Composition Dependence of Viscosity in Binary Silicate Melts Using Double Exponential Function

Photorefractive two-beam coupling is examined experimentally for the case of high modulation depth. It is seen that the dynamics of signal growth and decay are best described by a double exponential function. The properties of this function with respect to interaction angle and modulation depth are studied. It is suggested that the equations governing photorefractive dynamics may be reduced to a pair of coupled bilinear rate equations which adequately describe photorefractive dynamics for high modulation depth.

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Resolution enhancement in FT NMR through the use of a double exponential function

Journal of Magnetic Resonance (1969) ◽

10.1016/0022-2364(78)90197-x ◽

1978 ◽

Vol 31 (2) ◽

pp. 337-340 ◽

Cited By ~ 41

Author(s):

A.G Ferrige ◽

J.C Lindon

Keyword(s):

Exponential Function ◽

Resolution Enhancement ◽

Double Exponential ◽

Double Exponential Function

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The Hardness Changing Regularity of Quenched-Steel in Tempering Process and Its Double-Exponential Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.146-147.1578 ◽

2010 ◽

Vol 146-147 ◽

pp. 1578-1582

Author(s):

Cong Sheng Guo ◽

Shu Ming Long ◽

Hai Wa Bo ◽

Hong Bin Tan

Keyword(s):

Phase Transformation ◽

Exponential Function ◽

Optimization Design ◽

Hardness Test ◽

Exponential Model ◽

Physical Metallurgy ◽

Double Exponential ◽

Quenched Steel ◽

Double Exponential Function ◽

Tempering Process

The transformation of tempering for quenched steel corresponded to complicated process of phase transformation, and mechanical properties of quenched-and-tempered steel were related to the phase transformation. In practice, hardness test was adopted to judge whether the properties of tempered-parts qualified because of its facility. Numerous researches indicated that, there existed correlativity expressed by different function forms between tempering hardness of quenched-steel and its tempering parameters. However, considering physical metallurgy of tempering process, the adoption of double-exponential function would help to describe regularity of hardness changing more exactly for quenched-steel during tempering process. Additionally, results of hardness tests for isothermal tempering and molding/simulation researches have shown that, the model of double-exponential function, which can reflect decline law of tempering hardness for quenched-steel, would provide basis for optimization design of tempering parameters, performance prediction of tempered-parts, and energy-saving heat-treatment on tempering process.

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El proceso de difusión para variedades mejoradas de Phaseolus vulgaris L. en Guatemala.

Agronomía Mesoamericana ◽

10.15517/am.v5i0.25039 ◽

2016 ◽

Vol 5 ◽

pp. 08

Author(s):

Marco Baltensweiler

Keyword(s):

Diffusion Process ◽

Exponential Function ◽

Good Description ◽

Marginal Rate ◽

Marginal Rate Of Substitution ◽

Lack Of Information ◽

Double Exponential ◽

Acquisition Costs ◽

Relationship Of ◽

Double Exponential Function

A double exponential function provides a good description of this diffusion process. This function was derived from the data concerning the diffusion process of the two improved varieties ICT A-Ostua and ICT ASan Martin V.B. in Guatemala in the years 1990-1992. The two relevant parameters may be interpreted in the following way: Parameter a1 reflects the marginal rate of substitution between the yields obtained from both, the improved and the farmer' s bean varieties. Parameter a2 considers the relationship of the acquisition costs among the two varieties, which are based on the seed price plus the transaction's costs. This concept allows to discern the difficulties faced by the farmers, such as the lack of information of where and when to acquire the improved seed, the delivery costs and so on. Unfortunately, this function no~ only tends to over-estimate the number of farmers who buy the improved seed during the year of maximum demand but al so the time span of this maximum demando A third degree polynome would be more appropiated, but its inter-dependent parameters are more difficult to interptet, in contrast to the easy interpretation of the double exponential function.

