9,162 research outputs found
Tensor-scalar gravity and binary-pulsar experiments
Some recently discovered nonperturbative strong-field effects in
tensor-scalar theories of gravitation are interpreted as a scalar analog of
ferromagnetism: "spontaneous scalarization". This phenomenon leads to very
significant deviations from general relativity in conditions involving strong
gravitational fields, notably binary-pulsar experiments. Contrary to
solar-system experiments, these deviations do not necessarily vanish when the
weak-field scalar coupling tends to zero. We compute the scalar "form factors"
measuring these deviations, and notably a parameter entering the pulsar timing
observable gamma through scalar-field-induced variations of the inertia moment
of the pulsar. An exploratory investigation of the confrontation between
tensor-scalar theories and binary-pulsar experiments shows that nonperturbative
scalar field effects are already very tightly constrained by published data on
three binary-pulsar systems. We contrast the probing power of pulsar
experiments with that of solar-system ones by plotting the regions they exclude
in a generic two-dimensional plane of tensor-scalar theories.Comment: 35 pages, REVTeX 3.0, uses epsf.tex to include 9 Postscript figure
The Mid-Pleistocene Transition induced by delayed feedback and bistability
The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr
glacial-interglacial cycles that occurred roughly 1 Myr ago, is often
considered as a change in internal climate dynamics. Here we revisit the model
of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988).
We show that it is quantitatively similar to a scalar equation for the ice
dynamics only when combining the remaining components into a single delayed
feedback term. The delay is the sum of the internal times scales of ocean
transport and ice sheet dynamics, which is on the order of 10 kyr. We find
that, in the absence of astronomical forcing, the delayed feedback leads to
bistable behaviour, where stable large-amplitude oscillations of ice volume and
an equilibrium coexist over a large range of values for the delay. We then
apply astronomical forcing. We perform a systematic study to show how the
system response depends on the forcing amplitude. We find that over a wide
range of forcing amplitudes the forcing leads to a switch from small-scale
oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr
without any change of other parameters. The transition in the forced model
consistently occurs near the time of the Mid-Pleistocene Transition as observed
in data records. This provides evidence that the MPT could have been primarily
a forcing-induced switch between attractors of the internal dynamics. Small
additional random disturbances make the forcing-induced transition near 800 kyr
BP even more robust. We also find that the forced system forgets its initial
history during the small-scale oscillations, in particular, nearby initial
conditions converge prior to transitioning. In contrast to this, in the regime
of large-amplitude oscillations, the oscillation phase is very sensitive to
random perturbations, which has a strong effect on the timing of the
deglaciation events
Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
Reaction-diffusion systems can describe a wide class of rhythmic
spatiotemporal patterns observed in chemical and biological systems, such as
circulating pulses on a ring, oscillating spots, target waves, and rotating
spirals. These rhythmic dynamics can be considered limit cycles of
reaction-diffusion systems. However, the conventional phase-reduction theory,
which provides a simple unified framework for analyzing synchronization
properties of limit-cycle oscillators subjected to weak forcing, has mostly
been restricted to low-dimensional dynamical systems. Here, we develop a
phase-reduction theory for stable limit-cycle solutions of infinite-dimensional
reaction-diffusion systems. By generalizing the notion of isochrons to
functional space, the phase sensitivity function - a fundamental quantity for
phase reduction - is derived. For illustration, several rhythmic dynamics of
the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase
response properties and synchronization dynamics are revealed, reflecting their
complex spatiotemporal organization. Our theory will provide a general basis
for the analysis and control of spatiotemporal rhythms in various
reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio
Tensorial Reconstruction at the Integrand Level
We present a new approach to the reduction of one-loop amplitudes obtained by
reconstructing the tensorial expression of the scattering amplitudes. The
reconstruction is performed at the integrand level by means of a sampling in
the integration momentum. There are several interesting applications of this
novel method within existing techniques for the reduction of one-loop multi-leg
amplitudes: to deal with numerically unstable points, such as in the vicinity
of a vanishing Gram determinant; to allow for a sampling of the numerator
function based on real values of the integration momentum; to optimize the
numerical reduction in the case of long expressions for the numerator
functions.Comment: 20 pages, 2 figure
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