The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates

Analytical solutions to problems in finite elasticity are most often derived using the semi-inverse approach along with the spatial form of the equations of motion involving the Cauchy stress tensor. This procedure is somewhat indirect since the spatial equations involve derivatives with respect to spatial coordinates while the unknown functions are in terms of material coordinates, thus necessitating the use of the chain rule. In this classroom note, we derive compact expressions for the components of the divergence, with respect to orthogonal material coordinates, of the first Piola-Kirchhoff stress tensor. The spatial coordinate system is also assumed to be an orthogonal curvilinear one, although, not necessarily of the same type as the material coordinate system. We show by means of some example applications how analytical solutions can be derived more directly using the derived results.

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the-cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Exact controllability of generalized Hammerstein type equation

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Quasichemical equations for oxygen and sulphur in liquid binary alloys

An equation has been derived for predicting the activity coefficient of oxygen or sulphur in dilute solution in binary alloys, based on the quasichemical approach, where the metal atoms and the oxygen atoms are assigned different bond numbers. This equation is an advance on Alcock and Richardson's earlier treatment where all the three types of atoms were assigned the same coordination number. However, the activity coefficients predicted by this new equation appear to be very similar to those obtained through Alcock and Richardson's equation for a number of alloy systems, when the coordination number of oxygen in the new model is the same as the average coordination number used in the earlier equation. A second equation based on the formation of “molecular species” of the type XnO and YnO in solution is also derived, where X and Y atoms attached to oxygen are assumed not to make any other bonds. This equation does not fit experimental data in all the systems considered for a fixed value of n. Howover, if the strong oxygen-metal bonds are assumed to distort the electronic configuation around the metal atoms bonded to oxygen and thus reduce the strength of the bonds formed by these atoms with neighbouring metal atoms by approximately a factor of two, the resulting equation is found to predict the activity coefficients of oxygen that are in good agreement with experimental data in a number of binary alloys.

Photoluminescence study of mixed doped Ge-Se-In-Bi glasses

Photoluminescence studies, carried out using the Fourier Transform method rather than the conventional monochromator-dispersion method,are reported on glassy samples of indium-bismuth mixed doped Ge (10) Se(90-x-y) In (x) Bi (y) system (x,y = 5,10). The amorphous Bi2Se3 is found to be n-type like the crystalline counterpart. The possible contributions from microscopic cluster-level phase separation of Bi2Se3 and from the defects to the change in conductivity from p- to n- typein this system is discussed. The similar situation in related systems is also pointed out.

Finite Element Method For A Nonlocal Problem Of Kirchhoff Type

The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton-Raphson method. This is because the Jacobian of the Newton-Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Solution nuclear magnetic resonance structure of the GATase subunit and structural Basis of the interaction between GATase and ATPPase subunits in a two-subunit-type GMPS from methanocaldococcus jannaschii

The solution structure of the monomeric glutamine amidotransferase (GATase) subunit of the Methanocaldococcus janaschii (Mj) guanosine monophosphate synthetase (GMPS) has been determined using high-resolution nuclear magnetic resonance methods. Gel filtration chromatography and N-15 backbone relaxation studies have shown that the Mj GATase subunit is present in solution as a 21 kDa (188-residue) monomer. The ensemble of 20 lowest-energy structures showed root-mean-square deviations of 0.35 +/- 0.06 angstrom for backbone atoms and 0.8 +/- 0.06 angstrom for all heavy atoms. Furthermore, 99.4% of the backbone dihedral angles are present in the allowed region of the Ramachandran map, indicating the stereochemical quality of the structure. The core of the tertiary structure of the GATase is composed of a seven-stranded mixed beta-sheet that is fenced by five alpha-helices. The Mj GATase is similar in structure to the Pyrococcus horikoshi (Ph) GATase subunit. Nuclear magnetic resonance (NMR) chemical shift perturbations and changes in line width were monitored to identify residues on GATase that were responsible for interaction with magnesium and the ATPPase subunit, respectively. These interaction studies showed that a common surface exists for the metal ion binding as well as for the protein-protein interaction. The dissociation constant for the GATase-Mg2+ interaction has been found to be similar to 1 mM, which implies that interaction is very weak and falls in the fast chemical exchange regime. The GATase-ATPPase interaction, on the other hand, falls in the intermediate chemical exchange regime on the NMR time scale. The implication of this interaction in terms of the regulation of the GATase activity of holo GMPS is discussed.

