Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

An infrared spectroscopic study of the low-spin-high-spin transition in FexMn1-x(Phen)2(NCS)2: A composition-induced change in the order of the spin-state transition

Infrared spectroscopy provides a valuable tool to investigate the spin-state transition in Fe(II) complexes of the type Fe(Phen)2(NCS)2. With progressive substitution of Fe by Mn, the first-order transition changes over to a second-order transition, with a high residual population of the high-spin state even at very low temperatures

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.

Conformation of substituted polyacetylenes in solution : relationship between electronic properties and local order

A study of the chain conformation in solutions of polyphenylacetylene and poly(2-octyne) has been performed. The two polymers differ in many ways : polyphenylacetylene gives a red solution while poly(2-octyne) is transparent and, a marked difference on the chain rigidity is observed : the statistical length are 45 Å and 135 Å respectively. From the study of these two systems, one deduces that curvature fluctuations play a minor role on the π electrons localization, and that the torsion between monomer units is the pertinent parameter to understand the chain conformation and the π electrons localization.

Determination of the sign of the order parameter from MAS spectra of oriented molecules

The use of the intensities of the spinning sidebands in the magic-angle spinning spectra of oriented molecules is proposed for the determination of the signs of the order parameters. The method is demonstrated for benzene and chloroform oriented in nematic phases of liquid crystals. On the basis of the theoretical expressions derived for the various order sidebands, the applicability of the method for different experimental conditions is discussed.

Activation barriers for d.c. conductivity in ionic glasses: Classical calculations using the small-cluster approximation

A small-cluster approximation has been used to calculate the activation barriers for the d.c. conductivity in ionic glasses. The main emphasis of this approach is on the importance of the hitherto ignored polarization energy contribution to the total activation energy. For the first time it has been demonstrated that the d.c. conductivity activation energy can be calculated by considering ionic migration to a neighbouring vacancy in a smali cluster of ions consisting of face-sharing anion polyhedra. The activation energies from the model calculations have been compared with the experimental values in the case of highly modified lithium thioborate glasses.

Electrical switching and short-range order in As-Te glasses

The local structural order in chalcogenide network glasses is known to change markedly at two critical compositions, namely, the percolation and chemical thresholds. In the AsxTe100-x glassy system, both the thresholds coincide at the composition x = 40 (40 at. % of arsenic). It is demonstrated that the electrical switching fields of As-Te glasses exhibit a distinct change at this composition.

Translational Up-Regulation and High-Level Protein Expression from Plasmid Vectors by mTOR Activation via Different Pathways in PC3 and 293T Cells

Background: Though 293T cells are widely used for expression of proteins from transfected plasmid vectors, the molecular basis for the high-level expression is yet to be understood. We recently identified the prostate carcinoma cell line PC3 to be as efficient as 293T in protein expression. This study was undertaken to decipher the molecular basis of high-level expression in these two cell lines. Methodology/Principal Findings: In a survey of different cell lines for efficient expression of platelet-derived growth factor-B (PDGF-B), beta-galactosidase (beta-gal) and green fluorescent protein (GFP) from plasmid vectors, PC3 was found to express at 5-50-fold higher levels compared to the bone metastatic prostate carcinoma cell line PC3BM and many other cell lines. Further, the efficiency of transfection and level of expression of the reporters in PC3 were comparable to that in 293T. Comparative analyses revealed that the high level expression of the reporters in the two cell lines was due to increased translational efficiency. While phosphatidic acid (PA)-mediated activation of mTOR, as revealed by drastic reduction in reporter expression by n-butanol, primarily contributed to the high level expression in PC3, multiple pathways involving PA, PI3K/Akt and ERK1/2 appear to contribute to the abundant reporter expression in 293T. Thus the extent of translational upregulation attained through the concerted activation of mTOR by multiple pathways in 293T could be achieved through its activation primarily by the PA pathway in PC3. Conclusions/Significance: Our studies reveal that the high-level expression of proteins from plasmid vectors is effected by translational up-regulation through mTOR activation via different signaling pathways in the two cell lines and that PC3 is as efficient as 293T for recombinant protein expression. Further, PC3 offers an advantage in that the level of expression of the protein can be regulated by simple addition of n-butanol to the culture medium.

Novel approach to estimate fringe order in Moire profilometry

A novel approach to estimate fringe order in Moire topography is proposed. Along with the light source used to create shadow of the grating on the object (as in conventional moire), proposed method uses a second light source which illuminates the object with color bands from the side. Width of each colored band is set to match that height which leads to a 2 pi phase shift in moire fringes. This facilitates one to rule the object with colored bands, which can be used to estimate fringe order using a color camera with relatively low spatial resolution with out any compromise in height sensitivity. Current proposal facilitates one to extract 3D profile of objects with surface discontinuities. It also deals with the possible usage of moire topography (when combined with the proposed method) in extracting 3D surface profile of many objects with height discontinuities using a single 2D image. Present article deals with theory and simulations of this novel side illumination based approach.

