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 $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ 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