2,043 research outputs found
On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing
We prove that for divergent series solutions of nonlinear (or linear)
differential systems near a generic irregular singularity, the common
prescription of summation to the least term is, if properly interpreted,
meaningful and correct, and we extend this method to transseries solutions. In
every direction in the complex plane at the singularity (Stokes directions {\em
not} excepted) there exists a nonempty set of solutions whose difference from
the ``optimally'' (i.e., near the least term) truncated asymptotic series is of
the same (exponentially small) order of magnitude as the least term of the
series. There is a family of generalized Borel summation formulas
which commute with the usual algebraic and analytic operations (addition,
multiplication, differentiation, etc). We show that there is exactly one of
them, , such that for any formal series solution ,
differs from the optimal truncation of
by at most the order of the least term of . We show in addition that
the Berry (1989) smoothing phenomenon is universal within this class of
differential systems. Whenever the terms ``beyond all orders'' {\em change} in
crossing a Stokes line, these terms vary smoothly on the Berry scale
and the transition is always given by the error
function; under the same conditions we show that Dingle's rule of signs for
Stokes transitions holds
A Logic for Non-Deterministic Parallel Abstract State Machines
We develop a logic which enables reasoning about single steps of
non-deterministic parallel Abstract State Machines (ASMs). Our logic builds
upon the unifying logic introduced by Nanchen and St\"ark for reasoning about
hierarchical (parallel) ASMs. Our main contribution to this regard is the
handling of non-determinism (both bounded and unbounded) within the logical
formalism. Moreover, we do this without sacrificing the completeness of the
logic for statements about single steps of non-deterministic parallel ASMs,
such as invariants of rules, consistency conditions for rules, or step-by-step
equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748
Rifts in Spreading Wax Layers
We report experimental results on the rift formation between two freezing wax
plates. The plates were pulled apart with constant velocity, while floating on
the melt, in a way akin to the tectonic plates of the earth's crust. At slow
spreading rates, a rift, initially perpendicular to the spreading direction,
was found to be stable, while above a critical spreading rate a "spiky" rift
with fracture zones almost parallel to the spreading direction developed. At
yet higher spreading rates a second transition from the spiky rift to a zig-zag
pattern occurred. In this regime the rift can be characterized by a single
angle which was found to be dependent on the spreading rate. We show that the
oblique spreading angles agree with a simple geometrical model. The coarsening
of the zig-zag pattern over time and the three-dimensional structure of the
solidified crust are also discussed.Comment: 4 pages, Postscript fil
On the physical meaning of Fermi coordinates
(Some Latex problems should be removed in this version) Fermi coordinates
(FC) are supposed to be the natural extension of Cartesian coordinates for an
arbitrary moving observer in curved space-time. Since their construction cannot
be done on the whole space and even not in the whole past of the observer we
examine which construction principles are responsible for this effect and how
they may be modified. One proposal for a modification is made and applied to
the observer with constant acceleration in the two and four dimensional
Minkowski space. The two dimensional case has some surprising similarities to
Kruskal space which generalize those found by Rindler for the outer region of
Kruskal space and the Rindler wedge. In perturbational approaches the
modification leads also to different predictions for certain physical systems.
