Energy Arguments Research Articles

In-situ and ex-situ characterization of TiO2 and Au nanoparticle incorporated TiO2 thin films for optical gas sensing at extreme temperatures

Sensor technologies that can operate under extreme conditions including high temperatures, high pressures, highly reducing and oxidizing environments, and corrosive gases are needed for process monitoring and control in advanced fossil energy applications. Sensor technologies based on optical waveguide-based techniques are highly attractive for passive, embedded, and remote sensing. A critical enabling technology for optical waveguide sensors is the development of advanced optical thin film coatings which have a desired set of optical properties that change in a rapid, selective, and sensitive manner to a particular quantity of interest. TiO2 and Au nanoparticle incorporated TiO2 nanocomposite thin films were prepared through sol-gel deposition techniques and their respective optical responses to a 4% H2/N2 mixture were investigated in the visible / near-IR range of 400–1000 nm. A tendency for Au nanoparticles to occupy special sites on the TiO2 microstructure, such as grain boundaries, twin boundaries, and triple points is rationalized in terms of basic surface energy arguments. The Au / TiO2 nanocomposite films showed a useful optical response due to a reversible, rapid, and repeatable shift in the localized surface plasma resonance peak of Au nanoparticles at a temperature of 650 °C and 850 °C. In contrast, high temperature exposure of TiO2 films to reducing gases at 850 °C resulted in the growth of abnormally large grains or “hillocks” that protruded from the sample surface and resulted in light scattering and an irreversible decrease in transmission at short wavelengths. The origin of the observed optical response of Au / TiO2 nanocomposite films is discussed in the context of work by prior investigators in the Au / yttria-stabilized Zirconia (YSZ) system and needs for future research in this area is highlighted.

On the existence of Eshelby’s equivalent ellipsoidal inclusion solution

The existence of Eshelby’s equivalent inclusion solution is proved for a non-degenerate ‘transformed’ ellipsoidal inhomogeneity in an infinite anisotropic linear elastic matrix. We prove the invertibility of the fourth rank tensor expression, , where C is the stiffness tensor of the matrix, C′ is the stiffness tensor of the inhomogeneity, I is the Eshelby tensor, and is the symmetric identity tensor. Taking advantage of the positive definiteness of certain tensor expressions, a proof-by-contradiction using energy arguments is posited that eliminates the possibility that the above expression is singular. Because the tensor expression is non-singular, it can always be inverted and Eshelby’s equivalent ellipsoidal inclusion method can be used to find the stress and strain fields in both the matrix and inhomogeneity.

Charge pumping by magnetization dynamics in magnetic and semimagnetic tunnel junctions with interfacial Rashba or bulk extrinsic spin-orbit coupling

We develop a time-dependent nonequilibrium Green function (NEGF) approach to the problem of spin pumping by precessing magnetization in one of the ferromagnetic layers within F$|$I$|$F magnetic tunnel junctions (MTJs) or F$|$I$|$N semi-MTJs in the presence of intrinsic Rashba spin-orbit coupling (SOC) at the F$|$I interface or the extrinsic SOC in the bulk of F layers of finite thickness (F, ferromagnet; N, normal metal; I, insulating barrier). To express the time-averaged pumped charge current, or the corresponding dc voltage signal in an open circuit, we construct a novel solution to double-time-Fourier-transformed NEGF equations. The two energy arguments of NEGFs in this representation are connected by the Floquet theorem describing multiphoton emission and absorption processes. Within this fully quantum-mechanical treatment of the conduction electrons, we find that (i) only in the presence of the interfacial Rashba SOC, the nonzero dc pumping voltage ${V}_{\mathrm{pump}}$ in F$|$I$|$N junctions can emerge at the adiabatic level (i.e., proportional to the microwave frequency), which could explain recent experiments on microwave-driven semi-MTJs [T. Moriyama et al., Phys. Rev. Lett. 100, 067602 (2008)]; (ii) a unique signature of this charge pumping phenomenon, where the Rashba SOC within the precessing F layer participates in the pumping process, is a ${V}_{\mathrm{pump}}$ that changes sign as the function of the precession cone angle; (iii) unlike conventional spin pumping in MTJs in the absence of any SOC, where one emitted or absorbed microwave photon is sufficient to match the exact solution in the frame rotating with the magnetization, the presence of the Rashba SOC requires taking into account up to 10 photons in order to reach the asymptotic value of pumped charge current; (iv) the disorder within F$|$I$|$F MTJs can enhance ${V}_{\mathrm{pump}}$ in the quasiballistic transport regime; and (v) the extrinsic SOC in F$|$I$|$F MTJs causes spin relaxation and eventually the decay of ${V}_{\mathrm{pump}}$, which becomes negligible when the ratio of F layer thickness to the spin-diffusion length is around five. Our formalism can also be applied to charge and spin propagation in any noninteracting open quantum system that is brought out of equilibrium by time-dependent periodic external fields of arbitrary strength or frequency.

