6,247 research outputs found
Convective Ripening and Initiation of Rainfall
This paper discusses the evolution of the droplet size distribution for a
liquid-in-gas aerosol contained in a Rayleigh-B\'enard cell. It introduces a
non-collisional model for broadening the droplet size distribution, termed
'convective ripening'. The paper also considers the initiation of rainfall from
ice-free cumulus clouds. It is argued that while collisional mechanisms cannot
explain the production of rain from clouds with water droplet diameters of $20\
\mu {\rm m}$, the non-collisional convective ripening mechanism gives a much
faster route to increasing the size of the small fraction of droplets that grow
into raindrops.Comment: 6 pages, no figure
An exact effective Hamiltonian for a perturbed Landau level
Considers the effect of a scalar potential V (x, y) on a Landau level in two dimensions. An exact effective Hamiltonian is derived which describes the effect of the potential on a single Landau level, expressed as a power series in V/Ec, where Ec is the cyclotron energy. The effective Hamiltonian can be represented as a function H (x, p) in a one-dimensional phase space. The function H (x, p) resembles the potential V (x, y): when the area of a flux quantum is much smaller than the square of the characteristic length scale of V, then H approximately=V. Also H (x, p) retains the translational and rotational symmetries of V(x, y) exactly, but reflection symmetries are not retained beyond the lowest order of the perturbation expansion
Narrowly avoided crossings
In order to create a degeneracy in a quantum mechanical system without symmetries one must vary two parameters in the Hamiltonian. When only one parameter, lambda say, is varied, there is only a finite closest approach Delta E of two eigenvalues, and never a crossing. Often the gaps Delta E in these avoided crossings are much smaller than the mean spacing between the eigenvalues, and it has been conjectured that in this case the gap results from tunnelling through classically forbidden regions of phase space and decreases exponentially as h(cross) to 0: Delta E=Ae-S/h(cross). The author reports the results of numerical calculations on a system with two parameters, epsilon , lambda , which is completely integrable when epsilon =0. It if found that the gaps Delta E obtained by varying lambda decrease exponentially as h(cross) to 0, consistent with the tunnelling conjecture. When epsilon =0, Delta E=0 because the system is completely integrable. As epsilon to 0, the gaps do not vanish because the prefactor A vanishes; instead it is found that S diverges logarithmically. Also, keeping h(cross) fixed, the gaps are of size Delta E=O( epsilon nu ), where nu is usually very close to an integer. Theoretical arguments are presented which explain this result
Non-adiabatic transitions in multi-level systems
In a quantum system with a smoothly and slowly varying Hamiltonian, which
approaches a constant operator at times , the transition
probabilities between adiabatic states are exponentially small. They are
characterized by an exponent that depends on a phase integral along a path
around a set of branch points connecting the energy level surfaces in complex
time. Only certain sequences of branch points contribute. We propose that these
sequences are determined by a topological rule involving the Stokes lines
attached to the branch points. Our hypothesis is supported by theoretical
arguments and results of numerical experiments.Comment: 25 pages RevTeX, 9 figures and 4 tables as Postscipt file
Planet Formation by Concurrent Collapse
After reviewing the difficulties faced by the conventional theory of planet
formation (based upon the aggregation of microscopic dust particles), we
describe an alternative hypothesis. We propose that planets form by
gravitational collapse at the same time as the star about which they orbit.
This 'concurrent collapse' hypothesis avoids theoretical difficulties
associated with the conventional model and suggests satisfying explanations for
various poorly understood phenomena. We introduce new explanations for FU
Orionis outbursts seen in young stars, the discovery of exoplanets with
eccentric orbits and the existence of small rocky objects such as chondrules in
the solar system.Comment: 16 pages, no figures, extended and refined version of earlier
submissio
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