1,143 research outputs found
Multielectron Redox Chemistry of Transition Metal Complexes Supported by a NonâInnocent N3P2 Ligand: Synthesis, Characterization, and Catalytic Properties
A new redoxâactive, diarylamidoâbased ligand (LN3P2) capable of Îș5âN,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(2âaminoâ4âmethylphenyl)amine, which undergoes condensation with two equivalents of 2â(diphenylphosphanyl)benzaldehyde to provide chelating arms with both arylphosphine and imine donors. Xâray structural, magnetic, and spectroscopic studies indicate that the N3P2 coordination environment generally promotes lowâspin configurations. Three quasiâreversible redox couples between +1.0 and â1.5 V (vs. Fc+/Fc) were observed in voltammetric studies of each complex, corresponding to MII/MIII oxidation, LN3P2âbased oxidation, and MII/MI reduction (in order of highest to lowest potential). Spectroscopic and computational analyses of 3ox â generated via chemical oneâelectron oxidation of 3 â 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 4âtertâbutylphenol as the proton source at potentials below â2.0 V. The insights gained here will assist in the future design of pentadentate mixed N/Pâbased 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
MultiphysicsÂź 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
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