169,233 research outputs found
Non-Gaussian statistical models of surface wave fields for remote sensing applications
Based on the complete Stokes wave model with the bias term and using a simple mapping approach and an iteration solution method, we established a formula for the joint probability density function of the surface slope elevation of a nonlinear random wave field. The formula requires three parameters to define the whole density function: the rms surface elevation and slope values and the significant slope. This model represents the dynamics of the wave in a more direct way than the Gram-Charlier approximation. Based on this new statistical model and laboratory experiments, formula and numerical values of EM bias and dynamics bias are derived. The results indicate that various biases should be considered seriously if accuracy of the altimeter measurement is required in centimeter range
Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain
Using computer simulations of over 100,000 atoms, the mechanism for the
hydrophobic collapse of an idealized hydrated chain is obtained. This is done
by coarse-graining the atomistic water molecule positions over 129,000
collective variables that represent the water density field and then using the
string method in these variables to compute the minimum free energy pathway
(MFEP) for the collapsing chain. The dynamical relevance of the MFEP (i.e. its
coincidence with the mechanism of collapse) is validated a posteriori using
conventional molecular dynamics trajectories. Analysis of the MFEP provides
atomistic confirmation for the mechanism of hydrophobic collapse proposed by
ten Wolde and Chandler. In particular, it is shown that lengthscale-dependent
hydrophobic dewetting is the rate-limiting step in the hydrophobic collapse of
the considered chain.Comment: 11 pages, 7 figures, including supporting informatio
The Near Field Refractor
We present an abstract method in the setting of compact metric spaces which
is applied to solve a number of problems in geometric optics. In particular, we
solve the one source near field refraction problem. That is, we construct
surfaces separating two homogenous media with different refractive indices that
refract radiation emanating from the origin into a target domain contained in
an n-1 dimensional hypersurface. The input and output energy are prescribed.
This implies the existence of lenses focusing radiation in a prescribed manner.Comment: 39 pages, 4 figures, Annales de l'Institut Henri Poincare (C) Analyse
Non Lineaire (to appear). Geometric optics, lens design, measure equations,
Descartes ovals, Monge-Ampere type equation
Canonical Filtrations of Gorenstein Injective Modules
The principle "Every result in classical homological algebra should have a
counterpart in Gorenstein homological algebra" is given in [3]. There is a
remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps
one of the most glaring exceptions is provided by the fact that tensor products
of Gorenstein projective modules need not be Gorenstein projective, even over
Gorenstein rings. So perhaps it is surprising that tensor products of
Gorenstein injective modules over Gorenstein rings of finite Krull dimension
are Gorenstein injective.
Our main result is in support of the principle. Over commutative, noetherian
rings injective modules have direct sum decompositions into indecomposable
modules. We will show that Gorenstein injective modules over Gorenstein rings
of finite Krull dimension have filtrations analogous to those provided by these
decompositions. This result will then provide us with the tools to prove that
all tensor products of Gorenstein injective modules over these rings are
Gorenstein injective.Comment: 9 pages; It has been accepted for publication in Proceedings of the
American Mathematical Societ
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