302 research outputs found
Constructing explicit magnetic analogies for the dynamics of glass forming liquids
By defining a spatially varying replica overlap parameter for a supercooled
liquid referenced to an ensemble of fiducial liquid state configurations we
explicitly construct a constrained replica free energy functional that maps
directly onto an Ising Hamiltonian with both random fields and random
interactions whose statistics depend on liquid structure. Renormalization group
results for random magnets when combined with these statistics for the
Lennard-Jones glass suggest that discontinuous replica symmetry breaking would
occur if a liquid with short range interactions could be equilibrated at a
sufficiently low temperature where its mean field configurational entropy would
vanish, even though the system strictly retains a finite configurational
entropy
Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings.
We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.We acknowledge useful discussions with Daniel Asenjo, Carl Goodrich, Silke Henkes, and Fabien Paillusson. S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. J.D.S. acknowledges support by Marie Curie Grant 275544. D.F. and D.J.W. acknowledge support by EPSRC Programme Grant EP/I001352/1, by EPSRC grant EP/I000844/1 (D.F.) and ERC Advanced Grant RG59508 (D.J.W.)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.01290
The Ultimate Fate of Supercooled Liquids
In recent years it has become widely accepted that a dynamical length scale
{\xi}_{\alpha} plays an important role in supercooled liquids near the glass
transition. We examine the implications of the interplay between the growing
{\xi}_{\alpha} and the size of the crystal nucleus, {\xi}_M, which shrinks on
cooling. We argue that at low temperatures where {\xi}_{\alpha} > {\xi}_M a new
crystallization mechanism emerges enabling rapid development of a large scale
web of sparsely connected crystallinity. Though we predict this web percolates
the system at too low a temperature to be easily seen in the laboratory, there
are noticeable residual effects near the glass transition that can account for
several previously observed unexplained phenomena of deeply supercooled liquids
including Fischer clusters, and anomalous crystal growth near T_g
Percolation and Schramm-Loewner evolution in the 2D random-field Ising model
The presence of random fields is well known to destroy ferromagnetic order in
Ising systems in two dimensions. When the system is placed in a sufficiently
strong external field, however, the size of clusters of like spins diverges.
There is evidence that this percolation transition is in the universality class
of standard site percolation. It has been claimed that, for small disorder, a
similar percolation phenomenon also occurs in zero external field. Using exact
algorithms, we study ground states of large samples and find little evidence
for a transition at zero external field. Nevertheless, for sufficiently small
random field strengths, there is an extended region of the phase diagram, where
finite samples are indistinguishable from a critical percolating system. In
this regime we examine ground-state domain walls, finding strong evidence that
they are conformally invariant and satisfy Schramm-Loewner evolution
() with parameter . These results add support to the
hope that at least some aspects of systems with quenched disorder might be
ultimately studied with the techniques of SLE and conformal field theory
Eigenspectra: A Framework for Identifying Spectra from 3D Eclipse Mapping
Planetary atmospheres are inherently 3D objects that can have strong
gradients in latitude, longitude, and altitude. Secondary eclipse mapping is a
powerful way to map the 3D distribution of the atmosphere, but the data can
have large correlations and errors in the presence of photon and instrument
noise. We develop a technique to mitigate the large uncertainties of eclipse
maps by identifying a small number of dominant spectra to make them more
tractable for individual analysis via atmospheric retrieval. We use the
eigencurves method to infer a multi-wavelength map of a planet from
spectroscopic secondary eclipse light curves. We then apply a clustering
algorithm to the planet map to identify several regions with similar emergent
spectra. We combine the similar spectra together to construct an
"eigenspectrum" for each distinct region on the planetary map. We demonstrate
how this approach could be used to isolate hot from cold regions and/or regions
with different chemical compositions in observations of hot Jupiters with the
James Webb Space Telescope (JWST). We find that our method struggles to
identify sharp edges in maps with sudden discontinuities, but generally can be
used as a first step before a more physically motivated modeling approach to
determine the primary features observed on the planet.Comment: 13 pages, 17 figures, accepted to MNRA
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