46 research outputs found
Optimal quality of exceptional points for the Lebesgue density theorem
In spite of the Lebesgue density theorem, there is a positive such
that, for every non-trivial measurable set of real numbers, there is a
point at which both the lower densities of and of the complement of are
at least . The problem of determining the supremum of possible values
of this was studied in a paper of V. I. Kolyada, as well as in some
recent papers. We solve this problem in the present work.Comment: 45 page
On Witten multiple zeta-functions associated with semisimple Lie algebras IV
In our previous work, we established the theory of multi-variable Witten
zeta-functions, which are called the zeta-functions of root systems. We have
already considered the cases of types , , , and . In
this paper, we consider the case of -type. We define certain analogues of
Bernoulli polynomials of -type and study the generating functions of them
to determine the coefficients of Witten's volume formulas of -type. Next
we consider the meromorphic continuation of the zeta-function of -type and
determine its possible singularities. Finally, by using our previous method, we
give explicit functional relations for them which include Witten's volume
formulas.Comment: 22 pag
Crater formation by fast ions: comparison of experiment with Molecular Dynamics simulations
An incident fast ion in the electronic stopping regime produces a track of
excitations which can lead to particle ejection and cratering. Molecular
Dynamics simulations of the evolution of the deposited energy were used to
study the resulting crater morphology as a function of the excitation density
in a cylindrical track for large angle of incidence with respect to the surface
normal. Surprisingly, the overall behavior is shown to be similar to that seen
in the experimental data for crater formation in polymers. However, the
simulations give greater insight into the cratering process. The threshold for
crater formation occurs when the excitation density approaches the cohesive
energy density, and a crater rim is formed at about six times that energy
density. The crater length scales roughly as the square root of the electronic
stopping power, and the crater width and depth seem to saturate for the largest
energy densities considered here. The number of ejected particles, the
sputtering yield, is shown to be much smaller than simple estimates based on
crater size unless the full crater morphology is considered. Therefore, crater
size can not easily be used to estimate the sputtering yield.Comment: LaTeX, 7 pages, 5 EPS figures. For related figures/movies, see:
http://dirac.ms.virginia.edu/~emb3t/craters/craters.html New version uploaded
5/16/01, with minor text changes + new figure
(0,2) Deformations of Linear Sigma Models
We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma
model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear
sigma model these correspond to some of the holomorphic deformations of the
tangent bundle on the hypersurface. Combinatorial formulas are given for the
number of these deformations, and we show that these numbers are exchanged by
mirror symmetry in a subclass of the models.Comment: 35 pages; uses xy-fig; typos fixed, acknowledgments adde
Parametric Polyhedra with at least Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
Given an integral matrix , the well-studied affine semigroup
\mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be
stratified by the number of lattice points inside the parametric polyhedra
. Such families of parametric polyhedra appear in
many areas of combinatorics, convex geometry, algebra and number theory. The
key themes of this paper are: (1) A structure theory that characterizes
precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{
Sg}(A) such that has at least solutions. We
demonstrate that this set is finitely generated, it is a union of translated
copies of a semigroup which can be computed explicitly via Hilbert bases
computations. Related results can be derived for those right-hand-side vectors
for which has exactly solutions or fewer
than solutions. (2) A computational complexity theory. We show that, when
, are fixed natural numbers, one can compute in polynomial time an
encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function,
using a short sum of rational functions. As a consequence, one can identify all
right-hand-side vectors of bounded norm that have at least solutions. (3)
Applications and computation for the -Frobenius numbers. Using Generating
functions we prove that for fixed the -Frobenius number can be
computed in polynomial time. This generalizes a well-known result for by
R. Kannan. Using some adaptation of dynamic programming we show some practical
computations of -Frobenius numbers and their relatives
Efficient Performance of Electrostatic Spray-Deposited TiO2 Blocking Layers in Dye-Sensitized Solar Cells after Swift Heavy Ion Beam Irradiation
A compact TiO2 layer (~1.1 μm) prepared by electrostatic spray deposition (ESD) and swift heavy ion beam (SHI) irradiation using oxygen ions onto a fluorinated tin oxide (FTO) conducting substrate showed enhancement of photovoltaic performance in dye-sensitized solar cells (DSSCs). The short circuit current density (Jsc = 12.2 mA cm-2) of DSSCs was found to increase significantly when an ESD technique was applied for fabrication of the TiO2 blocking layer, compared to a conventional spin-coated layer (Jsc = 8.9 mA cm-2). When SHI irradiation of oxygen ions of fluence 1 × 1013 ions/cm2 was carried out on the ESD TiO2, it was found that the energy conversion efficiency improved mainly due to the increase in open circuit voltage of DSSCs. This increased energy conversion efficiency seems to be associated with improved electronic energy transfer by increasing the densification of the blocking layer and improving the adhesion between the blocking layer and the FTO substrate. The adhesion results from instantaneous local melting of the TiO2 particles. An increase in the electron transport from the blocking layer may also retard the electron recombination process due to the oxidized species present in the electrolyte. These findings from novel treatments using ESD and SHI irradiation techniques may provide a new tool to improve the photovoltaic performance of DSSCs
Recrystallization of amorphous nano-tracks and uniform layers generated by swift-ion-beam irradiation in lithium niobate.
The thermal annealing of amorphous tracks of nanometer-size diameter generated in lithium niobate (LiNbO3) by Bromine ions at 45 MeV, i.e., in the electronic stopping regime, has been investigated by RBS/C spectrometry in the temperature range from 250°C to 350°C. Relatively low fluences have been used (<1012 cm−2) to produce isolated tracks. However, the possible effect of track overlapping has been investigated by varying the fluence between 3×1011 cm−2 and 1012 cm−2. The annealing process follows a two-step kinetics. In a first stage (I) the track radius decreases linearly with the annealing time. It obeys an Arrhenius-type dependence on annealing temperature with activation energy around 1.5 eV. The second stage (II) operates after the track radius has decreased down to around 2.5 nm and shows a much lower radial velocity. The data for stage I appear consistent with a solid-phase epitaxial process that yields a constant recrystallization rate at the amorphous-crystalline boundary. HRTEM has been used to monitor the existence and the size of the annealed isolated tracks in the second stage. On the other hand, the thermal annealing of homogeneous (buried) amorphous layers has been investigated within the same temperature range, on samples irradiated with Fluorine at 20 MeV and fluences of ∼1014 cm−2. Optical techniques are very suitable for this case and have been used to monitor the recrystallization of the layers. The annealing process induces a displacement of the crystalline-amorphous boundary that is also linear with annealing time, and the recrystallization rates are consistent with those measured for tracks. The comparison of these data with those previously obtained for the heavily damaged (amorphous) layers produced by elastic nuclear collisions is summarily discussed
A topologically twisted index for three-dimensional supersymmetric theories
We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2
7S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to \u3a9-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2
7 T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants