4,592 research outputs found
Duality and interval analysis over idempotent semirings
In this paper semirings with an idempotent addition are considered. These
algebraic structures are endowed with a partial order. This allows to consider
residuated maps to solve systems of inequalities . The
purpose of this paper is to consider a dual product, denoted , and the
dual residuation of matrices, in order to solve the following inequality . Sufficient conditions ensuring the
existence of a non-linear projector in the solution set are proposed. The
results are extended to semirings of intervals
Particle Creation by a Moving Boundary with Robin Boundary Condition
We consider a massless scalar field in 1+1 dimensions satisfying a Robin
boundary condition (BC) at a non-relativistic moving boundary. We derive a
Bogoliubov transformation between input and output bosonic field operators,
which allows us to calculate the spectral distribution of created particles.
The cases of Dirichlet and Neumann BC may be obtained from our result as
limiting cases. These two limits yield the same spectrum, which turns out to be
an upper bound for the spectra derived for Robin BC. We show that the particle
emission effect can be considerably reduced (with respect to the
Dirichlet/Neumann case) by selecting a particular value for the oscillation
frequency of the boundary position
Quantum radiation in a plane cavity with moving mirrors
We consider the electromagnetic vacuum field inside a perfect plane cavity
with moving mirrors, in the nonrelativistic approximation. We show that low
frequency photons are generated in pairs that satisfy simple properties
associated to the plane geometry. We calculate the photon generation rates for
each polarization as functions of the mechanical frequency by two independent
methods: on one hand from the analysis of the boundary conditions for moving
mirrors and with the aid of Green functions; and on the other hand by an
effective Hamiltonian approach. The angular and frequency spectra are discrete,
and emission rates for each allowed angular direction are obtained. We discuss
the dependence of the generation rates on the cavity length and show that the
effect is enhanced for short cavity lengths. We also compute the dissipative
force on the moving mirrors and show that it is related to the total radiated
energy as predicted by energy conservation.Comment: 17 pages, 1 figure, published in Physical Review
Inertial forces in the Casimir effect with two moving plates
We combine linear response theory and dimensional regularization in order to
derive the dynamical Casimir force in the low frequency regime. We consider two
parallel plates moving along the normal direction in dimensional space. We
assume the free-space values for the mass of each plate to be known, and obtain
finite, separation-dependent mass corrections resulting from the combined
effect of the two plates. The global mass correction is proportional to the
static Casimir energy, in agreement with Einstein's law of equivalence between
mass and energy for stressed rigid bodies.Comment: 9 pages, 1 figure; title and abstract changed; to appear in Physical
Review
Radiation Pressure as a Source of Decoherence
We consider the interaction of an harmonic oscillator with the quantum field
via radiation pressure. We show that a `Schrodinger cat' state decoheres in a
time scale that depends on the degree of `classicality' of the state
components, and which may be much shorter than the relaxation time scale
associated to the dynamical Casimir effect. We also show that decoherence is a
consequence of the entanglement between the quantum states of the oscillator
and field two-photon states. With the help of the fluctuation-dissipation
theorem, we derive a relation between decoherence and damping rates valid for
arbitrary values of the temperature of the field. Coherent states are selected
by the interaction as pointer states.Comment: 14 pages, 3 figures, RevTex fil
Dynamical Casimir effect with Dirichlet and Neumann boundary conditions
We derive the radiation pressure force on a non-relativistic moving plate in
1+1 dimensions. We assume that a massless scalar field satisfies either
Dirichlet or Neumann boundary conditions (BC) at the instantaneous position of
the plate. We show that when the state of the field is invariant under time
translations, the results derived for Dirichlet and Neumann BC are equal. We
discuss the force for a thermal field state as an example for this case. On the
other hand, a coherent state introduces a phase reference, and the two types of
BC lead to different results.Comment: 12 page
Lateral Casimir-Polder force with corrugated surfaces
We derive the lateral Casimir-Polder force on a ground state atom on top of a
corrugated surface, up to first order in the corrugation amplitude. Our
calculation is based on the scattering approach, which takes into account
nonspecular reflections and polarization mixing for electromagnetic quantum
fluctuations impinging on real materials. We compare our first order exact
result with two commonly used approximation methods. We show that the proximity
force approximation (large corrugation wavelengths) overestimates the lateral
force, while the pairwise summation approach underestimates it due to the
non-additivity of dispersion forces. We argue that a frequency shift
measurement for the dipolar lateral oscillations of cold atoms could provide a
striking demonstration of nontrivial geometrical effects on the quantum vacuum.Comment: 12 pages, 6 figures, contribution to QFEXT07 proceeding
The Seyfert Population in the Local Universe
The magnitude-limited catalog of the Southern Sky Redshift Survey (SSRS2), is
used to characterize the properties of galaxies hosting Active Galactic Nuclei.
Using emission-line ratios, we identify a total of 162 (3%) Seyfert galaxies
out of the parent sample with 5399 galaxies. The sample contains 121 Seyfert 2
galaxies and 41 Seyfert 1. The SSRS2 Seyfert galaxies are predominantly in
spirals of types Sb and earlier, or in galaxies with perturbed appearance as
the result of strong interactions or mergers. Seyfert galaxies in this sample
are twice as common in barred hosts than the non-Seyferts. By assigning
galaxies to groups using a percolation algorithm we find that the Seyfert
galaxies in the SSRS2 are more likely to be found in binary systems, when
compared to galaxies in the SSRS2 parent sample. However, there is no
statistically significant difference between the Seyfert and SSRS2 parent
sample when systems with more than 2 galaxies are considered. The analysis of
the present sample suggests that there is a stronger correlation between the
presence of the AGN phenomenon with internal properties of galaxies
(morphology, presence of bar, luminosity) than with environmental effects
(local galaxy density, group velocity dispersion, nearest neighbor distance).Comment: 35 pages, 13 figures, Accepted to be publised in Astronomical Journa
Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam
Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values
- âŠ