Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain

Probably the most informative description of the ground slate of a magnetic molecular species is provided by the spin density map. Such a map may be experimentally obtained from polarized neutron diffraction (PND) data or theoretically calculated using quantum chemical approaches. Density functional theory (DFT) methods have been proved to be well-adapted for this. Spin distributions in one-dimensional compounds may also be computed using the density matrix renormalization group (DMRG) formalism. These three approaches, PND, DFT, and DMRG, have been utilized to obtain new insights on the ground state of two antiferromagnetically coupled Mn2+Cu2+ compounds, namely [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) and MnCu(pba)(H2O)(3) . 2H(2)O, with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, oxpn = N,N'-bis(3-aminopropyl)oxamido and pba = 1,3-propylenebis(oxamato). Three problems in particular have been investigated: the spin distribution in the mononuclear precursors [Cu(oxpn)] and [Cu(pba)](2-), the spin density maps in the two Mn2+Cu2+ compounds, and the evolution of the spin distributions on the Mn2+ and Cu2+ sites when passing from a pair to a one-dimensional ferrimagnet.

Theory of polymer breaking under tension

We consider the breaking of a polymer molecule which is fixed at one end and is acted upon by a force at the other. The polymer is assumed to be a linear chain joined together by bonds which satisfy the Morse potential. The applied force is found to modify the Morse potential so that the minimum becomes metastable. Breaking is just the decay of this metastable bond, by causing it to go over the barrier. Increasing the force causes the potential to become more and more distorted and eventually leads to the disappearance of the barrier. The limiting force at which the barrier disappears is D(e)a/2,D-e with a the parameters characterizing the Morse potential. The rate of breaking is first calculated using multidimensional quantum transition state theory. We use the harmonic approximation to account for vibrations of all the units. It includes tunneling contributions to the rate, but is valid only above a certain critical temperature. It is possible to get an analytical expression for the rate of breaking. We have calculated the rate of breaking for a model, which mimics polyethylene. First we calculate the rate of breaking of a single bond, without worrying about the other bonds. Inclusion of other bonds under the harmonic approximation is found to lower this rate by at the most one order of magnitude. Quantum effects are found to increase the rate of breaking and are significant only at temperatures less than 150 K. At 300 K, the calculations predict a bond in polyethylene to have a lifetime of only seconds at a force which is only half the limiting force. Calculations were also done using the Lennard-Jones potential. The results for Lennard-Jones and Morse potentials were rather different, due to the different long-range behaviors of the two potentials. A calculation including friction was carried out, at the classical level, by assuming that each atom of the chain is coupled to its own collection of harmonic oscillators. Comparison of the results with the simulations of Oliveira and Taylor [J. Chem. Phys. 101, 10 118 (1994)] showed the rate to be two to three orders of magnitude higher. As a possible explanation of discrepancy, we consider the translational motion of the ends of the broken chains. Using a continuum approximation for the chain, we find that in the absence of friction, the rate of the process can be limited by the rate at which the two broken ends separate from one another and the lowering of the rate is at the most a factor of 2, for the parameters used in the simulation (for polyethylene). In the presence of friction, we find that the rate can be lowered by one to two orders of magnitude, making our results to be in reasonable agreement with the simulations.

Coupled electro-mechanical response of an electroactive polymer cantilever structure and its application in energy harvesting

Ionic polymer-metal composites (IPMC), piezoelectric polymer composites and nematic elastomer composites are materials, which exhibit characteristics of both sensors and actuators. Large deformation and curvature are observed in these systems when electric potential is applied. Effects of geometric non-linearity due to the chargeinduced motion in these materials are poorly understood. In this paper, a coupled model for understanding the behavior of an ionic polymer beam undergoing large deformation and large curvature is presented. Maxwell's equations and charge transport equations are considered which couple the distribution of the ion concentration and the pressure gradient along length of a cantilever beam with interdigital electrodes. A nonlinear constitutive model is derived accounting for the visco-elasto-plastic behavior of these polymers and based on the hypothesis that the presence of electrical charge stretches/contracts bonds, which give rise to electrical field dependent softening/hardening. Polymer chain orientation in statistical sense plays a role on such softening or hardening. Elementary beam kinematics with large curvature is considered. A model for understanding the deformation due to electrostatic repulsion between asymmetrical charge distributions across the cross-sections is presented. Experimental evidence that Silver(Ag) nanoparticle coated IPMCs can be used for energy harvesting is reported. An IPMC strip is vibrated in different environments and the electric power against a resistive load is measured. The electrical power generated was observed to vary with the environment with maximum power being generated when the strip is in wet state. IPMC based energy harvesting systems have potential applications in tidal wave energy harvesting, residual environmental energy harvesting to power MEMS and NEMS devices.

