4,875 research outputs found
Investigation of the utility of mean square approximation systems and in system response predictions
A method is presented for estimating the variability of a system's natural frequencies arising from the variability of the system's parameters. The only information required to obtain the estimates is the member variability, in the form of second order properties, and the natural frequencies and mode shapes of the mean system. Several examples are worked out in detail to illustrate how the method is applied
The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
We have observed the production of strings (disclination lines and loops) via
the Kibble mechanism of domain (bubble) formation in the isotropic to nematic
phase transition of a sample of uniaxial nematic liquid crystal. The probablity
of string formation per bubble is measured to be . This is in
good agreement with the theoretical value expected in two dimensions
for the order parameter space of a simple uniaxial nematic
liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request
Loop Groups and Discrete KdV Equations
A study is presented of fully discretized lattice equations associated with
the KdV hierarchy. Loop group methods give a systematic way of constructing
discretizations of the equations in the hierarchy. The lattice KdV system of
Nijhoff et al. arises from the lowest order discretization of the trivial,
lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are
also given, the lowest order discretization of the first nontrivial equation in
the hierarchy, and a "second order" discretization of b_t=b_x. The former,
which is given the name "full lattice KdV" has the (potential) KdV equation as
a standard continuum limit. For each discretization a Backlund transformation
is given and soliton content analyzed. The full lattice KdV system has, like
KdV itself, solitons of all speeds, whereas both other discretizations studied
have a limited range of speeds, being discretizations of an equation with
solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur
Hydrogen production by photoelectrolytic decomposition of H2O using solar energy
Photoelectrochemical systems for the efficient decomposition of water are discussed. Semiconducting d band oxides which would yield the combination of stability, low electron affinity, and moderate band gap essential for an efficient photoanode are sought. The materials PdO and Fe-xRhxO3 appear most likely. Oxygen evolution yields may also be improved by mediation of high energy oxidizing agents, such as CO3(-). Examination of several p type semiconductors as photocathodes revealed remarkable stability for p-GaAs, and also indicated p-CdTe as a stable H2 photoelectrode. Several potentially economical schemes for photoelectrochemical decomposition of water were examined, including photoelectrochemical diodes and two stage, four photon processes
Atom cooling by non-adiabatic expansion
Motivated by the recent discovery that a reflecting wall moving with a
square-root in time trajectory behaves as a universal stopper of classical
particles regardless of their initial velocities, we compare linear in time and
square-root in time expansions of a box to achieve efficient atom cooling. For
the quantum single-atom wavefunctions studied the square-root in time expansion
presents important advantages: asymptotically it leads to zero average energy
whereas any linear in time (constant box-wall velocity) expansion leaves a
non-zero residual energy, except in the limit of an infinitely slow expansion.
For finite final times and box lengths we set a number of bounds and cooling
principles which again confirm the superior performance of the square-root in
time expansion, even more clearly for increasing excitation of the initial
state. Breakdown of adiabaticity is generally fatal for cooling with the linear
expansion but not so with the square-root expansion.Comment: 4 pages, 4 figure
Contraction of broken symmetries via Kac-Moody formalism
I investigate contractions via Kac-Moody formalism. In particular, I show how
the symmetry algebra of the standard 2-D Kepler system, which was identified by
Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was
denoted by , gets reduced by the symmetry breaking term,
defined by the Hamiltonian For this I
define two symmetry loop algebras , by
choosing the `basic generators' differently. These
can be mapped isomorphically onto subalgebras of , of
codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras
, relative to the corresponding
energy-dependent ideals , are isomorphic to
and for , respectively, just as for the
pure Kepler case. However, they yield two different non-standard contractions
as , namely to the Heisenberg-Weyl algebra or to an abelian Lie algebra, instead of the Euclidean algebra
for the pure Kepler case. The above example suggests a
general procedure for defining generalized contractions, and also illustrates
the {\em `deformation contraction hysteresis'}, where contraction which involve
two contraction parameters can yield different contracted algebras, if the
limits are carried out in different order.Comment: 21 pages, 1 figur
WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials
In the present work the conditions appearing in the WKB approximation
formalism of quantum mechanics are analyzed. It is shown that, in general, a
careful definition of an approximation method requires the introduction of two
length parameters, one of them always considered in the text books on quantum
mechanics, whereas the second one is usually neglected. Afterwards we define a
particular family of potentials and prove, resorting to the aforementioned
length parameters, that we may find an energy which is a lower bound to the
ground energy of the system. The idea is applied to the case of a harmonic
oscillator and also to a particle freely falling in a homogeneous gravitational
field, and in both cases the consistency of our method is corroborated. This
approach, together with the Rayleigh--Ritz formalism, allows us to define an
energy interval in which the ground energy of any potential, belonging to our
family, must lie.Comment: Accepted in Modern Physics Letters
Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check
We show that when the Hornberger--Sipe calculation of collisional decoherence
is carried out with the squared delta function a delta of energy instead of a
delta of the absolute value of momentum, following a method introduced by
Di\'osi, the corrected formula for the decoherence rate is simply obtained. The
results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As
an independent cross-check, we calculate the mean squared coordinate diffusion
of a hard sphere implied by the corrected decoherence master equation, and show
that it agrees precisely with the same quantity as calculated by a classical
Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references
added 9/29/06: further minor revisions and references adde
Neural Network Model for Apparent Deterministic Chaos in Spontaneously Bursting Hippocampal Slices
A neural network model that exhibits stochastic population bursting is
studied by simulation. First return maps of inter-burst intervals exhibit
recurrent unstable periodic orbit (UPO)-like trajectories similar to those
found in experiments on hippocampal slices. Applications of various control
methods and surrogate analysis for UPO-detection also yield results similar to
those of experiments. Our results question the interpretation of the
experimental data as evidence for deterministic chaos and suggest caution in
the use of UPO-based methods for detecting determinism in time-series data.Comment: 4 pages, 5 .eps figures (included), requires psfrag.sty (included
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