90,367 research outputs found
Positivity and strong ellipticity
We consider second-order partial differential operators in divergence
form on \Ri^d with a positive-semidefinite, symmetric, matrix of real
-coefficients and establish that is strongly elliptic if and only
if the associated semigroup kernel satisfies local lower bounds, or, if and
only if the kernel satisfies Gaussian upper and lower bounds.Comment: 9 page
Coarse-Grained Picture for Controlling Complex Quantum Systems
We propose a coarse-grained picture to control ``complex'' quantum dynamics,
i.e., multi-level-multi-level transition with a random interaction. Assuming
that optimally controlled dynamics can be described as a Rabi-like oscillation
between an initial and final state, we derive an analytic optimal field as a
solution to optimal control theory. For random matrix systems, we numerically
confirm that the analytic optimal field steers an initial state to a target
state which both contains many eigenstates.Comment: jpsj2.cls, 2 pages, 3 figure files; appear in J. Phys. Soc. Jpn.
Vol.73, No.11 (Nov. 15, 2004
The energy spectrum symmetry of Heisenberg model in Fock space
We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry
of energy spectrum between its subspace and the subspace of the Fock
space. Our proof is completed by introducing two general quantum operations.
One is a flip operation of spin direction and another is a mirror reflection of
spin sites.Comment: Revising version, 7 preprint pages, no figures; Published version
contains some revisions in Languag
Second-order operators with degenerate coefficients
We consider properties of second-order operators on \Ri^d with bounded real symmetric
measurable coefficients. We assume that almost
everywhere, but allow for the possibility that is singular. We associate
with a canonical self-adjoint viscosity operator and examine
properties of the viscosity semigroup generated by . The
semigroup extends to a positive contraction semigroup on the -spaces with
. We establish that it conserves probability, satisfies
~off-diagonal bounds and that the wave equation associated with has
finite speed of propagation. Nevertheless is not always strictly
positive because separation of the system can occur even for subelliptic
operators. This demonstrates that subelliptic semigroups are not ergodic in
general and their kernels are neither strictly positive nor H\"older
continuous. In particular one can construct examples for which both upper and
lower Gaussian bounds fail even with coefficients in C^{2-\varepsilon}(\Ri^d)
with .Comment: 44 page
Integrated system to perform surrogate based aerodynamic optimisation for high-lift airfoil
This work deals with the aerodynamics optimisation of a generic two-dimensional three element high-lift configuration. Although the high-lift system is applied only during take-off and landing in the low speed phase of the flight the cost efficiency of the airplane is strongly influenced by it [1]. The ultimate goal of an aircraft high lift system design team is to define the simplest configuration which, for prescribed constraints, will meet the take-off, climb, and landing requirements usually expressed in terms of maximum L/D and/or maximum CL. The ability of the calculation method to accurately predict changes in objective function value when gaps, overlaps and element deflections are varied is therefore critical. Despite advances in computer capacity, the enormous computational cost of running complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimisation. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in place of the actual simulation models. This work outlines the development of integrated systems to perform aerodynamics multi-objective optimisation for a three-element airfoil test case in high lift configuration, making use of surrogate models available in MACROS Generic Tools, which has been integrated in our design tool. Different metamodeling techniques have been compared based on multiple performance criteria. With MACROS is possible performing either optimisation of the model built with predefined training sample (GSO) or Iterative Surrogate-Based Optimization (SBO). In this first case the model is build independent from the optimisation and then use it as a black box in the optimisation process. In the second case is needed to provide the possibility to call CFD code from the optimisation process, and there is no need to build any model, it is being built internally during the optimisation process. Both approaches have been applied. A detailed analysis of the integrated design system, the methods as well as th
Bogdanov-Takens resonance in time-delayed systems
We analyze the oscillatory dynamics of a time-delayed dynamical system
subjected to a periodic external forcing. We show that, for certain values of
the delay, the response can be greatly enhanced by a very small forcing
amplitude. This phenomenon is related to the presence of a Bogdanov- Takens
bifurcation and displays some analogies to other resonance phenomena, but also
substantial differences.Comment: 14 pages, 8 figure
Frequency comb vernier spectroscopy in the near infrared
We perform femtosecond frequency comb vernier spectroscopy in the near
infrared with a femtosecond Er doped fiber laser, a scanning high-finesse
cavity and an InGaAs camera. By utilizing the properties of a frequency comb
and a scanning high-finesse cavity such spectroscopy provides broad spectral
bandwidth, high spectral resolution, and high detection sensitivity on a short
time scale. We achieved an absorption sensitivity of ~8E-8 cm-1Hz-1/2
corresponding to a detection limit of ~70 ppbv for acetylene, with a resolution
of ~1.1 GHz in single images taken in 0.5 seconds and covering a frequency
range of ~5 THz. These measurements have broad applications for sensing other
greenhouse gases in this fingerprint near IR region with a simple apparatus.Comment: 14 pages, 5 figure
Quantum Algorithms for Finding Constant-sized Sub-hypergraphs
We develop a general framework to construct quantum algorithms that detect if
a -uniform hypergraph given as input contains a sub-hypergraph isomorphic to
a prespecified constant-sized hypergraph. This framework is based on the
concept of nested quantum walks recently proposed by Jeffery, Kothari and
Magniez [SODA'13], and extends the methodology designed by Lee, Magniez and
Santha [SODA'13] for similar problems over graphs. As applications, we obtain a
quantum algorithm for finding a -clique in a -uniform hypergraph on
vertices with query complexity , and a quantum algorithm for
determining if a ternary operator over a set of size is associative with
query complexity .Comment: 18 pages; v2: changed title, added more backgrounds to the
introduction, added another applicatio
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