Diffusion-controlled annihilation A+B→0A + B \to 0 with initially separated reactants: The death of an AA particle island in the BB particle sea

We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of particles in the island is large enough, then at any system's dimensionality $d$ the death of the majority of particles occurs in the {\it universal scaling regime} within which $\approx 4/5$ of the particles die at the island expansion stage and the remaining $\approx 1/5$ at the stage of its subsequent contraction. In the quasistatic approximation the scaling of the reaction zone has been obtained for the cases of mean-field ($d \geq d_{c}$) and fluctuation ($d < d_{c}$) dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur

Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

We study long-time properties of reversible reaction-diffusion systems of type A + B C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.Comment: 6 pages, no figures, to appear in PR

Contribution of a time-dependent metric on the dynamics of an interface between two immiscible electro-magnetically controllable Fluids

We consider the case of a deformable material interface between two immiscible moving media, both of them being magnetiable. The time dependence of the metric at the interface introduces a non linear term, proportional to the mean curvature, in the surface dynamical equations of mass momentum and angular momentum. We take into account the effects of that term also in the singular magnetic and electric fields inside the interface which lead to the existence of currents and charges densities through the interface, from the derivation of the Maxwell equations inside both bulks and the interface. Also, we give the expression for the entropy production and of the different thermo-dynamical fluxes. Our results enlarge previous results from other theories where the specific role of the time dependent surface metric was insufficiently stressed.Comment: 25 page

Impact of proteoglycan‐4 and parathyroid hormone on articular cartilage

Proteoglycan‐4 ( Prg4 ) protects synovial joints from arthropathic changes by mechanisms that are incompletely understood. Parathyroid hormone (PTH), known for its anabolic actions in bone, increases Prg4 expression and has been reported to inhibit articular cartilage degeneration in arthropathic joints. To investigate the effect of Prg4 and PTH on articular cartilage, 16‐week‐old Prg4 mutant and wild‐type mice were treated with intermittent PTH (1–34) or vehicle control daily for six weeks. Analyses included histology of the knee joint, micro‐CT of the distal femur, and serum biochemical analysis of type II collagen fragments (CTX‐II). Compared to wild‐type littermates, Prg4 mutant mice had an acellular layer of material lining the surfaces of the articular cartilage and menisci, increased articular cartilage degradation, increased serum CTX‐II concentrations, decreased articular chondrocyte apoptosis, increased synovium SDF‐1 expression, and irregularly contoured subchondral bone. PTH‐treated Prg4 mutant mice developed a secondary deposit overlaying the acellular layer of material lining the joint surfaces, but PTH‐treatment did not alter signs of articular cartilage degeneration in Prg4 mutant mice. The increased joint SDF‐1 levels and irregular subchondral bone found in Prg4 mutant mice introduce novel candidate mechanisms by which Prg4 protects articular cartilage. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 31: 183–190, 2013Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94686/1/22207_ftp.pd

Inflammatory bone loss associated with MFG‐E8 deficiency is rescued by teriparatide

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154457/1/fsb2fj201701238r-sup-0002.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154457/2/fsb2fj201701238r.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154457/3/fsb2fj201701238r-sup-0001.pd

Behavior of the reaction front between initially segregated species in a two-stage reaction

The large-time asymptotic behavior of a two-stage reaction (A+B→R, B+R→S) with initially segregated reactants is described. The concentration of the reactants is found to be significantly less than the initial concentrations in a depletion zone of width proportional to t[sup. 1/2], where t is time; the reaction takes place in a thinner zone of width proportional to t[sup. 1/6]. Similarity solutions for the chemical concentration profiles in the reaction zone are calculated, and are compared with numerical simulations of the full partial differential reaction-diffusion equations. The large-time asymptotic scalings reported here are the same as in the absence of the secondary reaction, but we find that the location of the reaction zone is significantly shifted due to the secondary reaction. The reaction zone may behave in an exotic fashion at large time, moving first one way, then reversing its direction.Stephen M. Cox and Matthew D. Fin

Academic freedom in Europe: time for a Magna Charta?

This paper is a preliminary attempt to establish a working definition of academic freedom for the European Union states. The paper details why such a definition is required for the European Union and then examines some of the difficulties of defining academic freedom. By drawing upon experience of the legal difficulties beset by the concept in the USA and building on previous analyses of constitutional and legislative protection for academic freedom, and of legal regulations concerning institutional governance and academic tenure, a working definition of academic freedom is then derived. The resultant definition which, it is suggested, could form the basis for a European Magna Charta Libertatis Academicae, goes beyond traditional discussions of academic freedom by specifying not only the rights inherent in the concept but also its accompanying duties, necessary limitations and safeguards. The paper concludes with proposals for how the definition might be tested and carried forward