26,494 research outputs found
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
Multipole polarizability of a graded spherical particle
We have studied the multipole polarizability of a graded spherical particle
in a nonuniform electric field, in which the conductivity can vary radially
inside the particle. The main objective of this work is to access the effects
of multipole interactions at small interparticle separations, which can be
important in non-dilute suspensions of functionally graded materials. The
nonuniform electric field arises either from that applied on the particle or
from the local field of all other particles. We developed a differential
effective multipole moment approximation (DEMMA) to compute the multipole
moment of a graded spherical particle in a nonuniform external field. Moreover,
we compare the DEMMA results with the exact results of the power-law graded
profile and the agreement is excellent. The extension to anisotropic DEMMA will
be studied in an Appendix.Comment: LaTeX format, 2 eps figures, submitted for publication
The economical 3-3-1 model revisited
We show that the economical 3-3-1 model poses a very high new physics scale
of the order of 1000~TeV due to the constraint on the flavor-changing neutral
current. The implications of the model for neutrino masses, inflation,
leptogenesis, and superheavy dark matter are newly recognized. Alternatively,
we modify the model by rearranging the third quark generation differently from
the first two quark generations, as well as changing the scalar sector. The
resultant model now predicts a consistent new physics at TeV scale unlike the
previous case and may be fully probed at the current colliders. Particularly,
due to the minimal particle contents, the models under consideration manifestly
accommodate dark matter candidates and neutrino masses, with novel and distinct
production mechanisms. The large flavor-changing neutral currents that come
from the ordinary and exotic quark mixings can be avoided due to the
approximate symmetry.Comment: 21 pages; english writing improved, dark matter stability stated, and
references added; matches journal versio
Spatio-temporal mapping of variation potentials in leaves of Helianthus annuus L. seedlings in situ using multi-electrode array.
Damaging thermal stimuli trigger long-lasting variation potentials (VPs) in higher plants. Owing to limitations in conventional plant electrophysiological recording techniques, recorded signals are composed of signals originating from all of the cells that are connected to an electrode. This limitation does not enable detailed spatio-temporal distributions of transmission and electrical activities in plants to be visualised. Multi-electrode array (MEA) enables the recording and imaging of dynamic spatio-temporal electrical activities in higher plants. Here, we used an 8 × 8 MEA with a polar distance of 450 μm to measure electrical activities from numerous cells simultaneously. The mapping of the data that were recorded from the MEA revealed the transfer mode of the thermally induced VPs in the leaves of Helianthus annuus L. seedlings in situ. These results suggest that MEA can enable recordings with high spatio-temporal resolution that facilitate the determination of the bioelectrical response mode of higher plants under stress
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
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