714 research outputs found
On inversions and Doob -transforms of linear diffusions
Let be a regular linear diffusion whose state space is an open interval
. We consider a diffusion which probability law is
obtained as a Doob -transform of the law of , where is a positive
harmonic function for the infinitesimal generator of on . This is the
dual of with respect to where is the speed measure of
. Examples include the case where is conditioned to stay above
some fixed level. We provide a construction of as a deterministic
inversion of , time changed with some random clock. The study involves the
construction of some inversions which generalize the Euclidean inversions.
Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page
Recent Advances in Modeling Stellar Interiors
Advances in stellar interior modeling are being driven by new data from
large-scale surveys and high-precision photometric and spectroscopic
observations. Here we focus on single stars in normal evolutionary phases; we
will not discuss the many advances in modeling star formation, interacting
binaries, supernovae, or neutron stars. We review briefly: 1) updates to input
physics of stellar models; 2) progress in two and three-dimensional evolution
and hydrodynamic models; 3) insights from oscillation data used to infer
stellar interior structure and validate model predictions (asteroseismology).
We close by highlighting a few outstanding problems, e.g., the driving
mechanisms for hybrid gamma Dor/delta Sct star pulsations, the cause of giant
eruptions seen in luminous blue variables such as eta Car and P Cyg, and the
solar abundance problem.Comment: Proceedings for invited talk at conference High Energy Density
Laboratory Astrophysics 2010, Caltech, March 2010, submitted for special
issue of Astrophysics and Space Science; 7 pages; 5 figure
Temperature dependence of magnetic anisotropy and domain wall tuning in BaTiO₃(111)/CoFeB multiferroics
Artificial multiferroics consist of two types of ferroic materials, typically a ferroelectric and a ferromagnet, often coupled interfacially by magnetostriction induced by the lattice elongations in the ferroelectric. In BaTiO3, the magnitude of strain induced by these elongations is heavily temperature dependent, varying greatly between each of the polar crystal phases and exerting a huge influence over the properties of a coupled magnetic film. Here, we demonstrate that temperature and, thus, strain are effective means of controlling the magnetic anisotropy in BaTiO3(111)/CoFeB heterostructures. We investigate the three polar phases of BaTiO3: tetragonal (T) at room temperature, orthorhombic (O) below 280 K, and rhombohedral (R) below 190 K across a total range of 77–420 K. We find two distinct responses: a step-like change in the anisotropy across the low-temperature phase transitions and a sharp high-temperature reduction around the ferroelectric Curie temperature, measured from hard axis hysteresis loops. Using our measurements of this anisotropy strength, we are then able to show by micromagnetic simulation the behavior of all possible magnetic domain wall states and determine their scaling as a function of temperature. The most significant changes occur in the head-to-head domain wall states, with a maximum change of 210 nm predicted across the entire range, effectively doubling the size of the domain wall as compared to room temperature. Notably, similar changes are seen for both high and low temperatures, which suggests different routes for potential control of magnetic anisotropy and elastically pinned magnetic domain walls
Hydrogen-Helium Mixtures at High Pressure
The properties of hydrogen-helium mixtures at high pressure are crucial to
address important questions about the interior of Giant planets e.g. whether
Jupiter has a rocky core and did it emerge via core accretion? Using path
integral Monte Carlo simulations, we study the properties of these mixtures as
a function of temperature, density and composition. The equation of state is
calculated and compared to chemical models. We probe the accuracy of the ideal
mixing approximation commonly used in such models. Finally, we discuss the
structure of the liquid in terms of pair correlation functions.Comment: Proceedings article of the 5th Conference on Cryocrystals and Quantum
Crystals in Wroclaw, Poland, submitted to J. Low. Temp. Phys. (2004
The maximum clique enumeration problem: algorithms, applications, and implementations
Background
The maximum clique enumeration (MCE) problem asks that we identify all maximum cliques in a finite, simple graph. MCE is closely related to two other well-known and widely-studied problems: the maximum clique optimization problem, which asks us to determine the size of a largest clique, and the maximal clique enumeration problem, which asks that we compile a listing of all maximal cliques. Naturally, these three problems are View MathML /\u3e-hard, given that they subsume the classic version of the View MathML /\u3e-complete clique decision problem. MCE can be solved in principle with standard enumeration methods due to Bron, Kerbosch, Kose and others. Unfortunately, these techniques are ill-suited to graphs encountered in our applications. We must solve MCE on instances deeply seeded in data mining and computational biology, where high-throughput data capture often creates graphs of extreme size and density. MCE can also be solved in principle using more modern algorithms based in part on vertex cover and the theory of fixed-parameter tractability (FPT). While FPT is an improvement, these algorithms too can fail to scale sufficiently well as the sizes and densities of our datasets grow. Results
