Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Development of mechanical methods for cell-tray propagation and field transplanting of dwarf napiergrass (Pennisetum purpureum Schumach.)

Since dwarf napiergrass (Pennisetum purpureum Schumach.) must be propagated vegetatively due to lack of viable seeds, root splitting and stem cuttings are generally used to obtain true-to-type plant populations. These ordinary methods are laborious and costly, and are the greatest barriers for expanding the cultivation area of this crop. The objectives of this research were to develop nursery production of dwarf napiergrass in cell trays and to compare the efficiency of mechanical versus manual methods for cell-tray propagation and field transplanting. After defoliation of herbage either by a sickle (manually) or hand-mowing machine, every potential aerial tiller bud was cut to a single one for transplanting into cell trays as stem cuttings and placed in a glasshouse over winter. The following June, nursery plants were trimmed to a 25–cm length and transplanted in an experimental field (sandy soil) with 20,000 plants ha^(−1) either by shovel (manually) or Welsh onion planter. Labour time was recorded for each process. The manual defoliation of plants required 44% more labour time for preparing the stem cuttings (0.73 person-min. stemcutting^(−1)) compared to using hand-mowing machinery (0.51 person-min. stem-cutting^(−1)). In contrast, labour time for transplanting required an extra 0.30 person-min. m^(−2) (14%) using the machinery compared to manual transplanting, possibly due to the limited plot size for machinery operation. The transplanting method had no significant effect on plant establishment or plant growth, except for herbage yield 110 days after planting. Defoliation of herbage by machinery, production using a cell-tray nursery and mechanical transplanting reduced the labour intensity of dwarf napiergrass propagation.

Belief Propagation and Revision in Networks with Loops

Local belief propagation rules of the sort proposed by Pearl(1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay the foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive ananalytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP estimate obtained by belief revisionat convergence is guaranteed to give the globally optimal sequence of states. The result is independent of the length of the cycle and the size of the statespace. For networks with multiple loops, we introduce the concept of a "balanced network" and show simulati.

Uncertainty Propagation in Model-Based Recognition

Building robust recognition systems requires a careful understanding of the effects of error in sensed features. Error in these image features results in a region of uncertainty in the possible image location of each additional model feature. We present an accurate, analytic approximation for this uncertainty region when model poses are based on matching three image and model points, for both Gaussian and bounded error in the detection of image points, and for both scaled-orthographic and perspective projection models. This result applies to objects that are fully three- dimensional, where past results considered only two-dimensional objects. Further, we introduce a linear programming algorithm to compute the uncertainty region when poses are based on any number of initial matches. Finally, we use these results to extend, from two-dimensional to three- dimensional objects, robust implementations of alignmentt interpretation- tree search, and ransformation clustering.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined

International propagation of shocks: an evaluation of contagion effects for some Latin American countries

In this paper we analyze the spread of shocks across assets markets in eight Latin American countries. First, we measure the extent of markets reactions with the Principal Components Analysis. And second, we investigate the volatility of assets markets based in ARCH-GARCH models in function of the principal components retained in the first stage. Our results do not support the existence of financial contagion, but of interdependence in most of the cases and a slight increase in the sensibility of markets to recent shocks.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Tissue culture propagation alters plant-microbe interactions in tobacco rhizosphere

We have compared properties of roots from different lines (genotypes) of tobacco raised either in tissue culture or grown from seed. The different lines included unmodified plants and plants modified to express reduced activity of the enzyme cinnamoyl-CoA reductase, which has a pivotal role in lignin biosynthesis. The size and structure of the rhizosphere microbial community, characterized by adenosine triphosphate and phospholipid fatty acid analyses, were related to root chemistry (specifically the soluble carbohydrate concentration) and decomposition rate of the roots. The root material from unmodified plants decomposed faster following tissue culture compared with seed culture, and the faster decomposing material had significantly higher soluble carbohydrate concentrations. These observations are linked to the larger microbial biomass and greater diversity of the rhizosphere communities of tissue culture propagated plants.

Tissue culture propagation alters plant-microbe interactions in tobacco rhizosphere

We have compared properties of roots from different lines (genotypes) of tobacco raised either in tissue culture or grown from seed. The different lines included unmodified plants and plants modified to express reduced activity of the enzyme cinnamoyl-CoA reductase, which has a pivotal role in lignin biosynthesis. The size and structure of the rhizosphere microbial community, characterized by adenosine triphosphate and phospholipid fatty acid analyses, were related to root chemistry (specifically the soluble carbohydrate concentration) and decomposition rate of the roots. The root material from unmodified plants decomposed faster following tissue culture compared with seed culture, and the faster decomposing material had significantly higher soluble carbohydrate concentrations. These observations are linked to the larger microbial biomass and greater diversity of the rhizosphere communities of tissue culture propagated plants.

Magnetic cloud distortion resulting from propagation through a structured solar wind: Models and observations

Numerical simulations of magnetic clouds (MCs) propagating through a structured solar wind suggest that MC-associated magnetic flux ropes are highly distorted by inhomogeneities in the ambient medium. In particular, a solar wind configuration of fast wind from high latitudes and slow wind at low latitudes, common at periods close to solar minimum, should distort the cross section of magnetic clouds into concave-outward structures. This phenomenon has been reported in observations of shock front orientations, but not in the body of magnetic clouds. In this study an analytical magnetic cloud model based upon a kinematically distorted flux rope is modified to simulate propagation through a structured medium. This new model is then used to identify specific time series signatures of the resulting concave-outward flux ropes. In situ observations of three well studied magnetic clouds are examined with comparison to the model, but the expected concave-outward signatures are not present. Indeed, the observations are better described by the convex-outward flux rope model. This may be due to a sharp latitudinal transition from fast to slow wind, resulting in a globally concave-outward flux rope, but with convex-outward signatures on a local scale.

The propagation mechanism of a vortex on the β plane

The propagation velocity and propagation mechanism for vortices on a β plane are determined for a reduced-gravity model by integrating the momentum equations over the β plane. Isolated vortices, vortices in a background current, and initial vortex propagation from rest are studied. The propagation mechanism for isolated anticyclones as well as cyclones, which has been lacking up to now, is presented. It is shown that, to first order, the vortex moves to generate a Coriolis force on the mass anomaly of the vortex to compensate for the force on the vortex due to the variation of the Coriolis parameter. Only the mass anomaly of the vortex is of importance, because the Coriolis force due to the motion of the bulk of the layer moving with the vortex is almost fully compensated by the Coriolis force on the motion of the exterior flow. Because the mass anomaly of a cyclone is negative the force and acceleration have opposite sign. The role of dipolar structures in steadily moving vortices is discussed, and it is shown that their overall structure is fixed by the steady westward motion of the mass anomaly. Furthermore, it is shown that reduced-gravity vortices are not advected with a background flow. The reason for this behavior is that the background flow changes the ambient vorticity gradient such that the vortex obtains an extra self-propagation term that exactly cancels the advection by the background flow. Last, it is shown that a vortex initially at rest will accelerate equatorward first, after which a westward motion is generated. This result is independent of the sign of the vortex.