612 research outputs found
Low frequency elastic measurements on solid He in Vycor using a torsional oscillator
Torsional oscillator experiments involving solid He confined in the
nanoscale pores of Vycor glass showed anomalous frequency changes at
temperatures below 200 mK. These were initially attributed to decoupling of
some of the helium's mass from the oscillator, the expected signature of a
supersolid. However, these and similar anomalous effects seen with bulk
He now appear to be artifacts arising from large shear modulus changes
when mobile dislocations are pinned by He impurities. We have used a
torsional oscillator (TO) technique to directly measure the shear modulus of
the solid He/Vycor system at a frequency (1.2 kHz) comparable to that
used in previous TO experiments. The shear modulus increases gradually as the
TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the
freezing out of thermally activated relaxation processes in the solid helium.
The absence of rapid changes below 200 mK is expected since mobile dislocations
could not exist in pores as small as those of Vycor. Our results support the
interpretation of a recent torsional oscillator experiment that showed no
anomaly when elastic effects in bulk helium were eliminated by ensuring that
there were no gaps around the Vycor sample.Comment: Accepted by Journal of Low Temperature Physic
Dislocation networks in helium-4 crystals
The mechanical behavior of crystals is dominated by dislocation networks,
their structure and their interactions with impurities or thermal phonons.
However, in classical crystals, networks are usually random with impurities
often forming non-equilibrium clusters when their motion freezes at low
temperature. Helium provides unique advantages for the study of dislocations:
crystals are free of all but isotopic impurities, the concentration of these
can be reduced to the ppb level, and the impurities are mobile at all
temperatures and therefore remain in equilibrium with the dislocations. We have
achieved a comprehensive study of the mechanical response of 4He crystals to a
driving strain as a function of temperature, frequency and strain amplitude.
The quality of our fits to the complete set of data strongly supports our
assumption of string-like vibrating dislocations. It leads to a precise
determination of the distribution of dislocation network lengths and to
detailed information about the interaction between dislocations and both
thermal phonons and 3He impurities. The width of the dissipation peak
associated with impurity binding is larger than predicted by a simple Debye
model, and much of this broadening is due to the distribution of network
lengths.Comment: accepted by Phys. Rev.
The symplectic origin of conformal and Minkowski superspaces
Supermanifolds provide a very natural ground to understand and handle
supersymmetry from a geometric point of view; supersymmetry in and
dimensions is also deeply related to the normed division algebras.
In this paper we want to show the link between the conformal group and
certain types of symplectic transformations over division algebras. Inspired by
this observation we then propose a new\,realization of the real form of the 4
dimensional conformal and Minkowski superspaces we obtain, respectively, as a
Lagrangian supermanifold over the twistor superspace and a
big cell inside it.
The beauty of this approach is that it naturally generalizes to the 6
dimensional case (and possibly also to the 10 dimensional one) thus providing
an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change
The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility
In this note we prove that the volume of a causal diamond associated with an
inertial observer in asymptotically de Sitter 4-dimensional space-time is
monotonically increasing function of cosmological time. The asymptotic value of
the volume is that of in maximally symmetric de Sitter space-time. The
monotonic property of the volume is checked in two cases: in vacuum and in the
presence of a massless scalar field. In vacuum, the volume flow (with respect
to cosmological time) asymptotically vanishes if and only if future space-like
infinity is 3-manifold of constant curvature. The volume flow thus represents
irreversibility of asymptotic evolution in spacetimes with positive
cosmological constant.Comment: 15 pages, no figures; v.2: conjecture 1 on p. 11 made more precise;
version published in jhe
Smooth extensions of functions on separable Banach spaces
Let be a Banach space with a separable dual . Let be
a closed subspace, and a -smooth function. Then we
show there is a extension of to .Comment: 19 pages. This version fixes a gap in the previous proof of Theorem 1
by providing a sharp version of Lemma
Measuring frequency fluctuations in nonlinear nanomechanical resonators
Advances in nanomechanics within recent years have demonstrated an always
expanding range of devices, from top-down structures to appealing bottom-up
MoS and graphene membranes, used for both sensing and component-oriented
applications. One of the main concerns in all of these devices is frequency
noise, which ultimately limits their applicability. This issue has attracted a