Error analysis of a modified discontinuous Galerkin recovery scheme for diffusion problems

A theoretical error analysis using standard Sobolev space energy arguments is furnished for a class of discontinuous Galerkin (DG) schemes that are modified versions of one of those introduced by van Leer and Nomura. These schemes, which use discontinuous piecewise polynomials of degree q, are applied to a family of one-dimensional elliptic boundary value problems. The modifications to the original method include definition of a recovery flux function via a symmetric L2-projection and the addition of a penalty or stabilization term. The method is found to have a convergence rate of O(hq) for the approximation of the first derivative and O(hq+1) for the solution. Computational results for the original and modified DG recovery schemes are provided contrasting them as far as complexity and cost. Numerical examples are given which exhibit sub-optimal convergence rates when the stabilization terms are omitted.

Mixing in the Barents Sea Polar Front near Hopen in spring

Observations were made of hydrography, nutrients and shear microstructure in the water column across the Barents Sea Polar Front near Hopen. Profiles were collected in early May 2008 along a 125-km section extending from the Hopen Trench, across the front between the Arctic and Atlantic origin waters, and on toward the Spitsbergenbanken. Additionally a 10-h time series station was undertaken near the front. The Polar Front was identified near the 150m isobath, coinciding with the 1°C isotherm, with strong horizontal gradients in the temperature and salinity fields, which compensated in density. A second tidally-generated front with a strong horizontal density gradient was detected on the bank, dominated by salinity gradients due to ice melt. Biological activity was elevated between the two fronts. Nutrients were depleted in the euphotic zone where the chlorophyll concentrations were significantly enhanced relative to the stations on the warm side of the Polar Front and in the tidally mixed area. Below a turbulent surface layer, the water column on the warm side of the front was quiescent. Farther on the bank the turbulent boundary layers near the surface and seabed merged and the entire water column was turbulent. Energy arguments show that tidal straining together with stirring due to wind and tides can overcome the stratification induced by melting and heating, maintaining the tidal front. A mechanism is proposed whereby high nitrate concentrations on the warm side of the front are transported along the isopycnals onto the bank where tidal mixing then effectively mixes the nutrient-rich deep water upward, sustaining the phytoplankton bloom.

Interplay of electrohydrodynamic structure formation and microphase alignment in lamellar block copolymers

Electrohydrodynamic (EHD) destabilisation of a lamellar-forming block-copolymer (BCP) film gives rise to hierarchical pattern formation on the micrometre and 10 nm length scale in one single step. Two BCP morphologies were found in the columns that formed from a homogeneous surface instability. At low electric field strength, coaxial concentric lamellae indicate the dominance of surface tension differences of the BCP components over electric field effects. Outward opening lamellae are caused by lateral electric field gradients at sufficiently high field strength. Nucleated instabilities at low field strength give rise to stable bulls-eye-type ring structures consisting of BCP lamellae aligned along the ring perimeter. This is explained in terms of a free energy argument, illustrating the role of the internal energy of the BCP stack, resisting the deformation of the ring. Finally, the EHD experimental configuration was used to fabricate large monodomains of standing oriented lamellae.

Attenuation of short surface waves by the sea floor via nonlinear sub-harmonic interaction

AbstractWe consider the indirect mechanism for dissipation of short surface waves through their near-resonant interactions with long sub-harmonic waves that are dissipated by the bottom. Using direct perturbation analysis and an energy argument, we obtain analytic predictions of the evolution of the amplitudes of two short primary waves and the long sub-harmonic wave which form a near-resonant triad, elucidating the energy transfer, from the short waves to the long wave, which may be significant over time. We obtain expressions for the rate of total energy loss of the system and show that this rate has an extremum corresponding to a specific value of the (bottom) damping coefficient (for a given pair of short wavelengths relative to water depth). These analytic results agree very well with direct numerical simulations developed for the general nonlinear wave–wave and wave–bottom interaction problem.

