541 research outputs found
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Fracture in Mode I using a Conserved Phase-Field Model
We present a continuum phase-field model of crack propagation. It includes a
phase-field that is proportional to the mass density and a displacement field
that is governed by linear elastic theory. Generic macroscopic crack growth
laws emerge naturally from this model. In contrast to classical continuum
fracture mechanics simulations, our model avoids numerical front tracking. The
added phase-field smoothes the sharp interface, enabling us to use equations of
motion for the material (grounded in basic physical principles) rather than for
the interface (which often are deduced from complicated theories or empirical
observations). The interface dynamics thus emerges naturally. In this paper, we
look at stationary solutions of the model, mode I fracture, and also discuss
numerical issues. We find that the Griffith's threshold underestimates the
critical value at which our system fractures due to long wavelength modes
excited by the fracture process.Comment: 10 pages, 5 figures (eps). Added 2 figures and some text. Removed one
section (and a figure). To be published in PR
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
A Supercooled Spin Liquid State in the Frustrated Pyrochlore Dy2Ti2O7
A "supercooled" liquid develops when a fluid does not crystallize upon
cooling below its ordering temperature. Instead, the microscopic relaxation
times diverge so rapidly that, upon further cooling, equilibration eventually
becomes impossible and glass formation occurs. Classic supercooled liquids
exhibit specific identifiers including microscopic relaxation times diverging
on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for
the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for
time-domain relaxation. Recently, the pyrochlore Dy2Ti2O7 has become of
interest because its frustrated magnetic interactions may, in theory, lead to
highly exotic magnetic fluids. However, its true magnetic state at low
temperatures has proven very difficult to identify unambiguously. Here we
introduce high-precision, boundary-free magnetization transport techniques
based upon toroidal geometries and gain a fundamentally new understanding of
the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7. We
demonstrate a virtually universal HN form for the magnetic susceptibility, a
general KWW form for the real-time magnetic relaxation, and a divergence of the
microscopic magnetic relaxation rates with precisely the VTF trajectory. Low
temperature Dy2Ti2O7 therefore exhibits the characteristics of a supercooled
magnetic liquid; the consequent implication is that this translationally
invariant lattice of strongly correlated spins is evolving towards an
unprecedented magnetic glass state, perhaps due to many-body localization of
spin.Comment: Version 2 updates: added legend for data in Figures 4A and 4B;
corrected equation reference in caption for Figure 4
What are the interactions in quantum glasses?
The form of the low-temperature interactions between defects in neutral
glasses is reconsidered. We analyse the case where the defects can be modelled
either as simple 2-level tunneling systems, or tunneling rotational impurities.
The coupling to strain fields is determined up to 2nd order in the displacement
field. It is shown that the linear coupling generates not only the usual
Ising-like interaction between the rotational tunneling defect modes,
which cause them to freeze around a temperature , but also a random field
term. At lower temperatures the inversion symmetric tunneling modes are still
active - however the coupling of these to the frozen rotational modes, now via
the 2nd-order coupling to phonons, generates another random field term acting
on the inversion symmetric modes (as well as shorter-range interactions
between them). Detailed expressions for all these couplings are given.Comment: 12 pages, 2 figures. Minor modifications, published versio
Homogeneous Nucleation Rate Measurements for Water Over a Wide Range of Temperature and Nucleation Rate
An expansion cloud chamber was used to measure the homogeneous nucleation rate for water over a wide range of temperature from 230-290 K and nucleation rates of 1-106 drops cm-3 s-1. The comprehensive and extensive nature of this data allows a much more detailed comparison between theory and experiment than has previously been possible. The expansion chamber technique employs continuous pressure measurement and an adiabatic pulse of supersaturation to give the time history of supersaturation and temperature during the nucleation. The resulting drop concentration is determined using photographic techniques. The experimental observations are presented in tabular form and from them an empirical nucleation rate formula is determined: J=S2 exp[328.124-5.582 43T+0.030 365T2-5. 0319E-5T3-(999.814-4.100 87T+3.010 84E-3 T2)ln -2S], where J is the nucleation rate in units of drops cm -1 s-1 is the supersaturation ratio and T is the temperature in K
State Scorecard on Long-Term Services and Supports for Older Adults, People with Physical Disabilities, and Family Caregivers
This State Long-Term Services and Supports (LTSS) Scorecard is a multidimensional approach to measure state-level performance of LTSS systems that assist older people, adults with disabilities, and their family caregivers. This second edition of the State LTSS Scorecard measures LTSS system performance across five key dimensions: (1) affordability and access, (2) choice of setting and provider, (3) quality of life and quality of care, (4) support for family caregivers, and (5) effective transitions. Performance varies tremendously across the states, with LTSS systems in leading states having markedly different characteristics than those in lagging states. LTSS performance is gradually improving, both nationally and in most states. Progress is notable in many areas where public policy has a direct impact, including performance of the Medicaid safety net and legal and system supports for family caregivers. But the pace of improvement must accelerate as the Baby Boom Generation moves toward advanced ages
Evidence for a Second Order Phase Transition in Glasses at Very Low Temperatures -- A Macroscopic Quantum State of Tunneling Systems
Dielectric measurements at very low temperature indicate that in a glass with
the eutectic composition BaO-AlO-SiO a phase transition occurs at
5.84 mK. Below that temperature small magnetic fields of the order of 10 T
cause noticeable changes of the dielectric constant although the glass is
insensitive to fields up to 20 T above 10 mK. The experimental findings may be
interpreted as the signature of the formation of a new phase in which many
tunneling systems perform a coherent motion resulting in a macroscopic wave
function.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let
Spatial geometry of the rotating disk and its non-rotating counterpart
A general relativistic description of a disk rotating at constant angular
velocity is given. It is argued that conceptually this direct approach poses
fewer problems than the special relativistic one. For observers on the disk,
the geometry of their proper space is hyperbolic. This has interesting
consequences concerning their interpretation of the geometry of a non-rotating
disk having the same radius. The influence of clock synchronization on spatial
measurements is discussed.Comment: 10 pages, 3 figures, this is the version accepted by American Journal
of Physics; I had to remove the special relativity part, which one of the
referees did not like; it is still available in v
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