1,775 research outputs found
An Eulerian projection method for quasi-static elastoplasticity
A well-established numerical approach to solve the Navier--Stokes equations
for incompressible fluids is Chorin's projection method, whereby the fluid
velocity is explicitly updated, and then an elliptic problem for the pressure
is solved, which is used to orthogonally project the velocity field to maintain
the incompressibility constraint. In this paper, we develop a mathematical
correspondence between Newtonian fluids in the incompressible limit and
hypo-elastoplastic solids in the slow, quasi-static limit. Using this
correspondence, we formulate a new fixed-grid, Eulerian numerical method for
simulating quasi-static hypo-elastoplastic solids, whereby the stress is
explicitly updated, and then an elliptic problem for the velocity is solved,
which is used to orthogonally project the stress to maintain the
quasi-staticity constraint. We develop a finite-difference implementation of
the method and apply it to an elasto-viscoplastic model of a bulk metallic
glass based on the shear transformation zone theory. We show that in a
two-dimensional plane strain simple shear simulation, the method is in
quantitative agreement with an explicit method. Like the fluid projection
method, it is efficient and numerically robust, making it practical for a wide
variety of applications. We also demonstrate that the method can be extended to
simulate objects with evolving boundaries. We highlight a number of
correspondences between incompressible fluid mechanics and quasi-static
elastoplasticity, creating possibilities for translating other numerical
methods between the two classes of physical problems.Comment: 49 pages, 20 figure
A study of the high-inclination population in the Kuiper belt - II. The Twotinos
As the second part of our study, in this paper we proceed to explore the
dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion
resonance (NMMR). Depending on the inclination , we show the existence of
two critical eccentricities and , which are lower limits of
the eccentricity for the resonant angle to exhibit libration and
asymmetric libration, respectively. Accordingly, we have determined the
libration centres for inclined orbits, which are strongly dependent
on . With initial on a fine grid of , the
stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is
shown that symmetric librators are totally unstable for ; while
stable asymmetric librators exist for up to .
We further investigate the 1:2 NMMR capture and retention of planetesimals
with initial inclinations in the planet migration model
using a time-scale of yr. We find that: (1) the capture
efficiency of the 1:2 NMMR decreases drastically with the increase of ,
and it goes to 0 when ; (2) the probability of discovering
Twotinos with , beyond observed values, is roughly estimated to
be per cent; (3) more particles are captured into the leading rather
than the trailing asymmetric resonance for , but this number
difference appears to be the opposite at and is continuously
varying for even larger ; (4) captured Twotinos residing in the trailing
resonance or having are practically outside the Kozai mechanism,
like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome
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
Application of a Brain-Inspired Deep Imitation Learning Algorithm in Autonomous Driving
Acknowledgements This work was was supported by the University of Aberdeen Internal Funding to Pump-Prime Interdisciplinary Research and Impact under grant number SF10206-57Peer reviewedPublisher PD
Localization of q-form fields on a de Sitter brane in chameleon gravity
Recently, it was found that the vector field can be naturally localized on
the thick brane in chameleon gravity. In this work, we extend this study to
encompass de Sitter brane scenario. We focus on the localization of q-form
fields. The scalar and vector fields can be localized on the de Sitter brane,
while the KR field cannot be localized. The condition for localization of the
scalar and vector fields is obtained. Furthermore, we investigate the
localization characteristics in two examples with given conformal factor
. In the first case, the effective potentials and KK modes of the
matter fields are obtained asymmetric even though the de Sitter brane has
symmetry. In the second case, volcano-like effective potentials are generated
in the de Sitter brane model.Comment: 14 pages, 8 figure
- β¦