Global well-posedness and scattering for a nonlinear Klein–Gordon system in low dimensions

This article investigates the global well-posedness and the scattering for a nonlinear Klein–Gordon system in spatial dimensions 1 and 2. We establish a Morawetz estimate for this system which is similar to the Morawetz estimate established by Nakanishi [K. Nakanishi, Energy scattering for nonlinear Klein–Gordon and Schrödinger equations in spatial dimensions 1 and 2, J. Funct. Anal. 169(1), pp. 201–225], combining this Morawetz estimate with the induction on energy argument developed by Bourgain [J. Bourgain, Global well-posedness of defocusing 3D critical NLS in the radial case, J. Am. Math. Soc. 12 (1999), pp. 145–171], the bound of a certain space-time norm and scattering result are obtained.

The inverse-Compton ghost HDF 130 and the giant radio galaxy 6C 0905+3955: matching an analytic model for double-lobed radio source evolution

We present new GMRT observations of HDF 130, an inverse-Compton (IC) ghost of a giant radio source that is no longer being powered by jets. We compare the properties of HDF 130 with the new and important constraint of the upper limit of the radio flux density at 240 MHz to an analytic model. We learn what values of physical parameters in the model for the dynamics and evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the cosmic microwave background (CMB)) of a Fanaroff-Riley II (FR II) source are able to describe a source with features (lobe length, axial ratio, X-ray luminosity, photon index and upper limit of radio luminosity) similar to the observations. HDF 130 is found to agree with the interpretation that it is an IC ghost of a powerful double-lobed radio source, and we are observing it at least a few Myr after jet activity (which lasted 5--100 Myr) has ceased. The minimum Lorentz factor of injected particles into the lobes from the hotspot is preferred to be $\gamma\sim10^3$ for the model to describe the observed quantities well, assuming that the magnetic energy density, electron energy density, and lobe pressure at time of injection into the lobe are linked by constant factors according to a minimum energy argument, so that the minimum Lorentz factor is constrained by the lobe pressure. We also apply the model to match the features of 6C 0905+3955, a classical double FR II galaxy thought to have a low-energy cutoff of $\gamma\sim10^4$ in the hotspot due to a lack of hotspot inverse-Compton X-ray emission. The models suggest that the low-energy cutoff in the hotspots of 6C 0905+3955 is $\gamma\gtrsim 10^3$, just slightly above the particles required for X-ray emission.

An Alternate Approach to Optimal L 2-Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for deriving optimal error estimates for finite element approximations to parabolic problems with smooth initial data and hence, it unifies both theories, that is, one for smooth initial data and other for nonsmooth data. Moreover, the proposed technique is also extended to a semidiscrete mixed method for linear parabolic problems. In both cases, optimal L 2-error estimates are derived, when the initial data is in L 2. A superconvergence phenomenon is also observed, which is then used to prove L ∞-estimates for linear parabolic problems defined on two-dimensional spatial domain again with rough initial data.

Tutorial View of Electromagnetic Wave Diffraction Through Small Apertures Based on Energy Considerations

Electromagnetic wave diffraction through small apertures on perfectly electrically conducting surfaces is revisited in a tutorial spirit. Using solely energy arguments and the concept of radiation reaction fields, polarization formulas are obtained for aperture equivalent electric and magnetic dipoles in the presence of arbitrary sources or other apertures. Apertures on cavities are also treated with special attention to the role of cavity loss. The theory is applied to formulate the Foldy-Lax-type multiple scattering equations for aperture arrays on conducting planes.

Epitaxial Growth of Si(111)/Er2O3 (111) Structure on Si(111) by Molecular Beam Epitaxy

The Si overlayers are grown by molecular beam epitaxy on atomically smooth Er2O3 (111) films prepared on Si(111) substrates. Single crystalline Si overlayers are achieved and are evident due to the spot-like reflective high energy electron diffraction (RHEED) patterns and x-ray diffraction patterns. The epitaxial relationship of the Si overlayer along the surface with respect to the orientation of Er2O3 and the Si substrate is as follows: overgrown Si(111)//Er2O3(111)//Si(111). The rough surface of Si overlayers, as identified by both RHEED patterns and atomic force microscopy images, indicates a three-dimensional growth mode. The reason for this is based on the interfacial energy argument. Further growth of Er2O3 films on this rough Si overlayer leads to the polycrystalline nature of the topmost Er2O3 layer.

