A derivation of thermodynamic quantities of liquid alloys from their structure factors

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

Ultrafast Raman loss spectroscopy (URLS): instrumentation and principle

In this paper, we report on the concept and the design principle of ultrafast Raman loss spectroscopy (URLS) as a structure-elucidating tool. URLS is an analogue of stimulated Raman scattering (SRS) but more sensitive than SRS with better signal-to-noise ratio. It involves the interaction of two laser sources, namely, a picosecond (ps) Raman pump pulse and a white-light (WL) continuum, with a sample, leading to the generation of loss signals on the higher energy (blue) side with respect to the wavelength of the Raman pump unlike the gain signal observed on the lower energy (red) side in SRS. These loss signals are at least 1.5 times more intense than the SRS signals. An experimental study providing an insight into the origin of this extra intensity in URLS as compared to SRS is reported. Furthermore, the very requirement of the experimental protocol for the signal detection to be on the higher energy side by design eliminates the interference from fluorescence, which appears on the red side. Unlike CARS, URLS signals are not precluded by the non-resonant background and, being a self-phase-matched process, URLS is experimentally easier. Copyright (C) 2011 John Wiley & Sons, Ltd.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

A Modified Fluorimetric Method for Determination of Hydrogen Peroxide Using Homovanillic Acid Oxidation Principle

Hydrogen peroxide (H2O2) level in biological samples is used as an important index in various studies. Quantification of H2O2 level in tissue fractions in presence of H2O2 metabolizing enzymes may always provide an incorrect result. A modification is proposed for the spectrofluorimetric determination of H2O2 in homovanillic acid (HVA) oxidation method. The modification was included to precipitate biological samples with cold trichloroacetic acid (TCA, 5% w/v) followed by its neutralization with K2HPO4 before the fluorimetric estimation of H2O2 is performed. TCA was used to precipitate the protein portions contained in the tissue fractions. After employing the above modification, it was observed that H2O2 content in tissue samples was >= 2 fold higher than the content observed in unmodified method. Minimum 2 h incubation of samples in reaction mixture was required for completion of the reaction. The stability of the HVA dimer as reaction product was found to be > 12 h. The method was validated by using known concentrations of H2O2 and catalase enzyme that quenches H2O2 as substrate. This method can be used efficiently to determine more accurate tissue H2O2 level without using internal standard and multiple samples can be processed at a time with additional low cost reagents such as TCA and K2HPO4.

Super-Resolution Reconstruction in Frequency-Domain Optical-Coherence Tomography Using the Finite-Rate-of-Innovation Principle

The standard approach to signal reconstruction in frequency-domain optical-coherence tomography (FDOCT) is to apply the inverse Fourier transform to the measurements. This technique offers limited resolution (due to Heisenberg's uncertainty principle). We propose a new super-resolution reconstruction method based on a parametric representation. We consider multilayer specimens, wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite-rate-of-innovation (FRI) signal model and is represented by a finite number of free parameters. We deploy the high-resolution Prony method and show that high-quality, super-resolved reconstruction is possible with fewer measurements (about one-fourth of the number required for the standard Fourier technique). To further improve robustness to noise in practical scenarios, we take advantage of an iterated singular-value decomposition algorithm (Cadzow denoiser). We present results of Monte Carlo analyses, and assess statistical efficiency of the reconstruction techniques by comparing their performance against the Cramer-Rao bound. Reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal-to-reconstruction noise offered by the proposed method in comparison with the standard approach.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Ellipse Fitting Using the Finite Rate of Innovation Sampling Principle

Standard approaches for ellipse fitting are based on the minimization of algebraic or geometric distance between the given data and a template ellipse. When the data are noisy and come from a partial ellipse, the state-of-the-art methods tend to produce biased ellipses. We rely on the sampling structure of the underlying signal and show that the x- and y-coordinate functions of an ellipse are finite-rate-of-innovation (FRI) signals, and that their parameters are estimable from partial data. We consider both uniform and nonuniform sampling scenarios in the presence of noise and show that the data can be modeled as a sum of random amplitude-modulated complex exponentials. A low-pass filter is used to suppress noise and approximate the data as a sum of weighted complex exponentials. The annihilating filter used in FRI approaches is applied to estimate the sampling interval in the closed form. We perform experiments on simulated and real data, and assess both objective and subjective performances in comparison with the state-of-the-art ellipse fitting methods. The proposed method produces ellipses with lesser bias. Furthermore, the mean-squared error is lesser by about 2 to 10 dB. We show the applications of ellipse fitting in iris images starting from partial edge contours, and to free-hand ellipses drawn on a touch-screen tablet.