lot of attention recently, and the origin of this noise remains elusive up to
date. In this Letter we present a very simple technique to measure frequency
noise in nonlinear mechanical devices, based on the presence of bistability. It
is illustrated on silicon-nitride high-stress doubly-clamped beams, in a
cryogenic environment. We report on the same dependence of the frequency
noise power spectra as reported in the literature. But we also find unexpected
{\it damping fluctuations}, amplified in the vicinity of the bifurcation
points; this effect is clearly distinct from already reported nonlinear
dephasing, and poses a fundamental limit on the measurement of bifurcation
frequencies. The technique is further applied to the measurement of frequency
noise as a function of mode number, within the same device. The relative
frequency noise for the fundamental flexure lies in the range
ppm (consistent with literature for cryogenic MHz devices), and
decreases with mode number in the range studied. The technique can be applied
to {\it any types} of nano-mechanical structures, enabling progresses towards
the understanding of intrinsic sources of noise in these devices.Comment: Published 7 may 201
How social learning shapes the efficacy of preventative health behaviors in an outbreak.
The global pandemic of COVID-19 revealed the dynamic heterogeneity in how individuals respond to infection risks, government orders, and community-specific social norms. Here we demonstrate how both individual observation and social learning are likely to shape behavioral, and therefore epidemiological, dynamics over time. Efforts to delay and reduce infections can compromise their own success, especially when disease risk and social learning interact within sub-populations, as when people observe others who are (a) infected and/or (b) socially distancing to protect themselves from infection. Simulating socially-learning agents who observe effects of a contagious virus, our modelling results are consistent with with 2020 data on mask-wearing in the U.S. and also concur with general observations of cohort induced differences in reactions to public health recommendations. We show how shifting reliance on types of learning affect the course of an outbreak, and could therefore factor into policy-based interventions incorporating age-based cohort differences in response behavior
Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
Fefferman and Graham showed some time ago that four dimensional conformal
geometries could be analyzed in terms of six dimensional, ambient, Riemannian
geometries admitting a closed homothety. Recently it was shown how conformal
geometry provides a description of physics manifestly invariant under local
choices of unit systems. Strikingly, Einstein's equations are then equivalent
to the existence of a parallel scale tractor (a six component vector subject to
a certain first order covariant constancy condition at every point in four
dimensional spacetime). These results suggest a six dimensional description of
four dimensional physics, a viewpoint promulgated by the two times physics
program of Bars. The Fefferman--Graham construction relies on a triplet of
operators corresponding, respectively to a curved six dimensional light cone,
the dilation generator and the Laplacian. These form an sp(2) algebra which
Bars employs as a first class algebra of constraints in a six-dimensional gauge
theory. In this article four dimensional gravity is recast in terms of six
dimensional quantum mechanics by melding the two times and tractor approaches.
This "parent" formulation of gravity is built from an infinite set of six
dimensional fields. Successively integrating out these fields yields various
novel descriptions of gravity including a new four dimensional one built from a
scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe
Coercivity and stability results for an extended Navier-Stokes system
In this article we study a system of equations that is known to {\em extend}
Navier-Stokes dynamics in a well-posed manner to velocity fields that are not
necessarily divergence-free. Our aim is to contribute to an understanding of
the role of divergence and pressure in developing energy estimates capable of
controlling the nonlinear terms. We address questions of global existence and
stability in bounded domains with no-slip boundary conditions. Even in two
space dimensions, global existence is open in general, and remains so,
primarily due to the lack of a self-contained energy estimate. However,
through use of new coercivity estimates for the linear equations, we
establish a number of global existence and stability results, including results
for small divergence and a time-discrete scheme. We also prove global existence
in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure
A classification of local Weyl invariants in D=8
Following a purely algebraic procedure, we provide an exhaustive
classification of local Weyl-invariant scalar densities in dimension D=8.Comment: LaTeX, 19 pages, typos corrected, one reference adde
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