Spatially discrete reaction-diffusion equations with discontinuous hysteresis

We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic nonlinearity. We analyze a new mechanism that leads to appearance of a spatio-temporal pattern called {\it rattling}: the solution exhibits a propagation phenomenon different from the classical traveling wave, while the hysteretic nonlinearity, loosely speaking, takes a different value at every second spatial point, independently of the grid size. Such a dynamics indicates how one should redefine hysteresis to make the continuous problem well-posed and how the solution will then behave. In the present paper, we develop main tools for the analysis of the spatially discrete model and apply them to a prototype case. In particular, we prove that the propagation velocity is of order $a t^{-1/2}$ as $t\to\infty$ and explicitly find the rate $a$.Comment: 46 pages, 8 figures, Update bibliographi reference

Anisotropy Reversal of the Upper Critical Field at Low Temperatures and Spin-Locked Superconductivity in K2Cr3As3

We report the first measurements of the anisotropic upper critical field $H_{c2}(T)$ for K$_{2}$Cr$_{3}$As$_{3}$ single crystals up to 60 T and $T > 0.6$ K. Our results show that the upper critical field parallel to the Cr chains, $H_{c2}^\parallel (T)$, exhibits a paramagnetically-limited behavior, whereas the shape of the $H_{c2}^\perp (T)$ curve (perpendicular to the Cr chains) has no evidence of paramagnetic effects. As a result, the curves $H_{c2}^\perp (T)$ and $H_{c2}^\parallel(T)$ cross at $T\approx 4$ K, so that the anisotropy parameter $\gamma_H(T)=H_{c2}^\perp/H_{c2}^\parallel (T)$ increases from $\gamma_H(T_c)\approx 0.35$ near $T_c$ to $\gamma_H(0)\approx 1.7$ at 0.6 K. This behavior of $H_{c2}^\|(T)$ is inconsistent with triplet superconductivity but suggests a form of singlet superconductivity with the electron spins locked onto the direction of Cr chains

Crystal Structure of β-Arrestin at 1.9 Å Possible Mechanism of Receptor Binding and Membrane Translocation

AbstractBackground: Arrestins are responsible for the desensitization of many sequence-divergent G protein-coupled receptors. They compete with G proteins for binding to activated phosphorylated receptors, initiate receptor internalization, and activate additional signaling pathways.Results: In order to understand the structural basis for receptor binding and arrestin's function as an adaptor molecule, we determined the X-ray crystal structure of two truncated forms of bovine β-arrestin in its cytosolic inactive state to 1.9 Å. Mutational analysis and chimera studies identify the regions in β-arrestin responsible for receptor binding specificity. β-arrestin demonstrates high structural homology with the previously solved visual arrestin. All key structural elements responsible for arrestin's mechanism of activation are conserved.Conclusions: Based on structural analysis and mutagenesis data, we propose a previously unappreciated part in β-arrestin's mode of action by which a cationic amphipathic helix may function as a reversible membrane anchor. This novel activation mechanism would facilitate the formation of a high-affinity complex between β-arrestin and an activated receptor regardless of its specific subtype. Like the interaction between β-arrestin's polar core and the phosphorylated receptor, such a general activation mechanism would contribute to β-arrestin's versatility as a regulator of many receptors

Enhanced Mutant Compensates for Defects in Rhodopsin Phosphorylation in the Presence of Endogenous Arrestin-1

We determined the effects of different expression levels of arrestin-1-3A mutant with enhanced binding to light-activated rhodopsin that is independent of phosphorylation. To this end, transgenic mice that express mutant rhodopsin with zero, one, or two phosphorylation sites, instead of six in the WT mouse rhodopsin, and normal complement of WT arrestin-1, were bred with mice expressing enhanced phosphorylation-independent arrestin-1-3A mutant. The resulting lines were characterized by retinal histology (thickness of the outer nuclear layer, reflecting the number of rod photoreceptors, and the length of the outer segments, which reflects rod health), as well as single- and double-flash ERG to determine the functionality of rods and the rate of photoresponse recovery. The effect of co-expression of enhanced arrestin-1-3A mutant with WT arrestin-1 in these lines depended on its level: higher (240% of WT) expression reduced the thickness of ONL and the length of OS, whereas lower (50% of WT) expression was harmless in the retinas expressing rhodopsin with zero or one phosphorylation site, and improved photoreceptor morphology in animals expressing rhodopsin with two phosphorylation sites. Neither expression level increased the amplitude of the a- and b-wave of the photoresponse in any of the lines. However, high expression of enhanced arrestin-1-3A mutant facilitated photoresponse recovery 2-3-fold, whereas lower level was ineffective. Thus, in the presence of normal complement of WT arrestin-1 only supra-physiological expression of enhanced mutant is sufficient to compensate for the defects of rhodopsin phosphorylation

Generation of tunable Terahertz out-of-plane radiation using Josephson vortices in modulated layered superconductors

We show that a moving Josephson vortex in spatially modulated layered superconductors generates out-of-plane THz radiation. Remarkably, the magnetic and in-plane electric fields radiated are of the same order, which is very unusual for any good-conducting medium. Therefore, the out-of-plane radiation can be emitted to the vacuum without the standard impedance mismatch problem. Thus, the proposed design can be more efficient for tunable THz emitters than previous proposals, for radiation only propagating along the ab-plane.Comment: 7 pages, 1 figure. Phys. Rev. B (2005), in pres