20,667 research outputs found
The exp-log normal form of types
Lambda calculi with algebraic data types lie at the core of functional
programming languages and proof assistants, but conceal at least two
fundamental theoretical problems already in the presence of the simplest
non-trivial data type, the sum type. First, we do not know of an explicit and
implemented algorithm for deciding the beta-eta-equality of terms---and this in
spite of the first decidability results proven two decades ago. Second, it is
not clear how to decide when two types are essentially the same, i.e.
isomorphic, in spite of the meta-theoretic results on decidability of the
isomorphism.
In this paper, we present the exp-log normal form of types---derived from the
representation of exponential polynomials via the unary exponential and
logarithmic functions---that any type built from arrows, products, and sums,
can be isomorphically mapped to. The type normal form can be used as a simple
heuristic for deciding type isomorphism, thanks to the fact that it is a
systematic application of the high-school identities.
We then show that the type normal form allows to reduce the standard beta-eta
equational theory of the lambda calculus to a specialized version of itself,
while preserving the completeness of equality on terms. We end by describing an
alternative representation of normal terms of the lambda calculus with sums,
together with a Coq-implemented converter into/from our new term calculus. The
difference with the only other previously implemented heuristic for deciding
interesting instances of eta-equality by Balat, Di Cosmo, and Fiore, is that we
exploit the type information of terms substantially and this often allows us to
obtain a canonical representation of terms without performing sophisticated
term analyses
Non-equilibrium Magnetization Dynamics in the Fe_8 Single-Molecule Magnet Induced by High-Intensity Microwave Radiation
Resonant microwave radiation applied to a single crystal of the molecular
magnet Fe_8 induces dramatic changes in the sample's magnetization. Transitions
between excited states are found even though at the nominal system temperature
these levels have negligible population. We find evidence that the sample heats
significantly when the resonance condition is met. In addition, heating is
observed after a short pulse of intense radiation has been turned off,
indicating that the spin system is out of equilibrium with the lattice.Comment: Version to appear in Europhysics Letters. Minor changes and updated
reference
Nonlinear r-modes in Rapidly Rotating Relativistic Stars
The r-mode instability in rotating relativistic stars has been shown recently
to have important astrophysical implications (including the emission of
detectable gravitational radiation, the explanation of the initial spins of
young neutron stars and the spin-distribution of millisecond pulsars and the
explanation of one type of gamma-ray bursts), provided that r-modes are not
saturated at low amplitudes by nonlinear effects or by dissipative mechanisms.
Here, we present the first study of nonlinear r-modes in isentropic, rapidly
rotating relativistic stars, via 3-D general-relativistic hydrodynamical
evolutions. Our numerical simulations show that (1) on dynamical timescales,
there is no strong nonlinear coupling of r-modes to other modes at amplitudes
of order one -- unless nonlinear saturation occurs on longer timescales, the
maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is
of the same order as the rotational velocity at the equator). An absolute upper
limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars)
is set by causality. (2) r-modes and inertial modes in isentropic stars are
predominantly discrete modes and possible associated continuous parts were not
identified in our simulations. (3) In addition, the kinematical drift
associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000),
appears to be present in our simulations, but an unambiguous confirmation
requires more precise initial data. We discuss the implications of our findings
for the detectability of gravitational waves from the r-mode instability.Comment: 4 pages, 4 eps figures, accepted in Physical Review Letter
Experimental Upper Bound on Superradiance Emission from Mn12 Acetate
We used a Josephson junction as a radiation detector to look for evidence of
the emission of electromagnetic radiation during magnetization avalanches in a
crystal assembly of Mn_12-Acetate. The crystal assembly exhibits avalanches at
several magnetic fields in the temperature range from 1.8 to 2.6 K with
durations of the order of 1 ms. Although a recent study shows evidence of
electromagnetic radiation bursts during these avalanches [J. Tejada, et al.,
Appl. Phys. Lett. {\bf 84}, 2373 (2004)], we were unable to detect any