An extensive testbed of benchmark graphs are created using publicly available transcriptomic datasets from the Gene Expression Omnibus (GEO). Empirical testing reveals crucial but latent features of such high-throughput biological data. In turn, it is shown that these features distinguish real data from random data intended to reproduce salient topological features. In particular, with real data there tends to be an unusually high degree of maximum clique overlap. Armed with this knowledge, novel decomposition strategies are tuned to the data and coupled with the best FPT MCE implementations. Conclusions
Several algorithmic improvements to MCE are made which progressively decrease the run time on graphs in the testbed. Frequently the final runtime improvement is several orders of magnitude. As a result, instances which were once prohibitively time-consuming to solve are brought into the domain of realistic feasibility
Presupernova Structure of Massive Stars
Issues concerning the structure and evolution of core collapse progenitor
stars are discussed with an emphasis on interior evolution. We describe a
program designed to investigate the transport and mixing processes associated
with stellar turbulence, arguably the greatest source of uncertainty in
progenitor structure, besides mass loss, at the time of core collapse. An
effort to use precision observations of stellar parameters to constrain
theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory
Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics
and Space Science, submitted for peer review: 7 pages, 3 figure
Rings and bars: unmasking secular evolution of galaxies
Secular evolution gradually shapes galaxies by internal processes, in
contrast to early cosmological evolution which is more rapid. An important
driver of secular evolution is the flow of gas from the disk into the central
regions, often under the influence of a bar. In this paper, we review several
new observational results on bars and nuclear rings in galaxies. They show that
these components are intimately linked to each other, and to the properties of
their host galaxy. We briefly discuss how upcoming observations, e.g., imaging
from the Spitzer Survey of Stellar Structure in Galaxies (S4G), will lead to
significant further advances in this area of research.Comment: Invited review at "Galaxies and their Masks", celebrating Ken
Freeman's 70-th birthday, Sossusvlei, Namibia, April 2010. To be published by
Springer, New York, editors D.L. Block, K.C. Freeman, & I. Puerari; minor
change
Magnetic Reconnection in Extreme Astrophysical Environments
Magnetic reconnection is a basic plasma process of dramatic rearrangement of
magnetic topology, often leading to a violent release of magnetic energy. It is
important in magnetic fusion and in space and solar physics --- areas that have
so far provided the context for most of reconnection research. Importantly,
these environments consist just of electrons and ions and the dissipated energy
always stays with the plasma. In contrast, in this paper I introduce a new
direction of research, motivated by several important problems in high-energy
astrophysics --- reconnection in high energy density (HED) radiative plasmas,
where radiation pressure and radiative cooling become dominant factors in the
pressure and energy balance. I identify the key processes distinguishing HED
reconnection: special-relativistic effects; radiative effects (radiative
cooling, radiation pressure, and Compton resistivity); and, at the most extreme
end, QED effects, including pair creation. I then discuss the main
astrophysical applications --- situations with magnetar-strength fields
(exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares
and magnetically-powered central engines and jets of GRBs. Here, magnetic
energy density is so high that its dissipation heats the plasma to MeV
temperatures. Electron-positron pairs are then copiously produced, making the
reconnection layer highly collisional and dressing it in a thick pair coat that
traps radiation. The pressure is dominated by radiation and pairs. Yet,
radiation diffusion across the layer may be faster than the global Alfv\'en
transit time; then, radiative cooling governs the thermodynamics and
reconnection becomes a radiative transfer problem, greatly affected by the
ultra-strong magnetic field. This overall picture is very different from our
traditional picture of reconnection and thus represents a new frontier in
reconnection research.Comment: Accepted to Space Science Reviews (special issue on magnetic
reconnection). Article is based on an invited review talk at the
Yosemite-2010 Workshop on Magnetic Reconnection (Yosemite NP, CA, USA;
February 8-12, 2010). 30 pages, no figure
Global Search for New Physics with 2.0/fb at CDF
Data collected in Run II of the Fermilab Tevatron are searched for
indications of new electroweak-scale physics. Rather than focusing on
particular new physics scenarios, CDF data are analyzed for discrepancies with
the standard model prediction. A model-independent approach (Vista) considers
gross features of the data, and is sensitive to new large cross-section
physics. Further sensitivity to new physics is provided by two additional
algorithms: a Bump Hunter searches invariant mass distributions for "bumps"
that could indicate resonant production of new particles; and the Sleuth
procedure scans for data excesses at large summed transverse momentum. This
combined global search for new physics in 2.0/fb of ppbar collisions at
sqrt(s)=1.96 TeV reveals no indication of physics beyond the standard model.Comment: 8 pages, 7 figures. Final version which appeared in Physical Review D
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