1,861 research outputs found
The lattice of varieties of implication semigroups
In 2012, the second author introduced and examined a new type of algebras as
a generalization of De Morgan algebras. These algebras are of type (2,0) with
one binary and one nullary operation satisfying two certain specific
identities. Such algebras are called implication zroupoids. They invesigated in
a number of articles by the second author and J.M.Cornejo. In these articles
several varieties of implication zroupoids satisfying the associative law
appeared. Implication zroupoids satisfying the associative law are called
implication semigroups. Here we completely describe the lattice of all
varieties of implication semigroups. It turns out that this lattice is
non-modular and consists of 16 elements.Comment: Compared with the previous version, we rewrite Section 3 and add
Appendixes A and
Nonlinear Hysteretic Torsional Waves
We theoretically study and experimentally report the propagation of nonlinear
hysteretic torsional pulses in a vertical granular chain made of cm-scale,
self-hanged magnetic beads. As predicted by contact mechanics, the torsional
coupling between two beads is found nonlinear hysteretic. This results in a
nonlinear pulse distortion essentially different from the distortion predicted
by classical nonlinearities, and in a complex dynamic response depending on the
history of the wave particle angular velocity. Both are consistent with the
predictions of purely hysteretic nonlinear elasticity and the
Preisach-Mayergoyz hysteresis model, providing the opportunity to study the
phenomenon of nonlinear dynamic hysteresis in the absence of other type of
material nonlinearities. The proposed configuration reveals a plethora of
interesting phenomena including giant amplitude-dependent attenuation, short
term memory as well as dispersive properties. Thus, it could find interesting
applications in nonlinear wave control devices such as strong
amplitude-dependent filters
Asymptotic behaviours of the heat kernel in covariant perturbation theory
The trace of the heat kernel is expanded in a basis of nonlocal curvature
invariants of th order. The coefficients of this expansion (the nonlocal
form factors) are calculated to third order in the curvature inclusive. The
early-time and late-time asymptotic behaviours of the trace of the heat kernel
are presented with this accuracy. The late-time behaviour gives the criterion
of analyticity of the effective action in quantum field theory. The latter
point is exemplified by deriving the effective action in two dimensions.Comment: 22 pages, REVTeX, Alberta Thy 45-9
Ultrafast Acousto-Plasmonics in Gold Nanoparticles Superlattice
We report the investigation of the generation and detection of GHz coherent
acoustic phonons in plasmonic gold nanoparticles superlattices (NPS). The
experiments have been performed from an optical femtosecond pump-probe scheme
across the optical plasmon resonance of the superlattice. Our experiments allow
to estimate the collective elastic response (sound velocity) of the NPS as well
as an estimate of the nano-contact elastic stiffness. It appears that the
light-induced coherent acoustic phonon pulse has a typical in-depth spatial
extension of about 45 nm which is roughly 4 times the optical skin depth in
gold. The modeling of the transient optical reflectivity indicates that the
mechanism of phonon generation is achieved through ultrafast heating of the NPS
assisted by light excitation of the volume plasmon. These results demonstrate
how it is possible to map the photon-electron-phonon interaction in
subwavelength nanostructures
Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium
Experiments with acoustic waves guided along the mechanically free surface of
an unconsolidated granular packed structure provide information on the
elasticity of granular media at very low pressures that are naturally
controlled by the gravitational acceleration and the depth beneath the surface.
Comparison of the determined dispersion relations for guided surface acoustic
modes with a theoretical model reveals the dependencies of the elastic moduli
of the granular medium on pressure. The experiments confirm recent theoretical
predictions that relaxation of the disordered granular packing through
non-affine motion leads to a peculiar scaling of shear rigidity with pressure
near the jamming transition corresponding to zero pressure. Unexpectedly, and
in disagreement with the most of the available theories, the bulk modulus
depends on pressure in a very similar way to the shear modulus
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