20,485 research outputs found
Time-resolved spectroscopic measurements behind incident and reflected shock waves in air and xenon
Time-resolved spectra have been obtained behind incident and reflected shock waves in air and xenon at initial pressures of 0.1 and 1.0 torr using a rotating drum spectrograph and the OSU (The Ohio State University) arc-driven shock tube. These spectra were used to determine the qualitative nature of the flow as well as for making estimates of the available test time. The (n+1,n) and (n,n) band spectra of N2(+) (1st negative) were observed in the test gas behind incident shock waves in air at p1=1.0 torr and Us=9-10 km/sec. Behind reflected shock waves in air, the continuum of spectra appeared to cover almost the entire wavelength of 2,500-7,000 A for the shock-heated test gas. For xenon, the spectra for the incident shock wave cases for p1=0.1 torr show an interesting structure in which two intensely bright regions are witnessed in the time direction. The spectra obtained behind reflected shock waves in xenon were also dominated by continuum radiation but included strong absorption spectra due to FeI and FeII from the moment the reflected shock passed and on
Exponents of 2-multiarrangements and multiplicity lattices
We introduce a concept of multiplicity lattices of 2-multiarrangements,
determine the combinatorics and geometry of that lattice, and give a criterion
and method to construct a basis for derivation modules effectively.Comment: 14 page
Freeness of hyperplane arrangements and related topics
This is the expanded notes of the lecture by the author in "Arrangements in
Pyrenees", June 2012. We are discussing relations of freeness and splitting
problems of vector bundles, several techniques proving freeness of hyperplane
arrangements, K. Saito's theory of primitive derivations for Coxeter
arrangements, their application to combinatorial problems and related
conjectures.Comment: 28 page
Resonant bands, Aomoto complex, and real 4-nets
The resonant band is a useful notion for the computation of the nontrivial
monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this
article, we develop the resonant band description for the cohomology of the
Aomoto complex. As an application, we prove that real 4-nets do not exist.Comment: 23 pages, 7 figure
A vanishing result for the first twisted cohomology of affine varieties and applications to line arrangements
A general vanishing result for the first cohomology group of affine smooth
complex varieties with values in rank one local systems is established. This is
applied to the determination of the monodromy action on the first cohomology
group of the Milnor fiber of some line arrangements, including the monomial
arrangement and the exceptional reflection arrangement of type
Logarithmic vector fields for quasihomogeneous curve configurations in P^2
Let A be a union of smooth plane curves C_i, such that each singular point of
A is quasihomogeneous. We prove that if C is a smooth curve such that each
singular point of A U C is also quasihomogeneous, then there is an elementary
modification of rank two bundles, which relates the O_{P^2} module Der(log A)
of vector fields on P^2 tangent to A to the module Der(log A U C). This yields
an inductive tool for studying the splitting of the bundles Der(log A) and
Der(log A U C), depending on the geometry of the divisor A|_C on C.Comment: 10 pages 2 figure
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