Relaxation-time limit of the three-dimensional hydrodynamic model with boundary effects

In this paper, we study three-dimensional (3D) unipolar and bipolar hydrodynamic models and corresponding drift-diffusion models from semiconductor devices on bounded domain. Based on the asymptotic behavior of the solutions to the initial boundary value problems with slip boundary condition, we investigate the relation between the 3D hydrodynamic semiconductor models and the corresponding drift-diffusion models. That is, we discuss the relation-time limit from the 3D hydrodynamic semiconductor models to the corresponding drift-diffusion models by comparing the large-time behavior of these two models. These results can be showed by energy arguments. Copyrightcopyright 2011 John Wiley & Sons, Ltd.

A SHOCK FRONT IN THE MERGING GALAXY CLUSTER A754: X-RAY AND RADIO OBSERVATIONS

We present new Chandra X-ray and Giant Meterwave Radio Telescope (GMRT) radio observations of the nearby merging galaxy cluster Abell 754. Our X-ray data confirm the presence of a shock front by obtaining the first direct measurement of a gas temperature jump across the X-ray brightness edge previously seen in the imaging data. A754 is only the fourth galaxy cluster with confirmed merger shock fronts, and it has the weakest shock of those, with a Mach number M=1.57+0.16-0.12. In our new GMRT observation at 330 MHz, we find that the previously-known centrally located radio halo extends eastward to the position of the shock. The X-ray shock front also coincides with the position of a radio relic previously observed at 74 MHz. The radio spectrum of the post-shock region, using our radio data and the earlier results at 74 MHz and 1.4 GHz, is very steep. We argue that acceleration of electrons at the shock front directly from thermal to ultrarelativistic energies is problematic due to energy arguments, while reacceleration of preexisting relativistic electrons is more plausible.

Error Analysis of the SUPG Finite Element Discretization of Evolutionary Convection-Diffusion-Reaction Equations

Conditions on the stabilization parameters are explored for different approaches in deriving error estimates for the streamline-upwind Petrov-Galerkin (SUPG) finite element stabilization of time-dependent convection-diffusion-reaction equations. Exemplarily, it is shown for the SUPG method combined with the backward Euler scheme that standard energy arguments lead to estimates for stabilization parameters that depend on the length of the time step. The stabilization vanishes in the time-continuous limit. However, based on numerical experience, this seems not to be the correct behavior. For this reason, the main focus of the paper consists in deriving estimates in which the stabilization parameters do not depend on the length of the time step. It is shown that such estimates can be obtained in the case of time-independent convection and reaction. An error estimate for the time-continuous case with the standard order of convergence is derived for stabilization parameters of the same form as they are optimal for the steady-state problem. Analogous estimates are obtained for the fully discrete case using the backward Euler method and the Crank-Nicolson scheme. Numerical studies support the analytical results.

Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in ℝ1+n

Using the same induction on energy argument in both the frequency space and the spatial space simultaneously as in [6, 33, 38], we obtain the global well-posedness and scattering of energy solutions of the defocusing energy-critical nonlinear Hartree equation in ℝ × ℝ n (n ≥ 5), which removes the radial assumption on the data in [25]. The new ingredients are that we use a modified long time perturbation theory to obtain the frequency localization (Proposition 3.1 and Corollary 3.1) of the minimal energy blow up solutions, which cannot be obtained from the classical long time perturbation and bilinear estimate and that we obtain the spatial concentration of minimal energy blow up solution after proving that -norm of minimal energy blow up solutions is bounded from below, the -norm is stronger than the potential energy.

