24,420 research outputs found
Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
The truncation method is a collective name for techniques that arise from
truncating a Laurent series expansion (with leading term) of generic solutions
of nonlinear partial differential equations (PDEs). Despite its utility in
finding Backlund transformations and other remarkable properties of integrable
PDEs, it has not been generally extended to ordinary differential equations
(ODEs). Here we give a new general method that provides such an extension and
show how to apply it to the classical nonlinear ODEs called the Painleve
equations. Our main new idea is to consider mappings that preserve the
locations of a natural subset of the movable poles admitted by the equation. In
this way we are able to recover all known fundamental Backlund transformations
for the equations considered. We are also able to derive Backlund
transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages
Electrically modulated photoluminescence in ferroelectric liquid crystal
Electrical modulation and switching of photoluminescence (PL) have been
demonstrated in pure deformed helix ferroelectric liquid crystal (DHFLC)
material. The PL intensity increases and peak position shifts towards lower
wavelength above a threshold voltage which continues up to a saturation
voltage. This is attributed to the helix unwinding phenomenon in the DHFLC on
the application of an electric field. Moreover, the PL intensity could be
switched between high intensity (field-on) and low intensity (field-off)
positions. These studies would add a new dimension to ferroelectric liquid
crystal's application in the area of optical devices.Comment: 4 figure
Wave propagation through a coherently amplifying random medium
We report a detailed and systematic numerical study of wave propagation
through a coherently amplifying random one-dimensional medium. The coherent
amplification is modeled by introducing a uniform imaginary part in the site
energies of the disordered single-band tight binding Hamiltonian. Several
distinct length scales (regimes), most of them new, are identified from the
behavior of transmittance and reflectance as a function of the material
parameters. We show that the transmittance is a non-self-averaging quantity
with a well defined mean value. The stationary distribution of the super
reflection differs qualitatively from the analytical results obtained within
the random phase approximation in strong disorder and amplification regime. The
study of the stationary distribution of the phase of the reflected wave reveals
the reason for this discrepancy. The applicability of random phase
approximation is discussed. We emphasize the dual role played by the lasing
medium, as an amplifier as well as a reflector.Comment: 33 pages RevTex, 14 EPS figures included, Accepted for publication in
IJMP-
Towards Semantic Fast-Forward and Stabilized Egocentric Videos
The emergence of low-cost personal mobiles devices and wearable cameras and
the increasing storage capacity of video-sharing websites have pushed forward a
growing interest towards first-person videos. Since most of the recorded videos
compose long-running streams with unedited content, they are tedious and
unpleasant to watch. The fast-forward state-of-the-art methods are facing
challenges of balancing the smoothness of the video and the emphasis in the
relevant frames given a speed-up rate. In this work, we present a methodology
capable of summarizing and stabilizing egocentric videos by extracting the
semantic information from the frames. This paper also describes a dataset
collection with several semantically labeled videos and introduces a new
smoothness evaluation metric for egocentric videos that is used to test our
method.Comment: Accepted for publication and presented in the First International
Workshop on Egocentric Perception, Interaction and Computing at European
Conference on Computer Vision (EPIC@ECCV) 201
On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust
We consider here the gravitational collapse of a spherically symmetric
inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a
general class of these models, we find that the end state of the collapse is
either a black hole or a naked singularity, depending on the parameters of the
initial density distribution, which are , the initial central density
of the massive body, and , the initial boundary. The collapse ends in a
black hole if the dimensionless quantity constructed out of this
initial data is greater than 0.0113, and it ends in a naked singularity if
is less than this number. A simple interpretation of this result can be
given in terms of the strength of the gravitational potential at the starting
epoch of the collapse.Comment: Original title changed, numerical range of naked singularity
corrected. Plain Tex File. 14 pages. To appear in Physical Review
Prediction of long and short time rheological behavior in soft glassy materials
We present an effective time approach to predict long and short time
rheological behavior of soft glassy materials from experiments carried out over
practical time scales. Effective time approach takes advantage of relaxation
time dependence on aging time that allows time-aging time superposition even
when aging occurs over the experimental timescales. Interestingly experiments
on variety of soft materials demonstrate that the effective time approach
successfully predicts superposition for diverse aging regimes ranging from
sub-aging to hyper-aging behaviors. This approach can also be used to predict
behavior of any response function in molecular as well as spin glasses.Comment: 13 pages, 4 figure
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