Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler-Feynman absorber

The altered spontaneous emission of an emitter near an arbitrary body can be elucidated using an energy balance of the electromagnetic field. From a classical point of view it is trivial to show that the field scattered back from any body should alter the emission of the source. But it is not at all apparent that the total radiative and non-radiative decay in an arbitrary body can add to the vacuum decay rate of the emitter (i.e.) an increase of emission that is just as much as the body absorbs and radiates in all directions. This gives us an opportunity to revisit two other elegant classical ideas of the past, the optical theorem and the Wheeler-Feynman absorber theory of radiation. It also provides us alternative perspectives of Purcell effect and generalizes many of its manifestations, both enhancement and inhibition of emission. When the optical density of states of a body or a material is difficult to resolve (in a complex geometry or a highly inhomogeneous volume) such a generalization offers new directions to solutions. (c) 2012 Elsevier Ltd. All rights reserved.

Spectral-envelope and group-delay models for transient signals—applications to castanets and stop consonants

We present a novel approach to represent transients using spectral-domain amplitude-modulated/frequency -modulated (AM-FM) functions. The model is applied to the real and imaginary parts of the Fourier transform (FT) of the transient. The suitability of the model lies in the observation that since transients are well-localized in time, the real and imaginary parts of the Fourier spectrum have a modulation structure. The spectral AM is the envelope and the spectral FM is the group delay function. The group delay is estimated using spectral zero-crossings and the spectral envelope is estimated using a coherent demodulator. We show that the proposed technique is robust to additive noise. We present applications of the proposed technique to castanets and stop-consonants in speech.

Sub-band envelope approach to obtain instants of significant excitation in speech

In this paper, we propose a new sub-band approach to estimate the glottal activity. The method is based on the spectral harmonicity and the sub-band temporal properties of voiced speech. We propose a method to represent glottal excitation signal using sub-band temporal envelope. Instants of maximum glottal excitation or Glottal Closure Instants (GCI) are extracted from the estimated glottal excitation pattern and the result is compared with a standard GCI computation method, DYPSA [1]. The performance of the algorithm is also compared for the noisy signal and it is shown that the proposed method is less variant to GCI estimation under noisy conditions compared to DYPSA. The algorithm is evaluated on the CMU-ARCTIC database.

Spectral-envelope-group-delay models for transients

Transient signals such as plosives in speech or Castanets in audio do not have a specific modulation or periodic structure in time domain. However, in the spectral domain they exhibit a prominent modulation structure, which is a direct consequence of their narrow time localization. Based on this observation, a spectral-domain AM-FM model for transients is proposed. The spectral AM-FM model is built starting from real spectral zero-crossings. The AM and FM correspond to the spectral envelope (SE) and group delay (GD), respectively. Taking into account the modulation structure and spectral continuity, a local polynomial regression technique is proposed to estimate the GD function from the real spectral zeros. The SE is estimated based on the phase function computed from the estimated GD. Since the GD estimation is parametric, the degree of smoothness can be controlled directly. Simulation results based on synthetic transient signals generated using a beta density function are presented to analyze the noise-robustness of the SEGD model. Three specific applications are considered: (1) SEGD based modeling of Castanet sounds; (2) appropriateness of the model for transient compression; and (3) determining glottal closure instants in speech using a short-time SEGD model of the linear prediction residue.

Temporal Envelope Fit of Transient Audio Signals

We address the problem of temporal envelope modeling for transient audio signals. We propose the Gamma distribution function (GDF) as a suitable candidate for modeling the envelope keeping in view some of its interesting properties such as asymmetry, causality, near-optimal time-bandwidth product, controllability of rise and decay, etc. The problem of finding the parameters of the GDF becomes a nonlinear regression problem. We overcome the hurdle by using a logarithmic envelope fit, which reduces the problem to one of linear regression. The logarithmic transformation also has the feature of dynamic range compression. Since temporal envelopes of audio signals are not uniformly distributed, in order to compute the amplitude, we investigate the importance of various loss functions for regression. Based on synthesized data experiments, wherein we have a ground truth, and real-world signals, we observe that the least-squares technique gives reasonably accurate amplitude estimates compared with other loss functions.

The projective plane, J-holomorphic curves and Desargues' theorem

By a theorem of Gromov, for an almost complex structure J on CP2 tamed by the standard symplectic structure, the J-holomorphic curves representing the positive generator of homology form a projective plane. We show that this satisfies the Theorem of Desargues if and only if J is isomorphic to the standard complex structure. This answers a question of Ghys. (C) 2013 Published by Elsevier Masson SAS on behalf of Academie des sciences.

Large deviation function and fluctuation theorem for classical particle transport

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.

Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings

In this paper, we extend the characterization of Zx]/(f), where f is an element of Zx] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us to extend the Grobner basis method of computing a k-vector space basis of residue class polynomial rings over a field k (Macaulay-Buchberger Basis Theorem) to rings, i.e. Ax(1), ... , x(n)]/a, where a subset of Ax(1), ... , x(n)] is an ideal. We give some insights into the characterization for two special cases, when A = Z and A = ktheta(1), ... , theta(m)]. As an application of this characterization, we show that the concept of Border bases can be extended to rings when the corresponding residue class ring is a finitely generated, free A-module. (C) 2014 Elsevier B.V. All rights reserved.

