22,501 research outputs found
Nucleation of colloids and macromolecules: does the nucleation pathway matter?
A recent description of diffusion-limited nucleation based on fluctuating
hydrodynamics that extends classical nucleation theory predicts a very
non-classical two-step scenario whereby nucleation is most likely to occur in
spatially-extended, low-amplitude density fluctuations. In this paper, it is
shown how the formalism can be used to determine the maximum probability of
observing \emph{any} proposed nucleation pathway, thus allowing one to address
the question as to their relative likelihood, including of the newly proposed
pathway compared to classical scenarios. Calculations are presented for the
nucleation of high-concentration bubbles in a low-concentration solution of
globular proteins and it is found that the relative probabilities (new theory
compared to classical result) for reaching a critical nucleus containing
molecules scales as thus indicating that for all but the smallest
nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure
Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole
Slice stretching effects such as slice sucking and slice wrapping arise when
foliating the extended Schwarzschild spacetime with maximal slices. For
arbitrary spatial coordinates these effects can be quantified in the context of
boundary conditions where the lapse arises as a linear combination of odd and
even lapse. Favorable boundary conditions are then derived which make the
overall slice stretching occur late in numerical simulations. Allowing the
lapse to become negative, this requirement leads to lapse functions which
approach at late times the odd lapse corresponding to the static Schwarzschild
metric. Demanding in addition that a numerically favorable lapse remains
non-negative, as result the average of odd and even lapse is obtained. At late
times the lapse with zero gradient at the puncture arising for the puncture
evolution is precisely of this form. Finally, analytic arguments are given on
how slice stretching effects can be avoided. Here the excision technique and
the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice
stretching can be avoided by using excision and/or shift
Level structures on the Weierstrass family of cubics
Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For
each N >= 2, we construct surfaces parametrizing the three standard kinds of
level N structures on the smooth fibers of W. We then complete these surfaces
to finite covers of A^2. Since W -> A^2 is the versal deformation space of a
cusp singularity, these surfaces convey information about the level structure
on any family of curves of genus g degenerating to a cuspidal curve. Our goal
in this note is to determine for which values of N these surfaces are smooth
over (0,0). From a topological perspective, the results determine the
homeomorphism type of certain branched covers of S^3 with monodromy in
SL_2(Z/N).Comment: LaTeX, 12 pages; added section giving a topological interpretation of
the result
Unstable Hadrons in Hot Hadron Gas in Laboratory and in the Early Universe
We study kinetic master equations for chemical reactions involving the
formation and the natural decay of unstable particles in a thermal bath. We
consider the decay channel of one into two particles, and the inverse process,
fusion of two thermal particles into one. We present the master equations the
evolution of the density of the unstable particles in the early Universe. We
obtain the thermal invariant reaction rate using as an input the free space
(vacuum) decay time and show the medium quantum effects on reaction relaxation time. As another laboratory example
we describe the process in thermal hadronic gas in
heavy-ion collisions. A particularly interesting application of our formalism
is the process in the early Universe.
We also explore the physics of and freeze-out in the
Universe.Comment: 13 pages, 9 figures, published in Physical Review
Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
To calculate the baryon asymmetry in the baryogenesis via leptogenesis
scenario one usually uses Boltzmann equations with transition amplitudes
computed in vacuum. However, the hot and dense medium and, potentially, the
expansion of the universe can affect the collision terms and hence the
generated asymmetry. In this paper we derive the Boltzmann equation in the
curved space-time from (first-principle) Kadanoff-Baym equations. As one
expects from general considerations, the derived equations are covariant
generalizations of the corresponding equations in Minkowski space-time. We find
that, after the necessary approximations have been performed, only the
left-hand side of the Boltzmann equation depends on the space-time metric. The
amplitudes in the collision term on the right--hand side are independent of the
metric, which justifies earlier calculations where this has been assumed
implicitly. At tree level, the matrix elements coincide with those computed in
vacuum. However, the loop contributions involve additional integrals over the
the distribution function.Comment: 14 pages, 5 figures, extended discussion of the constraint equations
and the solution for the spectral functio
Dynamic autonomous intelligent control of an asteroid lander
One of the future flagship missions of the European Space Agency (ESA) is the asteroid sample return mission Marco-Polo. Although there have been a number of past missions to asteroids, a sample has never been successfully returned. The return of asteroid regolith to the Earth's surface introduces new technical challenges. This paper develops attitude control algorithms for the descent phase onto an asteroid in micro-gravity conditions and draws a comparison between the algorithms considered. Two studies are also performed regarding the Fault Detection Isolation and Recovery (FDIR) of the control laws considered. The potential of using Direct Adaptive Control (DAC) as a controller for the surface sampling process is also investigated. Use of a DAC controller incorporates increased levels of robustness by allowing realtime variation of control gains. This leads to better response to uncertainties encountered during missions
The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)
Automorphic distributions for SL(2) arise as boundary values of modular forms
and, in a more subtle manner, from Maass forms. In the case of modular forms of
weight one or of Maass forms, the automorphic distributions have continuous
first antiderivatives. We recall earlier results of one of us on the Holder
continuity of these continuous functions and relate them to results of other
authors; this involves a generalization of classical theorems on Fourier series
by S. Bernstein and Hardy-Littlewood. We then show that the antiderivatives are
non-differentiable at all irrational points, as well as all, or in certain
cases, some rational points. We include graphs of several of these functions,
which clearly display a high degree of oscillation. Our investigations are
motivated in part by properties of "Riemann's nondifferentiable function", also
known as "Weierstrass' function".Comment: 27 pages, 6 Figures; version 2 corrects misprints and updates
reference
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