The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations

This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

Interference of Fock states in a single measurement

We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed with Bose-Einstein condensates. We also show that the noise level present in the statistics is slightly lower than for a respective measurement of phase states.Comment: 4 page

Damage caused by red deer (Cervus elaphus) & wild boar (Sus scrofa) in forest hunting grounds in Serbia

The systematic study and assessment of the damage by big game in forest hunting grounds in Serbia was infrequent, although the damage was evident. The objective of this paper is to identify the rates and types of damage by red deer and wild boar at three localities: (1) fenced part of the hunting ground 'Crni Lug' (Srem), (2) fenced part of the hunting ground 'Podunavsko Lovište Plavna' (Southwestern Bačka), and (3) fenced rearing centre 'Lomnička Reka' (Mt. Veliki Jastrebac). The damage was not recorded on locality (1). The damage on locality (2) (new polar plantations) and locality (3) (beech forests) was caused by red deer. The main causes of the damage were excessive density and disturbed population structure (sex and age), nonharmonised forest and hunting management, shortage of natural food, especially of pasture areas

Symmetry of k·p Hamiltonian in pyramidal InAs/GaAs quantum dots: Application to the calculation of electronic structure

A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C-4 symmetry of the 8-band k·p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasiangular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type, and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands

Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation

The abundance of clusters at the present epoch and weak gravitational lensing shear both constrain roughly the same combination of the power spectrum normalization sigma_8 and matter energy density Omega_M. The cluster constraint further depends on the normalization of the mass-temperature relation. Therefore, combining the weak lensing and cluster abundance data can be used to accurately calibrate the mass-temperature relation. We discuss this approach and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in the analysis move the cluster contours in Fig1 slightly upwards. No changes in the conclusion

City of London: Vulnerability of Infrastructure to Climate Change. Background Report #2: Hydraulic Modeling and Floodplain Mapping

The main objective of the research project currently under way is to provide an engineering assessment of the vulnerability of London’s public infrastructure under projected rates of climate change with special emphasis on flooding. An original systematic procedure is used to gather and examine available data in order to develop an understanding of the relevant climatic effects and their interaction with municipal infrastructure. Assessment of climate change impacts on municipal infrastructure requires floodplain maps and inundation that will correspond to examined climate change scenarios. This report presents the results of hydraulic analyses used in floodplain mapping under changing climate. Combined, climate and hydrologic modeling, were used to generate input flow data for hydraulic modelling. Standard computer software HEC-RAS is used for hydraulic computation of water elevation. The existing HEC-RAS models of the Upper Thames River basin are not georeferenced and therefore they cannot be used for hydraulic modeling under climate change. Consequently, it was necessary to develop new HEC-RAS models for the rivers and creeks of London that were considered in this project. Geometric input data for new HEC-RAS models were created using HEC-GeoRAS software, which is an extension of ArcGIS computer package for spatial analysis. In the preprocessing phase the HEC-GeoRAS is used to create a digital terrain model from the contour lines shape file provided by the city of London. In the next step the following geometric data layers were generated: river center line, bank lines, flowpaths, cross sections, and bridges. Required attributes were assigned to each of the layers. In the last step of the pre-processing stage the input file for the HEC-RAS hydraulic analysis was prepared. The hydraulic analysis starts with the geometric data import, followed with the preparation of the hydraulic structures data and flow data. A very detailed quality control was performed on the cross sections data generated during the pre-processing phase. The roughness coefficient values were determined using the existing HEC-RAS models and aerial photography of the basin. Data on bridges, taken from the existing models and drawings were integrated with the rest of the data. Two climate scenarios (historic and wet) developed by climate and hydrologic modeling (Eum and Simonovic, 2009) were used and water surface elevation profiles were calculated for 100- and 250- year return periods. The computation results were used to assemble the HEC-RAS GIS export file for floodplain mapping. The Arc Map software package was used to create water surface GIS layer. Overlaying this layer with the terrain provided for calculation of floodplain boundaries and inundation depths. The floodplain maps generated using this process are used in vulnerability assessments of London’s public infrastructure to climate change currently in progress. The results of water surface profile computations are presented in tabular form for the 250- year flood under historic and wet climate scenarios. The final floodplain maps along Main Thames for both scenarios show minor deviation of the floodplain boundaries when compared with the existing floodplain lines. However, the water depth difference is up to 50 cm. The area upstream from the culvert on Pottersburg Creek (close to the intersection of Trafalgar St. and Clarke St.) is identified as critical due to the high extent of flooding. The flooding at this location is caused by insufficient culvert opening that creates a backwater effect. Areas of special concern are identified where the floodplain mapping results are not sufficiently accurate due to inaccuracies in the contour lines. The main recommendation based on the work presented in this report is that new georeferenced cross sections should be surveyed in order to increase the accuracy of the floodplain mapping process. The hydraulic analyses should be repeated with more accurate input data and the resulting floodplain maps should be revised accordingly.https://ir.lib.uwo.ca/wrrr/1031/thumbnail.jp

Quantum transport in semiconductor quantum dot superlattices: electron-phonon resonances and polaron effects

Electron transport in periodic quantum dot arrays in the presence of interactions with phonons was investigated using the formalism of nonequilibrium Green's functions. The self-consistent Born approximation was used to model the self-energies. Its validity was checked by comparison with the results obtained by direct diagonalization of the Hamiltonian of interacting electrons and longitudinal optical phonons. The nature of charge transport at electron -- phonon resonances was investigated in detail and contributions from scattering and coherent tunnelling to the current were identified. It was found that at larger values of the structure period the main peak in the current -- field characteristics exhibits a doublet structure which was shown to be a transport signature of polaron effects. At smaller values of the period, electron -- phonon resonances cause multiple peaks in the characteristics. A phenomenological model for treatment of nonuniformities of a realistic quantum dot ensemble was also introduced to estimate the influence of nonuniformities on current -- field characteristics

The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects

We study the effect of primordial nongaussianity on large-scale structure, focusing upon the most massive virialized objects. Using analytic arguments and N-body simulations, we calculate the mass function and clustering of dark matter halos across a range of redshifts and levels of nongaussianity. We propose a simple fitting function for the mass function valid across the entire range of our simulations. We find pronounced effects of nongaussianity on the clustering of dark matter halos, leading to strongly scale-dependent bias. This suggests that the large-scale clustering of rare objects may provide a sensitive probe of primordial nongaussianity. We very roughly estimate that upcoming surveys can constrain nongaussianity at the level |fNL| <~ 10, competitive with forecasted constraints from the microwave background.Comment: 16 pages, color figures, revtex4. v2: added references and an equation. submitted to PRD. v3: simplified derivation, additional reference