35,401 research outputs found
Modeling the Influence of Antifreeze Proteins on Three-Dimensional Ice Crystal Melt Shapes using a Geometric Approach
The melting of pure axisymmetric ice crystals has been described previously
by us within the framework of so-called geometric crystal growth.
Nonequilibrium ice crystal shapes evolving in the presence of hyperactive
antifreeze proteins (hypAFPs) are experimentally observed to assume ellipsoidal
geometries ("lemon" or "rice" shapes). To analyze such shapes we harness the
underlying symmetry of hexagonal ice Ih and extend two-dimensional geometric
models to three-dimensions to reproduce the experimental dissolution process.
The geometrical model developed will be useful as a quantitative test of the
mechanisms of interaction between hypAFPs and ice.Comment: 15 pages, 5 figures; Proc. R. Soc. A, Published online before print
June 27, 201
Finite difference schemes for second order systems describing black holes
In the harmonic description of general relativity, the principle part of
Einstein's equations reduces to 10 curved space wave equations for the
componenets of the space-time metric. We present theorems regarding the
stability of several evolution-boundary algorithms for such equations when
treated in second order differential form. The theorems apply to a model black
hole space-time consisting of a spacelike inner boundary excising the
singularity, a timelike outer boundary and a horizon in between. These
algorithms are implemented as stable, convergent numerical codes and their
performance is compared in a 2-dimensional excision problem.Comment: 19 pages, 9 figure
Binary Black Hole Waveform Extraction at Null Infinity
In this work, we present a work in progress towards an efficient and
economical computational module which interfaces between Cauchy and
characteristic evolution codes. Our goal is to provide a standardized waveform
extraction tool for the numerical relativity community which will allow CCE to
be readily applied to a generic Cauchy code. The tool provides a means of
unambiguous comparison between the waveforms generated by evolution codes based
upon different formulations of the Einstein equations and different numerical
approximation.Comment: 11 pages, 7 figure
Reverse mathematics and properties of finite character
We study the reverse mathematics of the principle stating that, for every
property of finite character, every set has a maximal subset satisfying the
property. In the context of set theory, this variant of Tukey's lemma is
equivalent to the axiom of choice. We study its behavior in the context of
second-order arithmetic, where it applies to sets of natural numbers only, and
give a full characterization of its strength in terms of the quantifier
structure of the formula defining the property. We then study the interaction
between properties of finite character and finitary closure operators, and the
interaction between these properties and a class of nondeterministic closure
operators.Comment: This paper corresponds to section 4 of arXiv:1009.3242, "Reverse
mathematics and equivalents of the axiom of choice", which has been
abbreviated and divided into two pieces for publicatio
Testing the well-posedness of characteristic evolution of scalar waves
Recent results have revealed a critical way in which lower order terms affect
the well-posedness of the characteristic initial value problem for the scalar
wave equation. The proper choice of such terms can make the Cauchy problem for
scalar waves well posed even on a background spacetime with closed lightlike
curves. These results provide new guidance for developing stable characteristic
evolution algorithms. In this regard, we present here the finite difference
version of these recent results and implement them in a stable evolution code.
We describe test results which validate the code and exhibit some of the
interesting features due to the lower order terms.Comment: 22 pages, 15 figures Submitted to CQ
Some mathematical problems in numerical relativity
The main goal of numerical relativity is the long time simulation of highly
nonlinear spacetimes that cannot be treated by perturbation theory. This
involves analytic, computational and physical issues. At present, the major
impasses to achieving global simulations of physical usefulness are of an
analytic/computational nature. We present here some examples of how analytic
insight can lend useful guidance for the improvement of numerical approaches.Comment: 17 pages, 12 graphs (eps format
Topological aspects of poset spaces
We study two classes of spaces whose points are filters on partially ordered
sets. Points in MF spaces are maximal filters, while points in UF spaces are
unbounded filters. We give a thorough account of the topological properties of
these spaces. We obtain a complete characterization of the class of countably
based MF spaces: they are precisely the second-countable T_1 spaces with the
strong Choquet property. We apply this characterization to domain theory to
characterize the class of second-countable spaces with a domain representation.Comment: 29 pages. To be published in the Michigan Mathematical Journa
Reverse mathematics and equivalents of the axiom of choice
We study the reverse mathematics of countable analogues of several maximality
principles that are equivalent to the axiom of choice in set theory. Among
these are the principle asserting that every family of sets has a
-maximal subfamily with the finite intersection property and the
principle asserting that if is a property of finite character then every
set has a -maximal subset of which holds. We show that these
principles and their variations have a wide range of strengths in the context
of second-order arithmetic, from being equivalent to to being
weaker than and incomparable with . In
particular, we identify a choice principle that, modulo induction,
lies strictly below the atomic model theorem principle and
implies the omitting partial types principle
Harmonic Initial-Boundary Evolution in General Relativity
Computational techniques which establish the stability of an
evolution-boundary algorithm for a model wave equation with shift are
incorporated into a well-posed version of the initial-boundary value problem
for gravitational theory in harmonic coordinates. The resulting algorithm is
implemented as a 3-dimensional numerical code which we demonstrate to provide
stable, convergent Cauchy evolution in gauge wave and shifted gauge wave
testbeds. Code performance is compared for Dirichlet, Neumann and Sommerfeld
boundary conditions and for boundary conditions which explicitly incorporate
constraint preservation. The results are used to assess strategies for
obtaining physically realistic boundary data by means of Cauchy-characteristic
matching.Comment: 31 pages, 14 figures, submitted to Physical Review
Reverse mathematics and uniformity in proofs without excluded middle
We show that when certain statements are provable in subsystems of
constructive analysis using intuitionistic predicate calculus, related
sequential statements are provable in weak classical subsystems. In particular,
if a sentence of a certain form is provable using E-HA
along with the axiom of choice and an independence of premise principle, the
sequential form of the statement is provable in the classical system RCA. We
obtain this and similar results using applications of modified realizability
and the \textit{Dialectica} interpretation. These results allow us to use
techniques of classical reverse mathematics to demonstrate the unprovability of
several mathematical principles in subsystems of constructive analysis.Comment: Accepted, Notre Dame Journal of Formal Logi
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