Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.Comment: 14 pages, Latex, 10 figure

The shape evolution of cometary nuclei via anisotropic mass loss

Context. Breathtaking imagery recorded during the European Space Agency's Rosetta mission confirmed the bilobate nature of comet 67P/Churyumov-Gerasimenko's nucleus. Its peculiar appearance is not unique among comets. The majority of cometary cores imaged at high resolution exhibit a similar build. Various theories have been brought forward as to how cometary nuclei attain such peculiar shapes. Aims. We illustrate that anisotropic mass loss and local collapse of subsurface structures caused by non-uniform exposure of the nucleus to solar irradiation can transform initially spherical comet cores into bilobed ones. Methods. A mathematical framework to describe the changes in morphology resulting from non-uniform insolation during a nucleus' spin-orbit evolution is derived. The resulting partial differential equations that govern the change in the shape of a nucleus subject to mass loss and consequent collapse of depleted subsurface structures are solved analytically for simple insolation configurations and numerically for more realistic scenarios. Results. The here proposed mechanism is capable of explaining why a large fraction of periodic comets appear to have peanut-shaped cores and why light-curve amplitudes of comet nuclei are on average larger than those of typical main belt asteroids of the same size.Comment: 4 pages of the main text, 2 pages of appendix, 4 figure

Ion dynamics and acceleration in relativistic shocks

Ab-initio numerical study of collisionless shocks in electron-ion unmagnetized plasmas is performed with fully relativistic particle in cell simulations. The main properties of the shock are shown, focusing on the implications for particle acceleration. Results from previous works with a distinct numerical framework are recovered, including the shock structure and the overall acceleration features. Particle tracking is then used to analyze in detail the particle dynamics and the acceleration process. We observe an energy growth in time that can be reproduced by a Fermi-like mechanism with a reduced number of scatterings, in which the time between collisions increases as the particle gains energy, and the average acceleration efficiency is not ideal. The in depth analysis of the underlying physics is relevant to understand the generation of high energy cosmic rays, the impact on the astrophysical shock dynamics, and the consequent emission of radiation.Comment: 5 pages, 3 figure

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.Comment: 160 pages, LaTeX, 29 EPS figures. Lectures given by I.Ya.Aref'eva at the Swieca Summer School, Brazil, January 2001; Summer School in Modern Mathematical Physics, Sokobanja, Yugoslavia, August 2001; Max Born Symposium, Karpacz, Poland, September, 2001; Workshop "Noncommutative Geometry, Strings and Renormalization", Leipzig, Germany, September 2001. Typos corrected, references adde

The geometry of spontaneous spiking in neuronal networks

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a certain continuous function on the surface of the unit n-cube encodes the most likely activity patterns generated by the network. By studying how the minima of this function evolve under the variation of the coupling strength, we describe the principal transformations in the network dynamics. The minimization problem is also used for the quantitative description of the main dynamical regimes and transitions between them. In particular, for the weak and strong coupling regimes, we present asymptotic formulas for the network activity rate as a function of the coupling strength and the degree of the network. The variational analysis is complemented by the stability analysis of the synchronous state in the strong coupling regime. The stability estimates reveal the contribution of the network connectivity and the properties of the cycle subspace associated with the graph of the network to its synchronization properties. This work is motivated by the experimental and modeling studies of the ensemble of neurons in the Locus Coeruleus, a nucleus in the brainstem involved in the regulation of cognitive performance and behavior

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic \beta-cells, which in isolation are known to exhibit irregular spiking. At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity or small total effective resistance are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models