On homogenization of electromagnetic crystals formed by uniaxial resonant scatterers

Dispersion properties of electromagnetic crystals formed by small uniaxial resonant scatterers (magnetic or electric) are studied using the local field approach. The goal of the study is to determine the conditions under which the homogenization of such crystals can be made. Therefore the consideration is limited by the frequency region where the wavelength in the host medium is larger than the lattice periods. It is demonstrated that together with known restriction for the homogenization related with the large values of the material parameters there is an additional restriction related with their small absolute values. From the other hand, the homogenization becomes allowed in both cases of large and small material parameters for special directions of propagation. Two unusual effects inherent to the crystals under consideration are revealed: flat isofrequency contour which allows subwavelength imaging using canalization regime and birefringence of extraordinary modes which can be used for beam splitting.Comment: 16 pages, 12 figures, submitted to PR

Universal Uhrig dynamical decoupling for bosonic systems

We construct efficient deterministic dynamical decoupling schemes protecting continuous variable degrees of freedom. Our schemes target decoherence induced by quadratic system-bath interactions with analytic time-dependence. We show how to suppress such interactions to $N$-th order using only $N$ pulses. Furthermore, we show to homogenize a $2^m$-mode bosonic system using only $(N+1)^{2m+1}$ pulses, yielding - up to $N$-th order - an effective evolution described by non-interacting harmonic oscillators with identical frequencies. The decoupled and homogenized system provides natural decoherence-free subspaces for encoding quantum information. Our schemes only require pulses which are tensor products of single-mode passive Gaussian unitaries and SWAP gates between pairs of modes.Comment: 17 pages, 2 figures

Using meta-level inference to constrain search and to learn strategies in equation solving

This thesis addresses two questions:- How can search be controlled in domains with a large search space?- How can this control information be learned?It is argued that both problems can be tackled with the aid of a technique called meta-level inference.In this technique, the control information is separated from the factual information. The control information is expressed declaratively, i.e. the control information is represented as explicit rules. These rules are axioms in the meta-theory of the domain. This gives rise to a two level program, the factual information forms the object-level and the control information forms the meta-level. Inference is performed at the meta-level. and this induces inference at the object-level. Search at the object-level is replaced by search at the meta-level. This has several advantages, one of the most important being that the meta-level search space is usually much smaller than the object-level space, so the search problem is greatly reduced.Two programs are presented in this thesis to support this claim. Both programs operate in the domain of symbolic equation solving. However, the techniques used can be applied to a wide variety of domains.The first program. PRESS, solves symbolic, transcendental, non-differential equations. PRESS makes extensive use of meta-level inference to control search. This overcomes problems experienced by other approaches. For example, systems that apply rewrite rules exhaustively usually only use the rules one way round, to avoid looping. However, this often makes the system incomplete, and the techniques for completing this set are not easily mechanized. PRESS is able to use rules in both directions, using inference to decide which direction is appropriate.The second program, LP is also an equation solving program, but, unlike PRESS, it is capable of learning new equation-solving techniques. It embodies a new learning method, called Precondition Analysis. Precondition Analysis combines meta-level inference with concepts from the field of planning, and allows the program to learn even from a single example. This learning technique seems particularly suitable in domains where the operators don't have precisely defined effects and preconditions. Equation solving is such a domain

Relationship between eruptions of active-region filaments and associated flares and CMEs

To better understand the dynamical process of active-region filament eruptions and associated flares and CMEs, we carried out a statistical study of 120 events observed by BBSO, TRACE, and t(SOHO/EIT) from 1998 to 2007 and combined filament observations with the NOAA's flare reports, MDI magnetograms, and LASCO data, to investigate the relationship between active-region filament eruptions and other solar activities. We found that 115 out of 120 filament eruptions are associated with flares. 56 out of 105 filament eruptions are found to be associated with CMEs except for 15 events without corresponding LASCO data. We note the limitation of coronagraphs duo to geometry or sensitivity, leading to many smaller CMEs that are Earth-directed or well out of the plane of sky not being detected by near-Earth spacecraft. Excluding those without corresponding LASCO data, the CME association rate of active-region filament eruptions clearly increases with X-ray flare class from about 32% for C-class flares to 100% for X-class flares. The eruptions of active-region filaments associated with Halo CMEs are often accompanied by large flares. About 92% events associated with X-class flare are associated with Halo CMEs. Such a result is due to that the Earth-directed CMEs detected as Halo CMEs are often the larger CMEs and many of the smaller ones are not detected because of the geometry and low intensity. The average speed of the associated CMEs of filament eruptions increases with X-ray flare size from 563.7 km/s for C-class flares to 1506.6 km/s for X-class flares. Moreover, the magnetic emergence and cancellation play an important role in triggering filament eruptions. These findings may be instructive to not only in respect to the modeling of active-region filament eruptions but also in predicting flares and CMEs.Comment: 19 Pages, 7 figures, Accepted for publication in MNRA

A modified particle method for semilinear hyperbolic systems with oscillatory solutions

We introduce a modified particle method for semi-linear hyperbolic systems with highly oscillatory solutions. The main feature of this modified particle method is that we do not require different families of characteristics to meet at one point. In the modified particle method, we update the ith component of the solution along its own characteristics, and interpolate the other components of the solution from their own characteristic points to the ith characteristic point. We prove the convergence of the modified particle method essentially independent of the small scale for the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell model. Numerical evidence suggests that the modified particle method also converges essentially independent of the small scale for the original Broadwell model if a cubic spline interpolation is used