Dynamical Systems and Topological Surgery

In this paper we try to establish a connection between a three-dimensional Lotka--Volterra dynamical system and two-dimensional topological surgery. There are many physical phenomena exhibiting two-dimensional topological surgery through a `hole drilling' process. By our connection, such phenomena may be modelled mathematically by the above dynamical system.Comment: 16 pages, 14 figure

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Critical Fluctuations at RHIC

On the basis of universal scaling properties, we claim that in Au+Au collisions at RHIC, the QCD critical point is within reach. The signal turns out to be an extended plateau of net baryons in rapidity with approximate height of the net-baryon rapidity density approximately 15 and a strong intermittency pattern with index s_2=1/6 in rapidity fluctuations. A window also exists, to reach the critical point at the SPS, especially in Si+Si collisions at maximal energy.Comment: 8 pages, 3 figure

Critical Opalescence in Baryonic QCD Matter

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behaviour is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.Comment: 7 pages, 1 figur

A new theory of premixed flames in near-stoichiometric mixtures

In this dissertation, a new model of premixed flames in near-stoichiometric mixtures is derived. Unlike most previous theories, which are valid only for very lean or very rich, i.e. off-stoichiometric conditions, our model remains valid over the entire spectrum of mixture compositions, from lean to rich, including the near-stoichiometric regime. Since fuel-mixture composition is known to have a significant effect on flame behavior, such a model is expected to contribute new insights into classical problems in premixed combustion. In the first part of this dissertation, we describe the derivation of a model for premixed flames in two-reactant mixtures in a formal asymptotic way. Using the method of matched asymptotics we are able to simplify the complicated governing equations of combustion and effectively decouple the hydrodynamic equations from those of heat and mass transport. Our model considers a two reactant mixture in which one reactant is slightly in excess and the other deficient. We show that, if the initially excess reactant is less mobile, then it doesn\u27t diffuse as rapidly across a strained flow field and can be locally deficient, and hence consumed, at the reaction zone. This can have a significant effect on burning characteristics of the flame. There are two major differences between our model and previous models. First, we have an additional react ion-diffusion equation governing the transport of the second species. Second, the derived conditions relating the gradients across the reaction sheet are shown to take one of two different forms, depending on which of the two species is consumed in the reaction. In the second part of the thesis, we use our model to study the behavior of planar and strained flames. For the planar flame in uniform flow, we find that many of the results of single-reactant theory apply under near-stoichiometric conditions, provided an effective Lewis number is introduced. On the other hand, for a flame in a nonuniform flow, the dynamics depend significantly on the mass diffusivities as well as mixture strength. In particular, we have analyzed the structure of flame in stagnation point flow and given a complete description of the combustion process including extinction conditions. Results are shown to compare favorably with experiments

On the theory of SODAR measurement techniques (final reporting on WP1, EU WISE project NNE5-2001-297)

The need for alternative means to measure the wind speed for wind energy purposes has increased with the increase of the size of wind turbines. The cost and the technical difficulties for performing wind speed measurements has also increased with the size of the wind turbines, since it is demanded that the wind speed has to be measured at the rotor center of the turbine and the size of both the rotor and the hub height have grown following the increase in the size of the wind turbines. The SODAR (SOund Detection And Ranging) is an alternative to the use of cup anemometers and offers the possibility of measuring both the wind speed distribution with height and the wind direction. At the same time the SODAR presents a number of serious drawbacks such as the low number of measurements per time period, the dependence of the ability to measure on the atmospheric conditions and the difficulty of measuring at higher wind speeds due to either background noise or the neutral condition of the atmosphere. Within the WISE project (EU project number NNE5-2001-297), a number of work packages have been defined in order to deal with the SODAR. The present report is the result of the work package 1. Within this package the objective has been to present and achieve the following: - An accurate theoretic model that describes all the relevant aspects of the interaction of the sound beam with the atmosphere in the level of detail needed for wind energy applications. - Understanding of dependence of SODAR performance on hard- and software configuration. - Quantification of principal difference between SODAR wind measurement and wind speed measurements with cup anemometers with regard to power performance measurements. The work associated to the above is described in the work program as follows: a) Draw up an accurate model of the theoretic background of the SODAR. The necessary depth is reached when the influences of various variables in the model on the accuracy of the measurement have been assessed. b) Describe the general algorithm SODAR uses for sending the beam and measuring the reflections. Describe the influence of various settings on the working of the algorithm. c) Using the data set from work package two analyse the differences between point measurements and profile measurements. All the above issues are addressed in the following repor