414 research outputs found
Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates
We present a quantum mechanical treatment of the mechanical stirring of
Bose-Einstein condensates using classical field techniques. In our approach the
condensate and excited modes are described using a Hamiltonian classical field
method in which the atom number and (rotating frame) energy are strictly
conserved. We simulate a T = 0 quasi-2D condensate perturbed by a rotating
anisotropic trapping potential. Vacuum fluctuations in the initial state
provide an irreducible mechanism for breaking the initial symmetries of the
condensate and seeding the subsequent dynamical instability. Highly turbulent
motion develops and we quantify the emergence of a rotating thermal component
that provides the dissipation necessary for the nucleation and motional-damping
of vortices in the condensate. Vortex lattice formation is not observed, rather
the vortices assemble into a spatially disordered vortex liquid state. We
discuss methods we have developed to identify the condensate in the presence of
an irregular distribution of vortices, determine the thermodynamic parameters
of the thermal component, and extract damping rates from the classical field
trajectories.Comment: 22 pages, 15 figures. v2: Minor refinements made at suggestion of
referee. Discussion of other treatments revised. To appear in Phys. Rev.
Towards Real-Time Simulation Of Hyperelastic Materials
We propose a new method for physics-based simulation supporting many different types of hyperelastic materials from mass-spring systems to three-dimensional finite element models, pushing the performance of the simulation towards real-time. Fast simulation methods such as Position Based Dynamics exist, but support only limited selection of materials; even classical materials such as corotated linear elasticity and Neo-Hookean elasticity are not supported. Simulation of these types of materials currently relies on Newton\u27s method, which is slow, even with only one iteration per timestep. In this work, we start from simple material models such as mass-spring systems or as-rigid-as-possible materials. We express the widely used implicit Euler time integration as an energy minimization problem and introduce auxiliary projection variables as extra unknowns. After our reformulation, the minimization problem becomes linear in the node positions, while all the non-linear terms are isolated in individual elements. We then extend this idea to efficiently simulate a more general spatial discretization using finite element method. We show that our reformulation can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than ten times faster than one iteration of Newton\u27s method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton\u27s method. Our method is also easier to implement, implying reduced software development costs
Non-abelian instantons on a fuzzy four-sphere
We study the compatibility between the instanton and the fuzzy
four-sphere algebra. By using the projective module point of view as an
intermediate step, we are able to identify a non-commutative solution of the
matrix model equations of motion which minimally extends the SU(2) instanton
solution on the classical sphere . We also propose to extend the
non-trivial second Chern class with the five-dimensional noncommutative
Chern-Simons term
Multiframe Scene Flow with Piecewise Rigid Motion
We introduce a novel multiframe scene flow approach that jointly optimizes
the consistency of the patch appearances and their local rigid motions from
RGB-D image sequences. In contrast to the competing methods, we take advantage
of an oversegmentation of the reference frame and robust optimization
techniques. We formulate scene flow recovery as a global non-linear least
squares problem which is iteratively solved by a damped Gauss-Newton approach.
As a result, we obtain a qualitatively new level of accuracy in RGB-D based
scene flow estimation which can potentially run in real-time. Our method can
handle challenging cases with rigid, piecewise rigid, articulated and moderate
non-rigid motion, and does not rely on prior knowledge about the types of
motions and deformations. Extensive experiments on synthetic and real data show
that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
Multiframe Scene Flow with Piecewise Rigid Motion
We introduce a novel multiframe scene flow approach that jointly optimizes
the consistency of the patch appearances and their local rigid motions from
RGB-D image sequences. In contrast to the competing methods, we take advantage
of an oversegmentation of the reference frame and robust optimization
techniques. We formulate scene flow recovery as a global non-linear least
squares problem which is iteratively solved by a damped Gauss-Newton approach.
As a result, we obtain a qualitatively new level of accuracy in RGB-D based
scene flow estimation which can potentially run in real-time. Our method can
handle challenging cases with rigid, piecewise rigid, articulated and moderate
non-rigid motion, and does not rely on prior knowledge about the types of
motions and deformations. Extensive experiments on synthetic and real data show
that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
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