Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

Procedimiento conciliatorio en Colombia

La conciliación es uno de los mecanismos alternativos de solución de conflictos más importantes y desarrollados en Colombia. Pese a que las normas legales que rigen la materia son las mismas, en la práctica parece que los conciliadores y centros de conciliación aplican el procedimiento de manera diferente. El presente texto tiene como objetivo poner a disposición de las personas interesadas en la conciliación una descripción de las etapas que integran el procedimiento conciliatorio. El análisis jurídico del procedimiento empieza con los requisitos de la solicitud de conciliación y termina con el seguimiento que se debe hacer al resultado del servicio ofrecido. Para el desarrollo de la presente obra, se integra la legislación, la jurisprudencia y los conceptos de línea institucional del Ministerio del Interior y de Justicia con ejemplos sencillos que permiten un mejor entendimiento de los conceptos que se quieren dar a conocer

FROG characterisation of SOA-based wavelength conversion using XPM in conjunction with shifted filtering up to line rates of 80 GHz

The work we present here builds on recent work where we obtained 80 Gb/s error free performance using cross phase modulation (XPM) in an SOA in conjunction with a blue shifted bandpass filter. Here we present a detailed characterisation of this wavelength conversion scheme using a Frequency Resolved Optical Gating (FROG) measurement scheme for both red and blue shifted filtering. This type of characterisation has not been provided before to the best of our knowledge and is an important analysis firstly to achieve a full understanding of the gain and phase dynamics exploited by the wavelength conversion scheme presented and secondly to design a filter so that an optimum performance can be obtaine

Analysis of bit rate dependence up to 80 Gbit/s of a simple wavelength converter based on XPM in a SOA and a shifted filtering

This paper provides the analysis of wavelength converted pulses obtained with a simple semiconductor optical amplifier (SOA)-based wavelength conversion scheme, which exploits cross phase modulation (XPM) in an SOA in conjunction with shifted filtering. The analysis includes experimental measurements of the back-to-back system performances as well as frequency-resolved optical gating (FROG) characterisations of the wavelength converted pulses. These measurements are implemented at different bit rates up to 80 Gbit/s and for both red and blue-shifted filtering, particularly showing different patterning effect dependencies of red and blue-shifting techniques. This analysis is developed by the addition of a numerical study which corroborates the experimental results. A further understanding of the different performances of red and blue filtering techniques, presented in the literature, can thus be proposed. The placement of the filter to undertake red-shifted filtering (RSF) allows us to achieve very short pulse widths but high bit rate operation is limited by pattern effects. The blue-shifted filtering (BSF) technique shows optimum performance as regards to patterning effects even if the wavelength converted pulses can be larger

Study of the conformation of DARPP-32, a dopamine- and cAMP-regulated phosphoprotein, by fluorescence spectroscopy.

DARPP-32 is a potent inhibitor of protein phosphatase 1 when it is phosphorylated on Thr34 by cAMP-dependent protein kinase. DARPP-32 is also phosphorylated on Ser45 and Ser102 by casein kinase II, resulting in a facilitation of phosphorylation by cAMP-dependent protein kinase. We have studied the conformation of recombinant rat DARPP-32 by steady-state and time-resolved fluorescence. The steady-state emission spectra and quenching of the intrinsic (Trp163) and extrinsic fluorescence (acrylodan or lucifer yellow linked to Cys72) were consistent with a complete exposure of these residues to the aqueous environment. The intrinsic fluorescence of DARPP-32 was resolved into three decay components with lifetimes of 1, 3.4, and 7 ns, with the intermediate lifetime component giving the major contribution. The ratio between the amplitudes associated with the short and long decay constants was decreased upon denaturation. The rotational behavior of DARPP-32 measured by anisotropy decay revealed that Trp163 is located in a highly flexible peptide chain, whereas Cys72 is embedded in a more rigid environment. Phosphorylation by cAMP-dependent protein kinase did not alter any of the fluorescence parameters, whereas only minor effects were associated with casein kinase II phosphorylation. These findings indicate that DARPP-32 contains at least two distinct domains and that phosphorylation has no dramatic effects on its conformation

On the numerical approximation of p-biharmonic and ∞-biharmonic functions

In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in L∞. The associated equation, coined the ∞-Bilaplacian, is a \emph{third order} fully nonlinear PDE given by Δ2∞u:=(Δu)3|D(Δu)|2=0. In this work we build a numerical method aimed at quantifying the nature of solutions to this problem which we call ∞-Biharmonic functions. For fixed p we design a mixed finite element scheme for the pre-limiting equation, the p-Bilaplacian Δ2pu:=Δ(|Δu|p−2Δu)=0. We prove convergence of the numerical solution to the weak solution of Δ2pu=0 and show that we are able to pass to the limit p→∞. We perform various tests aimed at understanding the nature of solutions of Δ2∞u and in 1-d we prove convergence of our discretisation to an appropriate weak solution concept of this problem, that of -solutions

AC electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications

Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK) phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across the semiconductor-electrolyte interface (consisting of the electric double layer (EDL) inside the electrolyte solutions and the space charge layer (SCL) inside the semiconductors) under AC electric fields with arbitrary wave forms. The present electrokinetic boundary conditions allow for evaluation of induced zeta potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Subsequently, we demonstrate the applications of these boundary conditions in analyzing the ACEK phenomena around a semiconducting cylinder. It is concluded that the flow circulations exist around the semiconducting cylinder and are shown to be stronger under an AC field with lower frequency and around a cylinder with higher conductivity.Comment: 29 pages, 4 figure