Effects of a Delocalizable Cation on the Headgroup of Gemini Lipids on the Lipoplex-Type Nanoaggregates Directly Formed from Plasmid DNA

Lipoplex-type nanoaggregates prepared from pEGFP-C3 plasmid DNA (pDNA) and mixed liposomes, with a gemini cationic lipid (CL) 1,2-bis(hexadecyl imidazolium) alkanes], referred as (C(16)Im)(2)C-n (where C-n is the alkane spacer length, n = 2, 3, 5, or 12, between the imidazolium heads) and DOPE zwitterionic lipid, have been analyzed by zeta potential, gel electrophoresis, SAXS, cryo-TEM, fluorescence anisotropy, transfection efficiency, fluorescence confocal microscopy, and cell viability/cytotoxicity experiments to establish a structure-biological activity relationship. The study, carried out at several mixed liposome compositions, alpha, and effective charge ratios, rho(eff), of the lipoplex, demonstrates that the transfection of pDNA using CLs initially requires the determination of the effective charge of both. The electrochemical study confirms that CLs with a delocalizable positive charge in their headgroups yield an effective positive charge that is 90% of their expected nominal one, while pDNA is compacted yielding an effective negative charge which is only 10-25% than that of the linear DNA. SAXS diffractograms show that lipoplexes formed by CLs with shorter spacer (n = 2, 3, or 5) present three lamellar structures, two of them in coexistence, while those formed by CL with longest spacer (n = 12) present two additional inverted hexagonal structures. Cryo-TEM micrographs show nanoaggregates with two multilamellar structures, a cluster-type (at low alpha value) and a fingerprint-type, that coexist with the cluster-type at moderate alpha composition. The optimized transfection efficiency (TE) of pDNA, in HEK293T, HeLa, and H1299 cells was higher using lipoplexes containing gemini CLs with shorter spacers at low a value. Each lipid formulation did not show any significant levels of toxicity, the reported lipoplexes being adequate DNA vectors for gene therapy and considerably better than both Lipofectamine 2000 and CLs of the 1,2-bis(hexadecyl ammnoniun) alkane series, recently reported.

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

Spinning strings and minimal surfaces in AdS(3) with mixed 3-form fluxes

Motivated by the recent proposal for the S-matrix in AdS(3) x S-3 with mixed three form fluxes, we study classical folded string spinning in AdS(3) with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinning strings with large spin S acquires a term given by -root lambda/2 pi b(2) log(2) S in addition to the usual root lambda/pi log S term where root lambda is proportional to the square of the radius of AdS(3). Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS(3) with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b(2) log(2) S term in the dispersion relation of the spinning string. This result indicates that the coefficient of b(2) log(2) S has a property similar to the coefficient of the log S term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling lambda using the recent proposal for the S-matrix.

Simple three parameter equations for correlating liquid phase compositions in subcritical and supercritical systems

Two Chrastil type expressions have been developed to model the solubility of supercritical fluids/gases in liquids. The three parameter expressions proposed correlates the solubility as a function of temperature, pressure and density. The equation can also be used to check the self-consistency of the experimental data of liquid phase compositions for supercritical fluid-liquid equilibria. Fifty three different binary systems (carbon-dioxide + liquid) with around 2700 data points encompassing a wide range of compounds like esters, alcohols, carboxylic acids and ionic liquids were successfully modeled for a wide range of temperatures and pressures. Besides the test for self-consistency, based on the data at one temperature, the model can be used to predict the solubility of supercritical fluids in liquids at different temperatures. (C) 2014 Elsevier B.V. All rights reserved.

