7 research outputs found
q-breathers in Discrete Nonlinear Schroedinger lattices
-breathers are exact time-periodic solutions of extended nonlinear systems
continued from the normal modes of the corresponding linearized system. They
are localized in the space of normal modes. The existence of these solutions in
a weakly anharmonic atomic chain explained essential features of the
Fermi-Pasta-Ulam (FPU) paradox. We study -breathers in one- two- and
three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices --
theoretical playgrounds for light propagation in nonlinear optical waveguide
networks, and the dynamics of cold atoms in optical lattices. We prove the
existence of these solutions for weak nonlinearity. We find that the
localization of -breathers is controlled by a single parameter which depends
on the norm density, nonlinearity strength and seed wave vector. At a critical
value of that parameter -breathers delocalize via resonances, signaling a
breakdown of the normal mode picture and a transition into strong mode-mode
interaction regime. In particular this breakdown takes place at one of the
edges of the normal mode spectrum, and in a singular way also in the center of
that spectrum. A stability analysis of -breathers supplements these
findings. For three-dimensional lattices, we find -breather vortices, which
violate time reversal symmetry and generate a vortex ring flow of energy in
normal mode space.Comment: 19 pages, 9 figure
The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging
Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks—e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called “seven pillars of aging” combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research
The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging
Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks—e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called “seven pillars of aging” combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research