Debye temperature of disordered bcc-Fe-Cr alloys

Debye temperature, TD, of Fe100-xCrx disordered alloys with 0<x<99.9 was determined from the temperature dependence of the centre shift of 57Fe Mossbauer spectra recorded in the temperature range of 80-300K. Its compositional dependence shows an interesting non-monotonous behaviour. For 0<x<~45 as well as for ~75<x<~95 the Debye temperature is enhanced relative to its value of a metallic iron, and at x=~3 there is a local maximum having a relative height of ~12% compared to a pure iron. For ~45~95 the Debye temperature is smaller than the one for the metallic iron, with a local minimum at x=~55 at which the relative decrease of TD amounts to ~12%. The first maximum coincides quite well with that found for the spin-waves stiffness coefficient, D0, while the pretty steep decrease observed for x>~95 which is indicative of a decoupling of the probe Fe atoms from the underlying chromium matrix is likely related to the spin-density waves which constitute the magnetic structure of chromium in that interval of composition. The harmonic force constant calculated from the Debye temperature of the least Fe-concentrated alloy (x>99.9) amounts to only 23% of the one characteristic of a pure chromium.Comment: 15 pages, 7 figures, 26 reference

Sigma-phase in Fe-Cr and Fe-V alloy systems and its physical properties

A review is presented on physical properties of the sigma-phase in Fe-Cr and Fe-V alloy systems as revealed both with experimental -- mostly with the Mossbauer spectroscopy -- and theoretical methods. In particular, the following questions relevant to the issue have been addressed: identification of sigma and determination of its structural properties, kinetics of alpha-to-sigma and sigma-to-alpha phase transformations, Debye temperature and Fe-partial phonon density of states, Curie temperature and magnetization, hyperfine fields, isomer shifts and electric field gradients.Comment: 26 pages, 23 figures and 83 reference

A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus

We consider the stationary diffusion equation $-\mathrm{div} (\nabla u + bu )=f$ in $n$-dimensional torus $\mathbb{T}^n$, where $f\in H^{-1}$ is a given forcing and $b\in L^p$ is a divergence-free drift. Zhikov (Funkts. Anal. Prilozhen., 2004) considered this equation in the case of a bounded, Lipschitz domain $\Omega \subset \mathbb{R}^n$, and proved existence of solutions for $b\in L^{2n/(n+2)}$, uniqueness for $b\in L^2$, and has provided a point-singularity counterexample that shows nonuniqueness for $b\in L^{3/2-}$ and $n=3,4,5$. We apply a duality method and a DiPerna-Lions-type estimate to show uniqueness of the solutions constructed by Zhikov for $b\in W^{1,1}$. We use a Nash iteration to demonstrate sharpness of this result, and also show that solutions in $H^1\cap L^{p/(p-1)}$ are flexible for $b\in L^p$, $p\in [1,2(n-1)/(n+1))$; namely we show that the set of $b\in L^p$ for which nonuniqueness in the class $H^1\cap L^{p/(p-1)}$ occurs is dense in the divergence-free subspace of $L^p$.Comment: 16 page

Well-posedness of logarithmic spiral vortex sheets

We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vortr\"age aus dem Gebiete der Hydro- und Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We prove that for each such spiral the normal component of the velocity field remains continuous across the spiral. Moreover, we give a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we show that a spiral gives rise to such a solution if and only if two conditions hold across every spiral: a velocity matching condition and a pressure matching condition. Furthermore we show that these two conditions are equivalent to the imaginary part and the real part, respectively, of a single complex constraint on the coefficients of the spirals. This in particular provides a rigorous mathematical framework for logarithmic spirals, an issue that has remained open since their introduction by Prandtl in 1922. Another consequence of the main result is well-posedness of the symmetric Alexander spiral with two branches, despite recent evidence for the contrary. Our main tools are new explicit formulas for the velocity field and for the pressure function, as well as a notion of a winding number of a spiral, which gives a robust way of localizing the spirals' arms with respect to a given point in the plane.Comment: 25 pages, 3 figure

Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.Comment: 17 page

Dynamic Response Characteristics in Variable Stiffness Soft Inflatable Links

© Springer Nature Switzerland AG 2019. In soft robotics, there is the fundamental need to develop devices that are flexible and can change stiffness in order to work safely in the vicinity of humans. Moreover, these structures must be rigid enough to withstand the force application and accuracy in motion. To solve these issues, previous research proposed to add a compliance element between motor and load – Series Elastic Actuators (SEAs). This approach benefits from improved force control and shock tolerance due to the elasticity introduced at joint level. However, series compliance at the joint level comes at the cost of inferior position controllability and additional mechanical complexity. In this research, we move the elastic compliance to the link, and evaluate the characteristics of variable stiffness soft inflatable links. The detailed investigation of the dynamic behaviour of inflatable link takes into consideration different internal pressures and applied loads. Our results demonstrate that the use of soft inflatable links leads to good weight lifting capability whilst preserving compliance which is beneficial for safety critical applications

Adenosine A2A receptors in Parkinson’s disease treatment

Latest results on the action of adenosine A2A receptor antagonists indicate their potential therapeutic usefulness in the treatment of Parkinson’s disease. Basal ganglia possess high levels of adenosine A2A receptors, mainly on the external surfaces of neurons located at the indirect tracts between the striatum, globus pallidus, and substantia nigra. Experiments with animal models of Parkinson’s disease indicate that adenosine A2A receptors are strongly involved in the regulation of the central nervous system. Co-localization of adenosine A2A and dopaminergic D2 receptors in striatum creates a milieu for antagonistic interaction between adenosine and dopamine. The experimental data prove that the best improvement of mobility in patients with Parkinson’s disease could be achieved with simultaneous activation of dopaminergic D2 receptors and inhibition of adenosine A2A receptors. In animal models of Parkinson’s disease, the use of selective antagonists of adenosine A2A receptors, such as istradefylline, led to the reversibility of movement dysfunction. These compounds might improve mobility during both monotherapy and co-administration with L-DOPA and dopamine receptor agonists. The use of adenosine A2A receptor antagonists in combination therapy enables the reduction of the L-DOPA doses, as well as a reduction of side effects. In combination therapy, the adenosine A2A receptor antagonists might be used in both moderate and advanced stages of Parkinson’s disease. The long-lasting administration of adenosine A2A receptor antagonists does not decrease the patient response and does not cause side effects typical of L-DOPA therapy. It was demonstrated in various animal models that inhibition of adenosine A2A receptors not only decreases the movement disturbance, but also reveals a neuroprotective activity, which might impede or stop the progression of the disease. Recently, clinical trials were completed on the use of istradefylline (KW-6002), an inhibitor of adenosine A2A receptors, as an anti-Parkinson drug