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

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

Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily

A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows

In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independent from the time evolution step. We present a theoretical analysis of the method, and give results for several numerical tests on benchmark problems which both illustrate the theory and show the proposed method's effectiveness

CO2 capture and conversion: A homemade experimental approach

During the SARS-2-Covid pandemic our institution sought to continue the teaching and learning of experimental laboratories by designing, assembling, and delivering a microscale chemistry kit to the students’ homes. Thanks to this approach students were able to perform ~25 experiments during each one of the Fall 2020 and Spring 2021 semesters in an elective Electrochemistry and Corrosion course offered to Chemical Engineering undergraduates. In addition to performing traditional experiments, students were encouraged to design some of their own and have the entire group reproduce them. One of such student-designed experiments involved the capture of CO2 and its reduction with a readily available active metal (i.e., Al foil) in aqueous media to generate potentially useful products. The highly negative standard potential of Al is exploited for the reduction of lab-generated CO2, and the products are chemically tested. Al as a foil has been reported to be electrochemically inactive for carbon dioxide reduction. However, encouraged by an earlier report of the reduction of CO2 to CO, the Al surface is activated in the present experiment by removal of its natural oxide layer with a solution of CuCl 2 produced in an electrochemical cell. This procedure enables Al to react with CO2 and yield useful chemistry. This experiment turned to be a discovery trip. The detailed procedure is discussed here, as well as the teaching methodology, grading scheme, and student outcomesPeer Reviewe

Blue light effects on rose photosynthesis and photomorphogenesis

Through its impact on photosynthesis and morphogenesis, light is the environmental factor that most affects plant architecture. Using light rather than chemicals to manage plant architecture could reduce the impact on the environment. However, the understanding of how light modulates plant architecture is still poor and further research is needed. To address this question, we examined the development of two rose cultivars, Rosa hybrida‘Radrazz’ and Rosa chinensis‘Old Blush’, cultivated under two light qualities. Plants were grown from one-node cuttings for 6 weeks under white or blue light at equal photosynthetic efficiencies. While plant development was totally inhibited in darkness, blue light could sustain full development from bud burst until flowering. Blue light reduced the net CO2 assimilation rate of fully expanded leaves in both cultivars, despite increasing stomatal conductance and intercellular CO2 concentrations. In ‘Radrazz’, the reduction in CO2 assimilation under blue light was related to a decrease in photosynthetic pigment content, while in both cultivars, the chl a/b ratio increased. Surprisingly, blue light could induce the same organogenetic activity of the shoot apical meristem, growth of the metamers and flower development as white light. The normal development of rose plants under blue light reveals the strong adaptive properties of rose plants to their light environment. It also indicates that photomorphogenetic processes can all be triggered by blue wavelengths and that despite a lower assimilation rate, blue light can provide sufficient energy via photosynthesis to sustain normal growth and development in roses

Colored Petri Nets to Verify Extended Event-Driven Process Chains

Business processes are becoming more and more complex and at the same time their correctness is becoming a critical issue: The costs of errors in business information systems are growing due to the growing scale of their application and the growing degree of automation. In this paper we consider Extended Event-driven Process Chains (eEPCs), a language which is widely used for modeling business processes, documenting industrial reference models and designing workflows. We describe how to translate eEPCs into timed colored Petri nets in order to verify processes given by eEPCs with the CPN Tools