The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(k)) in the quenched (annealed) updating case, where kn is the nth moment of the degree distribution. Thus, the threshol...

A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there are self-similar “scaling” solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations. Here, the...

A theory is presented for the dispersion relations of the nonlinear phonon-polaritons arising when phonons are coupled to the electromagnetic waves in multilayered structures of nonlinear materials. The calculations are applied to a multilayered structure consisting of a thin film surrounded by semi-infinite bounding media where each layer may have a frequency dependent dielectric function and ...

A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillati...

This paper re-examines the problem of ambipolar diffusion as a mechanism for the production and runaway evolution of centrally condensed molecular cloud cores, a process that has been termed the gravomagneto catastrophe. Our calculation applies in the geometric limit of a highly flattened core and allows for a semi-analytic treatment of the full problem, although physical fixes are required to ...

The main aim of this study is to construct an explicit form of an analytic solution of a multidimensional difference equation. To this end, we present a nonlinear Cournot duopoly model with unimodal reaction functions, show that its dynamical system is double logistic when the production externalities involved get stronger, and then give a constructive proof of the existence of an analytic solu...

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...

Analytic solutions for the evolution of cosmological linear density perturbations in the baryonic gas and collisionless dark matter are derived. The solutions are expressed in a closed form in terms of elementary functions, for arbitrary baryonic mass fraction. They are obtained assuming Ω = 1 and a time independent comoving Jeans wavenumber, kJ . By working with a time variable τ ≡ ln(t), the ...

Motivated currently by the problem of coalescence of receptor clusters in mast cells in the general subject of immune reactions, and formerly by the investigation of exciton trapping and sensitized luminescence in molecular systems and aggregates, we present analytic expressions for survival probabilities of moving entities undergoing diffusion and reaction on encounter. Results we provide cove...