significant radiation at well-defined frequencies. A control experiment with
external radiation pulses allows us to determine that the energy released as
radiation during an avalanche is less than 1 part in 10^4 of the total energy
released. In addition, our avalanche data indicates that the magnetization
reversal process does not occur uniformly throughout the sample.Comment: 4 RevTeX pages, 3 eps figure
Ferromagnetism of He Films in the Low Field Limit
We provide evidence for a finite temperature ferromagnetic transition in
2-dimensions as in thin films of He on graphite, a model system
for the study of two-dimensional magnetism. We perform pulsed and CW NMR
experiments at fields of 0.03 - 0.48 mT on He at areal densities of 20.5 -
24.2 atoms/nm. At these densities, the second layer of He has a
strongly ferromagnetic tendency. With decreasing temperature, we find a rapid
onset of magnetization that becomes independent of the applied field at
temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR
linewidth grow rapidly as well, which is consistent with a large (order unity)
polarization of the He spins.Comment: 4 figure
A numerical study of the r-mode instability of rapidly rotating nascent neutron stars
The first results of numerical analysis of classical r-modes of {\it rapidly}
rotating compressible stellar models are reported. The full set of linear
perturbation equations of rotating stars in Newtonian gravity are numerically
solved without the slow rotation approximation. A critical curve of
gravitational wave emission induced instability which restricts the rotational
frequencies of hot young neutron stars is obtained. Taking the standard cooling
mechanisms of neutron stars into account, we also show the `evolutionary
curves' along which neutron stars are supposed to evolve as cooling and
spinning-down proceed. Rotational frequencies of stars suffering
from this instability decrease to around 100Hz when the standard cooling
mechanism of neutron stars is employed. This result confirms the results of
other authors who adopted the slow rotation approximation.Comment: 4 pages, 2 figures; MNRAS,316,L1(2000
How unprovable is Rabin's decidability theorem?
We study the strength of set-theoretic axioms needed to prove Rabin's theorem
on the decidability of the MSO theory of the infinite binary tree. We first
show that the complementation theorem for tree automata, which forms the
technical core of typical proofs of Rabin's theorem, is equivalent over the
moderately strong second-order arithmetic theory to a
determinacy principle implied by the positional determinacy of all parity games
and implying the determinacy of all Gale-Stewart games given by boolean
combinations of sets. It follows that complementation for
tree automata is provable from - but not -comprehension.
We then use results due to MedSalem-Tanaka, M\"ollerfeld and
Heinatsch-M\"ollerfeld to prove that over -comprehension, the
complementation theorem for tree automata, decidability of the MSO theory of
the infinite binary tree, positional determinacy of parity games and
determinacy of Gale-Stewart games are all
equivalent. Moreover, these statements are equivalent to the
-reflection principle for -comprehension. It follows in
particular that Rabin's decidability theorem is not provable in
-comprehension.Comment: 21 page
The effect of uniaxial pressure on the magnetic anisotropy of the Mn_{12}-Ac single-molecule magnet
We study the effect of uniaxial pressure on the magnetic hysteresis loops of
the single-molecule magnet Mn_{12}-Ac. We find that the application of pressure
along the easy axis increases the fields at which quantum tunneling of
magnetization occurs. The observations are attributed to an increase in the
molecule's magnetic anisotropy constant D of 0.142(1)%/kbar. The increase in D
produces a small, but measurable increase in the effective energy barrier for
magnetization reversal. Density-functional theory calculations also predict an
increase in the barrier with applied pressure.Comment: version accepted by EPL; 6 pages, including 7 figures. Small changes
and added reference
Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell
Recent studies have raised doubts about the occurrence of r modes in
Newtonian stars with a large degree of differential rotation. To assess the
validity of this conjecture we have solved the eigenvalue problem for
Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the
presence of differential rotation. The results obtained indicate that the
eigenvalue problem is never singular and that, at least for the case of a
thin-shell, the analogues of r modes can be found for arbitrarily large degrees
of differential rotation. This work clarifies the puzzling results obtained in
calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ
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