11,010 research outputs found
Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid
The advective Cahn-Hilliard equation describes the competing processes of
stirring and separation in a two-phase fluid. Intuition suggests that bubbles
will form on a certain scale, and previous studies of Cahn-Hilliard dynamics
seem to suggest the presence of one dominant length scale. However, the
Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we
show that, by stirring the mixture at a sufficiently large amplitude, we excite
the diffusion and overwhelm the segregation to create a homogeneous liquid. At
intermediate amplitudes we see regions of bubbles coexisting with regions of
hyperdiffusive filaments. Thus, the problem possesses two dominant length
scales, associated with the bubbles and filaments. For simplicity, we use use a
chaotic flow that mimics turbulent stirring at large Prandtl number. We compare
our results with the case of variable mobility, in which growth of bubble size
is dominated by interfacial rather than bulk effects, and find qualitatively
similar results.Comment: 20 pages, 27 figures. RevTeX
Nambu-Goldstone Modes in Gravitational Theories with Spontaneous Lorentz Breaking
Spontaneous breaking of Lorentz symmetry has been suggested as a possible
mechanism that might occur in the context of a fundamental Planck-scale theory,
such as string theory or a quantum theory of gravity. However, if Lorentz
symmetry is spontaneously broken, two sets of questions immediately arise: what
is the fate of the Nambu-Goldstone modes, and can a Higgs mechanism occur? A
brief summary of some recent work looking at these questions is presented here.Comment: 6 pages. Presented at the meeting "From Quantum to Cosmos,"
Washington, D.C., May 2006; published in Int. J. Mod. Phys. D16:2357-2363,
200
Black Holes in Einstein-Aether Theory
We study black hole solutions in general relativity coupled to a unit
timelike vector field dubbed the "aether". To be causally isolated a black hole
interior must trap matter fields as well as all aether and metric modes. The
theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four
coupling coefficients. We find that the full three-parameter family of local
spherically symmetric static solutions is always regular at a metric horizon,
but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic
flatness imposes another condition, leaving a one-parameter family of regular
black holes. These solutions are compared to the Schwarzschild solution using
numerical integration for a special class of coupling coefficients. They are
very close to Schwarzschild outside the horizon for a wide range of couplings,
and have a spacelike singularity inside, but differ inside quantitatively. Some
quantities constructed from the metric and aether oscillate in the interior as
the singularity is approached. The aether is at rest at spatial infinity and
flows into the black hole, but differs significantly from the the 4-velocity of
freely-falling geodesics.Comment: 22 pages, 6 figures; v2: minor editing; v3: corrected overall sign in
twist formula and an error in the equation for the aether stress tensor.
Results unchanged since correct form was used in calculations; v4: corrected
minor typ
Twisted k-graph algebras associated to Bratteli diagrams
Given a system of coverings of k-graphs, we show that the cohomology of the
resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the
system. We then consider Bratteli diagrams of 2-graphs whose twisted
C*-algebras are matrix algebras over noncommutative tori. For such systems we
calculate the ordered K-theory and the gauge-invariant semifinite traces of the
resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this
form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the
sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik
Measuring the relativistic perigee advance with Satellite Laser Ranging
One of the most famous classical tests of General Relativity is the
gravitoelectric secular advance of the pericenter of a test body in the
gravitational field of a central mass. In this paper we explore the possibility
of performing a measurement of the gravitoelectric pericenter advance in the
gravitational field of the Earth by analyzing the laser-ranged data to some
existing, or proposed, laser-ranged geodetic satellites. At the present level
of knowledge of various error sources, the relative precision obtainable with
the data from LAGEOS and LAGEOS II, suitably combined, is of the order of
. Nevertheless, these accuracies could sensibly be improved in the
near future when the new data on the terrestrial gravitational field from the
CHAMP and GRACE missions will be available. The use of the perigee of LARES
(LAser RElativity Satellite), in the context of a suitable combination of
