Special Case of Partial Fraction Expansion with Laplace Transform Application

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical systems

Point Defect Study in Fe75Al25 and Fe70Al25X5 X=(Cr, Ni) Alloys as a Function of Thermal Treatment by Positron Lifetime Spectroscopy

AbstractPositron lifetime spectroscopy (PALS) is employed to study retained vacancies in Fe75Al25 and Fe70Al25X5 X= (Cr, Ni) after various thermal treatments. The PALS spectra were analyzed with the two states trapping model. The positron lifetime in defects suggests that they are Fe-monovacancies. The vacancy concentration, determined by the rates of trapping positrons to vacancies, strongly depends on the cooling rate of the sample and the ternary addition. An addition of Cr lowers, whereas an addition of Ni increases the concentration of the retained vacancies in relation to Fe75Al25 samples after the same heat treatment

A Generalized Solution Method to Undamped Constant-Coefficient Second-Order ODEs Using Laplace Transforms and Fourier Series

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series and Laplace transforms also reinforces the understanding of function representation through a Fourier series and its potential limitations, the mechanics of finding the Laplace transform of a differential equation and inverse transforms, the operation of an undamped system, and through programming insight into the practical application of both tools including information on the influence of the number of terms in the series solution

Austempering transformation kinetics of austempered ductile iron obtained by Mössbauer Spectroscopy

The composition of metallic matrix in ductile iron as-cast and after austempering at temperatures of 280, 330 and 380oC (ADI) was examined. The study presents the results of these examinations obtained by Mössbauer spectroscopy. The specimens were taken from cast rods of 60mm diameter. Using calculated values of the parameters of hyperfine interactions (isomeric shift IS, quadrupole splitting QS and hyperfine effective magnetic field H), isolated by deconvolution of the experimental spectrum, the constituents of the metallic matrix were identified in terms of both quantity and quality. The measured values as well as the data compiled in literature indicate that component Z1 (the, so called, Zeeman spectrum sextet) is related with 57Fe atoms present in the structure of ferrite α1 (I stage of o→α1 + st transformation), component Z2 is typical of ferrite α2 (II stage of st→α2 + carbides transformation), while component Z3 has its origin in 57Fe atoms seated in the structure of carbides (Fe3C, Fe2C or Fe2,4C). On the other hand, by analysis of the parameters of hyperfine interactions describing the non-magnetic components (L and Q) it has been proved that they are typical of austenite

Surface structured platinum electrodes for the electrochemical reduction of carbon dioxide in imidazolium based ionic liquids

The direct CO2 electrochemical reduction on model platinum single crystal electrodes Pt(hkl) is studied in [C2mim+][NTf2−], a suitable room temperature ionic liquid (RTIL) medium due to its moderate viscosity, high CO2 solubility and conductivity. Single crystal electrodes represent the most convenient type of surface structured electrodes for studying the impact of RTIL ion adsorption on relevant electrocatalytic reactions, such as surface sensitive electrochemical CO2 reduction. We propose here based on cyclic voltammetry and in situ electrolysis measurements, for the first time, the formation of a stable adduct [C2mimH–CO2−] by a radical–radical coupling after the simultaneous reduction of CO2 and [C2mim+]. It means between the CO2 radical anion and the radical formed from the reduction of the cation [C2mim+] before forming the corresponding electrogenerated carbene. This is confirmed by the voltammetric study of a model imidazolium-2-carboxylate compound formed following the carbene pathway. The formation of that stable adduct [C2mimH–CO2−] blocks CO2 reduction after a single electron transfer and inhibits CO2 and imidazolium dimerization reactions. However, the electrochemical reduction of CO2 under those conditions provokes the electrochemical cathodic degradation of the imidazolium based RTIL. This important limitation in CO2 recycling by direct electrochemical reduction is overcome by adding a strong acid, [H+][NTf2−], into solution. Then, protons become preferentially adsorbed on the electrode surface by displacing the imidazolium cations and inhibiting their electrochemical reduction. This fact allows the surface sensitive electro-synthesis of HCOOH from CO2 reduction in [C2mim+][NTf2−], with Pt(110) being the most active electrode studied.This work has been partially financed by Generalitat Valenciana through Ayudas para la realización de proyectos de I+D para grupos de investigación emergentes (GV/2014/096) and by the MICINN (project CTQ2013-48280-C3-3-R)

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

Influence of Heat Treatment on Defect Structures in Single-Crystalline Blade Roots Studied by X-ray Topography and Positron Annihilation Lifetime Spectroscopy

Single-crystalline superalloy CMSX-4 is studied in the as-cast state and after heat treatment, with material being taken from turbine blade castings. The effect of the heat treatment on the defect structure of the root area near the selector/root connection is emphasized. Multiscale analysis is performed to correlate results obtained by X-ray topography and positron annihilation lifetime spectroscopy (PALS). Electron microscopy observations were also carried out to characterize the inhomogeneity in dendritic structure. The X-ray topography was used to compare defects of the misorientation nature, occurring in as-cast and treated states. The type and concentration of defects before and after heat treatment in different root areas were determined using the PALS method, which enables voids, mono-vacancies, and dislocations to be taken into account. In this way, differences in the concentration of defects caused by heat treatment are rationalized

The role of adsorbed ions during electrocatalysis in ionic liquids

The effects of electrode–adsorbate interactions on electrocatalysis at Pt in ionic liquids are described. The ionic liquids are diethylmethylammonium trifluoromethanesulfonate, [dema][TfO], dimethylethylammonium trifluoromethanesulfonate, [dmea][TfO], and diethylmethylammonium bis(trifluoromethanesulfonyl)imide, [dema][Tf2N]. Electrochemical analysis indicates that a monolayer of hydrogen adsorbs onto Pt during potential cycling in [dema][[TfO] and [dmea][TfO]. In addition, a prepeak is observed at lower potentials than that of the main oxidation peak during CO oxidation in the [TfO]−-based liquids. In contrast, hydrogen does not adsorb onto Pt during potential cycling in [dema][Tf2N] and no prepeak is observed during CO oxidation. By displacing adsorbed ions on Pt surfaces with CO at a range of potentials, and measuring the charge passed during ion displacement, the potentials of zero total charge of Pt in [dema][TfO] and [dmea][TfO] were measured as 271 ± 9 and 289 ± 10 mV vs RHE, respectively. CO displacement experiments also indicate that the [Tf2N]− ion is bound to the Pt surface at potentials above −0.2 V and the implications of ion adsorption on electrocatalysis of the CO oxidation reaction and O2 reduction reaction in the protic ionic liquids are discussed

The cytoskeleton in cell-autonomous immunity: structural determinants of host defence

Host cells use antimicrobial proteins, pathogen-restrictive compartmentalization and cell death in their defence against intracellular pathogens. Recent work has revealed that four components of the cytoskeleton — actin, microtubules, intermediate filaments and septins, which are well known for their roles in cell division, shape and movement — have important functions in innate immunity and cellular self-defence. Investigations using cellular and animal models have shown that these cytoskeletal proteins are crucial for sensing bacteria and for mobilizing effector mechanisms to eliminate them. In this Review, we highlight the emerging roles of the cytoskeleton as a structural determinant of cell-autonomous host defence