86,389 research outputs found
Constructing a Low Energy Transfer Between Jovian Moons
There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest
of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by Europa
presents formidable challenges to traditional conic analysis since the regimes of motion involved depend heavily on three-body dynamics. New three-body perspectives are required to design successful
and efficient missions which take full advantage of the natural dynamics. Not only does a three-body
approach provide low-fuel trajectories, but it also increases the flexibility and versatility of missions.
We apply this approach to design a new mission concept wherein a spacecraft "leap-frogs" between
moons, orbiting each for a desired duration in a temporary capture orbit. We call this concept the
"Petit Grand Tour."
For this application, we apply dynamical systems techniques developed in a previous paper to
design a Europa capture orbit. We show how it is possible, using a gravitional boost from Ganymede,
to go from a jovicentric orbit beyond the orbit of Ganymede to a ballistic capture orbit around
Europa. The main new technical result is the employment of dynamical channels in the phase space
- tubes in the energy surface which naturally link the vicinity of Ganymede to the vicinity of Europa.
The transfer V necessary to jump from one moon to another is less than half that required by a
standard Hohmann transfer
Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings
We discuss dynamics of approximate adiabatic invariants in several nonlinear
models being related to physics of Bose-Einstein condensates (BEC). We show
that nonadiabatic dynamics in Feshbach resonance passage, nonlinear
Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well
can be considered within a unifying approach based on the theory of separatrix
crossings. The separatrix crossing theory was applied previously to some
problems of classical mechanics, plasma physics and hydrodynamics, but has not
been used in the rapidly growing BEC-related field yet. We derive explicit
formulas for the change in the action in several models. Extensive numerical
calculations support the theory and demonstrate its universal character. We
also discovered a qualitatively new nonlinear phenomenon in a NLZ model which
we propose to call {\em separated adiabatic tunnelling}Comment: Accepted for publication in Physical Review E; Several misprints are
corrected; main results are emphasized in the end of Introduction (including
finite conversion efficiency in Feshbach resonance passage due to geometric
jump in the action); bibliography is extende
Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances
We consider a slowly rotating rectangular billiard with moving boundaries and
use the canonical perturbation theory to describe the dynamics of a billiard
particle. In the process of slow evolution certain resonance conditions can be
satisfied. Correspondingly, phenomena of scattering on a resonance and capture
into a resonance happen in the system. These phenomena lead to destruction of
adiabatic invariance and to unlimited acceleration of the particle.Comment: 20 pages. Presented on School-Conference "Mathematics and Physics of
Billiard-Like Systems" (Ubatuba, 2011). Accepted to Chao
Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis
By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components. Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear
Formation and transformation of the 3:1 mean-motion resonance in 55 Cancri System
We report in this paper the numerical simulations of the capture into the 3:1
mean-motion resonance between the planet b and c in the 55 Cancri system. The
results show that this resonance can be obtained by a differential planetary
migration. The moderate initial eccentricities, relatively slower migration and
suitable eccentricity damping rate increase significantly the probability of
being trapped in this resonance. Otherwise, the system crosses the 3:1
commensurability avoiding resonance capture, to be eventually captured into a
2:1 resonance or some other higher-order resonances. After the resonance
capture, the system could jump from one orbital configuration to another one if
the migration continues, making a large region of the configuration space
accessible for a resonance system. These investigations help us understand the
diversity of resonance configurations and put some constrains on the early
dynamical evolution of orbits in the extra-solar planetary systems.Comment: 6 pages with 2 figures. Submitted for publication in the proceedings
of IAU Symposium No.249. A paper telling much more details than this paper is
under preparin
Vortex formation and dynamics in two-dimensional driven-dissipative condensates
We investigate the real-time evolution of lattice bosons in two spatial
dimensions whose dynamics is governed by a Markovian quantum master equation.
We employ the Wigner-Weyl phase space quantization and derive the functional
integral for open quantum many-body systems that governs the time evolution of
the Wigner function. Using the truncated Wigner approximation, in which quantum
fluctuations are only taken into account in the initial state whereas the
dynamics is governed by classical evolution equations, we study the buildup of
long-range correlations due to the action of non-Hermitean quantum jump
operators that constitute a mechanism for dissipative cooling. Starting from an
initially disordered state corresponding to a vortex condensate, the
dissipative process results in the annihilation of vortex-antivortex pairs and
the establishment of quasi long-range order at late times. We observe that a
finite vortex density survives the cooling process which disagrees with the
analytically constructed vortex-free Bose-Einstein condensate at asymptotic
times. This indicates that quantum fluctuations beyond the truncated Wigner
approximation need to be included to fully capture the physics of dissipative
Bose-Einstein condensation.Comment: 11 pages, 3 figures. Revised version: Derivation and discussion
extended, accepted for publication in PR
Hydrodynamics of the Oscillating Wave Surge Converter in the open ocean
A potential flow model is derived for a large flap-type oscillating wave
energy converter in the open ocean. Application of the Green's integral theorem
in the fluid domain yields a hypersingular integral equation for the jump in
potential across the flap. Solution is found via a series expansion in terms of
the Chebyshev polynomials of the second kind and even order. Several
relationships are then derived between the hydrodynamic parameters of the
system. Comparison is made between the behaviour of the converter in the open
ocean and in a channel. The degree of accuracy of wave tank experiments aiming
at reproducing the performance of the device in the open ocean is quantified.
Parametric analysis of the system is then undertaken. It is shown that
increasing the flap width has the beneficial effect of broadening the bandwidth
of the capture factor curve. This phenomenon can be exploited in random seas to
achieve high levels of efficiency.Comment: Submitted to: EJMB/Fluids, 16/07/201
Persistent Homology of Attractors For Action Recognition
In this paper, we propose a novel framework for dynamical analysis of human
actions from 3D motion capture data using topological data analysis. We model
human actions using the topological features of the attractor of the dynamical
system. We reconstruct the phase-space of time series corresponding to actions
using time-delay embedding, and compute the persistent homology of the
phase-space reconstruction. In order to better represent the topological
properties of the phase-space, we incorporate the temporal adjacency
information when computing the homology groups. The persistence of these
homology groups encoded using persistence diagrams are used as features for the
actions. Our experiments with action recognition using these features
demonstrate that the proposed approach outperforms other baseline methods.Comment: 5 pages, Under review in International Conference on Image Processin
- …