1,880 research outputs found
A Fast Algorithm for Computing the p-Curvature
We design an algorithm for computing the -curvature of a differential
system in positive characteristic . For a system of dimension with
coefficients of degree at most , its complexity is \softO (p d r^\omega)
operations in the ground field (where denotes the exponent of matrix
multiplication), whereas the size of the output is about . Our
algorithm is then quasi-optimal assuming that matrix multiplication is
(\emph{i.e.} ). The main theoretical input we are using is the
existence of a well-suited ring of series with divided powers for which an
analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo
Supergeometry and Arithmetic Geometry
We define a superspace over a ring as a functor on a subcategory of the
category of supercommutative -algebras. As an application the notion of a
-adic superspace is introduced and used to give a transparent construction
of the Frobenius map on -adic cohomology of a smooth projective variety over
the ring of -adic integers.Comment: 14 pages, expanded introduction, more detail
Sound propagation over uneven ground and irregular topography
The goal of this research is to develop theoretical, computational, and experimental techniques for predicting the effects of irregular topography on long range sound propagation in the atmosphere. Irregular topography here is understood to imply a ground surface that is not idealizable as being perfectly flat or that is not idealizable as having a constant specific acoustic impedance. The interest of this study focuses on circumstances where the propagation is similar to what might be expected for noise from low-attitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence. The activities and developments that have resulted during the period, August 1986 through February 1987, are discussed
Sound propagation over uneven ground and irregular topography
Theoretical, computational, and experimental techniques were developed for predicting the effects of irregular topography on long range sound propagation in the atmosphere. Irregular topography is understood to imply a ground surface that: (1) is not idealizable as being perfectly flat, or (2) that is not idealizable as having a constant specific acoustic impedance. The focus is on circumstances where the propagation is similar to what might be expected for noise from low altitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence
Ice Formation on Kaolinite: Insights from Molecular Dynamics Simulations
The formation of ice affects many aspects of our everyday life as well as
technologies such as cryotherapy and cryopreservation. Foreign substances
almost always aid water freezing through heterogeneous ice nucleation, but the
molecular details of this process remain largely unknown. In fact, insight into
the microscopic mechanism of ice formation on different substrates is difficult
to obtain even via state-of-the-art experimental techniques. At the same time,
atomistic simulations of heterogeneous ice nucleation frequently face
extraordinary challenges due to the complexity of the water-substrate
interaction and the long timescales that characterize nucleation events. Here,
we have investigated several aspects of molecular dynamics simulations of
heterogeneous ice nucleation considering as a prototypical ice nucleating
material the clay mineral kaolinite, which is of relevance in atmospheric
science. We show via seeded molecular dynamics simulations that ice nucleation
on the hydroxylated (001) face of kaolinite proceeds exclusively via the
formation of the hexagonal ice polytype. The critical nucleus size is two times
smaller than that obtained for homogeneous nucleation at the same supercooling.
Previous findings suggested that the flexibility of the kaolinite surface can
alter the time scale for ice nucleation within molecular dynamics simulations.
However, we here demonstrate that equally flexible (or non flexible) kaolinite
surfaces can lead to very different outcomes in terms of ice formation,
according to whether or not the surface relaxation of the clay is taken into
account. We show that very small structural changes upon relaxation
dramatically alter the ability of kaolinite to provide a template for the
formation of a hexagonal overlayer of water molecules at the water-kaolinite
interface, and that this relaxation therefore determines the nucleation ability
of this mineral
3D-printed system optimizing dissolution of hyperpolarized gaseous species for micro-sized NMR
International audienceDissolution of hyperpolarized species in liquids of interest for NMR is often hampered by the presence of bubbles that degrade the field homogeneity. Here a device constituted by a bubble pump and a miniaturized NMR cell fitting both inside the narrow bore of an NMR magnet is built by 3D printing. 129Xe NMR experiments performed with hyperpolarized xenon reveal high and homogeneous dissolution of the gas in water
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