31,666 research outputs found
Quantum Continuum Mechanics Made Simple
In this paper we further explore and develop the quantum continuum mechanics
(CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it
simpler to use in practice. Our simplifications relate to the non-interacting
part of the CM equations, and primarily refer to practical implementations in
which the groundstate stress tensor is approximated by its Kohn-Sham version.
We use the simplified approach to directly prove the exactness of CM for
one-electron systems via an orthonormal formulation. This proof sheds light on
certain physical considerations contained in the CM theory and their
implication on CM-based approximations. The one-electron proof then motivates
an approximation to the CM (exact under certain conditions) expanded on the
wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to
the relationships between transitions from occupied to unoccupied KS orbitals
and their approximations under the CM. We also demonstrate the simplified CM
semi-analytically on an example system
From continuum mechanics to general relativity
Using ideas from continuum mechanics we construct a theory of gravity. We
show that this theory is equivalent to Einstein's theory of general relativity;
it is also a much faster way of reaching general relativity than the
conventional route. Our approach is simple and natural: we form a very general
model and then apply two physical assumptions supported by experimental
evidence. This easily reduces our construction to a model equivalent to general
relativity. Finally, we suggest a simple way of modifying our theory to
investigate non-standard space-time symmetries.Comment: 7 pages, this essay received a honorable mention in the 2014 essay
competition of the Gravity Research Foundatio
Continuum Mechanics
Continuum Mechanics is the foundation for Applied Mechanics. There are numerous books on Continuum Mechanics with the main focus on the macroscale mechanical behavior of materials. Unlike classical Continuum Mechanics books, this book summarizes the advances of Continuum Mechanics in several defined areas. Emphasis is placed on the application aspect. The applications described in the book cover energy materials and systems (fuel cell materials and electrodes), materials removal, and mechanical response/deformation of structural components including plates, pipelines etc. Researchers from different fields should be benefited from reading the mechanics approached to real engineering problems
Fractional Calculus for Continuum Mechanics - anisotropic non-locality
In this paper the generalisation of previous author's formulation of
fractional continuum mechanics to the case of anisotropic non-locality is
presented. The considerations include the review of competitive formulations
available in literature. The overall concept bases on the fractional
deformation gradient which is non-local, as a consequence of fractional
derivative definition. The main advantage of the proposed formulation is its
analogical structure to the general framework of classical continuum mechanics.
In this sense, it allows, to give similar physical and geometrical meaning of
introduced objects
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