1,442 research outputs found
Linear-quadratic stochastic differential games for distributed parameter systems
A linear-quadratic differential game with infinite dimensional state space is considered. The system state is affected by disturbance and both players have access to different measurements. Optimal linear strategies for the pursuer and the evader, when they exist, are explicitly determined
Reduced-dimension linear transform coding of distributed correlated signals with incomplete observations
We study the problem of optimal reduced-dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal. In the mean square estimation context this involves finding he optimal signal representation based on multiple incomplete or only partial observations that are correlated. In particular this leads to the study of finding the optimal Karhunen-Loeve basis based on the censored observations. The problem has been considered previously by Gestpar, Dragotti and Vitterli in the context of jointly Gaussian random variables based on using conditional covariances. In this paper, we derive the estimation results in the more general setting of second-order random variables with arbitrary distributions, using entirely different techniques based on the idea of innovations. We explicitly solve the single transform coder case, give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problm
Supersymmetric Extension of GCA in 2d
We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra
(SGCA) in the case of two spacetime dimensions by performing group contraction
on 2d superconformal algebra. We also obtain the representations of the
generators in terms of superspace coordinates. Here we find realisations of the
SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary
and have their left and right central charges become large in magnitude and
opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and
develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the
representation theory based on SGCA primaries, Ward identities for their
correlation functions and their descendants which are null states.Comment: La TeX file, 32 pages; v2: typos corrected, journal versio
GCA in 2d
We make a detailed study of the infinite dimensional Galilean Conformal
Algebra (GCA) in the case of two spacetime dimensions. Classically, this
algebra is precisely obtained from a contraction of the generators of the
relativistic conformal symmetry in 2d. Here we find quantum mechanical
realisations of the (centrally extended) GCA by considering scaling limits of
certain 2d CFTs. These parent CFTs are non-unitary and have their left and
right central charges become large in magnitude and opposite in sign. We
therefore develop, in parallel to the usual machinery for 2d CFT, many of the
tools for the analysis of the quantum mechanical GCA. These include the
representation theory based on GCA primaries, Ward identities for their
correlation functions and a nonrelativistic Kac table. In particular, the null
vectors of the GCA lead to differential equations for the four point function.
The solution to these equations in the simplest case is explicitly obtained and
checked to be consistent with various requirements.Comment: 45 pages; v2: 47 pages. Restructured introduction, minor corrections,
added references. Journal versio
Vibrational dynamics and boson peak in a supercooled polydisperse liquid
Vibrational density of states (VDOS) in a supercooled polydisperse liquid is
computed by diagonalizing the Hessian matrix evaluated at the potential energy
minima for systems with different values of polydispersity. An increase of
polydispersity leads to an increase in relative population of the localized
high-frequency modes. At low frequencies, the density of states show an excess
compared to the Debye squared-frequency law, which has been identified with the
boson peak. The height of the boson peak increases with polydispersity. The
values of the participation ratio as well as the level spacing statistics
demonstrate that the modes comprising the boson peak are largely delocalized.
Interestingly, the intensity of the boson peak shows a rather narrow
sensitivity to changes in temperature and is seen to persist even at high
temperatures. Study of the difference spectrum at two different polydispersity
reveals that the increase in the height of boson peak is due to a population
shift from modes with frequencies above the maximum in the VDOS to that below
the maximum, indicating an increase in the fraction of the unstable modes in
the system. The latter is further supported by the facilitation of the observed
dynamics by polydispersity. Since the strength of the liquid increases with
polydispersity, the present result provides an evidence that the intensity of
boson peak correlates positively with the strength of the liquid, as observed
earlier in many experimental systems
Angular momentum dependent friction slows down rotational relaxation under non-equilibrium conditions
It has recently been shown that relaxation of the rotational energy of hot
non-equlibrium photofragments (i) slows down significantly with the increase of
their initial rotational temperature and (ii) differs dramatically from the
relaxation of the equilibrium rotational energy correlation function,
manifesting thereby breakdown of the linear response description [Science 311,
1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular
momentum dependence of rotational friction. We have developed the generalized
Fokker-Planck equation whose rotational friction depends upon angular momentum
algebraically. The calculated rotational correlation functions correspond well
to their counterparts obtained via molecular dynamics simulations in a broad
range of initial non-equilibrium conditions. It is suggested that the angular
momentum dependence of friction should be taken into account while describing
rotational relaxation far from equilibrium
Entropy of three-dimensional asymptotically flat cosmological solutions
The thermodynamics of three-dimensional asymptotically flat cosmological
solutions that play the same role than the BTZ black holes in the anti-de
Sitter case is derived and explained from holographic properties of flat space.
It is shown to coincide with the flat-space limit of the thermodynamics of the
inner black hole horizon on the one hand and the semi-classical approximation
to the gravitational partition function associated to the entropy of the outer
horizon on the other. This leads to the insight that it is the Massieu function
that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1
reference adde
Dielectric response of a polar fluid trapped in a spherical nanocavity
We present extensive Molecular Dynamics simulation results for the structure,
static and dynamical response of a droplet of 1000 soft spheres carrying
extended dipoles and confined to spherical cavities of radii , 3, and 4
nm embedded in a dielectric continuum of permittivity . The
polarisation of the external medium by the charge distribution inside the
cavity is accounted for by appropriate image charges. We focus on the influence
of the external permittivity on the static and dynamic properties
of the confined fluid. The density profile and local orientational order
parameter of the dipoles turn out to be remarkably insensitive to .
Permittivity profiles inside the spherical cavity are calculated
from a generalised Kirkwood formula. These profiles oscillate in phase with the
density profiles and go to a ``bulk'' value away from the
confining surface; is only weakly dependent on , except
for (vacuum), and is strongly reduced compared to the
permittivity of a uniform (bulk) fluid under comparable thermodynamic
conditions.
The dynamic relaxation of the total dipole moment of the sample is found to
be strongly dependent on , and to exhibit oscillatory behaviour when
; the relaxation is an order of magnitude faster than in the bulk.
The complex frequency-dependent permittivity is sensitive to
at low frequencies, and the zero frequency limit
is systematically lower than the ``bulk'' value
of the static primitivity.Comment: 12 pages including 17 figure
Nilpotent Classical Mechanics
The formalism of nilpotent mechanics is introduced in the Lagrangian and
Hamiltonian form. Systems are described using nilpotent, commuting coordinates
. Necessary geometrical notions and elements of generalized differential
-calculus are introduced. The so called geometry, in a special case
when it is orthogonally related to a traceless symmetric form, shows some
resemblances to the symplectic geometry. As an example of an -system the
nilpotent oscillator is introduced and its supersymmetrization considered. It
is shown that the -symmetry known for the Graded Superfield Oscillator (GSO)
is present also here for the supersymmetric -system. The generalized
Poisson bracket for -variables satisfies modified Leibniz rule and
has nontrivial Jacobiator.Comment: 23 pages, no figures. Corrected version. 2 references adde
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