267 research outputs found
Structural controllability: an undirected graph approach
This paper addresses questions regarding controllability for `generic
parameter' dynamical systems, i.e. the question whether a dynamical system is
`structurally controllable'. Unlike conventional methods that deal with
structural controllability, our approach uses an undirected graph: the
behavioral approach to modelling dynamical systems allows this. Given a system
of linear, constant coefficient, ordinary differential equations of any order,
we formulate necessary and sufficient conditions for controllability in terms
of weights of the edges in a suitable bipartite graph constructed from %
components with equal bipartite cardinality in the differential-algebraic
system. % of equations. A key notion that helps formulate the conditions is
that of a `redundant edge'. Removal of all redundant edges makes the inferring
of structural controllability a straightforward exercise. We use standard graph
algorithms as ingredients to check these conditions and hence obtain an
algorithm to check for structural controllability. We provide an analysis of
the running time of our algorithm. When our results are applied to the familiar
state space description of a system, we obtain a novel necessary and sufficient
condition to check structural controllability for this description.Comment: 17 pages, 2 figure
Gravitational Wave Detection with Michelson Interferometers
Electromagnetic methods recently proposed for detecting gravitational waves
modify the Michelson phase shift analysis (historically employed for special
relativity). We suggest that a frequency modulation analysis is more suited to
general relativity. An incident photon in the presence of a very long
wavelength gravitational wave will have a finite probability of being returned
as a final photon with a frequency shift whose magnitude is equal to the
gravitational wave frequency. The effect is due to the non-linear coupling
between electromagnetic and gravitational waves. The frequency modulation is
derived directly from the Maxwell-Einstein equations.Comment: 4 pages, 3 *.eps figures, RevTeX 4 forma
Temperature of a Compressed Bubble with Application to Sonoluminescence
The rise in temperature from the adiabatic compression of a bubble is
computed in thermodynamic mean field (van der Waals) theory. It is shown that
the temperature rise is higher for the noble gas atoms than for more complex
gas molecules. The adiabatic temperature rise is shown to be sufficient for
producing sonoluminescence via the excited electronic states of the atoms.Comment: 7 pages, 3 figure
Biological Nuclear Transmutations as a Source of Biophotons
Soft multi-photon radiation from hard higher energy reaction sources can be
employed to describe three major well established properties of biophoton
radiation; Namely, (i) the mild radiation intensity decreases for higher
frequencies, (ii) the coherent state Poisson counting statistics, and (iii) the
time delayed luminescence with a hyperbolic time tail. Since the soft photon
frequencies span the visible to the ultraviolet frequency range, the hard
reaction sources have energies extending into the nuclear transmutation regime.Comment: 5 Pages and 1 figur
Radiation Induced Landau-Lifshitz-Gilbert Damping in Ferromagnets
The Landau-Lifshitz-Gilbert damping coefficient employed in the analysis of
spin wave ferromagnetic resonance is related to the electrical conductivity of
the sample. The changing magnetization (with time) radiates electromagnetic
fields. The electromagnetic energy is then absorbed by the sample and the
resulting heating effect describes magnetic dissipative damping. The
ferromagnetic resonance relaxation rate theoretically depends on the geometry
(shape and size) of the sample as well as temperature in agreement with
experiment.Comment: 3 pages ReVTeX 4 forma
Thermal Superradiance and the Clausius-Mossotti Lorentz-Lorenz Equations
Electric polarization phenomena in insulating systems have long been
described in mean field theory by the (static) Clausius-Mossotti or (dynamic)
Lorentz-Lorenz polarizabilities. It is here shown, in the strong coupling
regime, that a thermodynamic phase instability exists in these models. The
resulting thermodynamic phase diagram coincides with that obtained from
Dicke-Preparata model of thermal superradiance.Comment: 6 pages LaTeX and 1 figure *.ep
The Clausius-Mossotti Phase Transition in Polar Liquids
The conventional Clausius-Mossotti polarization equation of state is known to
be unstable for polar liquids having molecules with high polarizability. Room
temperature water is an important example. The instability in the polarization
equation of state is of the typical loop form requiring an ``equal area''
construction for studying the stable ordered phase. The ordered phase of a
Clausius-Mossotti polar liquid then consists of domains each having a net
polarization. The polarization may vary in direction from domain to domain. The
ordered phases are quite similar to those previously discussed on the basis of
Dicke superradiance.Comment: ReVTeX format, 3 figure
Gravitational Waves and the Sagnac Effect
We consider light waves propagating clockwise and other light waves
propagating counterclockwise around a closed path in a plane (theoretically
with the help of stationary mirrors). The time difference between the two light
propagating path orientations constitutes the Sagnac effect. The general
relativistic expression for the Sagnac effect is discussed. It is shown that a
gravitational wave incident to the light beams at an arbitrary angle will not
induce a Sagnac effect so long as the wave length of the weak gravitational
wave is long on the length scale of the closed light beam paths. The
gravitational wave induced Sagnac effect is thereby null.Comment: LaTeX format 1 *.eps figur
Thermodynamic QED Coherence in Condensed Matter: Microscopic Basis of Thermal Superradiance
Electromagnetic superradiant field coherence exists in a condensed matter
system if the electromagnetic field oscillators undergo a mean displacement.
Transitions into thermal states with ordered superradiant phases have been
shown to theoretically exist in Dicke-Preparata models. The theoretical
validity of these models for condensed matter has been called into question due
to non-relativistic diamagnetic terms in the electronic Hamiltonian. The
microscopic bases of Dicke-Preparata thermal superradiance for realistic
macroscopic systems are explored in this work. The impossibility of diaelectric
correlations in condensed matter systems (via the Landau-Lifshitz theorem)
provides a strong theoretical basis for understanding the physical reality of
condensed matter thermodynamic superradiant phases.Comment: 11 pages, no figures, LaTeX forma
Maxwell Tension Supports the Water Bridge
A cylindrical flexible cable made up of pure fluid water can be
experimentally spanned across a spatial gap with cable endpoints fixed to the
top edges of two glass beakers. The cable has been called a water bridge in
close analogy to iron cables employed to build ordinary span bridges. A
necessary condition for the construction of a water bridge is that a large
electric field exists parallel to and located within the water cable.
Presently, there is no accepted detailed theory which quantitatively explains
the forces which hold up the bridge. Our purpose is to present such theory
based on the Maxwell pressure tensor induced by the electric field albeit
within the condensed matter dielectric fluid cable
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