On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Nonlinear (magnetic) correction to the field of a static charge in an external field

We find the first nonlinear correction to the field produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor-the nonlinear response function-is written within the local approximation of the effective action in an otherwise model-and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included. DOI: 10.1103/PhysRevD.86.125028

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

Nonlinear/electromagnetic co-simulation of microwaves and millimeter-waves links

The Ph.D. thesis describes the simulations of different microwave links from the transmitter to the receiver intermediate-frequency ports, by means of a rigorous circuit-level nonlinear analysis approach coupled with the electromagnetic characterization of the transmitter and receiver front ends. This includes a full electromagnetic computation of the radiated far field which is used to establish the connection between transmitter and receiver. Digitally modulated radio-frequency drive is treated by a modulation-oriented harmonic-balance method based on Krylov-subspace model-order reduction to allow the handling of large-size front ends. Different examples of links have been presented: an End-to-End link simulated by making use of an artificial neural network model; the latter allows a fast computation of the link itself when driven by long sequences of the order of millions of samples. In this way a meaningful evaluation of such link performance aspects as the bit error rate becomes possible at the circuit level. Subsequently, a work focused on the co-simulation an entire link including a realistic simulation of the radio channel has been presented. The channel has been characterized by means of a deterministic approach, such as Ray Tracing technique. Then, a 2x2 multiple-input multiple-output antenna link has been simulated; in this work near-field and far-field coupling between radiating elements, as well as the environment factors, has been rigorously taken into account. Finally, within the scope to simulate an entire ultra-wideband link, the transmitting side of an ultrawideband link has been designed, and an interesting Front-End co-design technique application has been setup.

Nonlinear / electromagnetic co-simulation and co-design of microwave links in highly polluted and / or strongly inhomogeneous environments

The objective of the Ph.D. thesis is to put the basis of an all-embracing link analysis procedure that may form a general reference scheme for the future state-of-the-art of RF/microwave link design: it is basically meant as a circuit-level simulation of an entire radio link, with – generally multiple – transmitting and receiving antennas examined by EM analysis. In this way the influence of mutual couplings on the frequency-dependent near-field and far-field performance of each element is fully accounted for. The set of transmitters is treated as a unique nonlinear system loaded by the multiport antenna, and is analyzed by nonlinear circuit techniques. In order to establish the connection between transmitters and receivers, the far-fields incident onto the receivers are evaluated by EM analysis and are combined by extending an available Ray Tracing technique to the link study. EM theory is used to describe the receiving array as a linear active multiport network. Link performances in terms of bit error rate (BER) are eventually verified a posteriori by a fast system-level algorithm. In order to validate the proposed approach, four heterogeneous application contexts are provided. A complete MIMO link design in a realistic propagation scenario is meant to constitute the reference case study. The second one regards the design, optimization and testing of various typologies of rectennas for power generation by common RF sources. Finally, the project and implementation of two typologies of radio identification tags, at X-band and V-band respectively. In all the cases the importance of an exhaustive nonlinear/electromagnetic co-simulation and co-design is demonstrated to be essential for any accurate system performance prediction.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

The effects of hypocalcemia on spatial alternans and ventricular fibrillation studied with the optical mapping technique

The heart is a wonderful but complex organ: it uses electrochemical mechanisms in order to produce mechanical energy to pump the blood throughout the body and allow the life of humans and animals. This organ can be subject to several diseases and sudden cardiac death (SCD) is the most catastrophic manifestation of these diseases, responsible for the death of a large number of people throughout the world. It is estimated that 325000 Americans annually die for SCD. SCD most commonly occurs as a result of reentrant tachyarrhythmias (ventricular tachycardia (VT) and ventricular fibrillation (VF)) and the identification of those patients at higher risk for the development of SCD has been a difficult clinical challenge. Nowadays, a particular electrocardiogram (ECG) abnormality, “T-wave alternans” (TWA), is considered a precursor of lethal cardiac arrhythmias and sudden death, a sensitive indicator of risk for SCD. TWA is defined as a beat-to-beat alternation in the shape, amplitude, or timing of the T-wave on the ECG, indicative of the underlying repolarization of cardiac cells [5]. In other words TWA is the macroscopic effect of subcellular and celluar mechanisms involving ionic kinetics and the consequent depolarization and repolarization of the myocytes. Experimental activities have shown that TWA on the ECG is a manifestation of an underlying alternation of long and short action potential durations (APDs), the so called APD-alternans, of cardiac myocytes in the myocardium. Understanding the mechanism of APDs-alternans is the first step for preventing them to occur. In order to investigate these mechanisms it’s very important to understand that the biological systems are complex systems and their macroscopic properties arise from the nonlinear interactions among the parts. The whole is greater than the sum of the parts, and it cannot be understood only by studying the single parts. In this sense the heart is a complex nonlinear system and its way of working follows nonlinear dynamics; alternans also, they are a manifestation of a phenomenon typical in nonlinear dynamical systems, called “period-dubling bifurcation”. Over the past decade, it has been demonstrated that electrical alternans in cardiac tissue is an important marker for the development of ventricular fibrillation and a significant predictor for mortality. It has been observed that acute exposure to low concentration of calcium does not decrease the magnitude of alternans and sustained ventricular Fibrillation (VF) is still easily induced under these condition. However with prolonged exposure to low concentration of calcium, alternans disappears, but VF is still inducible. This work is based on this observation and tries to make it clearer. The aim of this thesis is investigate the effect of hypocalcemia spatial alternans and VF doing experiments with canine hearts and perfusing them with a solution with physiological ionic concentration and with a solution with low calcium concentration (hypocalcemia); in order to investigate the so called memory effect, the experimental activity was modified during the way. The experiments were performed with the optical mapping technique, using voltage-sensitive dye, and a custom made Java code was used in post-processing. Finding the Nolasco and Dahlen’s criterion [8] inadequate for the prediction of alternans, and takin into account the experimental results, another criterion, which consider the memory effect, has been implemented. The implementation of this criterion could be the first step in the creation of a method, AP-based, discriminating who is at risk if developing VF. This work is divided into four chapters: the first is a brief presentation of the physiology of the heart; the second is a review of the major theories and discovers in the study of cardiac dynamics; the third chapter presents an overview on the experimental activity and the optical mapping technique; the forth chapter contains the presentation of the results and the conclusions.

