3,369 research outputs found
Improvements in estimating proportions of objects from multispectral data
Methods for estimating proportions of objects and materials imaged within the instantaneous field of view of a multispectral sensor were developed further. Improvements in the basic proportion estimation algorithm were devised as well as improved alien object detection procedures. Also, a simplified signature set analysis scheme was introduced for determining the adequacy of signature set geometry for satisfactory proportion estimation. Averaging procedures used in conjunction with the mixtures algorithm were examined theoretically and applied to artificially generated multispectral data. A computationally simpler estimator was considered and found unsatisfactory. Experiments conducted to find a suitable procedure for setting the alien object threshold yielded little definitive result. Mixtures procedures were used on a limited amount of ERTS data to estimate wheat proportion in selected areas. Results were unsatisfactory, partly because of the ill-conditioned nature of the pure signature set
Hypercomplex quantum mechanics
The fundamental axioms of the quantum theory do not explicitly identify the
algebraic structure of the linear space for which orthogonal subspaces
correspond to the propositions (equivalence classes of physical questions). The
projective geometry of the weakly modular orthocomplemented lattice of
propositions may be imbedded in a complex Hilbert space; this is the structure
which has traditionally been used. This paper reviews some work which has been
devoted to generalizing the target space of this imbedding to Hilbert modules
of a more general type. In particular, detailed discussion is given of the
simplest generalization of the complex Hilbert space, that of the quaternion
Hilbert module.Comment: Plain Tex, 11 page
Towards a Realistic Equation of State of Strongly Interacting Matter
We consider a relativistic strongly interacting Bose gas. The interaction is
manifested in the off-shellness of the equilibrium distribution. The equation
of state that we obtain for such a gas has the properties of a realistic
equation of state of strongly interacting matter, i.e., at low temperature it
agrees with the one suggested by Shuryak for hadronic matter, while at high
temperature it represents the equation of state of an ideal ultrarelativistic
Stefan-Boltzmann gas, implying a phase transition to an effectively weakly
interacting phase.Comment: LaTeX, figures not include
Galilean limit of equilibrium relativistic mass distribution for indistinguishable events
The relativistic distribution for indistinguishable events is considered in
the mass-shell limit where is a given intrinsic property of
the events. The characteristic thermodynamic quantities are calculated and
subject to the zero-mass and the high-temperature limits. The results are shown
to be in agreement with the corresponding expressions of an on-mass-shell
relativistic kinetic theory. The Galilean limit which
coincides in form with the low-temperature limit, is considered. The theory is
shown to pass over to a nonrelativistic statistical mechanics of
indistinguishable particles.Comment: Report TAUP-2136-9
INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION
It is shown that the existence of a time operator in the Liouville space
representation of both classical and quantum evolution provides a mechanism for
effective entropy change of physical states. In particular, an initially
effectively pure state can evolve under the usual unitary evolution to an
effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at
[email protected] (internet)
Direct Interactions in Relativistic Statistical Mechanics
Directly interacting particles are considered in the multitime formalism of
predictive relativistic mechanics. When the equations of motion leave a
phase-space volume invariant, it turns out that the phase average of any first
integral, covariantly defined as a flux across a -dimensional surface, is
conserved. The Hamiltonian case is discussed, a class of simple models is
exhibited, and a tentative definition of equilibrium is proposed.Comment: Plain Tex file, 26 page
Semigroup evolution in Wigner Weisskopf pole approximation with Markovian spectral coupling
We establish the relation between the Wigner-Weisskopf theory for the
description of an unstable system and the theory of coupling to an environment.
According to the Wigner-Weisskopf general approach, even within the pole
approximation (neglecting the background contribution) the evolution of a total
system subspace is not an exact semigroup for the multi-channel decay, unless
the projectors into eigesntates of the reduced evolution generator are
orthogonal. In this case these projectors must be evaluated at different pole
locations . Since the orthogonality relation does not
generally hold at different values of , for example, when there is symmetry
breaking, the semigroup evolution is a poor approximation for the multi-channel
decay, even for a very weak coupling. Nevertheless, there exists a possibility
not only to ensure the orthogonality of the projectors regardless the
number of the poles, but also to simultaneously suppress the effect of the
background contribution. This possibility arises when the theory is generalized
to take into account interactions with an environment. In this case , and
hence its eigenvectors as well, are {\it independent} of , which corresponds
to a structure of the coupling to the continuum spectrum associated with the
Markovian limit.Comment: 9 pages, 3 figure
Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems
An effective characterization of chaotic conservative Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor derived from
the structure of the Hamiltonian has been extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model
through an inverse map in the tangent space. The second covariant derivative of
the geodesic deviation in this space generates a dynamical curvature, resulting
in (energy dependent) criteria for unstable behavior different from the usual
Lyapunov criteria. We show here that this criterion can be constructively used
to modify locally the potential of a chaotic Hamiltonian model in such a way
that stable motion is achieved. Since our criterion for instability is local in
coordinate space, these results provide a new and minimal method for achieving
control of a chaotic system
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
Covariant Uniform Acceleration
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only
partially covariant. To achieve full Lorentz covariance, we replace the
four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By
taking this tensor to be constant, we obtain a covariant definition of
uniformly accelerated motion. We compute explicit solutions for uniformly
accelerated motion which are divided into four types: null, linear, rotational,
and general. For null acceleration, the worldline is cubic in the time. Linear
acceleration covariantly extends 1D hyperbolic motion, while rotational
acceleration covariantly extends pure rotational motion.
We use Generalized Fermi-Walker transport to construct a uniformly
accelerated family of inertial frames which are instantaneously comoving to a
uniformly accelerated observer. We explain the connection between our approach
and that of Mashhoon. We show that our solutions of uniformly accelerated
motion have constant acceleration in the comoving frame. Assuming the Weak
Hypothesis of Locality, we obtain local spacetime transformations from a
uniformly accelerated frame K' to an inertial frame K. The spacetime
transformations between two uniformly accelerated frames with the same
acceleration are Lorentz. We compute the metric at an arbitrary point of a
uniformly accelerated frame.
We obtain velocity and acceleration transformations from a uniformly
accelerated system K' to an inertial frame K. We derive the general formula for
the time dilation between accelerated clocks. We obtain a formula for the
angular velocity of a uniformly accelerated object. Every rest point of K' is
uniformly accelerated, and its acceleration is a function of the observer's
acceleration and its position. We obtain an interpretation of the
Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page
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