29,937 research outputs found
Polarity-dependent dielectric torque in nematic liquid crystals
The dielectric dispersion in the uniaxial nematic liquid crystals affects the
switching dynamics of the director, as the dielectric torque is determined by
not only the present values of the electric field and director but also by
their past values. We demonstrate that this dielectric memory leads to an
unusual contribution to the dielectric torque that is linear in the present
field and thus polarity-sensitive. This torque can be used to accelerate the
switch-off phase of director dynamics.Comment: 12 pages, 4 figure
Complete classification of 1D gapped quantum phases in interacting spin systems
Quantum phases with different orders exist with or without breaking the
symmetry of the system. Recently, a classification of gapped quantum phases
which do not break time reversal, parity or on-site unitary symmetry has been
given for 1D spin systems in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B
\textbf{83}, 035107 (2011); arXiv:1008.3745]. It was found that, such symmetry
protected topological (SPT) phases are labeled by the projective
representations of the symmetry group which can be viewed as a symmetry
fractionalization. In this paper, we extend the classification of 1D gapped
phases by considering SPT phases with combined time reversal, parity, and/or
on-site unitary symmetries and also the possibility of symmetry breaking. We
clarify how symmetry fractionalizes with combined symmetries and also how
symmetry fractionalization coexists with symmetry breaking.
In this way, we obtain a complete classification of gapped quantum phases in
1D spin systems. We find that in general, symmetry fractionalization, symmetry
breaking and long range entanglement(present in 2 or higher dimensions)
represent three main mechanisms to generate a very rich set of gapped quantum
phases. As an application of our classification, we study the possible SPT
phases in 1D fermionic systems, which can be mapped to spin systems by
Jordan-Wigner transformation.Comment: 15 pages, 3 figure
Nonlinear alternating current responses of graded materials
When a composite of nonlinear particles suspended in a host medium is
subjected to a sinusoidal electric field, the electrical response in the
composite will generally consist of alternating current (AC) fields at
frequencies of higher-order harmonics. The situation becomes more interesting
when the suspended particles are graded, with a spatial variation in the
dielectric properties. The local electric field inside the graded particles can
be calculated by the differential effective dipole approximation, which agrees
very well with a first-principles approach. In this work, a nonlinear
differential effective dipole approximation and a perturbation expansion method
have been employed to investigate the effect of gradation on the nonlinear AC
responses of these composites. The results showed that the fundamental and
third-harmonic AC responses are sensitive to the dielectric-constant and/or
nonlinear-susceptibility gradation profiles within the particles. Thus, by
measuring the AC responses of the graded composites, it is possible to perform
a real-time monitoring of the fabrication process of the gradation profiles
within the graded particles.Comment: 18 pages, 4 figure
A spatio-temporal entropy-based approach for the analysis of cyber attacks (demo paper)
Computer networks are ubiquitous systems growing exponentially with a predicted 50 billion devices connected by 2050. This dramatically increases the potential attack surface of Internet networks. A key issue in cyber defense is to detect, categorize and identify these attacks, the way they are propagated and their potential impacts on the systems affected. The research presented in this paper models cyber attacks at large by considering the Internet as a complex system in which attacks are propagated over a network. We model an attack as a path from a source to a target, and where each attack is categorized according to its intention. We setup an experimental testbed with the concept of honeypot that evaluates the spatiotemporal distribution of these Internet attacks. The preliminary results show a series of patterns in space and time that illustrate the potential of the approach, and how cyber attacks can be categorized according to the concept and measure of entropy
Tensor-product representations for string-net condensed states
We show that general string-net condensed states have a natural
representation in terms of tensor product states (TPS) . These TPS's are built
from local tensors. They can describe both states with short-range entanglement
(such as the symmetry breaking states) and states with long-range entanglement
(such as string-net condensed states with topological/quantum order). The
tensor product representation provides a kind of 'mean-field' description for
topologically ordered states and could be a powerful way to study quantum phase
transitions between such states. As an attempt in this direction, we show that
the constructed TPS's are fixed-points under a certain wave-function
renormalization group transformation for quantum states.Comment: 11 pages. RevTeX
Tensor product representation of topological ordered phase: necessary symmetry conditions
The tensor product representation of quantum states leads to a promising
variational approach to study quantum phase and quantum phase transitions,
especially topological ordered phases which are impossible to handle with
conventional methods due to their long range entanglement. However, an
important issue arises when we use tensor product states (TPS) as variational
states to find the ground state of a Hamiltonian: can arbitrary variations in
the tensors that represent ground state of a Hamiltonian be induced by local
perturbations to the Hamiltonian? Starting from a tensor product state which is
the exact ground state of a Hamiltonian with topological order,
we show that, surprisingly, not all variations of the tensors correspond to the
variation of the ground state caused by local perturbations of the Hamiltonian.
Even in the absence of any symmetry requirement of the perturbed Hamiltonian,
one necessary condition for the variations of the tensors to be physical is
that they respect certain symmetry. We support this claim by
calculating explicitly the change in topological entanglement entropy with
different variations in the tensors. This finding will provide important
guidance to numerical variational study of topological phase and phase
transitions. It is also a crucial step in using TPS to study universal
properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure
Eigenstructure Assignment Based Controllers Applied to Flexible Spacecraft
The objective of this paper is to evaluate the behaviour of a controller designed using a parametric Eigenstructure Assignment method and to evaluate its suitability for use in flexible spacecraft. The challenge of this objective lies in obtaining a suitable controller that is specifically designated to alleviate the deflections and vibrations suffered by external appendages in flexible spacecraft while performing attitude manoeuvres. One of the main problems in these vehicles is the mechanical cross-coupling that exists between the rigid and flexible parts of the spacecraft. Spacecraft with fine attitude pointing requirements need precise control of the mechanical coupling to avoid undesired attitude misalignment. In designing an attitude controller, it is necessary to consider the possible vibration of the solar panels and how it may influence the performance of the rest of the vehicle. The nonlinear mathematical model of a flexible spacecraft is considered a close approximation to the real system. During the process of controller evaluation, the design process has also been taken into account as a factor in assessing the robustness of the system
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