scholarly journals A homogenisation strategy for micromorphic continua based on particle mechanics

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 515-516
Author(s):  
Sami Bidier ◽  
Wolfgang Ehlers
Keyword(s):  
Particle Mechanics ◽  
Micromorphic Continua

scholarly journals Cosmic Analogues of Classic Variational Problems

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 71 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Relativistic Particle ◽  
Friedmann Equation ◽  
Variational Calculus ◽  
Variational Problems ◽  
Particle Mechanics ◽  
One Dimensional ◽  
Spatially Homogeneous

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.

scholarly journals Axiomatic Foundations of Classical Particle Mechanics

1953 ◽  
Vol 2 (2) ◽  
pp. 253-272 ◽  
Author(s):  
J. McKinsey ◽  
A. Sugar ◽  
Patrick Suppes
Keyword(s):  
Classical Particle ◽  
Particle Mechanics

scholarly journals Analogues of glacial valley profiles in particle mechanics and in cosmology

FACETS ◽  
2017 ◽  
Vol 2 (1) ◽  
pp. 286-300 ◽  
Author(s):  
Valerio Faraoni ◽  
Adriana M. Cardini
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Positive Curvature ◽  
Friedmann Equation ◽  
Theoretical Models ◽  
Point Particle ◽  
Relativistic Cosmology ◽  
Future Singularity ◽  
Particle Mechanics ◽  
Curvature Index

An ordinary differential equation describing the transverse profiles of U-shaped glacial valleys has two formal analogies, which we explore in detail, bridging these different areas of research. First, an analogy with point particle mechanics completes the description of the solutions. Second, an analogy with the Friedmann equation of relativistic cosmology shows that the analogue of a glacial valley profile is a universe with a future singularity of interest in theoretical models of cosmology. A Big Freeze singularity, which was not previously observed for positive curvature index, is also contained in the dynamics.

Hamiltonians in Relativistic Classical Particle Mechanics

1968 ◽  
Vol 166 (5) ◽  
pp. 1308-1316 ◽  
Author(s):  
Thomas F. Jordan
Keyword(s):  
Classical Particle ◽  
Particle Mechanics
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