Existence and convergence of the length-preserving elastic flow of clamped curves.

We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L 2 -gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Lojasiewicz-Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.

Curvature-dependent Eulerian interfaces in elastic solids.

We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large curvature of the interface, we include a geometric term featuring a curvature varifold. Equilibrium solutions are proved to exist via minimization. We then use this model in an Eulerian topology optimization problem that incorporates a curvature penalization. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

Li-Yau inequalities for the Helfrich functional and applications.

We prove a general Li-Yau inequality for the Helfrich functional where the spontaneous curvature enters with a singular volume type integral. In the physically relevant cases, this term can be converted into an explicit energy threshold that guarantees embeddedness. We then apply our result to the spherical case of the variational Canham-Helfrich model. If the infimum energy is not too large, we show existence of smoothly embedded minimizers. Previously, existence of minimizers was only known in the classes of immersed bubble trees or curvature varifolds.

A luminescent Pt2Fe spin crossover complex.

A heterotrinuclear [Pt2Fe] spin crossover (SCO) complex was developed and synthesized employing a ditopic bridging bpp-alkynyl ligand L and alkynyl coordinated PtII terpy units: [FeII(L-PtII)2]2(BF4)2 (1). We identified two different types of crystals of 1 which differ in their molecular packing and the number of co-crystallized solvent molecules: 1H (1·3.5CH2Cl2 in P1[combining macron]) and 1L (1·10CH2Cl2 in C2/c); while 1L shows a reversible SCO with a transition temperature of 268 K, the analogous compound 1H does not show any SCO and remains blocked in the HS state. The temperature-dependent magnetic properties of 1H and 1L were complementarily studied by Mössbauer spectroscopy. It has been shown that 1L performs thermal spin crossover and that 1L can be excited to a LIESST state. The vibrational properties of 1 were investigated by experimental nuclear resonance vibrational spectroscopy. The experimentally determined partial density of vibrational states (pDOS) was compared to a DFT-based simulation of the pDOS. The vibrational modes of the different components were assigned and visualized. In addition, the photophysical properties of 1 and L-Pt were investigated in the solid state and in solution. The ultrafast transient absorption spectroscopy of 1 in solution was carried out to study the PL quenching channel via energy transfer from photoexcited PtII terpy units to the FeII-moiety.

Spectroscopic, Structural, and Kinetic Investigation of the Ultrafast Spin Crossover in an Unusual Cobalt(II) Semiquinonate Radical Complex.

A comprehensive spectroscopic and structural investigation of [CoII (l-N4 tBu2 )(dbsq)][B(p-C6 H4 Cl)4 ] (1, l-N4 tBu2 =N,N'-di-tert-butyl-2,11-diaza[3.3](2,6)pyridinophane, dbsq1- =3,5-di-tert-butylsemiquinonate), the first known octahedral complex with a low-spin (ls) CoII semiquinonate ground state, is reported. Above 200 K, solids as well as solutions of 1 exhibit thermally induced spin-crossover (SCO) from the ls to the high-spin (hs) CoII semiquinonate state instead of the frequently observed valence tautomerism from ls CoIII catecholate to hs CoII semiquinonate. DFT calculations demonstrate that the (closed shell) CoIII catecholate suffers from a triplet instability leading to the ls CoII semiquinonate ground state. The thorough temperature-dependent spectroscopic study of the SCO enables a photophysical investigation. Thus, by selective photoexcitation of the ls fraction of 1 in solution at room temperature, ultrafast conversion to the hs state is observed using femtosecond electronic and IR-vibrational (infrared) transient absorption spectroscopy. The kinetics of the photocycle is described by a stretched exponential with τ=3.3-3.6 ps and ß=0.52-0.54, representing an upper limit for the hs-ls relaxation time. This is, to our knowledge, the fastest interconversion ever determined for a SCO complex, and is attributed to the special situation that in 1 a CoII complex is coordinated to a π-radical ligand allowing very efficient coupling between the ls and hs spin states.

Hydrothermal carbonization of anaerobically digested maize silage.

Hydrochars were prepared by hydrothermal carbonization (HTC) of maize silage previously treated at 55 °C in a two-stage solid-state reactor system. The HTC was carried out in a 1-L stirred pressure reactor with pH regulation by citric acid. The treated silage carbonized at relatively mild conditions (190 °C, 2 h), and the hydrochars showed mainly amorphous macro-size features with a carbon content of 59-79% (ash-free, dry) and a higher heating value of 25-36 MJ kg⁻¹. Temperature was the main influencing factor. The surface area according to Brunauer-Emmett-Teller (BET) analysis was highest at 190 °C (12.3 m²) g⁻¹). Based on these results, the hydrochars are potentially interesting for applications such as an alternative fuel or a soil conditioner.