6,260 research outputs found
Expert systems and finite element structural analysis - a review
Finite element analysis of many engineering systems is practised more as an art than as a science . It involves high level expertise (analytical as well as heuristic) regarding problem modelling (e .g. problem specification,13; choosing the appropriate type of elements etc .), optical mesh design for achieving the specified accuracy (e .g . initial mesh selection, adaptive mesh refinement), selection of the appropriate type of analysis and solution13; routines and, finally, diagnosis of the finite element solutions . Very often such expertise is highly dispersed and is not available at a single place with a single expert. The design of an expert system, such that the necessary expertise is available to a novice to perform the same job even in the absence of trained experts, becomes an attractive proposition. 13; In this paper, the areas of finite element structural analysis which require experience and decision-making capabilities are explored . A simple expert system, with a feasible knowledge base for problem modelling, optimal mesh design, type of analysis and solution routines, and diagnosis, is outlined. Several efforts in these directions, reported in the open literature, are also reviewed in this paper
Spectral Singularities and Whispering Gallery Modes of a Cylindrical Gain Medium
Complex scattering potentials can admit scattering states that behave exactly
like a zero-width resonance. Their energy is what mathematicians call a
spectral singularity. This phenomenon admits optical realizations in the form
of lasing at the threshold gain, and its time-reversal is responsible for
antilasing. We study spectral singularities and whispering gallery modes (WGMs)
of a cylindrical gain medium. In particular, we introduce a new class of WGMs
that support a spectral singularity and, as a result, have a divergent quality
factor. These singular gallery modes (SGMs) are excited only if the system has
a positive gain coefficient, but typically the required gain is extremely
small. More importantly given any amount of gain, there are SGMs requiring
smaller gain than this amount. This means that, in principle, the system lacks
a lasing threshold. Furthermore, the abundance of these modes allows for
configurations where a particular value of the gain coefficient yields an
effective excitation of two distant SGMs. This induces lasing at two different
wavelengths.Comment: 12 pages, 6 figures, 3 tables; to appear in Phys. Rev.
A Simple Analytical Model of the Angular Momentum Transformation in Strongly Focused Light Beams
A ray-optics model is proposed to describe the vector beam transformation in
a strongly focusing optical system. In contrast to usual approaches basing on
the focused field distribution near the focal plane, we employ the transformed
beam pattern formed immediately near the exit pupil. In this cross section,
details of the output field distribution are of minor physical interest but
proper allowance is made for transformation of the incident beam polarization
state. This enables to obtain the spin and orbital angular momentum
representations which are valid everywhere in the transformed beam space.
Simple analytical results are available for the transversely homogeneous
circularly polarized incident beam limited only by the circular aperture.
Behavior of the spin and orbital angular momenta of the output beam and their
dependences on the focusing strength (aperture angle) are analyzed. The
obtained analytical results are in good qualitative and reasonable quantitative
agreement to the calculation performed for the spatially inhomogeneous Gaussian
and Laguerre-Gaussian beams. In application to Laguerre-Gaussian beams, the
model provides possibility for analyzing the angular momentum transformation in
beams already possessing some mixture of the spin and orbital angular momenta.
The model supplies efficient and physically transparent means for qualitative
analysis of the spin-to-orbital angular momentum conversion. It can be
generalized to incident beams with complicated spatial and polarization
structure.Comment: 18 pages, 5 figures. The paper has appeared as an attempt to clearly
understand transformations of the light beam polarization in the course of
strong focusing. It provides description of the optical vortex formation
after focusing a circularly polarized beam and explains why the the orbital
angular momentum emerges in the focused bea
A study of blow-ups in the Keller-Segel model of chemotaxis
We study the Keller-Segel model of chemotaxis and develop a composite
particle-grid numerical method with adaptive time stepping which allows us to
accurately resolve singular solutions. The numerical findings (in two
dimensions) are then compared with analytical predictions regarding formation
and interaction of singularities obtained via analysis of the stochastic
differential equations associated with the Keller-Segel model
Changing Practices, Changing Identities: A Study with Students at Risk of Educational Exclusion
This study discusses how students at risk of educational exclusion can restore their identity and improve learning and scientific literacy. This qualitative research adopts an interpretative orientation. Twenty-eight secondary school students, aged 16 to 20 participated. Data was collected of the interactions between students in lessons, focus group interview and written documents. Data analysis was inductive, consistent with a naturalistic research paradigm, and consisted of uncovering salient patterns, singularities, and themes associated with research aims. Several students, at risk of educational exclusion, value this kind of practice. By changing practice, the learning social context varied, as well as students’ identities and their relationships with knowledge, teachers and school
- …