126 research outputs found
Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
Spatially confined rigid membranes reorganize their morphology in response to
the imposed constraints. A crumpled elastic sheet presents a complex pattern of
random folds focusing the deformation energy while compressing a membrane
resting on a soft foundation creates a regular pattern of sinusoidal wrinkles
with a broad distribution of energy. Here, we study the energy distribution for
highly confined membranes and show the emergence of a new morphological
instability triggered by a period-doubling bifurcation. A periodic
self-organized focalization of the deformation energy is observed provided an
up-down symmetry breaking, induced by the intrinsic nonlinearity of the
elasticity equations, occurs. The physical model, exhibiting an analogy with
parametric resonance in nonlinear oscillator, is a new theoretical toolkit to
understand the morphology of various confined systems, such as coated materials
or living tissues, e.g., wrinkled skin, internal structure of lungs, internal
elastica of an artery, brain convolutions or formation of fingerprints.
Moreover, it opens the way to new kind of microfabrication design of
multiperiodic or chaotic (aperiodic) surface topography via self-organization.Comment: Submitted for publicatio
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Study of pulsatile pressure-driven electroosmotic flows through an elliptic cylindrical microchannel with the Navier slip condition
This paper aims to study an unsteady electric field-driven and pulsatile pressure-driven flow of a Newtonian fluid in an elliptic cylindrical microchannel with Navier boundary wall slip. The governing equations of the slip flow and distributions of electric potential and charge densities are the modified Navier-Stokes equations, the Poisson equation and the Nernst-Planck equations, respectively. Analytical and numerical analyses based on the Mathieu and modified Mathieu equations are performed to investigate the interplaying effects of pulsatile pressure gradients and the slip lengths on the electroosmotic flow
f(R) theories
Over the past decade, f(R) theories have been extensively studied as one of
the simplest modifications to General Relativity. In this article we review
various applications of f(R) theories to cosmology and gravity - such as
inflation, dark energy, local gravity constraints, cosmological perturbations,
and spherically symmetric solutions in weak and strong gravitational
backgrounds. We present a number of ways to distinguish those theories from
General Relativity observationally and experimentally. We also discuss the
extension to other modified gravity theories such as Brans-Dicke theory and
Gauss-Bonnet gravity, and address models that can satisfy both cosmological and
local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in
Relativity, Published version, Comments are welcom
Atom Optics Quantum Pendulum
We explain the dynamics of cold atoms, initially trapped and cooled in a
magneto-optic trap, in a monochromatic stationary standing electromagnetic wave
field. In the large detuning limit the system is modeled as a nonlinear quantum
pendulum. We show that wave packet evolution of the quantum particle probes
parametric regimes in the quantum pendulum which support classical period,
quantum mechanical revival and super revival phenomena. Interestingly, complete
reconstruction in particular parametric regime at quantum revival times is
independent of potential height.Comment: 14 pages, 7 figure
Publisher Correction: Sex-dimorphic genetic effects and novel loci for fasting glucose and insulin variability.
Correction to: Nature Communications https://doi.org/10.1038/s41467-020-19366-9, published online 5 January 2021.
The original version of this Article contained an error in Fig. 2, in which panels a and b were inadvertently swapped.
This has now been corrected in the PDF and HTML versions of the Article
Publisher Correction: Sex-dimorphic genetic effects and novel loci for fasting glucose and insulin variability.
Correction to: Nature Communications https://doi.org/10.1038/s41467-020-19366-9, published online 5 January 2021.
The original version of this Article contained an error in Fig. 2, in which panels a and b were inadvertently swapped.
This has now been corrected in the PDF and HTML versions of the Article
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