Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

Nonlinear signal transformations:path to capacity above the linear AWGN Shannon limit

We present a methodology for simultaneous optimization of modulation format and regenerative transformations in nonlinear communication channels. We derived analytically the maximum regenerative Shannon capacity, towards which any regenerative channel tends at high SNR and large number of regenerators.

Optimization and characterization of femtosecond laser inscribed in-fiber microchannels for liquid sensing

In-fiber microchannels were fabricated directly in standard single mode fiber using the femtosecond laser inscribe and etch technique. This method of creating in-fiber microchannels offers great versatility, since it allows complex three-dimensional structures to be inscribed and then preferentially etched with hydrofluoric acid. In addition, inscription does not require a photosensitive fiber; the modification is induced through nonlinear processes triggered by an ultrashort laser pulse. Four in-fiber microchannel designs were experimentally investigated using this technique - microhole, microslot channel along the core, microslot channel perpendicular to the core and helical channel around the core. Each device design was evaluated through monitoring the optical spectral change while inserting a range of index matching oils into each microchannel; an R.I. sensitivity up to 1.55 dB/RIU was achieved in these initial tests. Furthermore, an all femtosecond laser inscribed Fabry-Pérot-based refractometer with an R.I. sensitivity of 2.75 nm/RIU was also demonstrated. The Fabry-Pérot refractometer was formed by positioning a microchannel between two femtosecond laser inscribed point-by-point fiber Bragg gratings.

Stable optical vortices in nonlinear multicore fibers

The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF.

Mode-locking intracavity dynamics:modeling nonlinear power and energy fluctuations

Modern high-power, pulsed lasers are driven by strong intracavity fluctuations. Critical in driving the intracavity dynamics is the nontrivial phase profiles generated and their periodic modification from either nonlinear mode-coupling, spectral filtering or dispersion management. Understanding the theoretical origins of the intracavity fluctuations helps guide the design, optimization and construction of efficient, high-power and high-energy pulsed laser cavities. Three specific mode-locking component are presented for enhancing laser energy: waveguide arrays, spectral filtering and dispersion management. Each component drives a strong intracavity dynamics that is captured through various modeling and analytic techniques.

Optimization models for selecting bus stops for accessibility improvements for people with disabilities

Bus stops are key links in the journeys of transit patrons with disabilities. Inaccessible bus stops prevent people with disabilities from using fixed-route bus services, thus limiting their mobility. The Americans with Disabilities Act (ADA) of 1990 prescribes the minimum requirements for bus stop accessibility by riders with disabilities. Due to limited budgets, transit agencies can only select a limited number of bus stop locations for ADA improvements annually. These locations should preferably be selected such that they maximize the overall benefits to patrons with disabilities. In addition, transit agencies may also choose to implement the universal design paradigm, which involves higher design standards than current ADA requirements and can provide amenities that are useful for all riders, like shelters and lighting. Many factors can affect the decision to improve a bus stop, including rider-based aspects like the number of riders with disabilities, total ridership, customer complaints, accidents, deployment costs, as well as locational aspects like the location of employment centers, schools, shopping areas, and so on. These interlacing factors make it difficult to identify optimum improvement locations without the aid of an optimization model. This dissertation proposes two integer programming models to help identify a priority list of bus stops for accessibility improvements. The first is a binary integer programming model designed to identify bus stops that need improvements to meet the minimum ADA requirements. The second involves a multi-objective nonlinear mixed integer programming model that attempts to achieve an optimal compromise among the two accessibility design standards. Geographic Information System (GIS) techniques were used extensively to both prepare the model input and examine the model output. An analytic hierarchy process (AHP) was applied to combine all of the factors affecting the benefits to patrons with disabilities. An extensive sensitivity analysis was performed to assess the reasonableness of the model outputs in response to changes in model constraints. Based on a case study using data from Broward County Transit (BCT) in Florida, the models were found to produce a list of bus stops that upon close examination were determined to be highly logical. Compared to traditional approaches using staff experience, requests from elected officials, customer complaints, etc., these optimization models offer a more objective and efficient platform on which to make bus stop improvement suggestions.

Optimization of waiting time at toll plazas

Toll plazas have several toll payment types such as manual, automatic coin machines, electronic and mixed lanes. In places with high traffic flow, the presence of toll plaza causes a lot of traffic congestion; this creates a bottleneck for the traffic flow, unless the correct mix of payment types is in operation. The objective of this research is to determine the optimal lane configuration for the mix of the methods of payment so that the waiting time in the queue at the toll plaza is minimized. A queuing model representing the toll plaza system and a nonlinear integer program have been developed to determine the optimal mix. The numerical results show that the waiting time can be decreased at the toll plaza by changing the lane configuration. For the case study developed an improvement in the waiting time as high as 96.37 percent was noticed during the morning peak hour.

