Port-Hamiltonian representation for pdes with second-order derivatives in the energy density

In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational multirate integration in multi-body dynamics

For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using two time grids consisting of micro and macro nodes. This formulation can be extended for multi-body systems. The rigid multi-body system is described by the so called director formulation and constraints describing the joints connecting the bodies. With the Lagrange multiplier method, the constraints are introduced into the equations of motion. A way to implement the null space method into the variational multirate framework is shown and the influence on the number of unknowns is investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimization- and Saddle-Point-Based Modeling of Diffusion-Deformation-Processes in Hydrogels

Hydrogels have gained importance during the last years due to their wide range of synthetically fabricable elastic properties as well their increasing meaning in biomedical applications. Future exploitation of the vast prospects of hydrogels is however only feasible by establishing reliable material models that precisely capture their behavior in different environments. To this end, we propose a consistent variational framework for deformation-diffusion processes, offering a canonically compact approach to the chemo-mechanical coupling of hydrogels via a saddle-point as well as a new minimization formulation. The work depicts the construction of rate-type potentials for the chemo-mechanical evolution problem and their transformation into time-discrete incremental potentials. In terms of spatial discretization, the finite element method is employed, benefiting from the intrinsic symmetric structure of the variational foundation. While the saddle-point formulation yields the well-known LBB condition as a constraint for finite element interpolations, on the part of its minimizing counterpart H(Div, ℬ︁)-conforming elements have to be chosen. We illustrate appropriate solutions to both challenges, using mixed Taylor-Hood for the saddle-point and Raviart-Thomas elements for the minimization formulation and discuss advantages of the new approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-quadratic defect energy: A comparison of gradient plasticity simulations to discrete dislocation dynamics results

A small-deformation strain gradient plasticity (GP) model for single-crystals has been proposed in [1], including a grain boundary (GB) yield condition without hardening. It has been extended by a hardening term for the GBs after a comparison to discrete dislocation dynamics (DDD) results in [2]. Differences between the strain gradients of the GP results and the DDD results motivate the consideration of a non-quadratic defect energy [3] in the GP model. It is shown that the gradients in the GP model can be improved using an exponent different from two. Remaining discrepancies in the strain profiles, compared to the DDD results, are attributed to the neglect of the individual gradients of plastic slip and due to the lack of a mechanism for the misorientation-dependent elastic interactions of dislocations across GBs [4] in the GP model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New Cyclic and Polycyclic Ring Systems Containing Group 14 (Si,Ge, Sn) and 16 (S,Se, Te) Elements

The reactions of Me₂MCl₂ (M = Si, Ge, Sn), Si₂Me₄Cl₂, Si₂Me₂Cl₃, Si₂Me₂Cl₄ and CH₂(SiCl₂Me)₂, and suitable mixtures thereof, with H₂S / NEt₃ and Li₂E (E = Se, Te) have been investigated and lead to a variety of new group 14 chalcogenide systems.     

Some Unusual Reactions in Organophosphorus Chemistry

Methylenephosphinophosphorane 1 reacts with azides without evolution of nitrogen to give zwitterionic phosphorazide 3 and iminophosphorazide 4 , which are in equilibrium to each other; 1 reacts with hexafluoroacetone (HFA) in a different way to give zwitterionic product 5 , which may have the ylidic structure 5' . HFA and thio-HFA react analogously with methylenediphosphines 6 to give corbodiphosphoranes 7 . Reaction of 6 with activated alkenes 9 gives monoylide 10 , which is a useful synthone for the synthesis of fluorosubstituted conjugated triene 12 and diylides 13 and 14 . Reaction of 10 with TOB gives unusually stable betaine 15 . Reaction of the other activated alkene 16 with 6 unexpectedly gave the unusual zwitterionic compound 17 .     

Experimental and Quantum Chemical Studies of 5-Fluoroisatin-3-(N-Cyclohexylthiosemicarbazone) and Its Metal Complexes

Abstract

Zn(II) and Ni(II) complexes of 5-fluoroisatin-3-[-(N-cyclohexylthiosemicarbazone)] (H₂FIC) have been prepared and characterized structurally by means of elemental analyses, FTIR, electronic, and ¹H NMR spectra. The theoretical wavenumbers, IR intensities, and molecular parameters have been calculated by the ab-initio Hartree–Fock (HF) method with the LanL2DZ basis set. The theoretical wavenumbers show a good agreement with experimental data. The bond lengths, bond angles, the highest occupied molecular orbital energy (E_HOMO), the lowest unoccupied molecular orbital energy (E_LUMO), the energy gap between E_HOMO and E_LUMO (ΔE_HOMO-LUMO), dipole moment, and charges on the atoms of H₂FIC as monomer form were studied by the density functional theory/Becke-3-Lee-Yang-Parr (DFT/B3LYP) and ab-initio HF methods using 6-31G(d,p) basis set. The trimeric possible structure of H₂FIC was also investigated using HF method. The observed IR wavenumbers of the H₂FIC were analyzed in the light of the computed vibrational spectra of its monomer and trimer forms.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Imides of 2-Trifluoroacetylphenol and other Trifluoracetic acid Esters: Novel Reactions with Phosphorus(III) Derivates

Abstract

The imido derivates of 2-trifluoroacetylphenol, 1 (R¹=H, Me, iPr) react with the isocyanatophosphites (R²O)₂PNCO, 2 (R²[dbnd]Et, R²-R²[dbnd]CMe₂-CMe₂) to yield the bicyclic compounds 3, wheras in case of 1 (R¹[dbnd](CH₂)₂NMe2) the λ³σ³P compounds 4 are found. The phosphorus(III) chlorides R3PC12 (R³[dbnd]Ph, OEt) and 1 (R¹[dbnd]H, Me) give rise to furnish the tricyclic phosphoranes 5. However with 1 (R¹[dbnd]iPr) phosphite 6 is obtained, which adds hexafluoracetone to give the 1,3,2λ⁵σ⁵-dioxaphospholane 7. 2-(Trifluoracetoxy)pyridine 8. reacts with Tris(trimethylsily1)phosphite to yield the bis(phosph0nate) 10. Some molecular structures are discussed on the basis of x-ray diffraction results.     

New Organophosphorus Proligands and Amide Precursors: Crystal and Molecular Structures of Ph2P(X)NH(C6H3Pri 2-2,6) (X = O,S) and (OPPh2)(O2SMe)N(C6H3Pri 2-2,6)

The new organophosphorus proligand (OPPh₂)(O₂SMe)NR (R = C₆H₃Prⁱ ₂–2,6) (3) was prepared as a white crystalline solid by reacting the lithiated compound Li[Ph₂P(O)NR] with MeSO₂Cl in a 1:1 molar ratio. The precursor Ph₂P(O)NHR (1), as well as its thio analogue Ph₂P(S)NHR (2), were obtained in the reaction between the lithiated amine RNHLi and the corresponding organophosphorus chloride. All compounds were characterized by multinuclear (¹H, ¹³C, and ³¹P) NMR spectroscopy. The molecular structures of 1–3 were established by single-crystal X-ray diffraction. A zigzag polymeric chain is formed in the crystals of 1 and 2 by hydrogen N–H···X (X = O, S) bonding, while the crystal of 3 contains discrete monomeric units with a syn–syn conformation of the O?P(C)₂–N–S(C)(?O)₂ skeleton.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.