orbital residuals including also LAGEOS II, should further raise the precision
of the measurement. As a secondary outcome of the proposed experiment, with the
so obtained value of \ppn and with \et=4\beta-\gamma-3 from Lunar Laser
Ranging it could be possible to obtain an estimate of the PPN parameters
and at the level.Comment: LaTex2e, 14 pages, no figures, 2 tables. To appear in Classical and
Quantum Gravit
Perceived importance of components of asynchronous music in circuit training
This study examined regular exercisersâ perceptions of specific components of music
during circuit training. Twenty-four men (38.8 years, s = 11.8 years) and 31 women
(32.4 years, s = 9.6 years) completed two questionnaires immediately after a circuit
training class. Participants rated the importance of 13 components of music (rhythm,
melody, etc.) in relation to exercise enjoyment, and each completed the Affect Intensity
Measure (Larsen, 1984) to measure emotional reactivity. Independent t tests were used
to evaluate gender differences in perceptions of musical importance. Pearson
correlations were computed to evaluate the relationships between affect intensity, age
and importance of musical components. Consistent with previous research and
theoretical predictions, rhythm response components (rhythm, tempo, beat) were rated
as most important. Women rated the importance of melody significantly higher than did
men, while men gave more importance to music associated with sport. Affect intensity
was found to be positively and significantly related to the perceived importance of
melody, lyrical content, musical style, personal associations and emotional content.
Results suggest that exercise leaders need to be sensitive to personal factors when
choosing music to accompany exercise. Qualitative research that focuses on the
personal meaning of music is encouraged
Rokhlin Dimension for Flows
This research was supported by GIF Grant 1137/2011, SFB 878 Groups, Geometry and Actions and ERC Grant No. 267079. Part of the research was conducted at the Fields institute during the 2014 thematic program on abstract harmonic analysis, Banach and operator algebras, and at the MittagâLeffler institute during the 2016 program on Classification of Operator Algebras: Complexity, Rigidity, and Dynamics.Peer reviewedPostprin
Vector vibrations and the Ioffe-Regel crossover in disordered lattices
The spectral density for vector vibrations in the f.c.c. lattice with
force-constant disorder is analysed within the coherent potential
approximation. The phase diagram showing the weak- and strong-scattering
regimes is presented and compared with that for electrons. The weak-scattering
regime for external long-wavelength vibrational plane waves is shown to be due
to sum-rule correlations in the dynamical matrix. A secondary peak below the
Brillouin peak for sufficiently large wavevectors is found for the lattice
models. The results obtained are supported by precise numerical solutions.Comment: 21 pages, 13 figure
Model for Spreading of Liquid Monolayers
Manipulating fluids at the nanoscale within networks of channels or chemical
lanes is a crucial challenge in developing small scale devices to be used in
microreactors or chemical sensors. In this context, ultra-thin (i.e.,
monolayer) films, experimentally observed in spreading of nano-droplets or upon
extraction from reservoirs in capillary rise geometries, represent an extreme
limit which is of physical and technological relevance since the dynamics is
governed solely by capillary forces. In this work we use kinetic Monte Carlo
(KMC) simulations to analyze in detail a simple, but realistic model proposed
by Burlatsky \textit{et al.} \cite{Burlatsky_prl96,Oshanin_jml} for the
two-dimensional spreading on homogeneous substrates of a fluid monolayer which
is extracted from a reservoir. Our simulations confirm the previously predicted
time-dependence of the spreading, , with as
the average position of the advancing edge at time , and they reveal a
non-trivial dependence of the prefactor on the strength of
inter-particle attraction and on the fluid density at the reservoir as
well as an -dependent spatial structure of the density profile of the
monolayer. The asymptotic density profile at long time and large spatial scale
is carefully analyzed within the continuum limit. We show that including the
effect of correlations in an effective manner into the standard mean-field
description leads to predictions both for the value of the threshold
interaction above which phase segregation occurs and for the density profiles
in excellent agreement with KMC simulations results.Comment: 21 pages, 9 figures, submitted to Phys. Rev.
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