Multielectron Redox Chemistry of Transition Metal Complexes Supported by a Non‐Innocent N3P2 Ligand: Synthesis, Characterization, and Catalytic Properties

A new redox‐active, diarylamido‐based ligand (LN3P2) capable of κ5‐N,N,N,P,P chelation has been used to prepare a series of complexes with the general formula [MII(LN3P2)]X, where M = Fe (1; X = OTf), Co (2; X = ClO4), or Ni (3; X = ClO4). The diarylamido core of monoanionic LN3P2 is derived from bis(2‐amino‐4‐methylphenyl)amine, which undergoes condensation with two equivalents of 2‐(diphenylphosphanyl)benzaldehyde to provide chelating arms with both arylphosphine and imine donors. X‐ray structural, magnetic, and spectroscopic studies indicate that the N3P2 coordination environment generally promotes low‐spin configurations. Three quasi‐reversible redox couples between +1.0 and –1.5 V (vs. Fc+/Fc) were observed in voltammetric studies of each complex, corresponding to MII/MIII oxidation, LN3P2‐based oxidation, and MII/MI reduction (in order of highest to lowest potential). Spectroscopic and computational analyses of 3ox – generated via chemical one‐electron oxidation of 3 – revealed that a stable diarylaminyl radical (LN3P2·) is formed upon oxidation. The ability of the CoII complex (2) to function as an electrocatalyst for H2 generation was evaluated in the presence of weak acids. Moderate activity was observed using 4‐tert‐butylphenol as the proton source at potentials below –2.0 V. The insights gained here will assist in the future design of pentadentate mixed N/P‐based chelates for catalytic processes

The Rhie-Chow stabilized Box Method for the Stokes problem

The Finite Volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the Rhie-Chow stabilized Box Method (RCBM) for the approximation of the Stokes problem. The Box Method (BM) is a piecewise linear Petrov-Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the Rhie-Chow (RC) stabilization is a well known stabilization technique for FVM. The first part of the paper provides a variational formulation of the RC stabilization and discusses the validity of crucial properties relevant for the well-posedeness and convergence of RCBM. Moreover, a numerical exploration of the convergence properties of the method on 2D and 3D test cases is presented. The last part of the paper considers the theoretically justification of the well-posedeness of RCBM and the experimentally observed convergence rates. This latter justification hinges upon suitable assumptions, whose validity is numerically explored.Comment: 27 pages, 6 figures, 4 table

A numerical investigation on the use of the virtual element method for topology optimization on polygonal meshes

A classical formulation of topology optimization addresses the problem of finding the best distribution of an assigned amount of isotropic material that minimizes the work of the external forces at equilibrium. In general, the discretization of the volume-constrained minimum compliance problem resorts to the adoption of four node displacement-based finite elements, coupled with element-wise density unknowns. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboarded patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of the members of the arising optimal design with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In light of the above remarks, in this contribution we consider polygonal meshes and implement the virtual element method (VEM) to solve two classes of topology optimization problems. The robustness of the adopted discretization is exploited to address problems governed by (nearly incompressible and compressible) linear elasticity and problems governed by Stokes equations. Numerical results show the capabilities of the proposed polygonal VEM-based approach with respect to more conventional discretizations

VEM and topology optimization on polygonal meshes

Topology optimization is a fertile area of research that is mainly concerned with the automatic generation of optimal layouts to solve design problems in Engineering. The classical formulation addresses the problem of finding the best distribution of an isotropic material that minimizes the work of the external loads at equilibrium, while respecting a constraint on the assigned amount of volume. This is the so-called minimum compliance formulation that can be conveniently employed to achieve stiff truss-like layout within a two-dimensional domain. A classical implementation resorts to the adoption of four node displacement-based finite elements that are coupled with an elementwise discretization of the (unknown) density field. When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboard patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of truss-like members with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts. In this paper we will consider several benchmarks of truss design and explore the performance of the recently proposed technique known as the Virtual Element Method (VEM) in driving the topology optimization procedure. In particular, we will show how the capability of VEM of efficiently approximating elasticity equations on very general polygonal meshes can contribute to overcome the aforementioned mesh-dependent instabilities exhibited by classical finite element based discretization technique

Diffuse Interface Models for Metal Foams

le interest because of their potential applications in many fields of the industry. To produce a metal foam, a well-established process is starting with a molten metal, then introducing blowing agents to create gas bubbles inside the metal. In this work we use COMSOL Multiphysics® and apply the diffuse interface methods of the phase field technique, in order to model the properties of metal foams and describe the movement of the gas-liquid interfaces. A metal foam represented by a number of bubbles moving in a laminar flow is modeled and simulated. Surface tension effects are considered and repulsive forces between neighboring bubbles are expressed through the disjoining pressure. The numerical results show that diffuse interface methods are effective to model this kind of complex phenomena and that fundamental mechanisms due to surface tension effects an