Interpolation of nonlinear positive or order preserving operators on Banach lattices

Positivity - We study the relationship between exact interpolation spaces for positive, linear operators, for order preserving, Lipschitz continuous operators, and for positive...     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

Equality of two spectra arising in harmonic analysis and semigroup theory

We show that a new notion of a spectrum of a function ( is a Banach space), defined by B. Basit and the first author, coincides with the Arveson spectrum of some shift group, provided is uniformly continuous. We apply this result to prove a new version of a tauberian theorem.     

Asymptotic behaviour of linear evolutionary integral equations

The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX

Every ordinary differential equation with a strict Lyapunov function is a gradient system

We explain and prove the statement from the title. This allows us to formulate a new type of gradient inequality and to obtain a new stabilization result for gradient-like ordinary differential equations.     

Stabilization of solutions of dissipative Hamiltonian systems

We study the stabilization of solutions of damped Hamiltonian systems. We give sufficient conditions for convergence of these solutions, decay estimate and examples of applications.     

Self‐Assembled Cyclic d,l‐α‐Peptides as Generic Conformational Inhibitors of the α‐Synuclein Aggregation and Toxicity: In Vitro and Mechanistic Studies

Many peptides and proteins with large sequences and structural differences self‐assemble into disease‐causing amyloids that share very similar biochemical and biophysical characteristics, which may contribute to their cross‐interaction. Here, we demonstrate how the self‐assembled, cyclic d,l ‐α‐peptide CP‐2 , which has similar structural and functional properties to those of amyloids, acts as a generic inhibitor of the Parkinson′s disease associated α‐synuclein (α‐syn) aggregation to toxic oligomers by an ?off‐pathway“ mechanism. We show that CP‐2 interacts with the N‐terminal and the non‐amyloid‐β component region of α‐syn, which are responsible for α‐syn′s membrane intercalation and self‐assembly, thus changing the overall conformation of α‐syn. CP‐2 also remodels α‐syn fibrils to nontoxic amorphous species and permeates cells through endosomes/lysosomes to reduce the accumulation and toxicity of intracellular α‐syn in neuronal cells overexpressing α‐syn. Our studies suggest that targeting the common structural conformation of amyloids may be a promising approach for developing new therapeutics for amyloidogenic diseases.     

Database of atomistic reaction mechanisms with application to kinetic Monte Carlo

Kinetic Monte Carlo is a method used to model the state-to-state kinetics of atomic systems when all reaction mechanisms and rates are known a priori. Adaptive versions of this algorithm use saddle searches from each visited state so that unexpected and complex reaction mechanisms can also be included. Here, we describe how calculated reaction mechanisms can be stored concisely in a kinetic database and subsequently reused to reduce the computational cost of such simulations. As all accessible reaction mechanisms available in a system are contained in the database, the cost of the adaptive algorithm is reduced towards that of standard kinetic Monte Carlo.