9,138 research outputs found
State space formulas for stable rational matrix solutions of a Leech problem
Given stable rational matrix functions and , a procedure is presented
to compute a stable rational matrix solution to the Leech problem
associated with and , that is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
All solutions to the relaxed commutant lifting problem
A new description is given of all solutions to the relaxed commutant lifting
problem. The method of proof is also different from earlier ones, and uses only
an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
For the strictly positive case (the suboptimal case) the maximum entropy
solution to the Leech problem and
, with and stable rational
matrix functions, is proved to be a stable rational matrix function. An
explicit state space realization for is given, and turns out
to be strictly less than one. The matrices involved in this realization are
computed from the matrices appearing in a state space realization of the data
functions and . A formula for the entropy of is also given.Comment: 19 page
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
For the strictly positive case (the suboptimal case), given stable rational
matrix functions and , the set of all solutions to the
Leech problem associated with and , that is, and
, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions and . On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page
Irreversibility, steady state, and nonequilibrium physics in relativistic heavy ion collisions
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve according to Prigogine s steady states rather than towards statistical equilibrium. These results are general and can be easily checked by any microscopic string-, transport-, or cascade model for heavy ion collisions. The absence of pure equilibrium states sheds light on the di culties of thermal models in describing the yields and spectra of hadrons, especially mesons, in heavy ion collisions at bombarding energies above 10 GeV/nucleon. PACS numbers: 25.75.-q, 05.70.Ln, 24.10.L
Homogeneous nucleation of quark gluon plasma, finite size effects and longlived metastable objects
The general formalism of homogeneous nucleation theory is applied to study the hadronization pattern of the ultra-relativistic quark-gluon plasma (QGP) undergoing a first order phase transition. A coalescence model is proposed to describe the evolution dynamics of hadronic clusters produced in the nucle- ation process. The size distribution of the nucleated clusters is important for the description of the plasma conversion. The model is most sensitive to the initial conditions of the QGP thermalization, time evolution of the energy den- sity, and the interfacial energy of the plasma hadronic matter interface. The rapidly expanding QGP is first supercooled by about T = T Tc = 4 6%. Then it reheats again up to the critical temperature Tc. Finally it breaks up into hadronic clusters and small droplets of plasma. This fast dynamics occurs within the first 5 10 fm/c. The finite size e ects and fluctuations near the critical temperature are studied. It is shown that a drop of longitudinally expanding QGP of the transverse radius below 4.5 fm can display a long-lived metastability. However, both in the rapid and in the delayed hadronization scenario, the bulk pion yield is emitted by sources as large as 3 4.5 fm. This may be detected experimentally both by a HBT interferometry signal and by the analysis of the rapidity distributions of particles in narrow pT -intervals at small |pT | on an event-by-event basis. PACS numbers: 12.38.Mh, 24.10.Pa, 25.75.-q, 64.60.Q
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