983 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
A new approach to hyperbolic inverse problems II (Global step)
We study the inverse problem for the second order self-adjoint hyperbolic
equation with the boundary data given on a part of the boundary. This paper is
the continuation of the author's paper [E]. In [E] we presented the crucial
local step of the proof. In this paper we prove the global step. Our method is
a modification of the BC-method with some new ideas. In particular, the way of
the determination of the metric is new.Comment: 21 pages, 2 figure
A new approach to hyperbolic inverse problems
We present a modification of the BC-method in the inverse hyperbolic
problems. The main novelty is the study of the restrictions of the solutions to
the characteristic surfaces instead of the fixed time hyperplanes. The main
result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a
part of the boundary uniquely determines the coefficients of the self-adjoint
hyperbolic operator up to a diffeomorphism and a gauge transformation. In this
paper we prove the crucial local step. The global step of the proof will be
presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that
potentials A(x),V(x) are real value
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
Inverse hyperbolic problems and optical black holes
In this paper we give a more geometrical formulation of the main theorem in
[E1] on the inverse problem for the second order hyperbolic equation of general
form with coefficients independent of the time variable. We apply this theorem
to the inverse problem for the equation of the propagation of light in a moving
medium (the Gordon equation). Then we study the existence of black and white
holes for the general hyperbolic and for the Gordon equation and we discuss the
impact of this phenomenon on the inverse problems
Strong wavefront lemma and counting lattice points in sectors
We compute the asymptotics of the number of integral quadratic forms with
prescribed orthogonal decompositions and, more generally, the asymptotics of
the number of lattice points lying in sectors of affine symmetric spaces. A new
key ingredient in this article is the strong wavefront lemma, which shows that
the generalized Cartan decomposition associated to a symmetric space is
uniformly Lipschitz
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
Recommended from our members
A linear mixed model approach to gene expression-tumor aneuploidy association studies.
Aneuploidy, defined as abnormal chromosome number or somatic DNA copy number, is a characteristic of many aggressive tumors and is thought to drive tumorigenesis. Gene expression-aneuploidy association studies have previously been conducted to explore cellular mechanisms associated with aneuploidy. However, in an observational setting, gene expression is influenced by many factors that can act as confounders between gene expression and aneuploidy, leading to spurious correlations between the two variables. These factors include known confounders such as sample purity or batch effect, as well as gene co-regulation which induces correlations between the expression of causal genes and non-causal genes. We use a linear mixed-effects model (LMM) to account for confounding effects of tumor purity and gene co-regulation on gene expression-aneuploidy associations. When applied to patient tumor data across diverse tumor types, we observe that the LMM both accounts for the impact of purity on aneuploidy measurements and identifies a new association between histone gene expression and aneuploidy
Influence of melt feeding scheme and casting parameters during direct-chill casting on microstructure of an AA7050 billet
© The Minerals, Metals & Materials Society and ASM International 2012Direct-chill (DC) casting billets of an AA7050 alloy produced with different melt feeding schemes and casting speeds were examined in order to reveal the effect of these factors on the evolution of microstructure. Experimental results show that grain size is strongly influenced by the casting speed. In addition, the distribution of grain sizes across the billet diameter is mostly determined by melt feeding scheme. Grains tend to coarsen towards the center of a billet cast with the semi-horizontal melt feeding, while upon vertical melt feeding the minimum grain size was observed in the center of the billet. Computer simulations were preformed to reveal sump profiles and flow patterns during casting under different melt feeding schemes and casting speeds. The results show that solidification front and velocity distribution of the melt in the liquid and slurry zones are very different under different melt feeding scheme. The final grain structure and the grain size distribution in a DC casting billet is a result of a combination of fragmentation effects in the slurry zone and the cooling rate in the solidification range
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
- …