26,684 research outputs found
Dynamical N-body Equlibrium in Circular Dilaton Gravity
We obtain a new exact equilibrium solution to the N-body problem in a
one-dimensional relativistic self-gravitating system. It corresponds to an
expanding/contracting spacetime of a circle with N bodies at equal proper
separations from one another around the circle. Our methods are
straightforwardly generalizable to other dilatonic theories of gravity, and
provide a new class of solutions to further the study of (relativistic)
one-dimensional self-gravitating systems.Comment: 4 pages, latex, reference added, minor changes in wordin
Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
We develop the canonical formalism for a system of bodies in lineal
gravity and obtain exact solutions to the equations of motion for N=2. The
determining equation of the Hamiltonian is derived in the form of a
transcendental equation, which leads to the exact Hamiltonian to infinite order
of the gravitational coupling constant. In the equal mass case explicit
expressions of the trajectories of the particles are given as the functions of
the proper time, which show characteristic features of the motion depending on
the strength of gravity (mass) and the magnitude and sign of the cosmological
constant. As expected, we find that a positive cosmological constant has a
repulsive effect on the motion, while a negative one has an attractive effect.
However, some surprising features emerge that are absent for vanishing
cosmological constant. For a certain range of the negative cosmological
constant the motion shows a double maximum behavior as a combined result of an
induced momentum-dependent cosmological potential and the gravitational
attraction between the particles. For a positive cosmological constant, not
only bounded motions but also unbounded ones are realized. The change of the
metric along the movement of the particles is also exactly derived.Comment: 37 pages, Latex, 24 figure
New Types of Thermodynamics from -Dimensional Black Holes
For normal thermodynamic systems superadditivity , homogeneity \H and
concavity \C of the entropy hold, whereas for -dimensional black holes
the latter two properties are violated. We show that -dimensional black
holes exhibit qualitatively new types of thermodynamic behaviour, discussed
here for the first time, in which \C always holds, \H is always violated
and may or may not be violated, depending of the magnitude of the black
hole mass. Hence it is now seen that neither superadditivity nor concavity
encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to
appear in Class. Quant. Gra
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
N-body Gravity and the Schroedinger Equation
We consider the problem of the motion of bodies in a self-gravitating
system in two spacetime dimensions. We point out that this system can be mapped
onto the quantum-mechanical problem of an N-body generalization of the problem
of the H molecular ion in one dimension. The canonical gravitational
N-body formalism can be extended to include electromagnetic charges. We derive
a general algorithm for solving this problem, and show how it reduces to known
results for the 2-body and 3-body systems.Comment: 15 pages, Latex, references added, typos corrected, final version
that appears in CQ
Systematic innovation and the underlying principles behind TRIZ and TOC
Innovative developments in the design of product and manufacturing systems are often marked by simplicity, at least in retrospect, that has previously been shrouded by restrictive mental models or limited knowledge transfer. These innovative developments are often associated with the breaking of long established trade-off compromises, as in the paradigm shift associated with JIT & TQM, or the resolution of design contradictions, as in the case of the dual cyclone vacuum cleaner. The rate of change in technology and the commercial environment suggests the opportunity for innovative developments is accelerating, but what systematic support is there to guide this innovation process. This paper brings together two parallel, but independent theories on inventive problem solving; one in mechanical engineering, namely the Russian Theory of Inventive Problem Solving (TRIZ) and the other originating in manufacturing management as the Theory of Constraints (TOC). The term systematic innovation is used to describe the use of common underlying principles within these two approaches. The paper focuses on the significance of trade-off contradictions to innovation in these two fields and explores their relationship with manufacturing strategy development
Soliton Solutions to the Einstein Equations in Five Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,
with the added feature of having Lorentzian signatures. They provide an
affirmative answer to the open question as to whether or not there exist
solutions with negative cosmological constant that asymptotically approach
AdS, but have less energy than AdS. We present
evidence that these solutions are the lowest-energy states within their
asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title
changed by journal from original title "Eguchi-Hanson Solitons
Electron cyclotron maser emission mode coupling to the z-mode on a longitudinal density gradient in the context of solar type III bursts
Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. This article appeared in Physics of Plasmas 19, 110702 (2012) and may be found at .supplemental material at http://astro.qmul.ac.uk/~tsiklauri/sp.htmlsupplemental material at http://astro.qmul.ac.uk/~tsiklauri/sp.htm
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