4,751 research outputs found
How Wigner Functions Transform Under Symplectic Maps
It is shown that, while Wigner and Liouville functions transform in an
identical way under linear symplectic maps, in general they do not transform
identically for nonlinear symplectic maps. Instead there are ``quantum
corrections'' whose hbar tending to zero limit may be very complicated.
Examples of the behavior of Wigner functions in this limit are given in order
to examine to what extent the corresponding Liouville densities are recovered.Comment: 8 pages, 6 figures [RevTeX/epsfig, macro included]. To appear in
Proceedings of the Advanced Beam Dynamics Workshop on Quantum Aspects of Beam
Physics (Monterey, CA 1998
3LP: a linear 3D-walking model including torso and swing dynamics
In this paper, we present a new model of biped locomotion which is composed
of three linear pendulums (one per leg and one for the whole upper body) to
describe stance, swing and torso dynamics. In addition to double support, this
model has different actuation possibilities in the swing hip and stance ankle
which could be widely used to produce different walking gaits. Without the need
for numerical time-integration, closed-form solutions help finding periodic
gaits which could be simply scaled in certain dimensions to modulate the motion
online. Thanks to linearity properties, the proposed model can provide a
computationally fast platform for model predictive controllers to predict the
future and consider meaningful inequality constraints to ensure feasibility of
the motion. Such property is coming from describing dynamics with joint torques
directly and therefore, reflecting hardware limitations more precisely, even in
the very abstract high level template space. The proposed model produces
human-like torque and ground reaction force profiles and thus, compared to
point-mass models, it is more promising for precise control of humanoid robots.
Despite being linear and lacking many other features of human walking like CoM
excursion, knee flexion and ground clearance, we show that the proposed model
can predict one of the main optimality trends in human walking, i.e. nonlinear
speed-frequency relationship. In this paper, we mainly focus on describing the
model and its capabilities, comparing it with human data and calculating
optimal human gait variables. Setting up control problems and advanced
biomechanical analysis still remain for future works.Comment: Journal paper under revie
Push recovery with stepping strategy based on time-projection control
In this paper, we present a simple control framework for on-line push
recovery with dynamic stepping properties. Due to relatively heavy legs in our
robot, we need to take swing dynamics into account and thus use a linear model
called 3LP which is composed of three pendulums to simulate swing and torso
dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use
a particular time-projection method to adjust the next footstep location
on-line during the motion continuously. This adjustment, which is found based
on both pelvis and swing foot tracking errors, naturally takes the swing
dynamics into account. Suggested adjustments are added to the Cartesian 3LP
gaits and converted to joint-space trajectories through inverse kinematics.
Fixed and adaptive foot lift strategies also ensure enough ground clearance in
perturbed walking conditions. The proposed structure is robust, yet uses very
simple state estimation and basic position tracking. We rely on the physical
series elastic actuators to absorb impacts while introducing simple laws to
compensate their tracking bias. Extensive experiments demonstrate the
functionality of different control blocks and prove the effectiveness of
time-projection in extreme push recovery scenarios. We also show self-produced
and emergent walking gaits when the robot is subject to continuous dragging
forces. These gaits feature dynamic walking robustness due to relatively soft
springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our
proposed architecture.Comment: 20 pages journal pape
Imprecise dynamic walking with time-projection control
We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller
Approximating Steady States in Equilibrium and Nonequilibrium Condensates
We obtain approximations for the time-independent Gross-Pitaevskii (GP) and
complex GP equation in two and three spatial dimensions by generalizing the
divergence-free WKB method. The results include an explicit expression of a
uniformly valid approximation for the condensate density of an ultracold Bose
gas confined in a harmonic trap that extends into the classically forbidden
region. This provides an accurate approximation of the condensate density that
includes healing effects at leading order that are missing in the widely
adopted Thomas-Fermi approximation. The results presented herein allow us to
formulate useful approximations to a range of experimental systems including
the equilibrium properties of a finite temperature Bose gas and the
steady-state properties of a 2D nonequilibrium condensate. Comparisons between
our asymptotic and numerical results for the conservative and
forced-dissipative forms of the GP equations as applied to these systems show
excellent agreement between the two sets of solutions thereby illustrating the
accuracy of these approximations.Comment: 5 pages, 1 figur
Muon diffusion and electronic magnetism in YTiO
We report a SR study in a YTiO single crystal. We observe
slow local field fluctuations at low temperature which become faster as the
temperature is increased. Our analysis suggests that muon diffusion is present
in this system and becomes small below 40 K and therefore incoherent. A
surprisingly strong electronic magnetic signal is observed with features
typical for muons thermally diffusing towards magnetic traps below K and released from them above this temperature. We attribute the traps to
Ti defects in the diluted limit. Our observations are highly relevant to
the persistent spin dynamics debate on TiO pyrochlores and their
crystal quality
A minimal integer automaton behind crystal plasticity
Power law fluctuations and scale free spatial patterns are known to
characterize steady state plastic flow in crystalline materials. In this Letter
we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type
model of 2D plasticity which is largely free of arbitrariness, amenable to
analytical study and is capable of generating critical exponents matching
experiments. Our main observation concerns the possibility to reduce continuum
plasticity to an integer valued automaton revealing inherent discreteness of
the plastic flow.Comment: 4 pages, 5 figure
Breathers on quantized superfluid vortices
We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings
Magnetism in purple bronze LiMoO
Muon spin relaxation measurements around the 25 K metal-insulator transition
in LiMoO elucidate a profound role of disorder as a possible
mechanism for this transition. The relaxation rate and the muon Knight
shift are incompatible with the transition to a SDW state and thus exclude it.Comment: pages 2, fig 2, The conf. on strongly correlated electron systems,
SCES 2004, German
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