One-dimensional global attractor for strongly damped wave equations

We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve.     

Thioamides and selenoamides with chirality solely due to hindered rotation about the C–N bond: enantioselective complexation with optically active hosts

Several thioformamides and selenoformamides, with chirality solely due to restricted rotation about the C–N bond, were resolved to enantiomers by inclusion crystallization with optically active diols (TADDOLs). The absolute configuration of the guest molecules was deduced from the X-ray crystal structures of the inclusion complexes. The optical activity of the resolved compounds is manifested by their CD spectra showing relatively strong Cotton effects in the region of thioamide or selenoamide n–π* transition. The optically active thioformamides and selenoformamides are configurationally labile compounds and gradually racemize in solution but are stable in the form of the inclusion complexes. The first-order kinetics of the racemization in solution allowed us to assign the C–N rotation barriers of thioformamides by spectropolarimetric measurements.     

Photochemically-induced crystallization of protein

I demonstrate photochemically induced crystallization of metastable hen egg-white lysozyme solution by weak UV irradiation for several tens seconds. The most effective irradiation time range is 10–60 s, and in this range the enzyme activity is maintained. Intermediates, neutral radicals at tryptophan residual produced by one-photon absorption, enhance nucleation. When the intermediate is selectively excited by visible light, the intermediate is denatured. At that time the light-induced nucleation is inhibited. This result indicates the intermediate induces nucleation. The radical forms lysozyme dimer that is detected by an SDS-PAGE electrophoresis experiment. An addition of polyethylene glycol (PEG) greatly enhances light-induced nucleation. PEG affects to shorten the intermediate radical lifetime, which suggests that PEG assists to form dimer. We consider that the photochemical dimer behaves as smallest cluster to grow critical nucleus. The smallest cluster formation is the rate determining step in classical nucleation theory due to surface energy disadvantage. The photochemical dimer is formed by a covalent bond, and the nucleation is initiated from stable dimer. The nucleation enhancement is reasonably explained. The present researches results point out the development of a new method for controlling nucleation and growth that could be applied for structural genomics and pharmaceutical industry for instance.     

Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Microstructural model for cyclic hardening in F-actin networks crosslinked by α-actinin

The rheology of F-actin networks has attracted a great attention during the last years. In order to gain a complete understanding of the rheological properties of these novel materials, it is necessary the study in a large deformations regime to alter their internal structure. In this sense, Schmoller et al. (2010) showed that the reconstituted networks of F-actin crosslinked with α-actinin unexpectedly harden when they are subjected to a cyclical shear. This observation contradicts the expected Mullins effect observed in most soft materials, such as rubber and living tissues, where a pronounced softening is observed when they are cyclically deformed.We think that the key to understand this stunning effect is the gelation process. To define it, the most relevant constituents are the chemical crosslinks – α-actinin –, the physical crosslinks – introduced by the entanglement of the semiflexible network – and the interaction between them. As a consequence of this interaction, a pre-stressed network emerges and introduces a feedback effect, where the pre-stress also regulates the adhesion energy of the α-actinin, setting the structure in a metastable reference configuration. Therefore, the external loads and the evolvement of the trapped stress drive the microstructural changes during the cyclic loading protocol. In this work, we propose a micromechanical model into the framework of nonlinear continuum mechanics. The mechanics of the F-actin filaments is modelled using the wormlike chain model for semiflexible filaments and the gelation process is modelled as mesoscale dynamics for the α-actinin and physical crosslink. The model has been validated with reported experimental results.