Ligand 5,10,15,20-Tetra(N-methyl-4-pyridyl)porphine (TMPyP4) Prefers the Parallel Propeller-Type Human Telomeric G-Quadruplex DNA over Its Other Polymorphs

The binding of ligand 5,10,15,20-tetra(N-methyl-4-pyridyl)porphine (TMPyP4) with telomeric and genomic G-quadruplex DNA has been extensively studied. However, a comparative study of interactions of TMPyP4 with different conformations of human telomeric G-quadruplex DNA, namely, parallel propeller-type (PP), antiparallel basket-type (AB), and mixed hybrid-type (MH) G-quadruplex DNA, has not been done. We considered all the possible binding sites in each of the G-quadruplex DNA structures and docked TMPyP4 to each one of them. The resultant most potent sites for binding were analyzed from the mean binding free energy of the complexes. Molecular dynamics simulations were then carried out, and analysis of the binding free energy of the TMPyP4-G-quadruplex complex showed that the binding of TMPyP4 with parallel propeller-type G-quadruplex DNA is preferred over the other two G-quadruplex DNA conformations. The results obtained from the change in solvent excluded surface area (SESA) and solvent accessible surface area (SASA) also support the more pronounced binding of the ligand with the parallel propeller-type G-quadruplex DNA.

Sensitivity characteristics of Ag doped BaTiO3-CuO mixed oxide as Carbon-dioxide S ensor

Ag doped BaTiO3-CuO mixed oxide thin films are evaluated for their carbon-dioxide sensing characteristics. The metal oxide films of different thicknesses are deposited on oxidized p type Si < 100 > substrate by RF Sputtering. Sensing characteristics for different CO2 concentration, (300 ppm - 1000 ppm) are obtained for different operating temperatures, (100 degrees C - 400 degrees C). Optimum temperature for maximum sensitivity is found to be 250 degrees C. The effect of annealing on sensing properties is also evaluated. The unannealed films give better sensitivity than that of annealed films. Response time and recovery time are also calculated.

In-doped multifilled n-type skutterudites with ZT=1.8

In this paper we maximize the thermoelectric (TE) figure of merit, ZT, of n-type skutterudites, (In,Sr,Ba,Yb)(y)Co4Sb12, via three different routes: (i) find the optimum fraction of In as fourth filler (ii) check the influence of powder particle, grain, and crystallite size on the TE properties and (iii) check thermal stability. Filled n-type (Sr, Ba, Yb)(y)Co4Sb12 was mixed in three different proportions with In0.4Co4Sb12, ball milled (regular or high-energy (HB) ball milling) and hot-pressed. Particle size analyses and SEM pictures of the broken surfaces of the hot pressed samples document that only HB produces uniform particles/grains with average crystallite sizes similar to 100 nm, proven by transmission electron microscopy. X-ray Rietveld refinements combined with EDX indicate that in all cases indium entered the icosahedral voids of the skutterudite. Temperature dependent physical properties of all three regularly ball-milled samples show that increasing In-content infers an increasing electrical resistivity, increasing Seebeck coefficient but a decreasing total thermal conductivity. Although ZT (823 K) is in the same range as for the sample without In, the ZT values in the whole temperature range are higher and consequently the TE-conversion efficiency, eta is at least 10% higher. Annealing the samples at 600 degrees C for three days shows minor changes in structure and thermoelectric properties, indicating TE stability. The HB sample, due to uniformly small particles, equally sized grains and crystallites, exhibits a high power factor (4.4 mW/m K-2 at 730 K) and a very low thermal conductivity leading to an outstanding high ZT = 1.8 at 823 K (eta(max) = 17.5%). (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.