2,404 research outputs found
Lagrange-Fedosov Nonholonomic Manifolds
We outline an unified approach to geometrization of Lagrange mechanics,
Finsler geometry and geometric methods of constructing exact solutions with
generic off-diagonal terms and nonholonomic variables in gravity theories. Such
geometries with induced almost symplectic structure are modelled on
nonholonomic manifolds provided with nonintegrable distributions defining
nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and
Fedosov nonholonomic manifolds provided with almost symplectic connection
adapted to the nonlinear connection structure.
We investigate the main properties of generalized Fedosov nonholonomic
manifolds and analyze exact solutions defining almost symplectic Einstein
spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio
Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their
Legendre transforms to Hamilton and Cartan spaces into almost Kaehler
structures on tangent and cotangent bundles. In particular cases, the Hamilton
spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on
effective phase spaces. This allows us to define the corresponding Fedosov
operators and develop deformation quantization schemes for nonlinear mechanical
and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009
Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kahler
manifolds enabled with a metric compatible canonical distinguished connection
structure generalizing the Levi Civita connection. The goal of this paper is to
perform a natural Fedosov-type deformation quantization of such geometries. All
constructions are canonically derived for regular Lagrangians and/or
fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23
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Erosion in Extruder Flows: Analytical and Numerical Study
© 2017 Author(s). We consider the erosion of particles (e.g. carbonblack agglomerates) advected by the polymeric flow in a single screw extruder. We assume a particle to be made of primary fragments bound together. In the erosion process a primary fragment breaks out of a given particle. Particles disperse because of the shear stresses imparted by the fluid. The time evolution of the numbers of particles of different sizes is described by the Bateman coupled differential equations developed a century ago to model radioactivity. Using the particle size distribution we compute an entropic fragmentation index which varies from 0 for a monodisperse system to 1 for an extreme poly-disperse system. The time dependence of the index exhibits a maximum at some intermediate time as the system starts monodisperse (large size particle) and evolves through a poly-disperse regime at intermediate times to a monodisperse (small size particle) at late times
Analogy Between Thermodynamic Phase Transitions and Creeping Flows in Rectangular Cavities
© 2020, MDPI AG. All rights reserved. An analogy is found between the streamline function corresponding to Stokes flows in rectangular cavities and the thermodynamics of phase transitions and critical points. In a rectangular cavity flow, with no-slip boundary conditions at the walls, the corners are fixed points. The corners defined by a stationary and a moving wall, are found to be analogous to a thermodynamic first-order transition point. In contrast, the corners defined by two stationary walls correspond to thermodynamic critical points. Here, flow structures, also known as Moffatt eddies, form and act as stagnation regions where mixing is impeded. A third stationary point occurs in the middle region of the channel and it is analogous to a high temperature thermodynamic fixed point. The numerical results of the fluid flow modeling are correlated with analytical work in the proximity of the fixed points
Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity
We analyze local anisotropies induced by anholonomic frames and associated
nonlinear connections in general relativity and extensions to affine Poincare
and de Sitter gauge gravity and different types of Kaluza-Klein theories. We
construct some new classes of cosmological solutions of gravitational field
equations describing Friedmann-Robertson-Walker like universes with rotation
(ellongated and flattened) ellipsoidal or torus symmetry.Comment: 37 page
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