12,513 research outputs found
Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions
A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Based on the algebraico-categorical (:sheaf-theoretic and sheaf
cohomological) conceptual and technical machinery of Abstract Differential
Geometry, a new, genuinely background spacetime manifold independent, field
quantization scenario for vacuum Einstein gravity and free Yang-Mills theories
is introduced. The scheme is coined `third quantization' and, although it
formally appears to follow a canonical route, it is fully covariant, because it
is an expressly functorial `procedure'. Various current and future Quantum
Gravity research issues are discussed under the light of 3rd-quantization. A
postscript gives a brief account of this author's personal encounters with
Rafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating
Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly
written that the Editor for this volume is Daniele Oriti, with CUP as
publisher. I apologize for the mistake.
Active dynamics of tissue shear flow
We present a hydrodynamic theory to describe shear flows in developing
epithelial tissues. We introduce hydrodynamic fields corresponding to state
properties of constituent cells as well as a contribution to overall tissue
shear flow due to rearrangements in cell network topology. We then construct a
generic linear constitutive equation for the shear rate due to topological
rearrangements and we investigate a novel rheological behaviour resulting from
memory effects in the tissue. We identify two distinct active cellular
processes: generation of active stress in the tissue, and actively driven
topological rearrangements. We find that these two active processes can produce
distinct cellular and tissue shape changes, depending on boundary conditions
applied on the tissue. Our findings have consequences for the understanding of
tissue morphogenesis during development
Zero modes in magnetic systems: general theory and an efficient computational scheme
The presence of topological defects in magnetic media often leads to normal
modes with zero frequency (zero modes). Such modes are crucial for long-time
behavior, describing, for example, the motion of a domain wall as a whole.
Conventional numerical methods to calculate the spin-wave spectrum in magnetic
media are either inefficient or they fail for systems with zero modes. We
present a new efficient computational scheme that reduces the magnetic
normal-mode problem to a generalized Hermitian eigenvalue problem also in the
presence of zero modes. We apply our scheme to several examples, including
two-dimensional domain walls and Skyrmions, and show how the effective masses
that determine the dynamics can be calculated directly. These systems highlight
the fundamental distinction between the two types of zero modes that can occur
in spin systems, which we call special and inertial zero modes. Our method is
suitable for both conservative and dissipative systems. For the latter case, we
present a perturbative scheme to take into account damping, which can also be
used to calculate dynamical susceptibilities.Comment: 64 pages, 15 figure
In situ evidence for the structure of the magnetic null in a 3D reconnection event in the Earth's magnetotail
Magnetic reconnection is one of the most important processes in
astrophysical, space and laboratory plasmas. Identifying the structure around
the point at which the magnetic field lines break and subsequently reform,
known as the magnetic null point, is crucial to improving our understanding
reconnection. But owing to the inherently three-dimensional nature of this
process, magnetic nulls are only detectable through measurements obtained
simultaneously from at least four points in space. Using data collected by the
four spacecraft of the Cluster constellation as they traversed a diffusion
region in the Earth's magnetotail on 15 September, 2001, we report here the
first in situ evidence for the structure of an isolated magnetic null. The
results indicate that it has a positive-spiral structure whose spatial extent
is of the same order as the local ion inertial length scale, suggesting that
the Hall effect could play an important role in 3D reconnection dynamics.Comment: 14 pages, 4 figure
Effect of disorder and noise in shaping the dynamics of power grids
The aim of this paper is to investigate complex dynamic networks which can
model high-voltage power grids with renewable, fluctuating energy sources. For
this purpose we use the Kuramoto model with inertia to model the network of
power plants and consumers. In particular, we analyse the synchronization
transition of networks of phase oscillators with inertia (rotators) whose
natural frequencies are bimodally distributed, corresponding to the
distribution of generator and consumer power. First, we start from globally
coupled networks whose links are successively diluted, resulting in a random
Erd\"os-Renyi network. We focus on the changes in the hysteretic loop while
varying inertial mass and dilution. Second, we implement Gaussian white noise
describing the randomly fluctuating input power, and investigate its role in
shaping the dynamics. Finally, we briefly discuss power grid networks under the
impact of both topological disorder and external noise sources.Comment: 7 pages, 6 figure
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