Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation

Soliton solution of continuum magnetization-equation in conducting ferromagnet with a spin-polarized current

Exact soliton solutions of a modified Landau-Lifshitz equation for the magnetization of conducting ferromagnet in the presence of a spin-polarized current are obtained by means of inverse scattering transformation. From the analytical solution effects of spin-current on the frequency, wave number, and dispersion law of spin wave are investigated. The one-soliton solution indicates obviously current-driven precession and periodic shape-variation as well. The inelastic collision of solitons by which we mean the shape change before and after collision appears due to the spin current. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and current parameters. This may lead to a potential technique for shape control of spin wave.Comment: 8 pages, 2 figure

Amplifier for scanning tunneling microscopy at MHz frequencies

Conventional scanning tunneling microscopy (STM) is limited to a bandwidth of circa 1kHz around DC. Here, we develop, build and test a novel amplifier circuit capable of measuring the tunneling current in the MHz regime while simultaneously performing conventional STM measurements. This is achieved with an amplifier circuit including a LC tank with a quality factor exceeding 600 and a home-built, low-noise high electron mobility transistor (HEMT). The amplifier circuit functions while simultaneously scanning with atomic resolution in the tunneling regime, i.e. at junction resistances in the range of giga-ohms, and down towards point contact spectroscopy. To enable high signal-to-noise and meet all technical requirements for the inclusion in a commercial low temperature, ultra-high vacuum STM, we use superconducting cross-wound inductors and choose materials and circuit elements with low heat load. We demonstrate the high performance of the amplifier by spatially mapping the Poissonian noise of tunneling electrons on an atomically clean Au(111) surface. We also show differential conductance spectroscopy measurements at 3MHz, demonstrating superior performance over conventional spectroscopy techniques. Further, our technology could be used to perform impedance matched spin resonance and distinguish Majorana modes from more conventional edge states

Surface phase separation in nanosized charge-ordered manganites

Recent experiments showed that the robust charge-ordering in manganites can be weakened by reducing the grain size down to nanoscale. Weak ferromagnetism was evidenced in both nanoparticles and nanowires of charge-ordered manganites. To explain these observations, a phenomenological model based on surface phase separation is proposed. The relaxation of superexchange interaction on the surface layer allows formation of a ferromagnetic shell, whose thickness increases with decreasing grain size. Possible exchange bias and softening of the ferromagnetic transition in nanosized charge-ordered manganites are predicted.Comment: 4 pages, 3 figure

An analytical model of trilateration localization error

Trilateration and multilateration are important location estimation techniques used in a diverse range of networks and applications. The system of equations yielded by multilateration can be reduced to simpler linear equations which can be solved to arrive at a closed form analytic solution. Exploiting this solution technique, we develop a novel and unique analytical model for the localization error resulting from trilateration. The analytical model can be used for the analysis of the localization error in all applications wherever multilateration is used for position estimation including internet of things, wireless sensor networks and global navigation satellite system thereby increasing reliability and quality of localization. As an example, we use the analytical model to corroborate the fact that localization error is a function of topology of reference positions in addition to distance estimation errors. The analytical model is verified using simulation experiments

Suppressing longitudinal double-layer oscillations by using elliptically polarized laser pulses in the hole-boring radiation pressure acceleration regime

It is shown that well collimated mono-energetic ion beams with a large particle number can be generated in the hole-boring radiation pressure acceleration regime by using an elliptically polarized laser pulse with appropriate theoretically determined laser polarization ratio. Due to the $\bm{J}\times\bm{B}$ effect, the double-layer charge separation region is imbued with hot electrons that prevent ion pileup, thus suppressing the double-layer oscillations. The proposed mechanism is well confirmed by Particle-in-Cell simulations, and after suppressing the longitudinal double-layer oscillations, the ion beams driven by the elliptically polarized lasers own much better energy spectrum than those by circularly polarized lasers.Comment: 6 pages, 5 figures, Phys. Plasmas (2013) accepte