Bypass Modules of Shunting of Electromagnets with Energy Recuperation to the Grid

Physics of Particles and Nuclei Letters - When creating accelerators and storage-ring installations in a compact space, there is not always enough space for all the necessary magnet elements. In...     

Formation of Finely Dispersed Structures in Alloys of Aluminum with Cobalt and Zirconium

Russian Journal of Physical Chemistry A - Rapidly quenched alloys of aluminum with cobalt and zirconium are investigated using a combination of means of physicochemical analysis to study the...     

Attractors of 3D Systems in Basic Models of Mechanics*

International Applied Mechanics - The theorems (statements) on the existence of attractor are proved. A generalized Shilnikov theorem is formulated. In the expression for the saddle of a homoclinic...     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.