55 research outputs found
Reconstruction of Bandlimited Functions from Unsigned Samples
We consider the recovery of real-valued bandlimited functions from the
absolute values of their samples, possibly spaced nonuniformly. We show that
such a reconstruction is always possible if the function is sampled at more
than twice its Nyquist rate, and may not necessarily be possible if the samples
are taken at less than twice the Nyquist rate. In the case of uniform samples,
we also describe an FFT-based algorithm to perform the reconstruction. We prove
that it converges exponentially rapidly in the number of samples used and
examine its numerical behavior on some test cases
Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes
An improved method is given for the computation of the stress-energy tensor
of a quantized scalar field using adiabatic regularization. The method works
for fields with arbitrary mass and curvature coupling in Robertson-Walker
spacetimes and is particularly useful for spacetimes with compact spatial
sections. For massless fields it yields an analytic approximation for the
stress-energy tensor that is similar in nature to those obtained previously for
massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure
Regularizing Property of the Maximal Acceleration Principle in Quantum Field Theory
It is shown that the introduction of an upper limit to the proper
acceleration of a particle can smooth the problem of ultraviolet divergencies
in local quantum field theory. For this aim, the classical model of a
relativistic particle with maximal proper acceleration is quantized canonically
by making use of the generalized Hamiltonian formalism developed by Dirac. The
equations for the wave function are treated as the dynamical equations for the
corresponding quantum field. Using the Green's function connected to these wave
equations as propagators in the Feynman integrals leads to an essential
improvement of their convergence properties.Comment: 9 pages, REVTeX, no figures, no table
Cascades of subharmonic stationary states in strongly non-linear driven planar systems
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial
non-linearity subjected to an external periodic excitation is studied. The
sequences (cascades) of harmonic and subharmonic stationary solutions to the
equation of motion are obtained by using the harmonic balance approximation
adapted for arbitrary truncation numbers, powers of non-linearity, and orders
of subharmonics. A scheme for investigating the stability of the harmonic
balance stationary solutions of such a general form is developed on the basis
of the Floquet theorem. Besides establishing the stable/unstable nature of a
stationary solution, its stability analysis allows obtaining the regions of
parameters, where symmetry-breaking and period-doubling bifurcations occur.
Thus, for period-doubling cascades, each unstable stationary solution is used
as a base solution for finding a subsequent stationary state in a cascade. The
procedure is repeated until this stationary state becomes stable provided that
a stable solution can finally be achieved. The proposed technique is applied to
calculate the sequences of subharmonic stationary states in driven hardening
Duffing's oscillator. The existence of stable subharmonic motions found is
confirmed by solving the differential equation of motion numerically by means
of a time-difference method, with initial conditions being supplied by the
harmonic balance approximation.Comment: 37 pages, 11 figures, revised material on chaotic motio
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