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Principles and Utilization of the Electron Beam Damage of Synthetic Polymers

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135654 ◽

1990 ◽

Vol 48 (2) ◽

pp. 410-411

Author(s):

D. Vesely

Keyword(s):

Exponential Function ◽

Structural Investigations ◽

Rapid Decomposition ◽

Damage Rate ◽

Double Exponential ◽

Loss Of Mass ◽

Polymeric Samples ◽

Double Exponential Function ◽

Beam Damage ◽

Initial Intensity

The rapid decomposition of polymeric samples is a major problem in structural investigations of these materials, as the crystallographic information and mass/thickness contrast can be quickly lost. The X-ray elemental analysis can also be affected by loss of elements and often extrapolation to zero exposure is necessary. It is thus of great interest to know how quickly this decomposition occurs for a given polymer.The beam damage rate can be measured by loss of crystallinity, loss of mass or loss of elements. The measured decay curves can be approximated by a double exponential function for which only three constants are needed. This describes the behaviour of most polymers very well, however an accurate experimental evaluation of these constants is not easy. The most important and difficult parameters to measure are the initial intensity, exposure and size of the irradiated area. It is not clear why the double exponential function is suitable, if it is a chemical law or if it fits purely by coincidence.

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Study on Wear of Grinding Wheels: 1—Bond Fracture in Grinding Wheels

Journal of Engineering for Industry ◽

10.1115/1.3667580 ◽

1963 ◽

Vol 85 (1) ◽

pp. 39-42 ◽

Cited By ~ 15

Author(s):

Hiroyuki Yoshikawa ◽

Toshio Sata

Keyword(s):

Brittle Fracture ◽

Wear Rate ◽

Exponential Function ◽

Grinding Force ◽

Theoretical Interpretation ◽

Grinding Wheels ◽

Double Exponential ◽

Double Exponential Function ◽

Single Exponential Function ◽

Single Exponential

Fracturing of bond bridges in grinding wheels is explained from the standpoint of brittle-fracture. It is shown that the wear rate of grinding wheels can be expressed as the single exponential function of the grinding speed and as the double exponential function of the grinding force. Experimental results are shown to confirm the theoretical interpretation.

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The foundation and study of a new type of lattice inversion potential for Iridium

International Journal of Modern Physics B ◽

10.1142/s0217979215502203 ◽

2015 ◽

Vol 29 (30) ◽

pp. 1550220 ◽

Cited By ~ 1

Author(s):

Xianli Ren ◽

Song Chen ◽

Ming Xie ◽

Song Wang ◽

Jieqiong Hu ◽

...

Keyword(s):

Exponential Function ◽

First Principles ◽

Pair Potential ◽

Inversion Method ◽

Energy Curve ◽

Embedded Atom ◽

Phonon Spectra ◽

Double Exponential ◽

Eam Potential ◽

Double Exponential Function

In this paper, the lattice cohesive curve of iridium is investigated through first-principles calculations. The double-exponential function to fit the curve is presented. The inversion pair potential curve is generated through Chen’s inversion method. The accurate pair potential function is obtained through fitting by the new double-exponential function. The phonon spectra are calculated using the inversion potential data, the embedded atom method (EAM) potential theory and first-principles method, respectively, to verify the reliability of the inversion potential. The method combining Boltzmann statistics equation with accuracy fitting of lattice cohesive energy curve is proposed to calculate the thermal expansion coefficient. In addition, the bulk modulus and Grüneisen constant in the room temperature are calculated. The results are in good agreement with experiment results, which imply that the inversion potential is effective and accurate.

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A temperature response function for development of the chrysanthemum (Chrysanthemum x morifolium Ramat.)

Ciência Rural ◽

10.1590/s0103-84782004000100008 ◽

2004 ◽

Vol 34 (1) ◽

pp. 49-54 ◽

Cited By ~ 9

Author(s):

Nereu Augusto Streck

Keyword(s):

Response Function ◽

Exponential Function ◽

Management Practices ◽

Beta Function ◽

Temperature Response ◽

Published Data ◽

Developmental Models ◽

Biological Meaning ◽

Double Exponential ◽

Double Exponential Function

Developmental models can help growers to decide management practices, and to predict flowering and harvest time. Currently, a double exponential function is proposed as a generalized temperature response function for chrysanthemum. This function is not the most appropriate because its parameters lack biological meaning. The objective of this study was to develop a nonlinear temperature response function of chrysanthemum development that has parameters with biological meaning. The proposed function is a beta function with three parameters, the cardinal temperatures (minimum, optimum, and maximum temperatures for development), which were defined as 0, 22, and 35ºC. Published data of temperature response of development of three cultivars, which are independent data sets, were used to test the performance of the double exponential function and the beta function. Results showed that the beta function is better than the double exponential function to describe the temperature response of chrysanthemum development.

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