Nonlinear distortion generation mechanisms in Doherty amplifiers

Nowadays, wireless communications systems demand for greater mobility and higher data rates. Moreover, the need for spectral efficiency requires the use of non-constant envelope modulation schemes. Hence, power amplifier designers have to build highly efficient, broadband and linear amplifiers. In order to fulfil these strict requirements, the practical Doherty amplifier seems to be the most promising technique. However, due to its complex operation, its nonlinear distortion generation mechanisms are not yet fully understood. Currently, only heuristic interpretations are being used to justify the observed phenomena. Therefore, the main objective of this work is to provide a model capable of describing the Doherty power amplifier nonlinear distortion generation mechanisms, allowing the optimization of its design according to linearity and efficiency criteria. Besides that, this approach will allow a bridge between two different worlds: power amplifier design and digital pre-distortion since the knowledge gathered from the Doherty operation will serve to select the most suitable pre-distortion models.

Digital nonlinear equalization for optical transmission systems

This thesis focuses on digital equalization of nonlinear fiber impairments for coherent optical transmission systems. Building from well-known physical models of signal propagation in single-mode optical fibers, novel nonlinear equalization techniques are proposed, numerically assessed and experimentally demonstrated. The structure of the proposed algorithms is strongly driven by the optimization of the performance versus complexity tradeoff, envisioning the near-future practical application in commercial real-time transceivers. The work is initially focused on the mitigation of intra-channel nonlinear impairments relying on the concept of digital backpropagation (DBP) associated with Volterra-based filtering. After a comprehensive analysis of the third-order Volterra kernel, a set of critical simplifications are identified, culminating in the development of reduced complexity nonlinear equalization algorithms formulated both in time and frequency domains. The implementation complexity of the proposed techniques is analytically described in terms of computational effort and processing latency, by determining the number of real multiplications per processed sample and the number of serial multiplications, respectively. The equalization performance is numerically and experimentally assessed through bit error rate (BER) measurements. Finally, the problem of inter-channel nonlinear compensation is addressed within the context of 400 Gb/s (400G) superchannels for long-haul and ultra-long-haul transmission. Different superchannel configurations and nonlinear equalization strategies are experimentally assessed, demonstrating that inter-subcarrier nonlinear equalization can provide an enhanced signal reach while requiring only marginal added complexity.

Optimization of the Ion Source-Mass Spectrometry Parameters in Non-Steroidal Anti-Inflammatory and Analgesic Pharmaceuticals Analysis by a Design of Experiments Approach

The flow rates of drying and nebulizing gas, heat block and desolvation line temperatures and interface voltage are potential electrospray ionization parameters as they may enhance sensitivity of the mass spectrometer. The conditions that give higher sensitivity of 13 pharmaceuticals were explored. First, Plackett-Burman design was implemented to screen significant factors, and it was concluded that interface voltage and nebulizing gas flow were the only factors that influence the intensity signal for all pharmaceuticals. This fractionated factorial design was projected to set a full 2(2) factorial design with center points. The lack-of-fit test proved to be significant. Then, a central composite face-centered design was conducted. Finally, a stepwise multiple linear regression and subsequently an optimization problem solving were carried out. Two main drug clusters were found concerning the signal intensities of all runs of the augmented factorial design. p-Aminophenol, salicylic acid, and nimesulide constitute one cluster as a result of showing much higher sensitivity than the remaining drugs. The other cluster is more homogeneous with some sub-clusters comprising one pharmaceutical and its respective metabolite. It was observed that instrumental signal increased when both significant factors increased with maximum signal occurring when both codified factors are set at level +1. It was also found that, for most of the pharmaceuticals, interface voltage influences the intensity of the instrument more than the nebulizing gas flowrate. The only exceptions refer to nimesulide where the relative importance of the factors is reversed and still salicylic acid where both factors equally influence the instrumental signal. Graphical Abstract ᅟ.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Solid Lipid Nanoparticles For Hydrophilic Biotech Drugs: Optimization And Cell Viability Studies (caco-2 & Hepg-2 Cell Lines).

Insulin was used as model protein to developed innovative Solid Lipid Nanoparticles (SLNs) for the delivery of hydrophilic biotech drugs, with potential use in medicinal chemistry. SLNs were prepared by double emulsion with the purpose of promoting stability and enhancing the protein bioavailability. Softisan(®)100 was selected as solid lipid matrix. The surfactants (Tween(®)80, Span(®)80 and Lipoid(®)S75) and insulin were chosen applying a 2(2) factorial design with triplicate of central point, evaluating the influence of dependents variables as polydispersity index (PI), mean particle size (z-AVE), zeta potential (ZP) and encapsulation efficiency (EE) by factorial design using the ANOVA test. Therefore, thermodynamic stability, polymorphism and matrix crystallinity were checked by Differential Scanning Calorimetry (DSC) and Wide Angle X-ray Diffraction (WAXD), whereas the effect of toxicity of SLNs was check in HepG2 and Caco-2 cells. Results showed a mean particle size (z-AVE) width between 294.6 nm and 627.0 nm, a PI in the range of 0.425-0.750, ZP about -3 mV, and the EE between 38.39% and 81.20%. After tempering the bulk lipid (mimicking the end process of production), the lipid showed amorphous characteristics, with a melting point of ca. 30 °C. The toxicity of SLNs was evaluated in two distinct cell lines (HEPG-2 and Caco-2), showing to be dependent on the concentration of particles in HEPG-2 cells, while no toxicity in was reported in Caco-2 cells. SLNs were stable for 24 h in in vitro human serum albumin (HSA) solution. The resulting SLNs fabricated by double emulsion may provide a promising approach for administration of protein therapeutics and antigens.