53,500 research outputs found
Travelling waves in a tissue interaction model for skin pattern formation
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed
Thermal instabilities in protogalactic clouds
The means by which a protogalaxy can fragment to form the first generation of stars and globular clusters remains an important problem in astrophysics. Gravitational instabilities grow on timescales too long to drive fragmentation before the background density grows by many orders of magnitude (see Murray and Lin 1989a, and references therein). Thermal instability provides a much more likely mechanism. After its initial collapse, a protogalactic cloud is expected to be shock heated to its virial temperature approx. 10(exp 6) K. Cooling by H and He+ below 10(exp 6) K has a negative slope, so that the cloud is subject to strong thermal instabilities. Density enhancements may then grow rapidly, fragmenting the protogalaxy as it cools to lower temperatures. The role of dynamical effects upon the growth of perturbations is considered here. The method used is similar to that used in Murray and Lin (1989a; see also the Erratum to appear September 15), which examined the growth of thermal instabilities with a one-dimensional Lagrangian hydrodynamics code, written for spherical symmetry. Perturbed regions therefore take the form of shells. The dynamical variables are integrated explicitly, while the temperature, ionization fraction, and molecular fraction are integrated implicitly, and account is taken for non-equilibrium values of these quantities
Analog communication over selective fading channels Interim technical report
Demodulators for analog communication over slowly time varying, frequency selective fading channel
Relativistic Effects in Extrasolar Planetary Systems
This paper considers general relativistic (GR) effects in currently observed
extrasolar planetary systems. Although GR corrections are small, they can
compete with secular interactions in these systems and thereby play an
important role. Specifically, some of the observed multiple planet systems are
close to secular resonance, where the dynamics is extremely sensitive to GR
corrections, and these systems can be used as laboratories to test general
relativity. For the three-planet solar system Upsilon Andromedae, secular
interaction theory implies an 80% probability of finding the system with its
observed orbital elements if GR is correct, compared with only a 2% probability
in the absence of GR. In the future, tighter constraints can be obtained with
increased temporal coverage.Comment: Accepted for publication in International Journal of Modern Physics
D; this paper received ``Honorable Mention'' in the 2006 Essay Competition of
the Gravity Research Foundation; 9 pages including 1 figur
Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle
Using median-unbiased estimation based on Augmented-Dickey-Fuller (ADF) regressions, recent research has questioned the validity of Rogoff's "remarkable consensus" of 3-5 year half-lives of deviations from PPP. The confidence intervals of these half-life estimates, however, are extremely wide, with lower bounds of about one year and upper bounds of infinity. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that combining median-unbiased estimation with this regression has the potential to tighten confidence intervals for the half-lives. Using long horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just under 3 years. Thus, while previous confidence intervals for median-unbiased half-lives are consistent with virtually anything, our tighter confidence intervals are inconsistent with economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates and move us away from solving the PPP puzzle.PPP puzzle, median-unbiased, persistence.
Binaries and core-ring structures in self-gravitating systems
Low energy states of self-gravitating systems with finite angular momentum
are considered. A constraint is introduced to confine cores and other condensed
objects within the system boundaries by gravity alone. This excludes previously
observed astrophysically irrelevant asymmetric configurations with a single
core. We show that for an intermediate range of a short-distance cutoff and
small angular momentum, the equilibrium configuration is an asymmetric binary.
For larger angular momentum or for a smaller range of the short distance
cutoff, the equilibrium configuration consists of a central core and an
equatorial ring. The mass of the ring varies between zero for vanishing
rotation and the full system mass for the maximum angular momentum a
localized gravitationally bound system can have. The value of scales
as , where is a ratio of a short-distance cutoff range
to the system size. An example of the soft gravitational potential is
considered; the conclusions are shown to be valid for other forms of
short-distance regularization.Comment: 6 pages, 3 figure
Sequential pattern formation in a model for skin morphogenesis
During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in a two-dimensional domain by a tissue interaction mechanochemical model for skin pattern formation. It is shown that the model can exhibit travelling waves of complex spatial pattern formation. Two alternative mechanisms that can produce such sequential patterning are presented. In particular, it is demonstrated that the specification of a simple quasi-one-dimensional pattern is all that is required to determine a complex two-dimensional pattern. Finally, the model solutions are related to actual pattern propagation during chick feather primordia initiation
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