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

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

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

Impact of menopause-associated frailty on traumatic brain injury

Navigating menopause involves traversing a complex terrain of hormonal changes that extend far beyond reproductive consequences. Menopausal transition is characterized by a decrease in estradiol-17β (E2), and the impact of menopause resonates not only in the reproductive system but also through the central nervous system, musculoskeletal, and gastrointestinal domains. As women undergo menopausal transition, they become more susceptible to frailty, amplifying the risk and severity of injuries, including traumatic brain injury (TBI). Menopause triggers a cascade of changes leading to a decline in muscle mass, accompanied by diminished tone and excitability, thereby restricting the availability of irisin, a crucial hormone derived from muscles. Concurrently, bone mass undergoes reduction, culminating in the onset of osteoporosis and altering the dynamics of osteocalcin, a hormone originating from bones. The diminishing levels of E2 during menopause extend their influence on the gut microbiota, resulting in a reduction in the availability of tyrosine, tryptophan, and serotonin metabolites, affecting neurotransmitter synthesis and function. Understanding the interplay between menopause, frailty, E2 decline, and the intricate metabolisms of bone, gut, and muscle is imperative when unraveling the nuances of TBI after menopause. The current review underscores the significance of accounting for menopause-associated frailty in the incidence and consequences of TBI. The review also explores potential mechanisms to enhance gut, bone, and muscle health in menopausal women, aiming to mitigate frailty and improve TBI outcomes. •Menopause leads to a decline in 17β-estradiol (E2).•E2 decline aggravates frailty by weakening musculoskeletal and gut health.•Frailty increases vulnerability to traumatic brain injury and its consequences.•Understanding menopause-frailty interplay in TBI is vital for improving outcomes