scholarly journals Dynamical equations and Lagrange–Ricci flow evolution on prolongation Lie algebroids

2019 ◽  
Vol 97 (2) ◽  
pp. 145-154
Author(s):  
Laurenţiu Bubuianu ◽  
Sergiu I. Vacaru
Keyword(s):  
Lie Algebroids ◽  
Gravity Models ◽  
Geometric Mechanics ◽  
Dynamical Equations ◽  
Geometric Evolution ◽  
Ricci Flows ◽  
Hamilton Equations ◽  
Flow Evolution ◽  
Statistical Functionals ◽  
Math Phys

The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems (S. Vacaru. J. Math. Phys. 49, 043504 (2008); Ibid. Rep. Math. Phys. 63, 95 (2009)) is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometric mechanics and analogous gravity can be modeled as gradient flows characterized by generalized Perelman functionals if an equivalent geometrization of Lagrange mechanics (J. Kern. Arch. Math. (Basel), 25, 438 (1974)) is considered. The Hamilton equations on Lie algebroids describing Lagrange–Ricci flows are derived. Finally, we show that geometric evolution models on Lie algebroids are described by effective thermodynamical values derived from statistical functionals on prolongation Lie algebroids.

scholarly journals METRIC COMPATIBLE OR NON-COMPATIBLE FINSLER–RICCI FLOWS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250041 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Ricci Flow ◽  
Evolution Equations ◽  
Finsler Geometry ◽  
Flow Theory ◽  
Finsler Metric ◽  
Geometric Evolution ◽  
Ricci Flows ◽  
Canonical Metric ◽  
Self Consistent ◽  
Math Phys

There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-holonomic Hamilton evolution equations, when metric non-compatible Finsler connections are involved. Following such an approach, we have to consider distortion tensors, uniquely defined by the Finsler metric, from the Cartan and/or the canonical metric compatible connections. We conclude that, in general, it is not possible to elaborate self-consistent models of geometric evolution with arbitrary Finsler metric non-compatible connections.

scholarly journals Updated f(T) gravity constraints from high-redshift cosmography

2015 ◽  
Vol 24 (14) ◽  
pp. 1550100 ◽  
Author(s):  
Ester Piedipalumbo ◽  
Enrica Della Moglie ◽  
Roberto Cianci
Keyword(s):  
Gamma Ray ◽  
Probability Distributions ◽  
High Redshift ◽  
Teleparallel Gravity ◽  
Gravity Theory ◽  
Gravity Models ◽  
Acoustic Oscillations ◽  
Dynamical Equations ◽  
Data Set ◽  
The Universe

In the last dozen years, a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the universe from measured distances, only assuming that the geometry can be described by the Friedmann–Lemaitre–Robertson–Walker metric. In this paper, we perform a high-redshift analysis which allows us to put constraints on the cosmographic parameters up to the fifth-order, thus inducing indirect constraints on any gravity theory. Here, we are interested in the so-called teleparallel gravity theory, [Formula: see text]. Actually, we use the analytical expressions of the present day values of [Formula: see text] and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for [Formula: see text] and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some gamma ray bursts (GRB) luminosity distance indicators and Gaussian priors on the distance from the baryon acoustic oscillations (BAOs) and the Hubble constant [Formula: see text]. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters, we use the Markov chain Monte Carlo (MCMC) method.

Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

1974 ◽  
Vol 32 ◽  
pp. 402-403
Author(s):  
S. Nakahara ◽  
D. M. Maher
Keyword(s):  
Image Analysis ◽  
Computational Approach ◽  
Dislocation Loops ◽  
Plane Wave Expansion ◽  
Dynamical Equations ◽  
Bloch Waves ◽  
Linear Defects ◽  
Imperfect Crystal ◽  
Localized Defects ◽  
Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

Determinants of Brazilian Exports by Levels of Technological Intensity: A Gravity Model Analysis Using the PPML Estimator

2019 ◽  
Vol 10 (9) ◽  
pp. 861-879
Author(s):  
Edson Roberto Vieira ◽  
◽  
Daniel Henrique Alves Reis ◽  
Keyword(s):  
International Market ◽  
Positive Influence ◽  
Gravity Models ◽  
Transport Costs ◽  
Consumer Market ◽  
Technology Products ◽  
The Us ◽  
Trading Partners ◽  
Negative Impacts ◽  
Technological Intensity

The objective of this study is to analyze the determinants of Brazilian exports by levels of technological intensity in the period 2000-2015. Gravity models were estimated for total of the exports and for each type of exports by levels of technological intensity, using the PPML-estimator. The study indicates that there is a process of concentration of Brazilian exports in low technology and medium-low technology products, at the same period in which China's share of total Brazilian shipments abroad grew. Estimates of empirical gravity models have shown that the income and size of the consumer market of Brazil’s trading partners seem to have the greatest positive influence on the Brazilian exports. Indications of this study are that the Brazil should continue to diversify its trading partners to minimize the impacts of a possible reduction of the economic growth of large trading partners (such as China and the US) on its exports and increase its exports of products with greater technological intensity. The results also highlight the need for Brazil to make greater efforts to increase its competitiveness in the international market to reduce the negative impacts of transport costs on the final prices of products exported by the country.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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