142,508 research outputs found
Finite-Dimensional Turbulence of Planetary Waves
Finite-dimensional wave turbulence refers to the chaotic dynamics of
interacting wave `clusters' consisting of finite number of connected wave
triads with exact three-wave resonances. We examine this phenomenon using the
example of atmospheric planetary (Rossby) waves. It is shown that the dynamics
of the clusters is determined by the types of connections between neighboring
triads within a cluster; these correspond to substantially different scenarios
of energy flux between different triads. All the possible cases of the energy
cascade termination are classified. Free and forced chaotic dynamics in the
clusters are investigated: due to the huge fluctuations of the energy exchange
between resonant triads these two types of evolution have a lot in common. It
is confirmed that finite-dimensional wave turbulence in finite wave systems is
fundamentally different from kinetic wave turbulence in infinite systems; the
latter is described by wave kinetic equations that account for interactions
with overlapping quasi-resonances of finite amplitude waves. The present
results are directly applicable to finite-dimensional wave turbulence in any
wave system in finite domains with 3-mode interactions as encountered in
hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.Comment: 29 pages, 21 figures, submitted to PR
Holography as a highly efficient RG flow II: An explicit construction
We complete the reformulation of the holographic correspondence as a
\emph{highly efficient RG flow} that can also determine the UV data in the
field theory in the strong coupling and large limit. We introduce a special
way to define operators at any given scale in terms of appropriate
coarse-grained collective variables, without requiring the use of the
elementary fields. The Wilsonian construction is generalised by promoting the
cut-off to a functional of these collective variables. We impose three criteria
to determine the coarse-graining. The first criterion is that the effective
Ward identities for local conservation of energy, momentum, etc. should
preserve their standard forms, but in new scale-dependent background metric and
sources which are functionals of the effective single trace operators. The
second criterion is that the scale-evolution equations of the operators in the
actual background metric should be state-independent, implying that the
collective variables should not explicitly appear in them. The final criterion
is that the endpoint of the scale-evolution of the RG flow can be transformed
to a fixed point corresponding to familiar non-relativistic equations with a
finite number of parameters, such as incompressible non-relativistic
Navier-Stokes, under a certain universal rescaling of the scale and of the time
coordinate. Using previous work, we explicitly show that in the hydrodynamic
limit each such highly efficient RG flow reproduces a unique classical gravity
theory with precise UV data that satisfy our IR criterion. We obtain the
explicit coarse-graining which reproduces Einstein's equations. In a simple
example, we are also able to compute the beta function. Finally, we show how
our construction can be interpolated with the traditional Wilsonian RG flow at
a suitable scale, and can be used to develop new non-perturbative frameworks
for QCD-like theories.Comment: 1+59 pages; Introduction slightly expanded, Section V on beta
function in highly efficient RG flow added, version accepted in PR
Finite Euler Hierarchies And Integrable Universal Equations
Recent work on Euler hierarchies of field theory Lagrangians iteratively
constructed {}from their successive equations of motion is briefly reviewed. On
the one hand, a certain triality structure is described, relating arbitrary
field theories, {\it classical\ts} topological field theories -- whose
classical solutions span topological classes of manifolds -- and
reparametrisation invariant theories -- generalising ordinary string and
membrane theories. On the other hand, {\it finite} Euler hierarchies are
constructed for all three classes of theories. These hierarchies terminate with
{\it universal\ts} equations of motion, probably defining new integrable
systems as they admit an infinity of Lagrangians. Speculations as to the
possible relevance of these theories to quantum gravity are also suggested.Comment: (replaces previous unprintable version corrupted mailer) 13 p.,
(Plain TeX), DTP-92/3
A tracking algorithm for the stable spin polarization field in storage rings using stroboscopic averaging
Polarized protons have never been accelerated to more than about GeV. To
achieve polarized proton beams in RHIC (250GeV), HERA (820GeV), and the
TEVATRON (900GeV), ideas and techniques new to accelerator physics are needed.
In this publication we will stress an important aspect of very high energy
polarized proton beams, namely the fact that the equilibrium polarization
direction can vary substantially across the beam in the interaction region of a
high energy experiment when no countermeasure is taken. Such a divergence of
the polarization direction would not only diminish the average polarization
available to the particle physics experiment, but it would also make the
polarization involved in each collision analyzed in a detector strongly
dependent on the phase space position of the interacting particle. In order to
analyze and compensate this effect, methods for computing the equilibrium
polarization direction are needed. In this paper we introduce the method of
stroboscopic averaging, which computes this direction in a very efficient way.
Since only tracking data is needed, our method can be implemented easily in
existing spin tracking programs. Several examples demonstrate the importance of
the spin divergence and the applicability of stroboscopic averaging.Comment: 39 page
Growth with competing technologies and bounded rationality
I develop a model of growth based on three assumptions: first, a variety of technologies characterised by different degrees of labour skill intensity, where technological change is localized; second, agents are boundedly rational, and the aggregate rule of motion of their behaviour follows a replicator dynamics; third, markets do not clear instantaneously, with prices adjusting gradually. For simplicity, I study the case of two technologies and two labour markets, one for skilled and one for unskilled labour. The model is investigated by means of local stability and computer numerical analysis. Two types of steady states obtain, each characterised by the complete specialization of production into one of the two technologies. Convergence towards the low-growth steady state, associated with the unskilled labour intensive technology, occurs under adverse structural conditions, such as marked initial skill shortage and high skill upgrade costs. This result of lock-in to the inferior steady state is interpreted as co-ordination failure, in that market forces do not always provide sufficient incentives to ensure a high-growth path
Floppy swimming: Viscous locomotion of actuated elastica
Actuating periodically an elastic filament in a viscous liquid generally
breaks the constraints of Purcell's scallop theorem, resulting in the
generation of a net propulsive force. This observation suggests a method to
design simple swimming devices - which we call "elastic swimmers" - where the
actuation mechanism is embedded in a solid body and the resulting swimmer is
free to move. In this paper, we study theoretically the kinematics of elastic
swimming. After discussing the basic physical picture of the phenomenon and the
expected scaling relationships, we derive analytically the elastic swimming
velocities in the limit of small actuation amplitude. The emphasis is on the
coupling between the two unknowns of the problems - namely the shape of the
elastic filament and the swimming kinematics - which have to be solved
simultaneously. We then compute the performance of the resulting swimming
device, and its dependance on geometry. The optimal actuation frequency and
body shapes are derived and a discussion of filament shapes and internal
torques is presented. Swimming using multiple elastic filaments is discussed,
and simple strategies are presented which result in straight swimming
trajectories. Finally, we compare the performance of elastic swimming with that
of swimming microorganisms.Comment: 23 pages, 6 figure
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