Estimation of inverse temperature and other Lagrange multipliers: The dual distribution

1984 ◽  
Vol 25 (7) ◽  
pp. 2160-2168 ◽  
Author(s):  
Y. Tikochinsky ◽  
R. D. Levine
Keyword(s):  
Lagrange Multipliers ◽  
Inverse Temperature ◽  
Dual Distribution

Self-Assembly of Hydrogels From Elastin-Mimetic Block Copolymers

2002 ◽  
Vol 724 ◽  
Author(s):  
Elizabeth R. Wright ◽  
R. Andrew McMillan ◽  
Alan Cooper ◽  
Robert P. Apkarian ◽  
Vincent P. Conticello
Keyword(s):  
Block Copolymers ◽  
Self Assembly ◽  
Triblock Copolymers ◽  
Variable Temperature ◽  
Inverse Temperature ◽  
Temperature Transition ◽  
Scanning Calorimetry ◽  
Design Synthesis ◽  
Inverse Temperature Transition ◽  
Functional Biomaterials

AbstractTriblock copolymers have traditionally been synthesized with conventional organic components. However, triblock copolymers could be synthesized by the incorporation of two incompatible protein-based polymers. The polypeptides would differ in their hydrophobicity and confer unique physiochemical properties to the resultant materials. One protein-based polymer, based on a sequence of native elastin, that has been utilized in the synthesis of biomaterials is poly (Valine-Proline-Glycine-ValineGlycine) or poly(VPGVG) [1]. This polypeptide has been shown to have an inverse temperature transition that can be adjusted by non-conservative amino acid substitutions in the fourth position [2]. By combining polypeptide blocks with different inverse temperature transition values due to hydrophobicity differences, we expect to produce amphiphilic polypeptides capable of self-assembly into hydrogels. Our research examines the design, synthesis and characterization of elastin-mimetic block copolymers as functional biomaterials. The methods that are used for the characterization include variable temperature 1D and 2D High-Resolution-NMR, cryo-High Resolutions Scanning Electron Microscopy and Differential Scanning Calorimetry.

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

Some Explicit Results for the Mean Spherical Approximation for Mixtures of Yukawa Fluids

2008 ◽  
Vol 73 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Douglas J. Henderson ◽  
Osvaldo H. Scalise
Keyword(s):  
Integral Equation ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Yukawa Fluid ◽  
The Mean ◽  
Full Solution ◽  
Insight Into ◽  
Reasonable Model

The mean spherical approximation (MSA) is of interest because it produces an integral equation that yields useful analytical results for a number of fluids. One such case is the Yukawa fluid, which is a reasonable model for a simple fluid. The original MSA solution for this fluid, due to Waisman, is analytic but not explicit. Ginoza has simplified this solution. However, Ginoza's result is not quite explicit. Some years ago, Henderson, Blum, and Noworyta obtained explicit results for the thermodynamic functions of a single-component Yukawa fluid that have proven useful. They expanded Ginoza's result in an inverse-temperature expansion. Even when this expansion is truncated at fifth, or even lower, order, this expansion is nearly as accurate as the full solution and provides insight into the form of the higher-order coefficients in this expansion. In this paper Ginoza's implicit result for the case of a rather special mixture of Yukawa fluids is considered. Explicit results are obtained, again using an inverse-temperature expansion. Numerical results are given for the coefficients in this expansion. Some thoughts concerning the generalization of these results to a general mixture of Yukawa fluids are presented.

Room-temperature synthesis, growth mechanisms and opto-electronic properties of organic–inorganic halide perovskite CH3NH3PbX3 (X = I, Br, and Cl) single crystals

CrystEngComm ◽  
2021 ◽  
Author(s):  
Maryam Bari ◽  
Hua Wu ◽  
Alexei A. Bokov ◽  
Rana Faryad Ali ◽  
Hamel N. Tailor ◽  
...  
Keyword(s):  
Electronic Properties ◽  
Single Crystals ◽  
Room Temperature ◽  
Solubility Curve ◽  
Inverse Temperature ◽  
Growth Mechanisms ◽  
Temperature Synthesis ◽  
Room Temperature Synthesis ◽  
Halide Perovskite ◽  
Temperature Crystallization

Growth of MAPbX3 (X = I, Br, and Cl) single crystals by room temperature crystallization (RTC) method, and the crystallization pathway illustrated by the solubility curve of MAPbCl3 in DMSO, compared with inverse temperature crystallization (ITC) method.

Determination of eigenvectors with Lagrange multipliers

2021 ◽  
Author(s):  
Wooyong Han ◽  
Dong-Won Jung ◽  
Jungil Lee ◽  
Chaehyun Yu
Keyword(s):  
Lagrange Multipliers

Staggered solution of fluid-porous-media interaction using the method of local Lagrange multipliers

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 473-474 ◽  
Author(s):  
Seyedmohammad Zinatbakhsh ◽  
Wolfgang Ehlers
Keyword(s):  
Porous Media ◽  
Lagrange Multipliers ◽  
Media Interaction

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

Sign in / Sign up

Export Citation Format

Share Document