VAE allows addressing the problem of sampling zeros by generating agents that
are virtually different from those in the original data but have similar
statistical properties. The presented approach can support agent-based modeling
at all levels by enabling richer synthetic populations with smaller zones and
more detailed individual characteristics.Comment: 27 pages, 15 figures, 4 table
Quantized fields and gravitational particle creation in f(R) expanding universes
The problem of cosmological particle creation for a spatially flat,
homogeneous and isotropic Universes is discussed in the context of f(R)
theories of gravity. Different from cosmological models based on general
relativity theory, it is found that a conformal invariant metric does not
forbid the creation of massless particles during the early stages (radiation
era) of the Universe.Comment: 14 pages, 2 figure
Simulation of Transport and Gain in Quantum Cascade Lasers
Quantum cascade lasers can be modeled within a hierarchy of different
approaches: Standard rate equations for the electron densities in the levels,
semiclassical Boltzmann equation for the microscopic distribution functions,
and quantum kinetics including the coherent evolution between the states. Here
we present a quantum transport approach based on nonequilibrium Green
functions. This allows for quantitative simulations of the transport and
optical gain of the device. The division of the current density in two terms
shows that semiclassical transitions are likely to dominate the transport for
the prototype device of Sirtori et al. but not for a recent THz-laser with only
a few layers per period. The many particle effects are extremely dependent on
the design of the heterostructure, and for the case considered here, inclusion
of electron-electron interaction at the Hartree Fock level, provides a sizable
change in absorption but imparts only a minor shift of the gain peak.Comment: 12 pages, 5 figures included, to appear in in "Advances in Solid
State Physics", ed. by B. Kramer (Springer 2003
Conformal and gauge invariant spin-2 field equations
Using an approach based on the Casimir operators of the de Sitter group, the
conformal invariant equations for a fundamental spin-2 field are obtained, and
their consistency discussed. It is shown that, only when the spin-2 field is
interpreted as a 1-form assuming values in the Lie algebra of the translation
group, rather than a symmetric second-rank tensor, the field equation is both
conformal and gauge invariant.Comment: 12 pages, no figures; accepted for publication in Gravitation &
Cosmolog
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