Structure-function hierarchies and von Karman-Howarth relations for turbulence in magnetohydrodynamical equations

We generalize the method of A. M. Polyakov, Phys. Rev. E 52, 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension Eur. Phys. J.B 9, 725 (1999)], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Karman-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.

Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature. (C) 2014 Elsevier Ltd. All rights reserved.

Polarization-rotation resonances with subnatural widths using a control laser

We demonstrate extremely narrow resonances for polarization rotation in an atomic vapor. The resonances are created using a strong control laser on the same transition, which polarizes the atoms due to optical pumping among the magnetic sublevels. As the power in the control laser is increased, successively higher-order nested polarization-rotation resonances are created, with progressively narrower linewidths. We study these resonances in the D-2 line of Rb in a room temperature vapor cell, and demonstrate a width of 0.14 G for the third-order rotation. The physical basis for the observed resonances is that optical pumping results in a simplified. AV-type level structure with differential dressing of the levels by the control laser, which is why the control power has to be sufficiently high for each resonance to appear. This explanation is borne out by a density-matrix analysis of the system. The dispersive lineshape and subnatural width of the resonance lends itself naturally to applications such as laser locking to atomic transitions and precision measurements. Copyright (c) EPLA, 2014

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

Large deformation dynamic finite element analysis of delaminated composite plates using contact-impact conditions

A new C-0 composite plate finite element based on Reddy's third order theory is used for large deformation dynamic analysis of delaminated composite plates. The inter-laminar contact is modeled with an augmented Lagrangian approach. Numerical results show that the widely used ``unconditionally stable'' beta-Newmark method presents instability problems in the transient simulation of delaminated composite plate structures with large deformation. To overcome this instability issue, an energy and momentum conserving composite implicit time integration scheme presented by Bathe and Baig is used. It is found that a proper selection of the penalty parameter is very crucial in the contact simulation. (C) 2014 Elsevier Ltd. All rights reserved.

STM verification of the reduction of the Young's modulus of CdS nanoparticles at smaller sizes

We demonstrate the first STM evaluation of the Young's modulus (E) of nanoparticles (NPs) of different sizes. The sample deformation induced by tip-sample interaction has been determined using current-distance (I-Z) spectroscopy. As a result of tip-sample interaction, and the induced surface deformations, the I-z curves deviates from pure exponential dependence. Normally, in order to analyze the deformation quantitatively, the tip radius must be known. We show, that this necessity is eliminated by measuring the deformation on a substrate with a known Young's modulus (Au(111)) and estimating the tip radius, and afterwards, using the same tip (with a known radius) to measure the (unknown) Young's modulus of another sample (nanoparticles of CdS). The Young's modulus values found for 3 NP's samples of average diameters of 3.7, 6 and 7.5 nm, were E similar to 73%, 78% and 88% of the bulk value, respectively. These results are in a good agreement with the theoretically predicted reduction of the Young's modulus due to the changes in hydrostatic stresses which resulted from surface tension in nanoparticles with different sizes. Our calculation using third order elastic constants gives a reduction of E which scales linearly with 1/r (r is the NP's radius). This demonstrates the applicability of scanning tunneling spectroscopy for local mechanical characterization of nanoobjects. The method does not include a direct measurement of the tip-sample force but is rather based on the study of the relative elastic response. (C) 2014 Elsevier B.V. All rights reserved.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Enhanced nonlinear optical properties of graphene oxide-silver nanocomposites measured by Z-scan technique

Nonlinear optical properties (NLO) of a graphene oxide-silver (GO-Ag) nanocomposite have been investigated by the Z-scan setup at Q-switched Nd:YAG laser second harmonic radiation i.e., at 532 nm excitation in a nanosecond regime. A noteworthy enhancement in the NLO properties in the GO-Ag nanocomposite has been reported in comparison with those of the synthesized GO nanosheet. The extracted value of third order nonlinear susceptibility (chi(3)), at a peak intensity of I-0 = 0.2 GW cm(-2), for GO-Ag has been found to be 2.8 times larger than that of GO. The enhancement in NLO properties in the GO-Ag nanocomposite may be attributed to the complex energy band structures formed during the synthesis which promote resonant transition to the conduction band via surface plasmon resonance (SPR) at low laser intensities and excited state transition (ESA) to the conduction band of GO at higher intensities. Along with this photogenerated charge carriers in the conduction band of silver or the increase in defect states during the formation of the GO-Ag nanocomposite may contribute to ESA. Open aperture Z-scan measurement indicates reverse saturable absorption (RSA) behavior of the synthesized nanocomposite which is a clear indication of the optical limiting (OL) ability of the nanocomposite.

Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits

The angular-momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular-momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to nonlinear memory. We average the angular-momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular-momentum flux provides the final input needed for gravitational-wave phasing of binaries moving in quasi-elliptical orbits. We obtain the evolution of orbital elements under 3PN gravitational radiation reaction in the quasi-elliptic case. For small eccentricities, we give simpler limiting expressions relevant for phasing up to order e(2). This work is important for the construction of templates for quasi-eccentric binaries, and for the comparison of post-Newtonian results with the numerical relativity simulations of the plunge and merger of eccentric binaries.

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

Head-on infall of two compact objects: Third post-Newtonian energy flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails, and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.

Thermal Lipid Order−Disorder Transitions in Mixtures of Cationic Cholesteryl Lipid Analogues and Dipalmitoyl Phosphatidylcholine Membranes

Two types of cationic cholesteryl amphiphiles, one where the headgroup is attached to the steroid by an ester linkage and the second by an ether linkage, were synthesized. A third type of cholesteryl lipid bearing an oligoethylene glycol segment was also prepared. Each of these synthetic lipids generated vesicle-like aggregates with closed inner aqueous compartments from their aqueous suspensions. We examined their interaction with L-α-dipalmitoyl phosphatidylcholine (DPPC) membranes using fluorescence anisotropy, transmission electron microscopy (TEM), and differential scanning calorimetry (DSC). When included in membranes, the synthetic cholesteryl lipids were found to quench the chain motion of the acyl chains of DPPC. This suggests that these cationic cholesteryl derivatives act as filler molecules despite modification at the headgroup level from the molecular structure of natural cholesterol. Careful analyses of DSC and fluorescence anisotropy data suggest that the nature of perturbation induced by each of these cationic cholesterol derivatives is dependent on the details of their molecular structure and provides significant information on the nature of interaction of these derivatives with phospholipid molecules. In general, amphiphiles that support structured water at the interfacial region tend to rigidify the fluid phase more than others. Importantly, these cholesteryl amphiphiles behave less like cholesterol in that their incorporation in DPPC not only abolishes the phase transition but also depresses the phase transition temperature.

Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian (PN) order. We further extend these results for compact binaries in quasielliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current-type multipole moments, we compute the spin-weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasielliptical orbits.

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.