Optimal control of non-stationary differential linear repetitive processes

Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics

Viscosity Limits for Zeroth-Order Pseudodifferential Operators

Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators on tori, we consider viscosity limits in which zeroth-order operators, P, are replaced by P + iν Δ, ν > 0. By adapting the Helffer–Sjöstrand theory of scattering resonances, we show that, in a complex neighbourhood of the continuous spectrum, eigenvalues of P + iν Δ have limits as the viscosity ν goes to 0. In the simplified setting of tori, this justifies claims made in the physics literature. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC

Constrained optimal control theory for differential linear repetitive processes

Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and $\epsilon$-maximum principles to the

On the connection between discrete linear repetitive processes and 2-D discrete linear systems

A direct method is developed that reduces a polynomial system matrix describinga discrete linear repetitive process to a 2-D singular state-space form such that all the relevant properties, including the zero structure of the system matrix, are retained. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D singular form is zero coprime system equivalence. The exact nature of the resulting system matrix in singular form and the transformation involved are established

Revealing large-scale homogeneity and trace impurity sensitivity of GaAs nanoscale membranes

III-V nanostructures have the potential to revolutionize optoelectronics and energy harvesting. For this to become a reality, critical issues such as reproducibility and sensitivity to defects should be resolved. By discussing the optical properties of MBE grown GaAs nanomembranes we highlight several features that bring them closer to large scale applications. Uncapped membranes exhibit a very high optical quality, expressed by extremely narrow neutral exciton emission, allowing the resolution of the more complex excitonic structure for the first time. Capping of the membranes with an AlGaAs shell results in a strong increase of emission intensity but also to a shift and broadening of the exciton peak. This is attributed to the existence of impurities in the shell, beyond MBE-grade quality, showing the high sensitivity of these structures to the presence of impurities. Finally, emission properties are identical at the sub-micron and sub-millimeter scale, demonstrating the potential of these structures for large scale applications.Comment: just accepted in Nano Letters, http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b0025

Isotopic composition of daily precipitation along the southern foothills of the Himalayas: impact of marine and continental sources of atmospheric moisture

The flow of the Himalayan rivers, a key source of fresh water for more than a billion people primarily depends upon the strength, behaviour and duration of the Indian summer monsoon (ISM) and the western disturbances (WD), two contrasting circulation regimes of the regional atmosphere. An analysis of the 2H and 18O isotope composition of daily precipitation collected along the southern foothills of the Himalayas, combined with extensive backward trajectory modelling, was used to gain deeper insight into the mechanisms controlling the isotopic composition of precipitation and the origin of atmospheric moisture and precipitation during ISM and WD periods. Daily precipitation samples were collected during the period from September 2008 to December 2011 at six stations, extending from Srinagar in the west (Kashmir state) to Dibrugarh in the east (Assam state). In total, 548 daily precipitation samples were collected and analysed for their stable isotope composition. It is suggested that the gradual reduction in the 2H and 18O content of precipitation in the study region, progressing from δ18O values close to zero down to ca. −10 ‰ in the course of ISM evolution, stems from regional, large-scale recycling of moisture-driven monsoonal circulation. Superimposed on this general trend are short-term fluctuations of the isotopic composition of rainfall, which might have stem from local effects such as enhanced convective activity and the associated higher degree of rainout of moist air masses (local amount effect), the partial evaporation of raindrops, or the impact of isotopically heavy moisture generated in evapotranspiration processes taking place in the vicinity of rainfall sampling sites. Seasonal footprint maps constructed for three stations representing the western, central and eastern portions of the Himalayan region indicate that the influence of monsoonal circulation reaches the western edges of the Himalayan region. While the characteristic imprint of monsoonal air masses (increase of monthly rainfall amount) can be completely absent in the western Himalayas, the onset of the ISM period in this region is still clearly visible in the isotopic composition of daily precipitation. A characteristic feature of daily precipitation collected during the WD period is the gradual increase of 2H and 18O content, reaching positive δ2H and δ18O values towards the end of the period. This trend can be explained by the growing importance of moisture of continental origin as a source of daily precipitation. High deuterium-excess (d-excess) values of daily rainfall recorded at the monitoring stations (38 cases in total, range from 20.6 to 44.0 ‰) are attributed to moisture of continental origin released into the atmosphere during the evaporation of surface water bodies and/or soil water evaporation

Excitonic Properties of Low-Band-Gap Lead-Tin Halide Perovskites

The MAPb1–xSnxI3 (x = 0–1) (MA = methylammonium) perovskite family comprises a range of ideal absorber band gaps for single- and multijunction perovskite solar cells. Here, we use spectroscopic measurements to reveal a range of hitherto unknown fundamental properties of this materials family. Temperature-dependent transmission results show that the temperature of the tetragonal to orthorhombic structural transition decreases with increasing tin content. Through low-temperature magnetospectroscopy, we show that the exciton binding energy is lower than 16 meV, revealing that the dominant photogenerated species at typical operational conditions of optoelectronic devices are free charges rather than excitons. The reduced mass increases approximately proportionally to the band gap, and the mass values (0.075–0.090me) can be described with a two-band k·p perturbation model extended across the broad band gap range of 1.2–2.4 eV. Our findings can be generalized to predict values for the effective mass and binding energy for other members of this family of materials