Asymptotic profiles for a travelling front solution of a biological equation

We are interested in the existence of depolarization waves in the human brain. These waves propagate in the grey matter and are absorbed in the white matter. We consider a two-dimensional model u_t=\Delta u + f(u) \1_{|y|\leq R} - \alpha u \1_{|y|>R}, with $f$ a bistable nonlinearity taking effect only on the domain \Rm\times [-R,R], which represents the grey matter layer. We study the existence, the stability and the energy of non-trivial asymptotic profiles of possible travelling fronts. For this purpose, we present dynamical systems technics and graphic criteria based on Sturm-Liouville theory and apply them to the above equation. This yields three different behaviours of the solution $u$ after stimulation, depending of the thickness $R$ of the grey matter. This may partly explain the difficulties to observe depolarization waves in the human brain and the failure of several therapeutic trials

The Last Scientific Revolution

Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is proposed as a unified solution

From the end of Unitary Science Projection to the Causally Complete Complexity Science: Extended Mathematics, Solved Problems, New Organisation and Superior Purposes

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal the mathematically exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity

On the Cyclotomic Quantum Algebra of Time Perception

I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise. Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity. Squeezing of phase fluctuations close to the phase transition temperature may play a role in memory encoding and conscious activity

Quantum Theory as Universal Theory of Structures – Essentially from Cosmos to Consciousness

Quantum theory is the most successful physical theory ever. About one third of the gross national product in the developed countries results from its applications. These applications range from nuclear power to most of the high-tech tools for computing, laser, solar cells and so on. No limit for its range of validity has been found up to now..