Constructing Poisson and Dissipative Brackets of Mixtures by using Lagrangian-to-Eulerian Transformation

2010 ◽  
Vol 26 (2) ◽  
pp. 219-228
Author(s):  
K.-C. Chen
Keyword(s):  
Evolution Equations ◽  
Poisson Brackets ◽  
State Variables ◽  
Component Mixture ◽  
Dissipative Part ◽  
Canonical Variables ◽  
Lagrangian Variable ◽  
Two Component ◽  
Lagrangian Form

AbstractThis paper aims to construct the bracket formalism of mixture continua by using the method of Lagrangian- to-Eulerian (LE) transformation. The LE approach first builds up the transformation relations between the Eulerian state variables and the Lagrangian canonical variables, and then transforms the bracket in Lagrangian form to the bracket in Eulerian form. For the conservative part of the bracket formalism, this study systematically generates the noncanonical Poisson brackets of a two-component mixture. For the dissipative part, we deduce the Eulerian-variable-based dissipative brackets for viscous and diffusive mechanisms from their Lagrangian-variable-based counterparts. Finally, the evolution equations of a micromorphic fluid, which can be treated as a multi-component mixture, are derived by constructing its Poisson and dissipative brackets.

Fifth virial coefficient of a two-component mixture of hard discs

1997 ◽  
Vol 90 (4) ◽  
pp. 679-681
Author(s):  
F. SAIJA ◽  
G. FIUMARA ◽  
P.V. GIAQUINTA
Keyword(s):  
Virial Coefficient ◽  
Component Mixture ◽  
Two Component

scholarly journals Two-Component Mixture Model in the Presence of Covariates

2021 ◽  
pp. 1-15 ◽  
Author(s):  
Nabarun Deb ◽  
Sujayam Saha ◽  
Adityanand Guntuboyina ◽  
Bodhisattva Sen
Keyword(s):  
Mixture Model ◽  
Component Mixture ◽  
Two Component

scholarly journals Photoisomerization of 1-triphenylmethylcyclopentadiene. Di-π-methane rearrangement to 5,6,6-triphenylbicyclo[3.1.0]hex-2-ene

1977 ◽  
Vol 55 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Stefan Weigl ◽  
John Warkentin
Keyword(s):  
Component Mixture ◽  
Two Component ◽  
Rearrangement Mechanism

Triphenylmethylcyclopentadiene exists as a mixture of isomers, the minor and major components of which are shown to be 1-triphenylmethylcyclopentadiene (1) and 2-triphenylmethyl-cyclopentadiene (2), respectively.Direct irradiation of a mixture of 1 and 2 led to formation of 5,6,6,-triphenylbicyclo[3.1.0]hex-2-ene (3) via rearrangement of 1. Acetophenone-sensitized irradiation of the same mixture gave 3 as well as a two component mixture of photodimers of 1 and/or 2. Results are interpreted in terms of the di-π-methane rearrangement mechanism.

Analysing sport data with clusters of opposite preferences

2018 ◽  
Vol 18 (5-6) ◽  
pp. 505-524 ◽  
Author(s):  
Rosaria Simone ◽  
Maria Iannario
Keyword(s):  
Sport Participation ◽  
Sport Activity ◽  
Discrete Models ◽  
Component Mixture ◽  
Rating Data ◽  
Self Evaluation ◽  
Specific Policy ◽  
Two Component ◽  
Competing Models ◽  
Selection Of

In the analysis of questionnaire-based evaluation of sport preferences, measurements of sport participation, opinions on social implications such as resurgence of racism, violence in stadiums and doping, the need arises to establish connections among motivations, subjects’ characteristics and responses. In this setting, the article deals with a selection of statistical models suitable to analyse sport rating data in which clusters of opposite responses are observed. Specifically, a two-component mixture of inverse hypergeometric (MIHG) distributions will be introduced and tested against competing models in order to yield a multifold interpretation of results. The ultimate comparative analysis will consider discrete models with a specific focus on those accounting for both uncertainty and feeling of self-evaluation in presence of inflation at the extreme categories. After a brief review of the methods, the proposal will be discussed both on ranking and rating data on the basis of two surveys on sport preferences and on measurements of sport activity: the identification of clusters of respondents with opposite choices will be investigated also in terms of covariates by comparing fitting performances of the selected models. The conclusions and insights offered by the study can be exploited to design plans of action for some specific policy or marketing strategy.

