Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

Inter-helical Interactions in Membrane Proteins: Analysis Based on the Local Backbone Geometry and the Side Chain Interactions

The availability of a significant number of the Structures of helical membrane proteins has prompted us to investigate the mode of helix-helix packing. In the present study, we have considered a dataset of alpha-helical membrane proteins representing Structures solved from all the known superfamilies. We have described the geometry of all the helical residues in terms of local coordinate axis at the backbone level. Significant inter-helical interactions have been considered as contacts by weighing the number of atom-atom contacts, including all the side-chain atoms. Such a definition of local axis and the contact criterion has allowed us to investigate the inter-helical interaction in a systematic and quantitative manner. We show that a single parameter (designated as alpha), which is derived from the parameters representing the Mutual orientation of local axes, is able to accurately Capture the details of helix-helix interaction. The analysis has been carried Out by dividing the dataset into parallel, anti-parallel, and perpendicular orientation of helices. The study indicates that a specific range of alpha value is preferred for interactions among the anti-parallel helices. Such a preference is also seen among interacting residues of parallel helices, however to a lesser extent. No such preference is seen in the case of perpendicular helices, the contacts that arise mainly due to the interaction Of Surface helices with the end of the trans-membrane helices. The Study Supports the prevailing view that the anti-parallel helices are well packed. However, the interactions between helices of parallel orientation are non-trivial. The packing in alpha-helical membrane proteins, which is systematically and rigorously investigated in this study, may prove to be useful in modeling of helical membrane proteins.

Bounding Run-Times of Local Adiabatic Algorithms

A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ingredient in the adiabaticity condition. In this paper we present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic un-ordered search of van Dam et al. [17] and Roland and Cerf [15] when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in log N, where N is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

Investigation of the local Fe magnetic moments at the grain boundaries of the Ca2FeReO6 double perovskite

The local Fe ferromagnetic (FM) moment at the grain boundaries of a ceramic sample of Ca2FeReO6 double perovskite was investigated by means of x-ray magnetic circular dichroism spectroscopy at the Fe L-2,L-3 edges and compared to the overall bulk magnetization. We found that, at the grain boundaries, the Fe FM moments at H=5 T are much smaller than expected and that the MxH curve is harder than in the bulk magnetization. These results suggest a larger degree of Fe/Re antisite disorder at the grain boundaries of this sample, shedding light into the intriguing nonmetallic resistivity behavior despite the reported presence of free carriers. (c) 2007 American Institute of Physics.

Hot deformation behaviour of Mg–3Al alloy—A study using processing map

The hot deformation behaviour of Mg–3Al alloy has been studied using the processing-map technique. Compression tests were conducted in the temperature range 250–550 °C and strain rate range 3 × 10−4 to 102 s−1 and the flow stress data obtained from the tests were used to develop the processing map. The various domains in the map corresponding to different dissipative characteristics have been identified as follows: (i) grain boundary sliding (GBS) domain accommodated by slip controlled by grain boundary diffusion at slow strain-rates (<10−3 s−1) in the temperature range from 350 to 450 °C, (ii) two different dynamic recrystallization (DRX) domains with a peak efficiency of 42% at 550 °C/10−1 s−1 and 425 °C/102 s−1 governed by stress-assisted cross-slip and thermally activated climb as the respective rate controlling mechanisms and (iii) dynamic recovery (DRV) domain below 300 °C in the intermediate strain rate range from 3 × 10−2 to 3 × 10−1 s−1. The regimes of flow instability have also been delineated in the processing map using an instability criterion. Adiabatic shear banding at higher strain rates (>101 s−1) and solute drag by substitutional Al atoms at intermediate strain rates (3 × 10−2 to 3 × 10−1 s−1) in the temperature range (350–450 °C) are responsible for flow instability. The relevance of these mechanisms with reference to hot working practice of the material has been indicated. The processing maps of Mg–3Al alloy and as-cast Mg have been compared qualitatively to elucidate the effect of alloying with aluminum on the deformation behaviour of magnesium.

