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

System thermal-hydraulic modelling of the phénix dissymmetric test benchmark

Phénix is a French pool-type sodium-cooled prototype reactor; before the definitive shutdown, occurred in 2009, a final set of experimental tests are carried out in order to increase the knowledge on the operation and the safety aspect of the pool-type liquid metal-cooled reactors. One of the experiments was the Dissymmetric End-of-Life Test which was selected for the validation benchmark activity in the frame of SESAME project. The computer code validation plays a key role in the safety assessment of the innovative nuclear reactors and the Phénix dissymmetric test provides useful experimental data to verify the computer codes capability in the asymmetric thermal-hydraulic behaviour into a pool-type liquid metal-cooled reactor. This paper shows the comparison of the outcomes obtained with six different System Thermal-Hydraulic (STH) codes: RELAP5-3D©, SPECTRA, ATHLET, SAS4A/SASSYS-1, ASTEC-Na and CATHARE. The nodalization scheme of the reactor was individually achieved by the participants; during the development of the thermal-hydraulic model, the pool nodalization methodology had a special attention in order to investigate the capability of the STH codes to reproduce the dissymmetric effects which occur in each loop and into pools, caused by the azimuthal asymmetry of the boundary conditions. The modelling methodology of the participants is discussed and the main results are compared in this paper to obtain useful guide lines for the future modelling of innovative liquid metal pool-type reactors

Standard ion transfer potential at the water|butyronitrile interface

Butyronitrile is an organic solvent stable enough to be used in photochemical reactions at liquid/liquid interfaces. However, it provides a rather short polarisation window making the analysis of ion transfer across the water|butyronitrile interface challenging. Here, steady-state cyclic voltammetry, at microhole-supported micro-interfaces, was used to measure Gibbs energies of transfer. A linear relationship between the standard Gibbs energies of ion partition for the water|butyronitrile interface and the water|1,2-dichloroethane and water|nitrobencene interfaces was found, making easy to extrapolate the Gibbs energy of other ions from this empiric correlation.Fil: Riva, Julieta Soledad. Swiss Federal Institute Of Technology Epfl; Suiza. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Bassetto, V. C.. Swiss Federal Institute Of Technology Epfl; SuizaFil: Girault, Hubert. Swiss Federal Institute Of Technology Epfl; SuizaFil: Olaya, A. J.. Swiss Federal Institute Of Technology Epfl, Lausanne

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

Hydrovoltaic cells. Part II: Thermogalvanic cells and numerical simulations of thermal diffusion potentials

When two electrolyte solutions of different temperature are placed in contact, a thermal diffusion potential (TDP) is established. The phenomenon is studied numerically using finite element simulations of the temperature distribution within a hydrodynamic cell. Experimentally, the hydrovoltaic flow cell is used to demonstrate how a temperature difference can induce redox reactions at electrodes placed in the two liquids in order to extract a current continuously in an external circuit resulting in a power-generating unit. When the concentration of the redox couple introduced in the solution is moderated, it is shown that the TDP is not negligible, even if the main driving force is due to the temperature effect on the standard potential of the couple present. The numerical model may also be applied in more general situations involving thermal effects in microsystems

Numerical analysis and simulation of the dynamics of mountain glaciers

In this chapter, we analyze and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solutions are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice, which describes the time evolution of a glacier. The accumulation due to snow precipitation and melting are accounted for in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a two-grids method. As an illustration, we simulate the evolution of Aletsch glacier, Switzerland, over the 21st century by using realistic climatic conditions

Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systems

A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition. It is shown that intrachain fluctuations in the order parameter play a crucial role and must be treated exactly. The effect of these fluctuations is determined by a single dimensionless parameter. The three-dimensional transition temperature, the associated specific heat jump, coherence lengths, and width of the critical region, are computed assuming that the single chain Ginzburg-Landau coefficients are independent of temperature. The width of the critical region, estimated from the Ginzburg criterion, is virtually parameter independent, being about 5-8 per cent of the transition temperature. To appear in {\it Physical Review B,} March 1, 1995.Comment: 15 pages, RevTeX, 5 figures in uuencoded compressed tar file