10,023 research outputs found
On the particle paths and the stagnation points in small-amplitude deep-water waves
In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
arXiv:1106.382
Robust formation of morphogen gradients
We discuss the formation of graded morphogen profiles in a cell layer by
nonlinear transport phenomena, important for patterning developing organisms.
We focus on a process termed transcytosis, where morphogen transport results
from binding of ligands to receptors on the cell surface, incorporation into
the cell and subsequent externalization. Starting from a microscopic model, we
derive effective transport equations. We show that, in contrast to morphogen
transport by extracellular diffusion, transcytosis leads to robust ligand
profiles which are insensitive to the rate of ligand production
Influence of RANEY nickel on the formation of intermediates in the degradation of lignin
Lignin forms an important part of lignocellulosic biomass and is an abundantly available residue. It is a potential renewable source of phenol. Liquefaction of enzymatic hydrolysis lignin as well as catalytical hydrodeoxygenation of the main intermediates in the degradation of lignin, that is, catechol and guaiacol, was studied. The cleavage of the ether bonds, which are abundant in the molecular structure of lignin, can be realised in near-critical water (573 to 673 K, 20 to 30MPa). Hydrothermal treatment in this context provides high selectivity in respect to hydroxybenzenes, especially catechol. RANEY Nickel was found to be an adequate catalyst for hydrodeoxygenation. Although it does not influence the cleavage of ether bonds, RANEY Nickel favours the production of phenol from both lignin and catechol. The main product from hydrodeoxygenation of guaiacol with RANEY Nickel was cyclohexanol. Reaction mechanism and kinetics of the degradation of guaiacol were explored
Breeding Yellow-flowered Alfalfa for Combined Wildlife Habitat and Forage Purposes
The objectives of our research were to: • evaluate a wide array of alfalfa germplasm containing varied levels of M. sativa ssp. falcata for traits related to suitability for stockpiling and nesting cover for game birds, •compare yellow-flowered cultivars and germplasms to conventional hay- and pasture-type cultivars for forage yield and quality in a delayed single-harvest / production system, and • develop, by phenotypic selection, one or more synthetic cultivars of yellow-flowered alfalfa that would have high forage yield, tolerance to potato leafhopper yellowing, prolonged flowering, and good leaf retention under a stockpiling management system until mid-July
Morphogen Transport in Epithelia
We present a general theoretical framework to discuss mechanisms of morphogen
transport and gradient formation in a cell layer. Trafficking events on the
cellular scale lead to transport on larger scales. We discuss in particular the
case of transcytosis where morphogens undergo repeated rounds of
internalization into cells and recycling. Based on a description on the
cellular scale, we derive effective nonlinear transport equations in one and
two dimensions which are valid on larger scales. We derive analytic expressions
for the concentration dependence of the effective diffusion coefficient and the
effective degradation rate. We discuss the effects of a directional bias on
morphogen transport and those of the coupling of the morphogen and receptor
kinetics. Furthermore, we discuss general properties of cellular transport
processes such as the robustness of gradients and relate our results to recent
experiments on the morphogen Decapentaplegic (Dpp) that acts in the fruit fly
Drosophila
Steady water waves with multiple critical layers: interior dynamics
We study small-amplitude steady water waves with multiple critical layers.
Those are rotational two-dimensional gravity-waves propagating over a perfect
fluid of finite depth. It is found that arbitrarily many critical layers with
cat's-eye vortices are possible, with different structure at different levels
within the fluid. The corresponding vorticity depends linearly on the stream
function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid
Mec
Self-organization and Mechanical Properties of Active Filament Bundles
A phenomenological description for active bundles of polar filaments is
presented. The activity of the bundle results from crosslinks, that induce
relative displacements between the aligned filaments. Our generic description
is based on momentum conservation within the bundle. By specifying the internal
forces, a simple minimal model for the bundle dynamics is obtained, capturing
generic dynamic behaviors. In particular, contracted states as well as solitary
and oscillatory waves appear through dynamic instabilities. The introduction of
filament adhesion leads to self-organized persistent filament transport.
Furthermore, calculating the tension, homogeneous bundles are shown to be able
to actively contract and to perform work against external forces. Our
description is motivated by dynamic phenomena in the cytoskeleton and could
apply to stress-fibers and self-organization phenomena during cell-locomotion.Comment: 19 pages, 10 figure
The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
In the present study we prove rigorously that in the long-wave limit, the
unidirectional solutions of a class of nonlocal wave equations to which the
improved Boussinesq equation belongs are well approximated by the solutions of
the Camassa-Holm equation over a long time scale. This general class of
nonlocal wave equations model bidirectional wave propagation in a nonlocally
and nonlinearly elastic medium whose constitutive equation is given by a
convolution integral. To justify the Camassa-Holm approximation we show that
approximation errors remain small over a long time interval. To be more
precise, we obtain error estimates in terms of two independent, small, positive
parameters and measuring the effect of nonlinearity and
dispersion, respectively. We further show that similar conclusions are also
valid for the lower order approximations: the Benjamin-Bona-Mahony
approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System
- …