1,141 research outputs found
Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect
We study the inverse boundary value problems for the Schr\"{o}dinger
equations with Yang-Mills potentials in a bounded domain
containing finite number of smooth obstacles . We
prove that the Dirichlet-to-Neumann operator on determines
the gauge equivalence class of the Yang-Mills potentials. We also prove that
the metric tensor can be recovered up to a diffeomorphism that is identity on
.Comment: 15 page
Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach
We describe the general setting for the optical Aharonov-Bohm effect based on
the inverse problem of the identification of the coefficients of the governing
hyperbolic equation by the boundary measurements. We interpret the inverse
problem result as a possibility in principle to detect the optical
Aharonov-Bohm effect by the boundary measurements.Comment: 34 pages. Minor changes, references adde
Counting generalized Jenkins-Strebel differentials
We study the combinatorial geometry of "lattice" Jenkins--Strebel
differentials with simple zeroes and simple poles on and of the
corresponding counting functions. Developing the results of M. Kontsevich we
evaluate the leading term of the symmetric polynomial counting the number of
such "lattice" Jenkins-Strebel differentials having all zeroes on a single
singular layer. This allows us to express the number of general "lattice"
Jenkins-Strebel differentials as an appropriate weighted sum over decorated
trees.
The problem of counting Jenkins-Strebel differentials is equivalent to the
problem of counting pillowcase covers, which serve as integer points in
appropriate local coordinates on strata of moduli spaces of meromorphic
quadratic differentials. This allows us to relate our counting problem to
calculations of volumes of these strata . A very explicit expression for the
volume of any stratum of meromorphic quadratic differentials recently obtained
by the authors leads to an interesting combinatorial identity for our sums over
trees.Comment: to appear in Geometriae Dedicata. arXiv admin note: text overlap with
arXiv:1212.166
Triangulations and volume form on moduli spaces of flat surfaces
In this paper, we are interested in flat metric structures with conical
singularities on surfaces which are obtained by deforming translation surface
structures. The moduli space of such flat metric structures can be viewed as
some deformation of the moduli space of translation surfaces. Using geodesic
triangulations, we define a volume form on this moduli space, and show that, in
the well-known cases, this volume form agrees with usual ones, up to a
multiplicative constant.Comment: 42 page
Of (flying) pigs and (black) swans: strengths and limitations of a risk-based food safety system for handling potential emerging pork risks
‘Black swans’ are a widely used metaphor for surprising, extreme events, generally with devastating consequences, that lie far outside the realm of anticipated possibility. Because they are inherently challenging to predict using traditional probability theory, black swans pose formidable challenges to risk analysis and risk management, regardless of whether the event is truly unknown to the scientific community (‘unknown unknowns’) or whether it is merely not known or adequately considered by the relevant parties
Shear stress induced stimulation of mammalian cell metabolism
A flow apparatus was developed for the study of the metabolic response of anchorage dependent cells to a wide range of steady and pulsatile shear stresses under well controlled conditions. Human umbilical vein endothelial cell monolayers were subjected to steady shear stresses of up to 24 dynes/sq cm, and the production of prostacyclin was determined. The onset of flow led to a burst in prostacyclin production which decayed to a long term steady state rate (SSR). The SSR of cells exposed to flow was greater than the basal release level, and increased linearly with increasing shear stress. It is demonstrated that shear stresses in certain ranges may not be detrimental to mammalian cell metabolism. In fact, throughout the range of shear stresses studied, metabolite production is maximized by maximizing shear stress
Formation of hot tear under controlled solidification conditions
Aluminum alloy 7050 is known for its superior mechanical properties, and thus finds its application in aerospace industry. Vertical direct-chill (DC) casting process is typically employed for producing such an alloy. Despite its advantages, AA7050 is considered as a "hard-to-cast" alloy because of its propensity to cold cracking. This type of cracks occurs catastrophically and is difficult to predict. Previous research suggested that such a crack could be initiated by undeveloped hot tears (microscopic hot tear) formed during the DC casting process if they reach a certain critical size. However, validation of such a hypothesis has not been done yet. Therefore, a method to produce a hot tear with a controlled size is needed as part of the verification studies. In the current study, we demonstrate a method that has a potential to control the size of the created hot tear in a small-scale solidification process. We found that by changing two variables, cooling rate and displacement compensation rate, the size of the hot tear during solidification can be modified in a controlled way. An X-ray microtomography characterization technique is utilized to quantify the created hot tear. We suggest that feeding and strain rate during DC casting are more important compared with the exerted force on the sample for the formation of a hot tear. In addition, we show that there are four different domains of hot-tear development in the explored experimental window-compression, microscopic hot tear, macroscopic hot tear, and failure. The samples produced in the current study will be used for subsequent experiments that simulate cold-cracking conditions to confirm the earlier proposed model.This research was carried out within the Materials innovation institute (www.m2i.nl) research framework, project no. M42.5.09340
Inverse Scattering for Gratings and Wave Guides
We consider the problem of unique identification of dielectric coefficients
for gratings and sound speeds for wave guides from scattering data. We prove
that the "propagating modes" given for all frequencies uniquely determine these
coefficients. The gratings may contain conductors as well as dielectrics and
the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page
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