As an example we consider atomic interferometry and derive the deviation of the
acceleration-induced phase shift from the standard result in Fermi coordinates.Comment: 11 pages, KONS-RGKU-94/02 (Latex
Global properties of warped solutions in General Relativity
Assuming the four-dimensional space-time to be a general warped product of
two surfaces we reduce the four-dimensional Einstein equations to a
two-dimensional problem which can be solved. All global vacuum solutions are
explicitly constructed and analysed. The classification of the solutions
includes the Schwarzschild, the (anti-)de Sitter, and other well-known
solutions but also many exact ones whose detailed global properties to our
knowledge have not been discussed before. They have a natural physical
interpretation describing single or several wormholes, domain walls of
curvature singularities, cosmic strings, cosmic strings surrounded by domain
walls, solutions with closed timelike curves, etc.Comment: 35 pages, 5 eps figures, minor change
Gauge Field Back-reaction on a Black Hole
The order fluctuations of gauge fields in the vicinity of a blackhole
can create a repulsive antigravity region extending out beyond the renormalized
Schwarzschild horizon. If the strength of this repulsive force increases as
higher orders in the back-reaction are included, the formation of a
wormhole-like object could occur.Comment: 17 pages, three figures available on request, in RevTe
Nucleating Black Holes via Non-Orientable Instantons
We extend the analysis of black hole pair creation to include non- orientable
instantons. We classify these instantons in terms of their fundamental
symmetries and orientations. Many of these instantons admit the pin structure
which corresponds to the fermions actually observed in nature, and so the
natural objection that these manifolds do not admit spin structure may not be
relevant. Furthermore, we analyse the thermodynamical properties of
non-orientable black holes and find that in the non-extreme case, there are
interesting modifications of the usual formulae for temperature and entropy.Comment: 27 pages LaTeX, minor typos are correcte
Cosmological Surrealism: More than ``Eternal Reality" is Needed
Inflationary Cosmology makes the universe ``eternal" and provides for
recurrent universe creation, ad infinitum -- making it also plausible to assume
that ``our" Big Bang was also preceeded by others, etc.. However, GR tells us
that in the ``parent" universe's reference frame, the newborn universe's
expansion will never start. Our picture of ``reality" in spacetime has to be
enlarged.Comment: 7 pages, TAUP N23
Sampling a Littoral Fish Assemblage: Comparison of Small-Mesh Fyke Netting and Boat Electrofishing
We compared small-mesh (4-mm) fyke netting and boat electrofishing for sampling a littoral fish assemblage in Muskegon Lake, Michigan. We hypothesized that fyke netting selects for small-bodied fishes and electrofishing selects for large-bodied fishes. Three sites were sampled during May (2004 and 2005), July (2005 only), and September (2004 and 2005). We found that the species composition of captured fish differed considerably between fyke netting and electrofishing based on nonmetric multidimensional scaling (NMDS). Species strongly associated with fyke netting (based on NMDS and relative abundance) included the brook silverside Labidesthes sicculus, banded killifish Fundulus diaphanus, round goby Neogobius melanostomus, mimic shiner Notropis volucellus, and bluntnose minnow Pimephales notatus, whereas species associated with electrofishing included the Chinook salmon Oncorhynchus tshawytscha, catostomids (Moxostoma spp. and Catostomus spp.), freshwater drum Aplodinotus grunniens, walleye Sander vitreus, gizzard shad Dorosoma cepedianum, and common carp Cyprinus carpio. The total length of fish captured by electrofishing was 12.8 cm (95% confidence interval ¼ 5.5– 17.2 cm) greater than that of fish captured by fyke netting. Size selectivity of the gears contributed to differences in species composition of the fish captured, supporting our initial hypothesis. Thus, small-mesh fyke nets and boat electrofishers provided complementary information on a littoral fish assemblage. Our results support use of multiple gear types in monitoring and research surveys of fish assemblages.
Copyright by the American Fisheries Society 2007, Originally published in the North American Journal of Fisheries Management 27: 825-831, 2007
Black Holes in Modified Gravity (MOG)
The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified
gravity (MOG) have a static, spherically symmetric black hole solution
determined by the mass with two horizons. The strength of the gravitational
constant is where is a parameter. A regular
singularity-free MOG solution is derived using a nonlinear field dynamics for
the repulsive gravitational field component and a reasonable physical
energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole
solution is obtained. The Kerr-MOG black hole solution is determined by the
mass , the parameter and the spin angular momentum . The
equations of motion and the stability condition of a test particle orbiting the
MOG black hole are derived, and the radius of the black hole photosphere and
the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are
calculated. A traversable wormhole solution is constructed with a throat
stabilized by the repulsive component of the gravitational field.Comment: 14 pages, 3 figures. Upgraded version of paper to match published
version in European Physics Journal
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