Electron-beam irradiation effects on poly(ethylene-co-vinyl acetate) polymer

Poly(ethylene-co-vinyl acetate) (EVA) films were irradiated with a 1.2MeV electron beam at varied doses over the range 0-270kGy in order to investigate the modifications induced in its optical, electrical and thermal properties. It was observed that optical band gap and activation energy of EVA films decreased upon electron irradiation, whereas the transition dipole moment, oscillator strength and number of carbon atoms per cluster were found to increase upon irradiation. Further, the dielectric constant, the dielectric loss, and the ac conductivity of EVA films were found to increase with an increase in the dose of electron radiation. The result further showed that the thermal stability of EVA film samples increased upon electron irradiation.

Intracellular Pathogen Sensor NOD2 Programs Macrophages to Trigger Notch1 Activation

Intracellular pathogen sensor, NOD2, has been implicated in regulation of wide range of anti-inflammatory responses critical during development of a diverse array of inflammatory diseases; however, underlying molecular details are still imprecisely understood. In this study, we demonstrate that NOD2 programs macrophages to trigger Notch1 signaling. Signaling perturbations or genetic approaches suggest signaling integration through cross-talk between Notch1-PI3K during the NOD2-triggered expression of a multitude of immunological parameters including COX-2/PGE(2) and IL-10. NOD2 stimulation enhanced active recruitment of CSL/RBP-Jk on the COX-2 promoter in vivo. Intriguingly, nitric oxide assumes critical importance in NOD2-mediated activation of Notch1 signaling as iNOS(-/-) macrophages exhibited compromised ability to execute NOD2-triggered Notch1 signaling responses. Correlative evidence demonstrates that this mechanism operates in vivo in brain and splenocytes derived from wild type, but not from iNOS(-/-) mice. Importantly, NOD2-driven activation of the Notch1-PI3K signaling axis contributes to its capacity to impart survival of macrophages against TNF-alpha or IFN-gamma-mediated apoptosis and resolution of inflammation. Current investigation identifies Notch1-PI3K as signaling cohorts involved in the NOD2-triggered expression of a battery of genes associated with anti-inflammatory functions. These findings serve as a paradigm to understand the pathogenesis of NOD2-associated inflammatory diseases and clearly pave a way toward development of novel therapeutics.

Holographic optical element based single-mode hybrid fiber optic interferometer for realizing zero-order fringe

A holographic optical element (HOE) based single-mode hybrid fiber optic interferometer for realizing the zero-order fringe is described. The HOE proposed and used integrates the actions of a beam combiner and a lens, and endows the interferometer with high tolerance for repositioning errors. The proposed method is simple and offers advantages such as the elimination of in situ processing for the hologram.

A Non-contact measurement technique to measure micro surface stress and obtain deformation profiles of the order of 1nm in Micro-cantilever based structures by single image Optical Diffraction method

A new method based on analysis of a single diffraction pattern is proposed to measure deflections in micro-cantilever (MC) based sensor probes, achieving typical deflection resolutions of 1nm and surface stress changes of 50 mu N/m. The proposed method employs a double MC structure where the deflection of one of the micro-cantilevers relative to the other due to surface stress changes results in a linear shift of intensity maxima of the Fraunhofer diffraction pattern of the transilluminated MC. Measurement of such shifts in the intensity maxima of a particular order along the length of the structure can be done to an accuracy of 0.01mm leading to the proposed sensitivity of deflection measurement in a typical microcantilever. This method can overcome the fundamental measurement sensitivity limit set by diffraction and pointing stability of laser beam in the widely used Optical Beam Deflection method (OBDM).

Distribution of ionic charge carriers and migration barriers in binary alkali silicate glasses

Likely spatial distributions of network-modifying (and mobile) cations in (oxide) glasses are discussed here. At very low modifier concentrations, the ions form dipoles with non-bridging oxygen centres while, at higher levels of modification, the cations tend to order as a result of Coulombic interactions. Activation energies for cation migration are calculated, assuming that the ions occupy (face-sharing) octahedral sites. It is found that conductivity activation energy decreases markedly with increasing modifier content, in agreement with experiment.

Higher twist and higher order contributions to the pion electromagnetic form factor

The O(m(pi)4/(m(u) + (d))2Q2) and O(alpha(S)2) corrections to the leading term of the perturbative QCD calculation of the pion electromagnetic form factor are examined numerically. Both sets of terms provide significant corrections for values of Q2 between 1 and 15 GeV2/c2.