943 research outputs found
Uncovering Ramanujan's "Lost" Notebook: An Oral History
Here we weave together interviews conducted by the author with three
prominent figures in the world of Ramanujan's mathematics, George Andrews,
Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the
"lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's
notes, and recent breakthroughs by Ono and others carrying certain important
aspects of the Indian mathematician's work into the future. Also presented are
historical details related to Ramanujan and his mathematics, perspectives on
the impact of his work in contemporary mathematics, and a number of interesting
personal anecdotes from Andrews, Berndt and Ono
Hamiltonian Analysis of Non-Linear Sigma Model on Supercoset Target
This paper is devoted to the study of the Hamiltonian formulation of
non-linear sigma models on supercoset targets. We calculate the Poisson
brackets of left-invariant currents. Then we introduce the Hamiltonian of the
system and determine the equations of motion for left-invariant currents. We
also determine the charge corresponding to the invariance of the action under
global left multiplication.Comment: 17. pages,v2: references added, v3: references added, minor
correction
Recommended from our members
Vacancy and interstitial loops in irradiated copper
Significant advances have been made in diffuse scattering studies of irradiation induced dislocation loops in metals. Numerical calculational procedures have been developed that provide accurate diffuse scattering cross sections for vacancy and interstitial loops, and these cross sections have been used in conjunction with x-ray diffuse scattering studies of neutron and ion irradiated copper. Size distributions and concentrations have been obtained for both vacancy and interstitial loops and these results are compared with electron microscopy measurements. The size distributions obtained from diffuse scattering measurements show the vacancy loops to be smaller and more numerous than the interstitial loops, and indicate that equal numbers of vacancies and interstitials are in loops. The diffuse scattering and microscopy size distributions agree at the larger sizes, but the diffuse scattering method identifies more loops of the smaller sizes
Nonlocal charges of T-dual strings
We obtain sets of infinite number of conserved nonlocal charges of strings in
a flat space and pp-wave backgrounds, and compare them before and after
T-duality transformation. In the flat background the set of nonlocal charges is
the same before and after the T-duality transformation with interchanging odd
and even-order charges. In the IIB pp-wave background an infinite number of
nonlocal charges are independent, contrast to that in a flat background only
the zero-th and first order charges are independent. In the IIA pp-wave
background, which is the T-dualized compactified IIB pp-wave background, the
zero-th order charges are included as a part of the set of nonlocal charges in
the IIB background. To make this correspondence complete a variable conjugate
to the winding number is introduced as a Lagrange multiplier in the IIB action
a la Buscher's transformation.Comment: 23 pages, 1 figur
Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux
in various dimensions. We realize the backgrounds as supercosets and analyze
explicitly two classes of models: non-critical superstrings on AdS_{2d} and
critical superstrings on AdS_p\times S^p\times CY. We work both in the
Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter
family of flat currents (a Lax connection) leading to an infinite number of
conserved non-local charges, which imply the classical integrability of both
sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove
the quantum integrability of the sigma-model. We discuss how classical
\kappa-symmetry implies one-loop conformal invariance. We consider the addition
of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos
fixed in some equations; v3: typos fixed to match the published versio
Mineral exploration in the Cockermouth area, Cumbria. Part 2: follow-up surveys
This report describes the results of geochemical, geological and geophysical surveys across three
small areas of Carboniferous and Lower Palaeozoic rocks along the northern margin of the English
Lake District. The areas were chosen from the appraisal of regional-scale survey data described by
Cooper et al. (1991). In two of the areas, Ruthwaite and Tallentire, the objective was to provide
more information on the extent and magnitude of fracture-controlled epigenetic baryte and base
metal mineralisation. In the third area, at Whitrigg, brief surveys were carried out to aid the
interpretation of unexplained geochemical and geophysical anomalies found during two projects
carried out under the Mineral Exploration and Investment Grants Act (MEIGA).
At Ruthwaite, where a mine formerly worked baryte from a fault separating Lower Palaeozoic and
Carboniferous rocks, surface indications of further baryte mineralisation were found. Soil analyses
indicated that mineralisation may be present along the continuation of the faultline worked at
Ruthwaite and in the Eycott Volcanic Group rocks to the south of it. In this area relatively small,
but in some circumstances perhaps economically attractive, deposits of baryte may be present
under drift cover.