An integral fluctuation theorem for systems with unidirectional transitions

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where R-ij > 0 but R-ji = 0, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution, which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically and found to show the same qualitative features as systems exhibiting microreversibility.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.

A gap theorem for Ricci-flat 4-manifolds

Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K-min(p)) denote the maximum (respectively the minimum) of sectional curvatures at p. We prove that if K-max(p) <= -cK(min)(P) for all p is an element of M, for some constant c with 0 <= c < 2+root 6/4 then (M, g) is fiat. We prove a similar result for compact Ricci-flat Kahler surfaces. Let (M, g) be such a surface and for p is an element of M let H-max(p) (respectively H-min(P)) denote the maximum (respectively the minimum) of holomorphic sectional curvatures at p. If H-max(P) <= -cH(min)(P) for all p is an element of M, for some constant c with 0 <= c < 1+root 3/2, then (M, g) is flat. (C) 2015 Elsevier B.V. All rights reserved.

Genesis of workpiece roughness generated in surface grinding and polishing of metals

Assuming the grinding wheel surface to be fractal in nature, the maximum envelope profile of the wheel and contact deflections are estimated over a range of length scales. This gives an estimate of the 'no wear' roughness of a surface ground metal. Four test materials, aluminum, copper, titanium, and steel are surface ground and their surface power spectra were estimated. The departure of this power spectra from the 'no wear' estimates is studied in terms of the traction-induced wear damage of the surfaces. The surface power spectra in grinding are influenced by hardness and the power is enhanced by wear damage. No such correlation with hardness was found for the polished surface, the roughness of which is insensitive to mechanical properties and appears to be influenced by microstructure and physical properties of the material.

Structural and optical investigations of TiO2 films deposited on transparent substrates by sol-gel technique

An inexpensive and effective simple method for the preparation of nano-crystalline titanium oxide (anatase) thin films at room temperature on different transparent substrates is presented. This method is based on the use of peroxo-titanium complex, i.e. titanium isopropoxide as a single initiating organic precursor. Post-annealing treatment is necessary to convert the deposited amorphous film into titanium oxide (TiO2) crystalline (anatase) phase. These films have been characterized for X-ray diffraction (XRD) studies, atomic force microscopic (AFM) studies and optical measurements. The optical constants such as refractive index and extinction coefficient have been estimated by using envelope technique. Also, the energy gap values have been estimated using Tauc's formula for on glass and quartz substrates are found to be 3.35 eV and 3.39 eV, respectively.

Heat shock protein 70 on Neuro2a cells is a putative receptor for Japanese encephalitis virus

Japanese encephalitis virus (JEV) envelope (E) protein has been shown to play a critical role in attachment to cells. However, the receptor interacting with envelope protein has not been conclusively identified. Using mouse neuroblastoma (Neuro2a) cells and purified JEV-E protein in `Virus Overlay Protein Binding Assay' followed by MALDI-TOF analysis, we identified `heat shock protein 70' (Hsp70) as a possible receptor for JEV. Indirect immunofluorescence and flow-cytometry analysis demonstrated localization of Hsp70 on Neuro2a cell surface. Co-immunoprecipitation followed by Western blot analysis reconfirmed the interaction between Hsp70 and JEV-E protein. Further, anti-Hsp70 polyclonal-antibodies were able to block JEV entry into Neuro2a cells. Additionally, using the bioinformatic tool - FTDOCK, clocking between the proteins was performed. Amongst six interacting structural poses studied one pose involving RGD motif on JEV-E and leucine(539) on Hsp70 displayed stable interaction. These observations indicate that Hsp70 serves as putative receptor for JEV in Neuro2A cells.

Synthesis, structure and spectroscopic studies on hydroxo-bridged heterotrinuclear complexes of cobalt(m) with ethane-l,2-diamine and ammonia as terminal ligands

Hydroxo-bridged homo- and hetero-trinuclear cobalt(III) complexes of the type [MII(H2O)2{(OH)2CoIII(N4)}2]X2·nH2O [MII= a divalent metal ion such as CoII, NiII or ZnII; N4=(en)2(en = ethane-1,2-diamine) or (NH3)4; X = SO4 or (ClO4)2; n= 3 or 5] have been prepared and spectroscopically characterized. The structure of [Cu{(OH)2Co(en)2}2][SO4]2·2H2O 1 has been determined. The geometry around copper atom is a pseudo-square-based pyramid, with the basal sites occupied by four bridging hydroxide oxygens and the apical site is occupied by a weakly co-ordinated sulfate anion [Cu–O 2.516(4)Å]. The hydroxo groups bridge pairs of cobalt(III) ions which are in near-octahedral environments. The ethylenediamine chelate rings have the twist conformation. In the crystal structure of [Cu{(OH)2Co(en)2}2][ClO4]4·2H2O 2 the perchlorate ion is not co-ordinated and the en ligands have envelope conformations. The sulfate ion in [Cu{(OH)2Co(NH3)4}2][SO4]2·4H2O 3 is not co-ordinated to the central copper ion. Electronic, infrared and variable-temperature EPR spectral data are discussed.