10,215 research outputs found
Consecutive primes in tuples
In a recent advance towards the Prime -tuple Conjecture, Maynard and Tao
have shown that if is sufficiently large in terms of , then for an
admissible -tuple of linear forms in
, the set contains at
least primes for infinitely many . In this note, we
deduce that contains at least
consecutive primes for infinitely many . We answer an old
question of Erd\H os and Tur\'an by producing strings of consecutive
primes whose successive gaps form an increasing
(resp. decreasing) sequence. We also show that such strings exist with
for . For any coprime integers
and we find arbitrarily long strings of consecutive primes with bounded
gaps in the congruence class .Comment: Revised versio
Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors
In this paper, we will show that a periodic nonlinear, time-varying
dissipative system that is defined on a genus-p surface contains one or more
invariant sets which act as attractors. Moreover, we shall generalize a result
in [Martins, 2004] and give conditions under which these invariant sets are not
homeomorphic to a circle individually, which implies the existence of chaotic
behaviour. This is achieved by studying the appearance of inversely unstable
solutions within each invariant set.Comment: 19 pages with 20 figures, AMS La-TeX, to be published in
International Journal of Bifurcation and Chao
Out of equilibrium: understanding cosmological evolution to lower-entropy states
Despite the importance of the Second Law of Thermodynamics, it is not
absolute. Statistical mechanics implies that, given sufficient time, systems
near equilibrium will spontaneously fluctuate into lower-entropy states,
locally reversing the thermodynamic arrow of time. We study the time
development of such fluctuations, especially the very large fluctuations
relevant to cosmology. Under fairly general assumptions, the most likely
history of a fluctuation out of equilibrium is simply the CPT conjugate of the
most likely way a system relaxes back to equilibrium. We use this idea to
elucidate the spacetime structure of various fluctuations in (stable and
metastable) de Sitter space and thermal anti-de Sitter space.Comment: 27 pages, 11 figure
Ten Dimensional Black Hole and the D0-brane Threshold Bound State
We discuss the ten dimensional black holes made of D0-branes in the regime
where the effective coupling is large, and yet the 11D geometry is unimportant.
We suggest that these black holes can be interpreted as excitations over the
threshold bound state. Thus, the entropy formula for the former is used to
predict a scaling region of the wave function of the latter. The horizon radius
and the mass gap predicted in this picture agree with the formulas derived from
the classical geometry.Comment: 11 pages, harvmac; v2: typos corrected, argument for the convergence
of two integrals improved, v3: one ref. adde
Nonsingular Lagrangians for Two Dimensional Black Holes
We introduce a large class of modifications of the standard lagrangian for
two dimensional dilaton gravity, whose general solutions are nonsingular black
holes. A subclass of these lagrangians have extremal solutions which are
nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is
possible that quantum deformations of these extremal solutions are the endpoint
of Hawking evaporation when the models are coupled to matter, and that the
resulting evolution may be studied entirely within the framework of the
semiclassical approximation. Numerical work to verify this conjecture is in
progress. We point out however that the solutions with non-negative mass always
contain Cauchy horizons, and may be sensitive to small perturbations.Comment: 27 pages, three figures, RU-92-61. (Replaced version contains some
corrections to incorrect equations. The zero temperature extremal geometry
(the conjectured end-point of the Hawking evaporation) is not as stated in
the previous version, but rather is a nonsingular analogue of the zero
temperature Reissner-Nordstrom space-time.
Comments on information loss and remnants
The information loss and remnant proposals for resolving the black hole
information paradox are reconsidered. It is argued that in typical cases
information loss implies energy loss, and thus can be thought of in terms of
coupling to a spectrum of ``fictitious'' remnants. This suggests proposals for
information loss that do not imply planckian energy fluctuations in the low
energy world. However, if consistency of gravity prevents energy
non-conservation, these remnants must then be considered to be real. In either
case, the catastrophe corresponding to infinite pair production remains a
potential problem. Using Reissner-Nordstrom black holes as a paradigm for a
theory of remnants, it is argued that couplings in such a theory may give
finite production despite an infinite spectrum. Evidence for this is found in
analyzing the instanton for Schwinger production; fluctuations from the
infinite number of states lead to a divergent stress tensor, spoiling the
instanton calculation. Therefore naive arguements for infinite production fail.Comment: 30 pages (harvmac l mode) UCSBTH-93-35 (minor reference and typo
corrections
On the Possibility of Large Axion Decay Constants
The decay constant of the QCD axion is required by observation to be small
compared to the Planck scale. In theories of "natural inflation," and certain
proposed anthropic solutions of the cosmological constant problem, it would be
interesting to obtain a large decay constant for axion-like fields from
microscopic physics. String theory is the only context in which one can
sensibly address this question. Here we survey a number of periodic fields in
string theory in a variety of string vacua. In some examples, the decay
constant can be parameterically larger than the Planck scale but the effective
action then contains appreciable harmonics of order . As a result,
these fields are no better inflaton candidates than Planck scale axions.Comment: 17 pages, no figures, minor change mad
Report from space plasma science
Space plasma science, especially plasma experiments in space, is discussed. Computational simulations, wave generation and propagation, wave-particle interactions, charged particle acceleration, particle-particle interactions, radiation transport in dense plasmas, macroscopic plasma flow, plasma-magnetic field interactions, plasma-surface interactions, prospects for near-term plasma science experiments in space and three-dimensional plasma experiments are among the topics discussed
Comment about quasi-isotropic solution of Einstein equations near cosmological singularity
We generalize for the case of arbitrary hydrodynamical matter the
quasi-isotropic solution of Einstein equations near cosmological singularity,
found by Lifshitz and Khalatnikov in 1960 for the case of radiation-dominated
universe. It is shown that this solution always exists, but dependence of terms
in the quasi-isotropic expansion acquires a more complicated form.Comment: 7 pages, The collective of authors is enlarged and some comments and
references are adde
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