27,899 research outputs found
Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance
Pairs of migrating extrasolar planets often lock into mean motion resonance
as they drift inward. This paper studies the convergent migration of giant
planets (driven by a circumstellar disk) and determines the probability that
they are captured into mean motion resonance. The probability that such planets
enter resonance depends on the type of resonance, the migration rate, the
eccentricity damping rate, and the amplitude of the turbulent fluctuations.
This problem is studied both through direct integrations of the full 3-body
problem, and via semi-analytic model equations. In general, the probability of
resonance decreases with increasing migration rate, and with increasing levels
of turbulence, but increases with eccentricity damping. Previous work has shown
that the distributions of orbital elements (eccentricity and semimajor axis)
for observed extrasolar planets can be reproduced by migration models with
multiple planets. However, these results depend on resonance locking, and this
study shows that entry into -- and maintenance of -- mean motion resonance
depends sensitively on migration rate, eccentricity damping, and turbulence.Comment: 43 pages including 14 figures; accepted for publication in The
Astrophysical Journa
Modeling the secular evolution of migrating planet pairs
The subject of this paper is the secular behaviour of a pair of planets
evolving under dissipative forces. In particular, we investigate the case when
dissipative forces affect the planetary semi-major axes and the planets move
inward/outward the central star, in a process known as planet migration. To
perform this investigation, we introduce fundamental concepts of conservative
and dissipative dynamics of the three-body problem. Based on these concepts, we
develop a qualitative model of the secular evolution of the migrating planetary
pair. Our approach is based on analysis of the energy and the orbital angular
momentum exchange between the two-planet system and an external medium; thus no
specific kind of dissipative forces is invoked. We show that, under assumption
that dissipation is weak and slow, the evolutionary routes of the migrating
planets are traced by the Mode I and Mode II stationary solutions of the
conservative secular problem. The ultimate convergence and the evolution of the
system along one of these secular modes of motion is determined uniquely by the
condition that the dissipation rate is sufficiently smaller than the proper
secular frequency of the system. We show that it is possible to reassemble the
starting configurations and migration history of the systems on the basis of
their final states and consequently to constrain the parameters of the physical
processes involved.Comment: 20 pages, 17 figures. Accepted for publication in MNRA
A general model of resonance capture in planetary systems: First and second order resonances
Mean motion resonances are a common feature of both our own Solar System and
of extrasolar planetary systems. Bodies can be trapped in resonance when their
orbital semi-major axes change, for instance when they migrate through a
protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the
capture behaviour for first and second order resonances. Using this method, all
resonances of the same order can be described by one equation, with
applications to specific resonances by appropriate scaling. We focus on the
limit where one body is a massless test particle and the other a massive
planet. We quantify how the the probability of capture into a resonance depends
on the relative migration rate of the planet and particle, and the particle's
eccentricity. Resonant capture fails for high migration rates, and has
decreasing probability for higher eccentricities. More massive planets can
capture particles at higher eccentricities and migration rates. We also
calculate libration amplitudes and the offset of the libration centres for
captured particles, and the change in eccentricity if capture does not occur.
