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

Work Function of Single-wall Silicon Carbide Nanotube

Using first-principles calculations, we study the work function of single wall silicon carbide nanotube (SiCNT). The work function is found to be highly dependent on the tube chirality and diameter. It increases with decreasing the tube diameter. The work function of zigzag SiCNT is always larger than that of armchair SiCNT. We reveal that the difference between the work function of zigzag and armchair SiCNT comes from their different intrinsic electronic structures, for which the singly degenerate energy band above the Fermi level of zigzag SiCNT is specifically responsible. Our finding offers potential usages of SiCNT in field-emission devices.Comment: 3 pages, 3 figure

QUANTITATIVE MONITORING OF CEFRADINE IN HUMAN URINE USING A LUMINOL/SULFOBUTYLETHER-beta-CYCLODEXTRIN CHEMILUMINESCENCE SYSTEM

In this paper, a sensitive, rapid, and simple flow-injection chemiluminescence (FI-CL) technique is described for determining cefradine in human urine and capsule samples at the picogram level. The results show that cefradine within 0.1-100.0 nmol/L quantitatively quenches the CL intensity of the luminol/sulfo butylether-beta-cyclodextrin (SBE-beta-CD) system, with a relative correlation coefficient r of 0.9931. Subsequently, the possible mechanism for the quenching phenomenon is discussed in detail using the FI-CL and molecular docking methods. The proposed CL method, with a detection limit of 0.03 nmol/L (3 sigma) and relative standard deviations < 3.0% (N = 7), is then implemented to monitor the excretion of cefradine in human urine. After orally administration, the cefradine reaches a maximum value of 1.37 +/- 0.02 mg/mL at 2.0 h in urine, and the total excretion is 4.41 +/- 0.03 mg/mL within 8.0 h. The absorption rate constant k(a), the elimination rate constant k(e), and the half-life t(1/2) are 0.670 +/- 0.008 h(-1), 0.744 +/- 0.005 h(-1), and 0.93 +/- 0.05 h, respectively

Thermal Performance Analysis of High-temperature Heat Transfer Process of Solar Energy

Volumetric solar receivers (VSR) have become a promising technology for the solar thermal conversion. The absorption of the concentrated solar radiation and the heat transfer to the working fluid are the two dominant processes. Firstly, the effects of two typical modeling approaches of the concentrated solar radiation for receiver are compared in view of porosity and mean cell size. Then, the radiation transport within the solar window and the porous absorber is fully simulated. The effects of porous structure parameters, slope error of the concentrator, and the alignment error of the receiver are analyzed. Keywords: volumetric solar receivers (VSR), Monte Carlo ray tracing method, concentrated solar radiation, heat transfe

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozieres and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.Comment: 7 pages, 4 figures, published version in Europhysics Letters, a long preprint with details will appear soo

Communication-constrained distributed quantile regression with optimal statistical guarantees

We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. This is challenging due to the non-smooth nature of the quantile regression (QR) loss function, which invalidates the use of existing methodology. The difficulties are resolved through a double-smoothing approach that is applied to the local (at each data source) and global objective functions. Despite the reliance on a delicate combination of local and global smoothing parameters, the quantile regression model is fully parametric, thereby facilitating interpretation. In the low-dimensional regime, we establish a finite-sample theoretical framework for the sequentially defined distributed QR estimators. This reveals a trade-off between the communication cost and statistical error. We further discuss and compare several alternative confidence set constructions, based on inversion of Wald and score-type tests and resampling techniques, detailing an improvement that is effective for more extreme quantile coefficients. In high dimensions, a sparse framework is adopted, where the proposed doubly-smoothed objective function is complemented with an ℓ1-penalty. We show that the corresponding distributed penalized QR estimator achieves the global convergence rate after a near-constant number of communication rounds. A thorough simulation study further elucidates our findings