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Possible crater-based pingos, paleolakes and periglacial landscapes in the high latitudes of Utopia Planitia, Mars
Experimental Investigation of Gully Formation Under Low Pressure and Low Temperature Conditions
International audienceIntroduction: A large morphological diversity of gullies is observed on Earth and on Mars. Debris flow – a non-newtonian flow comprising a sediment-water mix – is a common process attributed to gully formation on both planets [1, 2]. Many variables can influence the morphology of debris flows (grainsizes, discharge , slope, soil moisture, etc) and their respective influences are difficult to disentangle in the field. Furthermore effects specific to the martian environment have not yet been explored in detail. Some preliminary laboratory simulations have already been performed that isolate some of these variables. Cold room experiments [3] were already perfomed to test the effect of a melted surface layer on the formation of linear gullies over sand dunes. Low pressure experiments [4] were performed to test the effect of the atmospheric pressure on erosional capacity and runout distance of the flows. Our aim is to develop a new set of experiments both under Martian atmospheric pressure and terrestrial atmospheric pressure in order to reproduce the variability of the observed morphologies under well constrained experimental conditions
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
A new method is presented for Fourier decomposition of the Helmholtz Green
Function in cylindrical coordinates, which is equivalent to obtaining the
solution of the Helmholtz equation for a general ring source. The Fourier
coefficients of the Helmholtz Green function are split into their half
advanced+half retarded and half advanced-half retarded components. Closed form
solutions are given for these components in terms of a Horn function and a
Kampe de Feriet function, respectively. The systems of partial differential
equations associated with these two-dimensional hypergeometric functions are
used to construct a fourth-order ordinary differential equation which both
components satisfy. A second fourth-order ordinary differential equation for
the general Fourier coefficent is derived from an integral representation of
the coefficient, and both differential equations are shown to be equivalent.
Series solutions for the various Fourier coefficients are also given, mostly in
terms of Legendre functions and Bessel/Hankel functions. These are derived from
the closed form hypergeometric solutions or an integral representation, or
both. Numerical calculations comparing different methods of calculating the
Fourier coefficients are presented
Application of Edwards' statistical mechanics to high dimensional jammed sphere packings
The isostatic jamming limit of frictionless spherical particles from Edwards'
statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629
(2008)] is generalized to arbitrary dimension using a liquid-state
description. The asymptotic high-dimensional behavior of the self-consistent
relation is obtained by saddle-point evaluation and checked numerically. The
resulting random close packing density scaling is
consistent with that of other approaches, such as replica theory and density
functional theory. The validity of various structural approximations is
assessed by comparing with three- to six-dimensional isostatic packings
obtained from simulations. These numerical results support a growing accuracy
of the theoretical approach with dimension. The approach could thus serve as a
starting point to obtain a geometrical understanding of the higher-order
correlations present in jammed packings.Comment: 13 pages, 7 figure
A Non-supersymmetric Interpretation of the CDF e+e-\gamma\gamma + missing E_T Event
The \eegg event reported recently by the CDF Collaboration has been
interpreted as a signal of supersymmetry in several recent papers. In this
article, we report on an alternative non-supersymmetric interpretation of the
event using an extension of the standard model which contains new physics at
the electroweak scale that does not effect the existing precision electroweak
data. We extend the standard model by including an extra sequential generation
of fermions, heavy right-handed neutrinos for all generations and an extra
singly charged SU(2)-singlet Higgs boson. We discuss possible ways to
discriminate this from the standard supersymemtric interpretations.Comment: 7 pages, Latex, no figure
Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum
Every completely positive map G that commutes which the Hamiltonian time
evolution is an integral or sum over (densely defined) CP-maps G_\sigma where
\sigma is the energy that is transferred to or taken from the environment. If
the spectrum is non-degenerated each G_\sigma is a dephasing channel followed
by an energy shift. The dephasing is given by the Hadamard product of the
density operator with a (formally defined) positive operator. The Kraus
operator of the energy shift is a partial isometry which defines a translation
on R with respect to a non-translation-invariant measure.
As an example, I calculate this decomposition explicitly for the rotation
invariant gaussian channel on a single mode.
I address the question under what conditions a covariant channel destroys
superpositions between mutually orthogonal states on the same orbit. For
channels which allow mutually orthogonal output states on the same orbit, a
lower bound on the quantum capacity is derived using the Fourier transform of
the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly
specified. Presentation more detailed. Implementing the shift after the
dephasing is sometimes more convenien
Collapse models with non-white noises II: particle-density coupled noises
We continue the analysis of models of spontaneous wave function collapse with
stochastic dynamics driven by non-white Gaussian noise. We specialize to a
model in which a classical "noise" field, with specified autocorrelator, is
coupled to a local nonrelativistic particle density. We derive general results
in this model for the rates of density matrix diagonalization and of state
vector reduction, and show that (in the absence of decoherence) both processes
are governed by essentially the same rate parameters. As an alternative route
to our reduction results, we also derive the Fokker-Planck equations that
correspond to the initial stochastic Schr\"odinger equation. For specific
models of the noise autocorrelator, including ones motivated by the structure
of thermal Green's functions, we discuss the qualitative and qantitative
dependence on model parameters, with particular emphasis on possible
cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision
A method for dense packing discovery
The problem of packing a system of particles as densely as possible is
foundational in the field of discrete geometry and is a powerful model in the
material and biological sciences. As packing problems retreat from the reach of
solution by analytic constructions, the importance of an efficient numerical
method for conducting \textit{de novo} (from-scratch) searches for dense
packings becomes crucial. In this paper, we use the \textit{divide and concur}
framework to develop a general search method for the solution of periodic
constraint problems, and we apply it to the discovery of dense periodic
packings. An important feature of the method is the integration of the unit
cell parameters with the other packing variables in the definition of the
configuration space. The method we present led to improvements in the
densest-known tetrahedron packing which are reported in [arXiv:0910.5226].
Here, we use the method to reproduce the densest known lattice sphere packings
and the best known lattice kissing arrangements in up to 14 and 11 dimensions
respectively (the first such numerical evidence for their optimality in some of
these dimensions). For non-spherical particles, we report a new dense packing
of regular four-dimensional simplices with density
and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure
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