402 research outputs found
Frustration driven structural distortion in VOMoO4
Nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR),
magnetization measurements and electronic structure calculations in VOMoO4 are
presented. It is found that VOMoO4 is a frustrated two-dimensional
antiferromagnet on a square lattice with competing exchange interactions along
the side J1 and the diagonal J2 of the square. From magnetization measurements
J1+J2 is estimated around 155 K, in satisfactory agreement with the values
derived from electronic structure calculations. Around 100 K a structural
distortion, possibly driven by the frustration, is evidenced. This distortion
induces significant modifications in the NMR and EPR spectra which can be
accounted for by valence fluctuations. The analysis of the spectra suggests
that the size of the domains where the lattice is distorted progressively grows
as the temperature approaches the transition to the magnetic ground state at
Tc=42 K
On formal verification of arithmetic-based cryptographic primitives
Cryptographic primitives are fundamental for information security: they are
used as basic components for cryptographic protocols or public-key
cryptosystems. In many cases, their security proofs consist in showing that
they are reducible to computationally hard problems. Those reductions can be
subtle and tedious, and thus not easily checkable. On top of the proof
assistant Coq, we had implemented in previous work a toolbox for writing and
checking game-based security proofs of cryptographic primitives. In this paper
we describe its extension with number-theoretic capabilities so that it is now
possible to write and check arithmetic-based cryptographic primitives in our
toolbox. We illustrate our work by machine checking the game-based proofs of
unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and
semantic security of the public-key cryptographic scheme of Goldwasser and
Micali.Comment: 13 page
Contribution of pulsars to the gamma-ray background and their observation with the space telescopes GLAST and AGILE
Luminosities and uxes of the expected population of galactic gamma-ray
pulsars become foreseeable if physical distributions at birth and evolutive
history are assigned. In this work we estimate the contribution of pulsar uxes
to the gamma-ray background, which has been measured by the EGRET experiment on
board of the CGRO. For pulsar luminosities we select some of the most important
gamma-ray emission models, taking into account both polar cap and outer gap
scenarios. We nd that this contribution strongly depends upon controversial
neutron star birth properties. A comparison between our simulation results and
EGRET data is presented for each model, nding an average contribution of about
10%. In addition, we perform the calculation of the number of new gamma-ray
pulsars detectable by GLAST and AGILE, showing a remarkable di erence between
the two classes of models. Finally, we suggest some improvements in the
numerical code, including more sophisticated galactic m odels and di erent
populations of pulsars like binaries, milliseconds, anomalous pulsars and
magnetars.Comment: 6 pages, 6 figures, to be published in the Proceedings of the 6th
International Symposium ''Frontiers of Fundamental and Computational
Physics'' (FFP6), Udine (Italy), Sep. 26-29, 200
Population statistics study of radio and gamma-ray pulsars in the Galactic plane
We present results of our pulsar population synthesis of ordinary isolated
and millisecond pulsars in the Galactic plane. Over the past several years, a
program has been developed to simulate pulsar birth, evolution and emission
using Monte Carlo techniques. We have added to the program the capability to
simulate millisecond pulsars, which are old, recycled pulsars with extremely
short periods. We model the spatial distribution of the simulated pulsars by
assuming that they start with a random kick velocity and then evolve through
the Galactic potential. We use a polar cap/slot gap model for -ray
emission from both millisecond and ordinary pulsars. From our studies of radio
pulsars that have clearly identifiable core and cone components, in which we
fit the polarization sweep as well as the pulse profiles in order to constrain
the viewing geometry, we develop a model describing the ratio of radio
core-to-cone peak fluxes. In this model, short period pulsars are more
cone-dominated than in our previous studies. We present the preliminary results
of our recent study and the implications for observing these pulsars with GLAST
and AGILE.Comment: 6 pages, 3 figures, 1 table, accepted in Astrophysics and Space
Scienc
Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker
Since the proof of the four color theorem in 1976, computer-generated proofs
have become a reality in mathematics and computer science. During the last
decade, we have seen formal proofs using verified proof assistants being used
to verify the validity of such proofs.
