Size-Dependent Melting of Finite-Length Nanowires

We report on the size-dependent melting of nanowires with finite length based on the thermodynamic as well as liquid drop model. It has been inferred that the length dependency cannot be ignored, unlike the case of infinite length nanowires. To validate the length dependency, we have analyzed a few experimental results reported in the literature.

Theoretical Estimation of Length Dependent In-Plane Stiffness of Single Walled Carbon Nanotubes Using the Nonlocal Elasticity Theory

In the present paper, Eringen's nonlocal elasticity theory is employed to evaluate the length dependent in-plane stiffness of single-walled carbon nanotubes (SWCNTs). The SWCNT is modeled as an Euler-Bernoulli beam and is analyzed for various boundary conditions to evaluate the length dependent in-plane stiffness. It has been found that the nonlocal scaling parameter has a significant effect on the length dependent in-plane stiffness of SWCNTs. It has been observed that as the nonlocal scale parameter increases the stiffness ratio of SWCNT decreases. In nonlocality, the cantilever SWCNT has high in-plane stiffness as compared to the simply-supported and the clamped cases.

Bond length distortions associated with torsion potentials; ab-initio studies on methanedio

The 4-31G basis set is used to study the bond length variations as functions of dihedral angels in methanediol. This study is compared with O---C---O bond angle optimization studies by Gorenstein and Kar and the possible reason for bond length shorteing in the trans---trans configuration is analysed.

Length-independent voltage fluctuations in small conductors

The mean-squared voltage fluctuation of a disordered conductor of lengthL smaller than the phase coherence lengthL ϕ, is independent of the distance between the probes. We obtain this result using the voltage additivity and the known results for the conductance fluctuation. Our results complement the recent theoretical and experimental findings.

A XANES study of the K-absorption edge of copper in some of its compounds and use of the same in the determination of bond length

XANES in the K-edge of copper in the systems CuO, Cu(OH)2, La2CuO4, Cu3AsO4 and CuOHF have been investigated and transitions have been assigned to the observed structures. The measurements have been used for calculating the first coordination bond distance in the above systems. It is observed that the values so determined agree fairly well with crystallographic values.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

A2MoTiO7−x (Atriple bond; length as m-dashrare earth or Y): a new series of oxide pyrochlores prepared by topochemical reduction of A2MoTiO8 scheelites

A series of anion-deficient pyrochlore oxides of the formula A2MoTiO7−x (xless-than-or-equals, slant0.5), where Atriple bond; length as m-dashSm, Gd, Tb, Dy, Ho, Er, Lu and Y, has been prepared by reduction of A2MoTiO8 scheelites. The scheelite-to-pyrochlore conversion is reversible, indicating that the reaction is likely to be topochemical. The oxidation states of molybdenum and titanium are most probably Mo(III) and Ti(IV) for the limiting composition of the pyrochlores A2MoTiO6.5. The new pyrochlores are non-metallic and paramagnetic as expected.

Theory of the effects of destruction of localization by inelastic scattering in the resistivity of pure thin potassium wires

Measurements of the electrical resistivity of thin potassium wires at temperatures near 1 K have revealed a minimum in the resistivity as a function of temperature. By proposing that the electrons in these wires have undergone localization, albeit with large localization length, and that inelastic-scattering events destroy the coherence of that state, we can explain both the magnitude and shape of the temperature-dependent resistivity data. Localization of electrons in these wires is to be expected because, due to the high purity of the potassium, the elastic mean free path is comparable to the diameters of the thinnest samples, making the Thouless length lT (or inelastic diffusion length) much larger than the diameter, so that the wire is effectively one dimensional. The inelastic events effectively break the wire into a series of localized segments, whose resistances can be added to obtain the total resistance of the wire. The ensemble-averaged resistance for all possible segmented wires, weighted with a Poisson distribution of inelastic-scattering lengths along the wire, yields a length dependence for the resistance that is proportional to [L3/lin(T)], provided that lin(T)?L, where L is the sample length and lin(T) is some effective temperature-dependent one-dimensional inelastic-scattering length. A more sophisticated approach using a Poisson distribution in inelastic-scattering times, which takes into account the diffusive motion of the electrons along the wire through the Thouless length, yields a length- and temperature-dependent resistivity proportional to (L/lT)4 under appropriate conditions. Inelastic-scattering lifetimes are inferred from the temperature-dependent bulk resistivities (i.e., those of thicker, effectively three-dimensional samples), assuming that a minimum amount of energy must be exchanged for a collision to be effective in destroying the phase coherence of the localized state. If the dominant inelastic mechanism is electron-electron scattering, then our result, given the appropriate choice of the channel number parameter, is consistent with the data. If electron-phason scattering were of comparable importance, then our results would remain consistent. However, the inelastic-scattering lifetime inferred from bulk resistivity data is too short. This is because the electron-phason mechanism dominates in the inelastic-scattering rate, although the two mechanisms may be of comparable importance for the bulk resistivity. Possible reasons why the electron-phason mechanism might be less effective in thin wires than in bulk are discussed.

Performance study of a pressure transducer with meandering-path thin film strain gauges

The performance of a pressure transducer with meandering-path thin film strain gauges has been studied. Details of the procedure followed to prepare the thin film strain gauge system on the pressure transducer diaphragm are given. The effect of post-deposition heat treatment on the resistance of the sensing films of the strain gauges and the insulating base layers are discussed. The output of the pressure transducer was studied with various input pressures and excitation voltages. It was found that up to a maximum of 10 V bridge excitation the output was stable and repetitive. The maximum non-linearity and hysteresis observed are ±0.15%, ±0.16% and ±0.14% FSO (full-scale output) for 5, 7.5 and 10 V excitation respectively. Information on the output behaviour of the pressure transducer with temperature is also included.

Path integral quantisation of topological field theories

Conditions for quantum topological invariance of classically topological field theories in the path integral formulation are discussed. Both the three-dimensional Chern-Simons system and a Witten-type topological field theory are shown to satisfy these conditions.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

High accuracy curve fits for chirality, length and diameter dependent initial modulus of single walled carbon nanotubes

Many previous studies regarding the estimation of mechanical properties of single walled carbon nanotubes (SWCNTs) report that, the modulus of SWCNTs is chirality, length and diameter dependent. Here, this dependence is quantitatively described in terms of high accuracy curve fit equations. These equations allow us to estimate the modulus of long SWCNTs (lengths of about 100-120 nm) if the value at the prescribed low lengths (lengths of about 5-10 nm) is known. This is supposed to save huge computational time and expense. Also, based on the observed length dependent behavior of SWCNT initial modulus, we predict that, SWCNT mechanical properties such as Young's modulus, secant modulus, maximum tensile strength, failure strength, maximum tensile strain and failure strain might also exhibit the length dependent behavior along with chirality and length dependence. (C) 2010 Elsevier B.V. All rights reserved.

Length-scale-dependent ensemble-averaged conductance of a 1D disordered conductor: Conductance minimum

An exact numerical calculation of ensemble-averaged length-scale-dependent conductance for the one-dimensional Anderson model is shown to support an earlier conjecture for a conductance minimum. The numerical results can be understood in terms of the Thouless expression for the conductance and the Wigner level-spacing statistics.