41,853 research outputs found
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
Causality Violations in Cascade Models of Nuclear Collisions
Transport models have successfully described many aspects of intermediate
energy heavy-ion collision dynamics. As the energies increase in these models
to the ultrarelativistic regime, Lorentz covariance and causality are not
strictly respected. The standard argument is that such effects are not
important to final results; but they have not been seriously considered at high
energies. We point out how and why these happen, how serious of a problem they
may be and suggest ways of reducing or eliminating the undesirable effects.Comment: RevTeX, 23 pages, 9 (uuencoded) figures; to appear in Phys. Rev
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
Probing the circulation of ring-shaped Bose-Einstein condensates
This paper reports the results of a theoretical and experimental study of how
the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be
probed by time-of-flight (TOF) images. We have studied theoretically the
dynamics of a BEC after release from a toroidal trap potential by solving the
3D Gross-Pitaevskii (GP) equation. The trap and condensate characteristics
matched those of a recent experiment. The circulation, experimentally imparted
to the condensate by stirring, was simulated theoretically by imprinting a
linear azimuthal phase on the initial condensate wave function. The theoretical
TOF images were in good agreement with the experimental data. We find that upon
release the dynamics of the ring--shaped condensate proceeds in two distinct
phases. First, the condensate expands rapidly inward, filling in the initial
hole until it reaches a minimum radius that depends on the initial circulation.
In the second phase, the density at the inner radius increases to a maximum
after which the hole radius begins slowly to expand. During this second phase a
series of concentric rings appears due to the interference of ingoing and
outgoing matter waves from the inner radius. The results of the GP equation
predict that the hole area is a quadratic function of the initial circulation
when the condensate is released directly from the trap in which it was stirred
and is a linear function of the circulation if the trap is relaxed before
release. These scalings matched the data. Thus, hole size after TOF can be used
as a reliable probe of initial condensate circulation. This connection between
circulation and hole size after TOF will facilitate future studies of
atomtronic systems that are implemented in ultracold quantum gases.Comment: 9 pages, 9 figure
Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries
Lie group theory states that knowledge of a -parameters solvable group of
symmetries of a system of ordinary differential equations allows to reduce by
the number of equations. We apply this principle by finding some
\emph{affine derivations} that induces \emph{expanded} Lie point symmetries of
considered system. By rewriting original problem in an invariant coordinates
set for these symmetries, we \emph{reduce} the number of involved parameters.
We present an algorithm based on this standpoint whose arithmetic complexity is
\emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can
generally reduce the number of parameters defining the system behavior by
studying the system's Lie symmetrie
Modeling scenarios for water allocation in the Gediz Basin, Turkey
Water management / Water allocation / Models / River basin development / Hydrology / Decision making / Environmental effects / Water use efficiency / Climate / Irrigation water / Irrigated farming / Stream flow / Surface water / Salt water intrusion / Turkey / Gediz Basin
Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4
We describe three presentations relating to the X-ray pulsar GX 1+4 at a
workshop on magnetic fields and accretion at the Astrophysical Theory Centre,
Australian National University on 1998, November 12-13. Optical and X-ray
spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly
bound matter. We discuss an unstable negative feedback mechanism (originally
proposed by Kotani et al, 1999), based on X-ray heating of this matter which
controls the accretion rate when the source is in a low X-ray luminosity state.
A deep minimum lasting ~6 hours occurred during observations with the RXTE
satellite over 1996, July 19-21. The shape of the X-ray pulses changed
remarkably from before to after the minimum. These changes may be related to
the transition from neutron star spin-down to spin-up which occurred at about
the same time. Smoothed particle hydrodynamic simulations of the effect of
adding matter with opposite angular momentum to an existing disc, show that it
is possible for a number of concentric rings with alternating senses of
rotation to co-exist in a disc. This could provide an explanation for the
step-like changes in Pdot which are observed in GX 1+4. Changes at the inner
boundary of the disc occur at the same timescale as that imposed at the outer
boundary. Reversals of material torque on the neutron star occur at a minimum
in L_X.Comment: 10 pages, 5 figures; accepted for publication by PAS
Detection of continuous variable entanglement without coherent local oscillators
We propose three criteria for identifying continuous variable entanglement
between two many-particle systems with no restrictions on the quantum state of
the local oscillators used in the measurements. Mistakenly asserting a coherent
state for the local oscillator can lead to incorrectly identifying the presence
of entanglement. We demonstrate this in simulations with 100 particles, and
also find that large number fluctuations do not prevent the observation of
entanglement. Our results are important for quantum information experiments
with realistic Bose-Einstein condensates or in optics with arbitrary photon
states.Comment: 7 Pages, 4 Figure
Interplanetary propulsion using inertial fusion
Inertial fusion can be used to power spacecraft within the solar system and beyond. Such spacecraft have the potential for short-duration manned-mission performance exceeding other technologies. We are conducting a study to assess the systems aspects of inertial fusion as applied to such missions, based on the conceptual engine design of Hyde (1983) we describe the required systems for an entirely new spacecraft design called VISTA that is based on the use of DT fuel. We give preliminary design details for the power conversion and power conditioning systems for manned missions to Mars of total duration of about 100 days. Specific mission performance results will be published elsewhere, after the study has been completed
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