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

In situ transmission electron microscope study of single asperity sliding contacts

Direct observation of events taking place at the contacting interfaces is important to understand many tribological phenomena. Transmission electron microscope (TEM) has the ability to look through materials at very high magnifications. Most of the TEM observations are done long after the deforming loads and stresses have been relaxed and the material state is further disturbed during the specimen preparation. We have developed a specimen holder in which two electron transparent surfaces can be brought in contact and moved relative to each other in JEOL 2000FX microscope. This holder enables visualization of not only the contacting surfaces at nanoscale but also the subsurface deformation resulting from the contact interaction. Sliding experimentS have been carried out mimicking a single asperity sliding contact. A sharp tungsten probe is moved laterally against a tip mounted on a cantilever. Magnitude of the contact instability, when the contact is broken is found to be dependent on the local geometry of the contact.(C) 2009 Elsevier Ltd. All rights reserved.

Non local scale effects on ultrasonic wave characteristics nanorods

In this paper, the nonlocal elasticity theory has been incorporated into classical Euler-Bernoulli rod model to capture unique features of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behaviors of nanorods from those of macroscopic rods. Nonlocal Euler-Bernoulli bar model is developed for nanorods. Explicit expressions are derived for wavenumbers and wave speeds of nanorods. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial wave mode where no wave propagation occurs. This is manifested in the spectrum cures as the region where the wavenumber tends to infinite (or wave speed tends to zero). The results can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes. (C) 2010 Elsevier B.V. All rights reserved.

Stereochemical Analysis of Higher α,α-Dialkylglycine Containing Peptides. Characterization of Local Helical Conformations at Dipropylglycine Residues and Observation of a Novel Hydrated Multiple β-Turn Structure in Crystals of a Glycine Rich Peptide

The peptide Boc-Gly-Dpg-Gly-Gly-Dpg-Gly-NHMe (1) has been synthesized to examine the conformational preferences of Dpg residues in the context of a poor helix promoting sequence. Single crystals of 1 were obtained in the space group P21/c with a = 13.716(2) Å, b = 12.960(2) Å, c = 22.266(4) Å, and β = 98.05(1)°; R = 6.3% for 3660 data with |Fo| > 4σ. The molecular conformation in crystals revealed that the Gly(1)-Dpg(2) segment adopts φ, ψ values distorted from those expected for an ideal type II‘ β-turn (φGly(1) = +72.0°, ψGly(1) = −166.0°; φDpg(2) = −54.0°, ψDpg(2) = −46.0°) with an inserted water molecule between Boc-CO and Gly(3)NH. The Gly(3)-Gly(4) segment adopts φ, ψ values which lie broadly in the right handed helical region (φGly(3) = −78.0°, ψGly(3) = −9.0°; φGly(4) = −80.0°, ψGly(4) = −18.0°). There is a chiral reversal at Dpg(5) which takes up φ, ψ values in the left handed helical region. The Dpg(5)-Gly(6) segment closely resembles an ideal type I‘ β-turn (φDpg(5) = +56.0°, ψDpg(5) = +32.0°; φGly(6) = +85.0°, ψGly(6) = −3.0°). Molecules of both chiral senses are found in the centrosymmetric crystal. The C-terminus forms a hydrated Schellman motif, with water insertion into the potential 6 → 1 hydrogen bond between Gly(1)CO and Gly(6)NH. NMR studies in CDCl3 suggest substantial retention of the multiple turn conformation observed in crystals. In solution the observed NOEs support local helical conformation at the two Dpg residues.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

