26,745 research outputs found
Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence
The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field
The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays
For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed
Thermodynamic entropy production fluctuation in a two dimensional shear flow model
We investigate fluctuations in the momentum flux across a surface
perpendicular to the velocity gradient in a stationary shear flow maintained by
either thermostated deterministic or by stochastic boundary conditions. In the
deterministic system the Gallavotti-Cohen (GC)relation for the probability of
large deviations, which holds for the phase space volume contraction giving the
Gibbs ensemble entropy production, never seems to hold for the flux which gives
the hydrodynamic entropy production. In the stochastic case the GC relation is
found to hold for the total flux, as predicted by extensions of the GC theorem
but not for the flux across part of the surface. The latter appear to satisfy a
modified GC relation. Similar results are obtained for the heat flux in a
steady state produced by stochastic boundaries at different temperatures.Comment: 9 postscript figure
Reversibility of Red blood Cell deformation
The ability of cells to undergo reversible shape changes is often crucial to
their survival. For Red Blood Cells (RBCs), irreversible alteration of the cell
shape and flexibility often causes anemia. Here we show theoretically that RBCs
may react irreversibly to mechanical perturbations because of tensile stress in
their cytoskeleton. The transient polymerization of protein fibers inside the
cell seen in sickle cell anemia or a transient external force can trigger the
formation of a cytoskeleton-free membrane protrusion of micrometer dimensions.
The complex relaxation kinetics of the cell shape is shown to be responsible
for selecting the final state once the perturbation is removed, thereby
controlling the reversibility of the deformation. In some case, tubular
protrusion are expected to relax via a peculiar "pearling instability".Comment: 4 pages, 3 figure
Hydrodynamic phase-locking of swimming microorganisms
Some microorganisms, such as spermatozoa, synchronize their flagella when
swimming in close proximity. Using a simplified model (two infinite, parallel,
two-dimensional waving sheets), we show that phase-locking arises from
hydrodynamics forces alone, and has its origin in the front-back asymmetry of
the geometry of their flagellar waveform. The time-evolution of the phase
difference between co-swimming cells depends only on the nature of this
geometrical asymmetry, and microorganisms can phase-lock into conformations
which minimize or maximize energy dissipation
Multicomponent dynamical systems: SRB measures and phase transitions
We discuss a notion of phase transitions in multicomponent systems and
clarify relations between deterministic chaotic and stochastic models of this
type of systems. Connections between various definitions of SRB measures are
considered as well.Comment: 13 pages, LaTeX 2
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