Libration amplitudes are higher for larger initial eccentricity. The model
allows for a complete description of a particle's behaviour as it successively
encounters several resonances. We discuss implications for several scenarios:
(i) Planet migration through gas discs trapping other planets or planetesimals
in resonances. (ii) Planet migration through a debris disc. (iii) Dust
migration through PR drag. The Hamiltonian model will allow quick
interpretation of the resonant properties of extrasolar planets and Kuiper Belt
Objects, and will allow synthetic images of debris disc structures to be
quickly generated, which will be useful for predicting and interpreting disc
images made with ALMA, Darwin/TPF or similar missions. [Abridged]Comment: 19 pages, 14 figures; accepted to MNRA
Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model
Chemoattractant gradients are usually considered in terms of sources and sinks that are independent of the chemotactic cell. However, recent interest has focused on ‘self-generated’ gradients, in which cell populations create their own local gradients as they move. Here, we consider the interplay between chemoattractants and single cells. To achieve this, we extend a recently developed computational model to incorporate breakdown of extracellular attractants by membrane-bound enzymes. Model equations are parametrized, using the published estimates from Dictyostelium cells chemotaxing towards cyclic AMP. We find that individual cells can substantially modulate their local attractant field under physiologically appropriate conditions of attractant and enzymes. This means the attractant concentration perceived by receptors can be a small fraction of the ambient concentration. This allows efficient chemotaxis in chemoattractant concentrations that would be saturating without local breakdown. Similar interactions in which cells locally mould a stimulus could function in many types of directed cell motility, including haptotaxis, durotaxis and even electrotaxis
Fog-supported delay-constrained energy-saving live migration of VMs over multiPath TCP/IP 5G connections
The incoming era of the fifth-generation fog computing-supported radio access networks (shortly, 5G FOGRANs) aims at exploiting computing/networking resource virtualization, in order to augment the limited resources of wireless devices through the seamless live migration of virtual machines (VMs) toward nearby fog data centers. For this purpose, the bandwidths of the multiple wireless network interface cards of the wireless devices may be aggregated under the control of the emerging MultiPathTCP (MPTCP) protocol. However, due to the fading and mobility-induced phenomena, the energy consumptions of the current state-of-the-art VM migration techniques may still offset their expected benefits. Motivated by these considerations, in this paper, we analytically characterize and implement in software and numerically test the optimal minimum-energy settable-complexity bandwidth manager (SCBM) for the live migration of VMs over 5G FOGRAN MPTCP connections. The key features of the proposed SCBM are that: 1) its implementation complexity is settable on-line on the basis of the target energy consumption versus implementation complexity tradeoff; 2) it minimizes the network energy consumed by the wireless device for sustaining the migration process under hard constraints on the tolerated migration times and downtimes; and 3) by leveraging a suitably designed adaptive mechanism, it is capable to quickly react to (possibly, unpredicted) fading and/or mobility-induced abrupt changes of the wireless environment without requiring forecasting. The actual effectiveness of the proposed SCBM is supported by extensive energy versus delay performance comparisons that cover: 1) a number of heterogeneous 3G/4G/WiFi FOGRAN scenarios; 2) synthetic and real-world workloads; and, 3) MPTCP and wireless connections
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The influence of the atmospheric boundary layer on nocturnal layers of noctuids and other moths migrating over southern Britain
Insects migrating at high altitude over southern Britain have been continuously monitored by automatically-operating, vertical-looking radars over a period of several years. During some occasions in the summer months, the migrants were observed to form well-defined layer concentrations, typically at heights of 200-400 m, in the stable night-time atmosphere. Under these conditions, insects are likely to have control over their vertical movements and are selecting flight heights which are favourable for long-range migration. We therefore investigated the factors influencing the formation of these insect layers by comparing radar measurements of the vertical distribution of insect density with meteorological profiles generated by the UK Met. Office’s Unified Model (UM). Radar-derived measurements of mass and displacement speed, along with data from Rothamsted Insect Survey light traps provided information on the identity of the migrants. We present here three case studies where noctuid and pyralid moths contributed substantially to the observed layers. The major meteorological factors influencing the layer concentrations appeared to be: (a) the altitude of the warmest air, (b) heights corresponding to temperature preferences or thresholds for sustained migration and (c), on nights when air temperatures are relatively high, wind-speed maxima associated with the nocturnal jet. Back-trajectories indicated that layer duration may have been determined by the distance to the coast. Overall, the unique combination of meteorological data from the UM and insect data from entomological radar described here show considerable promise for systematic studies of high-altitude insect layering
Global existence for a degenerate haptotaxis model of tumor invasion under the go-or-grow dichotomy hypothesis
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer
cell invasion through a tissue network under the go-or-grow hypothesis
asserting that cancer cells can either move or proliferate. Hence our setting
features two interacting cell populations with their mutual transitions and
involves tissue-dependent degenerate diffusion and haptotaxis for the moving
subpopulation. The proliferating cells and the tissue evolution are
characterized by way of ODEs for the respective densities. We prove the global
existence of weak solutions and illustrate the model behaviour by numerical
simulations in a two-dimensional setting.Comment: arXiv admin note: text overlap with arXiv:1512.0428
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