In the Tallentire Hill area, geological mapping followed by traverse-based soil sampling showed
that fracture-controlled mineralisation is widespread in the Carboniferous (Dinantian and
Namurian) rocks. The fracture fillings consist dominantly of baryte, often accompanied by
carbonate, with traces of copper and mercury. Where seen at surface the fracture fillings are too
small, patchy and low-grade to be of any economic importance. Baryte mineralisation also occurs
locally as patchy impregnations in sandstones. These are considered to be epigenetic deposits
related to the fracture-controlled mineralisation. Trial geophysical surveys suggested that electrical
methods may be useful in determining the extent of the mineralised sandstone. There is a
possibility that more extensive baryte deposits may be present in the limestone succession
underlying the mineralised sandstones.
In the Whitrigg area, Carboniferous rocks are separated from Lower Palaeozoic rocks of the
Eycott Volcanic Group by the easterly-trending Boundary Fault and north-westerly-trending
Bothel Fault. Evidence from an old mineral working and the results of a soil survey indicate that
patchy, epigenetic, fracture-controlled baryte and base metal mineralisation occurs along the
Bothel Fault and, locally, in the adjacent rocks. A feature of this mineralisation is the presence of
mercury, which is most abundant in a sample of brecciated and altered rock from the Eycott
Volcanic Group. Prominent base metal in soil anomalies discovered by MEIGA-funded projects
near Stangerhill are not associated with barium anomalies. It was concluded that these soil
anomalies are most likely to be caused by secondary concentration in overburden, and that the
source of metals may be a sub-cropping metalliferous horizon within the Carboniferous succession
or, more probably, fracture-controlled mineralisation.
Trial geophysical surveys carried out in all three areas indicated that in ground free of artificial
sources the VLF(EM) and conductivity mapping methods could be useful for tracing faults beneath
drift and providing information on drift thickness. Closely-spaced soil sampling proved effective for
detecting mineralisation in areas where the drift cover is thin, and a trial soil-gas survey showed
that this technique could also be useful for tracing faults beneath drift
Determining Reheating Temperature at Colliders with Axino or Gravitino Dark Matter
After a period of inflationary expansion, the
Universe reheated and reached full thermal equilibrium at the reheating
temperature T_R. In this work we point out that, in the context of effective
low-energy supersymmetric models, LHC measurements may allow one to determine
T_R as a function of the mass of the dark matter particle assumed to be either
an axino or a gravitino. An upper bound on their mass may also be derived.Comment: 19 pages, some improvements, JHEP versio
Rms-flux relation in the optical fast variability data of BL Lacertae object S5 0716+714
The possibility that BL Lac S5 0716+714 exhibits a linear root mean square
(rms)-flux relation in its IntraDay Variability (IDV) is analysed. The results
may be used as an argument in the existing debate regarding the source of
optical IDV in Active Galactic Nuclei. 63 time series in different optical
bands were used. A linear rms-flux relation at a confidence level higher than
65% was recovered for less than 8% of the cases. We were able to check if the
magnitude is log-normally distributed for eight timeseries and found, with a
confidence > 95%, that this is not the case.Comment: Accepted by Astrophysics and Space Scienc
Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards
We present a simple method to stabilize the optical path length of an optical
fiber to an accuracy of about 1/100 of the laser wavelength. We study the
dynamic response of the path length to modulation of an electrically conductive
heater layer of the fiber. The path length is measured against the laser
wavelength by use of the Pound-Drever-Hall method; negative feedback is applied
via the heater. We apply the method in the context of a cryogenic resonator
frequency standard.Comment: Expanded introduction and outlook. 9 pages, 5 figure
A high stability semiconductor laser system for a Sr-based optical lattice clock
We describe a frequency stabilized diode laser at 698 nm used for high
resolution spectroscopy of the 1S0-3P0 strontium clock transition. For the
laser stabilization we use state-of-the-art symmetrically suspended optical
cavities optimized for very low thermal noise at room temperature. Two-stage
frequency stabilization to high finesse optical cavities results in measured
laser frequency noise about a factor of three above the cavity thermal noise
between 2 Hz and 11 Hz. With this system, we demonstrate high resolution remote
spectroscopy on the 88Sr clock transition by transferring the laser output over
a phase-noise-compensated 200 m-long fiber link between two separated
laboratories. Our dedicated fiber link ensures a transfer of the optical
carrier with frequency stability of 7 \cdot 10^{-18} after 100 s integration
time, which could enable the observation of the strontium clock transition with
an atomic Q of 10^{14}. Furthermore, with an eye towards the development of
transportable optical clocks, we investigate how the complete laser system
(laser+optics+cavity) can be influenced by environmental disturbances in terms
of both short- and long-term frequency stability.Comment: 9 pages, 9 figures, submitted to Appl. Phys.
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