630 research outputs found
Multipeakons and a theorem of Stieltjes
A closed form of the multi-peakon solutions of the Camassa-Holm equation is
found using a theorem of Stieltjes on continued fractions. An explicit formula
is obtained for the scattering shifts.Comment: 6 page
An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation
This paper employs a powerful argument, called an algorithmic argument, to
prove lower bounds of the quantum query complexity of a multiple-block ordered
search problem in which, given a block number i, we are to find a location of a
target keyword in an ordered list of the i-th block. Apart from much studied
polynomial and adversary methods for quantum query complexity lower bounds, our
argument shows that the multiple-block ordered search needs a large number of
nonadaptive oracle queries on a black-box model of quantum computation that is
also supplemented with advice. Our argument is also applied to the notions of
computational complexity theory: quantum truth-table reducibility and quantum
truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the
29th International Symposium on Mathematical Foundations of Computer Science,
Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27,
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Reactor Physics Modeling of Spent Nuclear Research Reactor Fuel for Snm Attribution and Nuclear Forensics
Nuclear research reactors are the least safeguarded type of reactor; in some cases this may be attributed to low risk and in most cases it is due to difficulty from dynamic operation. Research reactors vary greatly in size, fuel type, enrichment, power and burnup providing a significant challenge to any standardized safeguard system. If a whole fuel assembly was interdicted, based on geometry and other traditional forensics work, one could identify the material's origin fairly accurately. If the material has been dispersed or reprocessed, in-depth reactor physics models may be used to help with the identification. Should there be a need to attribute research reactor fuel material, the Savannah River National Laboratory would perform radiochemical analysis of samples of the material as well as other non-destructive measurements. In depth reactor physics modeling would then be performed to compare to these measured results in an attempt to associate the measured results with various reactor parameters. Several reactor physics codes are being used and considered for this purpose, including: MONTEBURNS/ORIGEN/MCNP5, CINDER/MCNPX and WIMS. In attempt to identify reactor characteristics, such as time since shutdown, burnup, or power, various isotopes are used. Complexities arise when the inherent assumptions embedded in different reactor physics codes handle the isotopes differently and may quantify them to different levels of accuracy. A technical approach to modeling spent research reactor fuel begins at the assembly level upon acquiring detailed information of the reactor to be modeled. A single assembly is run using periodic boundary conditions to simulate an infinite lattice which may be repeatedly burned to produce input fuel isotopic vectors of various burnups for a core level model. A core level model will then be constructed using the assembly level results as inputs for the specific fuel shuffling pattern in an attempt to establish an equilibrium cycle. The core level results may then be compared to the radiochemistry results from the dissolved fuel samples and a decision whether further more in-depth modeling should be performed. The SRNL is in the process of analyzing multiple research reactor fuels to determine the best means to provide forensic data for attribution and assess codes and modeling methods for attribution. As several fuel samples are analyzed, this work will allow improved SNM forensics of spent research reactor fuel. This will enable the establishment of a research reactor fuel database of SNM materials, and allow an attempt of an inverse analysis if research reactor material is diverted and seized
The inverse spectral problem for the discrete cubic string
Given a measure on the real line or a finite interval, the "cubic string"
is the third order ODE where is a spectral parameter. If
equipped with Dirichlet-like boundary conditions this is a nonselfadjoint
boundary value problem which has recently been shown to have a connection to
the Degasperis-Procesi nonlinear water wave equation. In this paper we study
the spectral and inverse spectral problem for the case of Neumann-like boundary
conditions which appear in a high-frequency limit of the Degasperis--Procesi
equation. We solve the spectral and inverse spectral problem for the case of
being a finite positive discrete measure. In particular, explicit
determinantal formulas for the measure are given. These formulas generalize
Stieltjes' formulas used by Krein in his study of the corresponding second
order ODE .Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse
Problems (http://www.iop.org/EJ/journal/IP
Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity
In this paper we give several global characterisations of the Hormander class
of pseudo-differential operators on compact Lie groups. The result is applied
to give criteria for the ellipticity and the global hypoellipticity of
pseudo-differential operators in terms of their matrix-valued full symbols.
Several examples of the first and second order globally hypoelliptic
differential operators are given. Where the global hypoelliptiticy fails, one
can construct explicit examples based on the analysis of the global symbols.Comment: 20 page
Scalability of quantum computation with addressable optical lattices
We make a detailed analysis of error mechanisms, gate fidelity, and
scalability of proposals for quantum computation with neutral atoms in
addressable (large lattice constant) optical lattices. We have identified
possible limits to the size of quantum computations, arising in 3D optical
lattices from current limitations on the ability to perform single qubit gates
in parallel and in 2D lattices from constraints on laser power. Our results
suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e.,
qubits) may be achievable, provided two-qubit gates can be performed with
sufficiently high precision and degree of parallelizability. Parallelizability
of long range interaction-based two-qubit gates is qualitatively compared to
that of collisional gates. Different methods of performing single qubit gates
are compared, and a lower bound of is determined on the
error rate for the error mechanisms affecting Cs in a blue-detuned
lattice with Raman transition-based single qubit gates, given reasonable limits
on experimental parameters.Comment: 17 pages, 5 figures. Accepted for publication in Physical Review
On the Cauchy problem for a nonlinearly dispersive wave equation
We establish the local well-posedness for a new nonlinearly dispersive wave
equation and we show that the equation has solutions that exist for indefinite
times as well as solutions which blowup in finite times. Furthermore, we derive
an explosion criterion for the equation and we give a sharp estimate from below
for the existence time of solutions with smooth initial data.Comment: arxiv version is already officia
Decay and Continuity of Boltzmann Equation in Bounded Domains
Boundaries occur naturally in kinetic equations and boundary effects are
crucial for dynamics of dilute gases governed by the Boltzmann equation. We
develop a mathematical theory to study the time decay and continuity of
Boltzmann solutions for four basic types of boundary conditions: inflow,
bounce-back reflection, specular reflection, and diffuse reflection. We
establish exponential decay in norm for hard potentials for
general classes of smooth domains near an absolute Maxwellian. Moreover, in
convex domains, we also establish continuity for these Boltzmann solutions away
from the grazing set of the velocity at the boundary. Our contribution is based
on a new decay theory and its interplay with delicate
decay analysis for the linearized Boltzmann equation, in the presence of many
repeated interactions with the boundary.Comment: 89 pages
Neumark Operators and Sharp Reconstructions, the finite dimensional case
A commutative POV measure with real spectrum is characterized by the
existence of a PV measure (the sharp reconstruction of ) with real
spectrum such that can be interpreted as a randomization of . This paper
focuses on the relationships between this characterization of commutative POV
measures and Neumark's extension theorem. In particular, we show that in the
finite dimensional case there exists a relation between the Neumark operator
corresponding to the extension of and the sharp reconstruction of . The
relevance of this result to the theory of non-ideal quantum measurement and to
the definition of unsharpness is analyzed.Comment: 37 page
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