On the effect of matrix cracks in composite helicopter rotor blade

This paper investigates the feasibility of an on-line damage detection capability for helicopter main rotor blades made of composite material. Damage modeled in the composite is matrix cracking. A box-beam with stiffness properties similar to a hingeless rotor blade is designed using genetic algorithm for the typical [+/-theta(m)/90(n)](s) family of composites. The effect of matrix cracks is included in an analytical model of composite box-beam. An aeroelastic analysis of the helicopter rotor based on finite elements in space and time is used to study the effects of matrix cracking in the rotor blade in forward flight. For global fault detection, rotating frequencies, tip bending and torsion response, and blade root loads are studied. It is observed that the effect of matrix cracking on lag bending and elastic twist deflection at the blade tip and blade root yawing moment is significant and these parameters can be monitored for online health monitoring. For implementation of local fault detection technique, the effect on axial and shear strain, for matrix cracks in the whole blade as well as matrix cracks occurring locally is studied. It is observed that using strain measurement along the blade it is possible to locate the matrix cracks as well as to predict density of matrix cracks. (C) 2004 Elsevier Ltd. All rights reserved.

Local structure in LaMnO3 and CaMnO3 perovskites: A quantitative structural refinement of mn K-edge XANES data

Hole-doped perovskites such as La1-xCaxMnO3 present special magnetic and magnetotransport properties, and it is commonly accepted that the local atomic structure around Mn ions plays a crucial role in determining these peculiar features. Therefore experimental techniques directly probing the local atomic structure, like x-ray absorption spectroscopy (XAS), have been widely exploited to deeply understand the physics of these compounds. Quantitative XAS analysis usually concerns the extended region [extended x-ray absorption fine structure (EXAFS)] of the absorption spectra. The near-edge region [x-ray absorption near-edge spectroscopy (XANES)] of XAS spectra can provide detailed complementary information on the electronic structure and local atomic topology around the absorber. However, the complexity of the XANES analysis usually prevents a quantitative understanding of the data. This work exploits the recently developed MXAN code to achieve a quantitative structural refinement of the Mn K-edge XANES of LaMnO3 and CaMnO3 compounds; they are the end compounds of the doped manganite series LaxCa1-xMnO3. The results derived from the EXAFS and XANES analyses are in good agreement, demonstrating that a quantitative picture of the local structure can be obtained from XANES in these crystalline compounds. Moreover, the quantitative XANES analysis provides topological information not directly achievable from EXAFS data analysis. This work demonstrates that combining the analysis of extended and near-edge regions of Mn K-edge XAS spectra could provide a complete and accurate description of Mn local atomic environment in these compounds.

Local structure of Sr(2)FeMoxW1-xO(6) double perovskites studied by EXAFS

Sr2FeMoO6 double perovskits display low field MR at a relatively high temperature and unusual ferromagnetic properties. These compounds depicts metal to insulator transition increasing x above x(c) similar to 0.25. A comparative analysis of the near edge regions (XANES) suggests that iron is Fe3+ in the metallic range. Checking the end compounds, we found that the doped samples can be viewn as inhomogeneous distributions of the end compounds. This could help to distinguish between the two scenarios proposed to explain the metal to insulator transition. Moreover, the local atomic structure of Sr2FeMoxW1-xO6 as a function of composition (0 <= x <= 1) has been investigated by Extended X-ray absorption spectroscopy (EXAFS) a the Fe, Mo, Sr K-edges andW L-III-edge.

Fracture analysis of stiffened panels under combined tensile, bending, and shear loads

The objective is to present the formulation of numerically integrated modified virtual crack closure integral technique for concentrically and eccentrically stiffened panels for computation of strain-energy release rate and stress intensity factor based on linear elastic fracture mechanics principles. Fracture analysis of cracked stiffened panels under combined tensile, bending, and shear loads has been conducted by employing the stiffened plate/shell finite element model, MQL9S2. This model can be used to analyze plates with arbitrarily located concentric/eccentric stiffeners, without increasing the total number of degrees of freedom, of the plate element. Parametric studies on fracture analysis of stiffened plates under combined tensile and moment loads have been conducted. Based on the results of parametric,studies, polynomial curve fitting has been carried out to get best-fit equations corresponding to each of the stiffener positions. These equations can be used for computation of stress intensity factor for cracked stiffened plates subjected to tensile and moment loads for a given plate size, stiffener configuration, and stiffener position without conducting finite element analysis.