Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity

1998 ◽  
Vol 49 (1) ◽  
pp. 137-155 ◽  
Author(s):  
S. Tokarzewski ◽  
J. J. Telega
Keyword(s):  
Analytical Continuation ◽  
Effective Moduli ◽  
Stieltjes Function

scholarly journals Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 477
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela
Keyword(s):  
Stochastic Processes ◽  
Spectral Function ◽  
Evolution Equations ◽  
Memory Function ◽  
Relaxation Phenomena ◽  
Stieltjes Function ◽  
Infinitely Divisible ◽  
Spectral Functions ◽  
Debye Relaxation ◽  
Relaxation Functions

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.

scholarly journals Analytical Continuation within the Freundlich Adsorption Model. Comment on Edet, U.A.; Ifelebuegu, A.O. Kinetics, Isotherms, and Thermodynamic Modeling of the Adsorption of Phosphates from Model Wastewater Using Recycled Brick Waste. Processes 2020, 8, 665

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1251
Author(s):  
Michael Vigdorowitsch ◽  
Alexander N. Pchelintsev ◽  
Liudmila E. Tsygankova
Keyword(s):  
Experimental Data ◽  
Power Function ◽  
Thermodynamic Modeling ◽  
Mathematical Theory ◽  
Surface Adsorption ◽  
Analytical Continuation ◽  
Adsorption Model ◽  
Saturation Regime

Using experimental data for the adsorption of phosphates out of wastewater on waste recycled bricks, published independently in MDPI Processes before (2020), this message re-visits the mathematical theory of the Freundlich adsorption model. It demonstrates how experimental data are to be deeper treated to model the saturation regime and to bridge a chasm between those areas where the data fit the Freundlich power function and where a saturation of surface adsorption centers occurs.

Anisotropic Effective Moduli of Cracked Short-Fiber Reinforced Composites

1999 ◽  
Vol 66 (3) ◽  
pp. 709-713 ◽  
Author(s):  
R. S. Feltman ◽  
M. H. Santare
Keyword(s):  
Short Fiber ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Effective Moduli ◽  
Fiber Reinforced ◽  
Fiber Fracture ◽  
Composite Systems ◽  
Reinforced Composite ◽  
Anisotropic Elastic ◽  
Energy Dissipated

A model is presented to analyze the effect of fiber fracture on the anisotropic elastic properties of short-fiber reinforced composite materials. The effective moduli of the material are modeled using a self-consistent scheme which includes the calculated energy dissipated through the opening of a crack in an arbitrarily oriented elliptical inclusion. The model is an extension of previous works which have modeled isotropic properties of short-fiber reinforced composites with fiber breakage and anisotropic properties of monolithic materials with microcracks. Two-dimensional planar composite systems are considered. The model allows for the calculation of moduli under varying degrees of fiber alignment and damage orientation. In the results, both aligned fiber systems and randomly oriented fiber systems with damage-induced anisotropy are examined.

The Stieltjes Function--Definition and Properties

1988 ◽  
Vol 51 (183) ◽  
pp. 281
Author(s):  
Jan Bohman ◽  
Carl-Erik Froberg
Keyword(s):  
Stieltjes Function ◽  
Function Definition

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

2019 ◽  
Vol 27 (3) ◽  
pp. 341-352
Author(s):  
Seyed Majid Saberi Fathi
Keyword(s):  
Inverse Problem ◽  
Transport Equation ◽  
Inversion Formula ◽  
Complex Analysis ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Radon Transforms ◽  
Photon Transport ◽  
X Ray ◽  
Several Variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from {\mathbb{R}^{3}} to {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

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