scholarly journals Doubly Censored Data from Two-Component Mixture of Inverse Weibull Distributions: Theory and Applications

2016 ◽  
Vol 15 (2) ◽  
pp. 322-349 ◽  
Author(s):  
Tabassum Naz Sindhu ◽  
Navid Feroze ◽  
Muhammad Aslam
Keyword(s):  
Censored Data ◽  
Weibull Distributions ◽  
Component Mixture ◽  
Doubly Censored Data ◽  
Two Component ◽  
Doubly Censored

scholarly journals A Statistical Framework for Evolutionary Analysis of Recurrent Somatic Mutations in Cancers

2020 ◽  
Author(s):  
Xun Gu
Keyword(s):  
Somatic Mutations ◽  
Cancer Genomics ◽  
Computational Procedure ◽  
The Cancer Genome Atlas ◽  
Component Model ◽  
Evolutionary Analysis ◽  
Cancer Genes ◽  
Component Mixture ◽  
Two Component ◽  
Empirical Bayesian Method

AbstractCurrent cancer genomics databases have accumulated millions of somatic mutations that remain to be further explored, faciltating enormous high throuput analyses to explore the underlying mechanisms that may contribute to malignant initiation or progression. In the context of over-dominant passenger mutations (unrelated to cancers), the challenge is to identify somatic mutations that are cancer-driving. Under the notion that carcinogenesis is a form of somatic-cell evolution, we developed a two-component mixture model that enables to accomplish the following analyses. (i) We formulated a quasi-likelihood approach to test whether the two-component model is significantly better than a single-component model, which can be used for new cancer gene predicting. (ii) We implemented an empirical Bayesian method to calculate the posterior probabilities of a site to be cancer-driving for all sites of a gene, which can be used for new driving site predicting. (iii) We developed a computational procedure to calculate the somatic selection intensity at driver sites and passenger sites, respectively, as well as site-specific profiles for all sites. Using these newly-developed methods, we comprehensively analyzed 294 known cancer genes based on The Cancer Genome Atlas (TCGA) database.

scholarly journals Time Impact on Residue in a Non-homogeneous Equation of Statics in the Theory of Elastic Mixture

2021 ◽  
Vol 09 (05) ◽  
Author(s):  
Ebikiton Ndiwari ◽  
Keyword(s):  
Meromorphic Function ◽  
Homogeneous Equation ◽  
Principal Component ◽  
Variable Coefficients ◽  
Component Mixture ◽  
Second Order Differential Equations ◽  
Elastic Mixture ◽  
The Earth ◽  
Time Relationship ◽  
Two Component

Residual stress in continuum has not been quantified because time relationship with residues has not been proven analytically. This is achieved in this paper by analyzing a two component mixture with the non-homogeneous equation of statics in the theory of elastic mixture, and second order differential equations with variable coefficients. A dry mixture of sand and cement is transformed into a continuum, which is been determined as an entire or a meromorphic function, as a result of the existence of residues that are contained in the principal component of the mixture obtained directly from the earth. The time relationship with residue, in these two functions are determined. Our result shows that time places a limit on residues, making the meromorphic function prone to implosion..

scholarly journals Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 907 ◽  
Author(s):  
Oğul Esen ◽  
Miroslav Grmela ◽  
Hasan Gümral ◽  
Michal Pavelka
Keyword(s):  
Kinetic Theory ◽  
Lie Algebra ◽  
Particle Motion ◽  
Evolution Equations ◽  
Poisson Brackets ◽  
Hamiltonian Approach ◽  
Symmetric Tensors ◽  
Field Equations ◽  
Algebra Homomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

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