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