4,410 research outputs found
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 of the cusp map
, (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
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment 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
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