111,750 research outputs found
Aerodynamic noise from rigid trailing edges with finite porous extensions
This paper investigates the effects of finite flat porous extensions to
semi-infinite impermeable flat plates in an attempt to control trailing-edge
noise through bio-inspired adaptations. Specifically the problem of sound
generated by a gust convecting in uniform mean steady flow scattering off the
trailing edge and permeable-impermeable junction is considered. This setup
supposes that any realistic trailing-edge adaptation to a blade would be
sufficiently small so that the turbulent boundary layer encapsulates both the
porous edge and the permeable-impermeable junction, and therefore the
interaction of acoustics generated at these two discontinuous boundaries is
important. The acoustic problem is tackled analytically through use of the
Wiener-Hopf method. A two-dimensional matrix Wiener-Hopf problem arises due to
the two interaction points (the trailing edge and the permeable-impermeable
junction). This paper discusses a new iterative method for solving this matrix
Wiener-Hopf equation which extends to further two-dimensional problems in
particular those involving analytic terms that exponentially grow in the upper
or lower half planes. This method is an extension of the commonly used "pole
removal" technique and avoids the needs for full matrix factorisation.
Convergence of this iterative method to an exact solution is shown to be
particularly fast when terms neglected in the second step are formally smaller
than all other terms retained. The final acoustic solution highlights the
effects of the permeable-impermeable junction on the generated noise, in
particular how this junction affects the far-field noise generated by
high-frequency gusts by creating an interference to typical trailing-edge
scattering. This effect results in partially porous plates predicting a lower
noise reduction than fully porous plates when compared to fully impermeable
plates.Comment: LaTeX, 20 pp., 19 graphics in 6 figure
Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems
We discuss exact analytical solutions of a variety of statistical models
recently obtained for finite systems by a novel powerful mathematical method,
the Laplace-Fourier transform. Among them are a constrained version of the
statistical multifragmentation model, the Gas of Bags Model and the Hills and
Dales Model of surface partition. Thus, the Laplace-Fourier transform allows
one to study the nuclear matter equation of state, the equation of state of
hadronic and quark gluon matter and surface partitions on the same footing. A
complete analysis of the isobaric partition singularities of these models is
done for finite systems. The developed formalism allows us, for the first time,
to exactly define the finite volume analogs of gaseous, liquid and mixed phases
of these models from the first principles of statistical mechanics and
demonstrate the pitfalls of earlier works. The found solutions may be used for
building up a new theoretical apparatus to rigorously study phase transitions
in finite systems. The strategic directions of future research opened by these
exact results are also discussed.Comment: Contribution to the ``World Consensus Initiative III, Texas A & M
University, College Station, Texas, USA, February 11-17, 2005, 21
Complete Wiener-Hopf Solution of the X-Ray Edge Problem
We present a complete solution of the soft x-ray edge problem within a
field-theoretic approach based on the Wiener-Hopf infinite-time technique. We
derive for the first time within this approach critical asymptotics of all the
relevant quantities for the x-ray problem as well as their nonuniversal
prefactors. Thereby we obtain the most complete field-theoretic solution of the
problem with a number of new experimentally relevant results. We make thorough
comparison of the proposed Wiener-Hopf technique with other approaches based on
finite-time methods. It is proven that the Fredholm, finite-time solution
converges smoothly to the Wiener-Hopf one and that the latter is stable with
respect to perturbations in the long-time limit. Further on we disclose a wide
interval of intermediate times showing quasicritical behavior deviating from
the Wiener-Hopf one. The quasicritical behavior of the core-hole Green function
is derived exactly from the Wiener-Hopf solution and the quasicritical exponent
is shown to match the result of Nozi\`eres and De Dominicis. The reasons for
the quasicritical behavior and the way of a crossover to the infinite-time
solution are expounded and the physical relevance of the Nozi\`eres and De
Dominicis as well as of the Winer-Hopf results are discussed.Comment: 19 pages, RevTex, no figure
Survival of interacting Brownian particles in crowded 1D environment
We investigate a diffusive motion of a system of interacting Brownian
particles in quasi-one-dimensional micropores. In particular, we consider a
semi-infinite 1D geometry with a partially absorbing boundary and the hard-core
inter-particle interaction. Due to the absorbing boundary the number of
particles in the pore gradually decreases. We present the exact analytical
solution of the problem. Our procedure merely requires the knowledge of the
corresponding single-particle problem. First, we calculate the simultaneous
probability density of having still a definite number of surviving
particles at definite coordinates. Focusing on an arbitrary tagged particle, we
derive the exact probability density of its coordinate. Secondly, we present a
complete probabilistic description of the emerging escape process. The survival
probabilities for the individual particles are calculated, the first and the
second moments of the exit times are discussed. Generally speaking, although
the original inter-particle interaction possesses a point-like character, it
induces entropic repulsive forces which, e.g., push the leftmost (rightmost)
particle towards (opposite) the absorbing boundary thereby accelerating
(decelerating) its escape. More importantly, as compared to the reference
problem for the non-interacting particles, the interaction changes the
dynamical exponents which characterize the long-time asymptotic dynamics.
Interesting new insights emerge after we interpret our model in terms of a)
diffusion of a single particle in a -dimensional space, and b) order
statistics defined on a system of independent, identically distributed
random variables
Effective action approach to strongly correlated fermion systems
We construct a new functional for the single particle Green's function, which
is a variant of the standard Baym Kadanoff functional.
The stability of the stationary solutions to the new functional is directly
related to aspects of the irreducible particle hole interaction through the
Bethe Salpeter equation.
A startling aspect of this functional is that it allows a simple and rigorous
derivation of both the standard and extended dynamical mean field (DMFT)
equations as stationary conditions. Though the DMFT equations were formerly
obtained only in the limit of infinite lattice coordination, the new functional
described in the work, presents a way of directly extending DMFT to finite
dimensional systems, both on a lattice and in a continuum. Instabilities of the
stationary solution at the bifurcation point of the functional, signal the
appearance of a zero mode at the Mott transition which then couples t o
physical quantities resulting in divergences at the transition.Comment: 9 page
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