Theoretical Investigation of Structural and Magnetic Properties of ZnnSen (n=6–13) Nanoclusters Doped with Manganese Atoms

With the generalized gradient approximation in first principle all‐electron calculations, the lowest energy structures of ZnnSen (n=6–13) nanoclusters were obtained as the pristine clusters. A number of configurations and structural isomers of ZnnSen (n=6–13) nanoclusters doped with single and two Mn atoms were used to investigate the structural and magnetic properties of manganese‐doped ZnnSen (n=6–13) nanoclusters. It arrives at a conclusion that Mn doping does not change the size‐dependent oscillating behavior in second‐order energy difference of ZnnSen (n=6–13) nanoclusters, but leads to the decrease of energy gap between lowest unoccupied molecular orbital and the highest occupied molecular orbital. Energy arguments indicate that Mn atoms prefer to substitute Zn atoms in Mn‐doped ZnnSen (n=6–13) nanoclusters. Owing the Mn–Mn short‐ranged superexchange mechanism, Mn atoms favor to locate at adjacent Zn atom sites in antiferromagnetic states of ZnnSen nanoclusters doped with two Mn atoms.

Guided ion beam and theoretical study of the reactions of Hf+ with H2, D2, and HD

The kinetic energy dependences of reactions of the third-row transition metal cation Hf(+) with H(2), D(2), and HD were determined using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Hf(+) in its (2)D (6s(2)5d(1)) electronic ground state level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependences of the cross sections for the endothermic formation of HfH(+) and HfD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Hf(+)-H)=2.11±0.08 eV. Quantum chemical calculations at several levels of theory performed here generally overestimate the experimental bond energy but results obtained using the Becke-half-and-half-LYP functional show good agreement. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. Results from the reactions with HD provide insight into the reaction mechanisms and indicates that Hf(+) reacts via a statistical mechanism. We also compare this third-row transition metal system with the first-row and second-row congeners, Ti(+) and Zr(+), and find that Hf(+) has a weaker M(+)-H bond. As most third-row transition metal hydride cation bonds exceed their lighter congeners, this trend is unusual but can be understood using promotion energy arguments.

Chemical Reasoning Based on an Invariance Property: Bond and Lone Pair Pictures in Quantum Structural Formulas

Chemists use one set of orbitals when comparing to a structural formula, hybridized AOs or NBOs for example, and another for reasoning in terms of frontier orbitals, MOs usually. Chemical arguments can frequently be made in terms of energy and/or electron density without the consideration of orbitals at all. All orbital representations, orthogonal or not, within a given function space are related by linear transformation. Chemical arguments based on orbitals are really energy or electron density arguments; orbitals are linked to these observables through the use of operators. The Valency Interaction Formula, VIF, offers a system of chemical reasoning based on the invariance of observables from one orbital representation to another. VIF pictures have been defined as one-electron density and Hamiltonian operators. These pictures are classified in a chemically meaningful way by use of linear transformations applied to them in the form of two pictorial rules and the invariance of the number of doubly, singly, and unoccupied orbitals or bonding, nonbonding, and antibonding orbitals under these transformations. The compatibility of the VIF method with the bond pair – lone pair language of Lewis is demonstrated. Different electron lone pair representations are related by the pictorial rules and have stability understood in terms of Walsh’s rules. Symmetries of conjugated ring systems are related to their electronic state by simple mathematical formulas. Description of lone pairs in conjugated systems is based on the strength and sign of orbital interactions around the ring. Simple models for bonding in copper clusters are tested, and the bonding of O2 to Fe(II) in hemoglobin is described. Arguments made are supported by HF, B3LYP, and MP2 computations.

The very steep spectrum radio halo in Abell 697

<i>Aims. <i/>We present a detailed study of the giant radio halo in the galaxy cluster Abell 697 to constrain its origin and connection with the cluster dynamics.<i>Methods. <i/>We performed high sensitivity GMRT observations at 325 MHz, which showed that the radio halo is much brighter and larger at this frequency than in previous 610 MHz observations. To derive the integrated spectrum in the frequency range 325 MHz-1.4 GHz, we reanalysed archival VLA data at 1.4 GHz and used proprietary GMRT data at 610 MHz.<i>Results. <i/>Our multifrequency analysis shows that the total radio spectrum of the giant radio halo in A 697 is very steep, with <i>≈<i/> 1.7–1.8. Owing to energy arguments, a hadronic origin of the halo is disfavoured by this steep spectrum. Very steep spectrum halos in merging clusters are predicted in the case that the emitting electrons are accelerated by turbulence. Observations with upcoming low frequency arrays will be able to test these expectations.