159 research outputs found
Kazhdan-Lusztig polynomials, tight quotients and Dyck superpartitions
We give an explicit combinatorial product formula for the parabolic Kazhdan–Lusztig polynomials of the tight quotients of the symmetric group. This formula shows that these polynomials are always either zero or a monic power of q and implies the main result in [F. Brenti, Kazhdan–Lusztig and R-polynomials, Youngʼs lattice, and Dyck partitions, Pacific J. Math. 207 (2002) 257–286] on the parabolic Kazhdan–Lusztig polynomials of the maximal quotients. The formula depends on a new class of superpartitions
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
The combination of Index of NASH score and liver stiffness improves the noninvasive diagnostic accuracy for severe liver fibrosis in patients with NonAlcoholic Fatty Liver Disease.
Increased hepatic glucose production and insulin resistance in subjects with non-alcoholic fatty liver disease is associated to increased plasma concentrations of glucogenic amino acids
Hepatic macrophage activation is associated with adipose tissue insulin resistance in non-diabetic patients with Non-Alcoholic Fatty Liver Disease
Angiopoietin like protein 4 (ANGPTL4): a marker of alteration in lipid metabolism, insulin resistance and ectopic fat accumulation
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