Wave dispersion in a cellular composite with modulated microstructure

In this paper we report a modeling technique and analysis of wave dispersion in a cellular composite laminate with spatially modulated microstructure, which can be modeled by parameterization and homogenization in an appropriate length scale. Higher order beam theory is applied and the system of wave equations are derived. Homogenization of these equations are carried out in the scale of wavelength and frequency of the individual wave modes. Smaller scale scattering below the order of cell size are filtered out in the present approach. The longitudinal dispersion relations for different values of a modulation parameter are analyzed which indicates the existence of stop and pass band patterns. Dispersion relations for flexural-shear case are also analyzed which indicates a tendency toward forming the stop and pass bands for increasing values of a shear stiffness modulation parameter. The effect the phase angle (θ) of the incident wave indicates the existence more number of alternative stop bands and pass bands for θ = 45°.

Model track studies on fouled ballast using ground penetrating radar and multichannel analysis of surface wave

Ballast fouling is created by the breakdown of aggregates or outside contamination by coal dust from coal trains, or from soil intrusion beneath rail track. Due to ballast fouling, the conditions of rail track can be deteriorated considerably depending on the type of fouling material and the degree of fouling. So far there is no comprehensive guideline available to identify the critical degree of fouling for different types of fouling materials. This paper presents the identification of degree of fouling and types of fouling using non-destructive testing, namely seismic surface-wave and ground penetrating radar (GPR) survey. To understand this, a model rail track with different degree of fouling has been constructed in Civil engineering laboratory, University of Wollongong, Australia. Shear wave velocity obtained from seismic survey has been employed to identify the degree of fouling and types of fouling material. It is found that shear wave velocity of fouled ballast increases initially, reaches optimum fouling point (OFP), and decreases when the fouling increases. The degree of fouling corresponding after which the shear wave velocity of fouled ballast will be smaller than that of clean ballast is called the critical fouling point (CFP). Ground penetrating radar with four different ground coupled antennas (500 MHz, 800 MHz, 1.6 GHz and 2.3 GHz) was also used to identify the ballast fouling condition. It is found that the 800 MHz ground coupled antenna gives a better signal in assessing the ballast fouling condition. Seismic survey is relatively slow when compared to GPR survey however it gives quantifiable results. In contrast, GPR survey is faster and better in estimating the depth of fouling. (C) 2011 Elsevier B.V. All rights reserved.

A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

Effect of pairing fluctuations on low-energy electronic spectra in cuprate superconductors

We describe here a minimal theory of tight-binding electrons moving on the square planar Cu lattice of the hole-doped cuprates and mixed quantum mechanically with their own Cooper pairs. The superconductivity occurring at the transition temperature T(c) is the long-range, d-wave symmetry phase coherence of these Cooper pairs. Fluctuations, necessarily associated with incipient long-range superconducting order, have a generic large-distance behavior near T(c). We calculate the spectral density of electrons coupled to such Cooper-pair fluctuations and show that features observed in angle resolved photoemission spectroscopy (ARPES) experiments on different cuprates above T(c) as a function of doping and temperature emerge naturally in this description. These include ``Fermi arcs'' with temperature-dependent length and an antinodal pseudogap, which fills up linearly as the temperature increases toward the pseudogap temperature. Our results agree quantitatively with experiment. Below T(c), the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with some recent ARPES experiments, especially the observed bending or deviation of the superconducting gap from the canonical d-wave form.

Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Study of non-local wave properties of nanotubes with surface effects

In macroscopic and even microscopic structural elements, surface effects can be neglected and classical theories are sufficient. As the structural size decreases towards the nanoscale regime, the surface-to-bulk energy ratio increases and surface effects must be taken into account. In the present work, the terahertz wave dispersion characteristics of a nanotube are studied with consideration of the surface effects as well as the non-local small scale effects. Non-local elasticity theory is used to derive the general governing differential equation based on equilibrium approach to include those scale effects. Scale and surface property dependent wave characteristic equations are obtained via spectral analysis. For the present study the material properties of an anodic alumina nanotube with crystallographic of < 111 > direction are considered. The present analysis shows that the effect of surface properties (surface integrated residual stress and surface integrated modulus) on the flexural wave characteristics of anodic nanotubes are more significant. It has been found that the flexural wavenumbers with surface effects are high as compared to that without surface effects. It has also been shown that, with consideration of surface effects the flexural wavenumbers are under compressive nature. The effect of the small scale and the size of the nanotube on wave dispersion properties are also captured in the present work. (C) 2012 Elsevier B.V. All rights reserved.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

Longitudinal Magnetic Field Effect on Nonlocal Ultrasonic Vibration Analysis of Single-Walled Carbon Nanotubes Based on Wave Propagation Approach

This paper studies the effect of longitudinal magnetic field on ultrasonic vibration in single walled carbon nanotubes (CNTs) based on nonlocal continuum medium theory. Governing partial differential equations of CNTs are derived by considering the Lorentz magnetic forces applied on CNTs induced by a longitudinal magnetic field through Maxwell equations. The vibration characteristics of CNTs under a longitudinal magnetic field are obtained by solving the governing equations via wave propagation approach. The effects of longitudinal magnetic field on vibration of CNTs are discussed through numerical experiments. The present analysis show that vibration frequencies of CNTs drops dramatically in the presence of the magnetic field for various circumferential wavenumbers. Such effect is also observed for various boundary conditions of the CNT. New features for the effect of longitudinal magnetic field on ultrasonic vibration of CNTs, presented in this paper are useful in the design of nano-drive device, nano-oscillator and actuators and nano-electron technology, where carbon nanotubes act as basic elements.

Ultrasonic Wave Dispersion Characteristics of Fluid-Filled Single-Walled Carbon Nanotubes Based on Nonclassical Shell Model

In this paper, ultrasonic wave propagation analysis in fluid filled single-walled carbon nanotube (SWCNT) is studied using nonlocal elasticity theory. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. The fluid inside the SWCNT is assumed as water. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The presence of fluid in SWCNT alters the ultrasonic wave dispersion behavior. The wavenumber and wave velocity are smaller in presence of fluid as compared to the empty SWCNT. The nonlocal elasticity calculation shows that the wavenumber tends to reach the continuum limit at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. It has been shown that the circumferential. waves will propagate non-dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the cut-off frequency depend on the nonlocal scaling parameter and also on the density of the fluid inside the SWCNT, and the axial wavenumber, as the fluid becomes denser the cut-off frequency decreases. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTS filled with water is also discussed.

Coupled phonons, magnetic excitations, and ferroelectricity in AlFeO3: Raman and first-principles studies

We determine the nature of coupled phonons and magnetic excitations in AlFeO3 using inelastic light scattering from 5 to 315 K covering a spectral range from 100 to 2200 cm(-1) and complementary first-principles density functional theory-based calculations. A strong spin-phonon coupling and magnetic ordering-induced phonon renormalization are evident in (1) anomalous temperature dependence of many modes with frequencies below 850 cm(-1), particularly near the magnetic transition temperature T-c approximate to 250 K, and (2) distinct changes in band positions of high-frequency Raman bands between 1100 and 1800 cm(-1); in particular, a broad mode near 1250 cm(-1) appears only below T-c, attributed to the two-magnon Raman scattering. We also observe weak anomalies in the mode frequencies similar to 100 K due to a magnetically driven ferroelectric phase transition. Understanding of these experimental observations has been possible on the basis of first-principles calculations of the phonons' spectrum and their coupling with spins.

Temperature effects on wave propagation in nanoplates

In this paper, the thermal effects on the ultrasonic wave propagation characteristics of a nanoplate are studied based on the nonlocal continuum theory. The nonlocal governing equations are derived for the nanoplate under thermal environment. The axial stress caused by the thermal effects is considered. The wave propagation analysis is carried out using spectral analysis. The influences of the nonlocal small scale coefficient, the room or low temperature, the high temperature and the axial half wave numbers on the wave dispersion properties of nanoplate are also discussed. Numerical results show that the small scale effects and the thermal effects are significant for larger half wavenumbers. The results are qualitatively different from those obtained based on the local plate theory and thus, are important for the development of graphene-based nanodevices such as strain sensor, mass and pressure sensors, atomic dust detectors, and enhancer of surface image resolution. (C) 2011 Elsevier Ltd. All rights reserved.