In this paper, we describe a formalized theory of size-optimal sorting
networks. From this formalization we extract a certified checker that
successfully verifies computer-generated proofs of optimality on up to 8
inputs. The checker relies on an untrusted oracle to shortcut the search for
witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c
Binary pattern tile set synthesis is NP-hard
In the field of algorithmic self-assembly, a long-standing unproven
conjecture has been that of the NP-hardness of binary pattern tile set
synthesis (2-PATS). The -PATS problem is that of designing a tile assembly
system with the smallest number of tile types which will self-assemble an input
pattern of colors. Of both theoretical and practical significance, -PATS
has been studied in a series of papers which have shown -PATS to be NP-hard
for , , and then . In this paper, we close the
fundamental conjecture that 2-PATS is NP-hard, concluding this line of study.
While most of our proof relies on standard mathematical proof techniques, one
crucial lemma makes use of a computer-assisted proof, which is a relatively
novel but increasingly utilized paradigm for deriving proofs for complex
mathematical problems. This tool is especially powerful for attacking
combinatorial problems, as exemplified by the proof of the four color theorem
by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and
Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by
Konev and Lisitsa using computer programs. We utilize a massively parallel
algorithm and thus turn an otherwise intractable portion of our proof into a
program which requires approximately a year of computation time, bringing the
use of computer-assisted proofs to a new scale. We fully detail the algorithm
employed by our code, and make the code freely available online
Spin-Dependent Cyclotron Decay Rates in Strong Magnetic Fields
Cyclotron decay and absorption rates have been well studied in the
literature, focusing primarily on spectral, angular and polarization
dependence. Astrophysical applications usually do not require retention of
information on the electron spin state, and these are normally averaged in
obtaining the requisite rates. In magnetic fields, higher order quantum
processes such as Compton scattering become resonant at the cyclotron frequency
and its harmonics, with the resonances being formally divergent. Such
divergences are usually eliminated by accounting for the finite lifetimes of
excited Landau states. This practice requires the use of spin-dependent
cyclotron rates in order to obtain accurate determinations of process rates
very near cyclotronic resonances, the phase space domain most relevant for
certain applications to pulsar models. This paper develops previous results in
the literature to obtain compact analytic expressions for cyclotron decay
rates/widths in terms of a series of Legendre functions of the second kind;
these expressions can be expediently used in astrophysical models. The rates
are derived using two popular eigenstate formalisms, namely that due to Sokolov
and Ternov, and that due to Johnson and Lippmann. These constitute two sets of
eigenfunctions of the Dirac equation that diagonalize different operators, and
accordingly yield different spin-dependent cyclotron rates. This paper
illustrates the attractive Lorentz transformation characteristics of the
Sokolov and Ternov formulation, which is another reason why it is preferable
when electron spin information must be explicitly retained.Comment: 11 pages, 2 embedded figures, apjgalley format, To appear in The
Astrophysical Journal, Vol 630, September 1, 2005 issu
Compton Scattering in Ultra-Strong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime
This paper explores the effects of strong magnetic fields on the Compton
scattering of relativistic electrons. Recent studies of upscattering and energy
loss by relativistic electrons that have used the non-relativistic, magnetic
Thomson cross section for resonant scattering or the Klein-Nishina cross
section for non-resonant scattering do not account for the relativistic quantum
effects of strong fields ( G). We have derived a
simplified expression for the exact QED scattering cross section for the
broadly-applicable case where relativistic electrons move along the magnetic
field. To facilitate applications to astrophysical models, we have also
developed compact approximate expressions for both the differential and total
polarization-dependent cross sections, with the latter representing well the
exact total QED cross section even at the high fields believed to be present in
environments near the stellar surfaces of Soft Gamma-Ray Repeaters and
Anomalous X-Ray Pulsars. We find that strong magnetic fields significantly
lower the Compton scattering cross section below and at the resonance, when the
incident photon energy exceeds in the electron rest frame. The cross
section is strongly dependent on the polarization of the final scattered
photon. Below the cyclotron fundamental, mostly photons of perpendicular
polarization are produced in scatterings, a situation that also arises above
this resonance for sub-critical fields. However, an interesting discovery is
that for super-critical fields, a preponderance of photons of parallel
polarization results from scatterings above the cyclotron fundamental. This
characteristic is both a relativistic and magnetic effect not present in the
Thomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for
publication in The Astrophysical Journa
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