The Crystallization Kinetics of Polylactic Acid (Pla) Processed Through Solid-State/Melt Extrusion

Polylactic acid (PLA) is a bio-derived, biodegradable polymer with a number of similar mechanical properties to commodity plastics like polyethylene (PE) and polyethylene terephthalate (PETE). There has recently been a great interest in using PLA to replace these typical petroleum-derived polymers because of the developing trend to use more sustainable materials and technologies. However, PLA¿s inherent slow crystallization behavior is not compatible with prototypical polymer processing techniques such as molding and extrusion, and in turn inhibits its widespread use in industrial applications. In order to make PLA into a commercially-viable material, there is a need to process the material in such a way that its tendency to form crystals is enhanced. The industry standard for producing PLA products is via twin screw extrusion (TSE), where polymer pellets are fed into a heated extruder, mixed at a temperature above its melting temperature, and molded into a desired shape. A relatively novel processing technique called solid-state shear pulverization (SSSP) processes the polymer in the solid state so that nucleation sites can develop and fast crystallization can occur. SSSP has also been found to enhance the mechanical properties of a material, but its powder output form is undesirable in industry. A new process called solid-state/melt extrusion (SSME), developed at Bucknell University, combines the TSE and SSSP processes in one instrument. This technique has proven to produce moldable polymer products with increased mechanical strength. This thesis first investigated the effects of the TSE, SSSP, and SSME polymer processing techniques on PLA. The study seeks to determine the process that yields products with the most enhanced thermal and mechanical properties. For characterization, percent crystallinity, crystallization half time, storage modulus, softening temperature, degradation temperature and molecular weight were analyzed for all samples. Through these characterization techniques, it was observed that SSME-processed PLA had enhanced properties relative to TSE- and SSSP-processed PLA. Because of the previous findings, an optimization study for SSME-processed PLA was conducted where throughput and screw design were varied. The optimization study determined PLA processed with a low flow rate and a moderate screw design in an SSME process produced a polymer product with the largest increase in thermal properties and a high retention of polymer structure relative to TSE-, SSSP-, and all other SSME-processed PLA. It was concluded that the SSSP part of processing scissions polymer chains, creating defects within the material, while the TSE part of processing allows these defects to be mixed thoroughly throughout the sample. The study showed that a proper SSME setup allows for both the increase in nucleation sites within the polymer and sufficient mixing, which in turn leads to the development of a large amount of crystals in a short period of time.

Modeling of transfer kinetics at the serum-cerebrospinal fluid barrier in rabbits with experimental meningitis: application to grepafloxacin

The goals of the present study were to model the population kinetics of in vivo influx and efflux processes of grepafloxacin at the serum-cerebrospinal fluid (CSF) barrier and to propose a simulation-based approach to optimize the design of dose-finding trials in the meningitis rabbit model. Twenty-nine rabbits with pneumococcal meningitis receiving grepafloxacin at 15 mg/kg of body weight (intravenous administration at 0 h), 30 mg/kg (at 0 h), or 50 mg/kg twice (at 0 and 4 h) were studied. A three-compartment population pharmacokinetic model was fit to the data with the program NONMEM (Nonlinear Mixed Effects Modeling). Passive diffusion clearance (CL(diff)) and active efflux clearance (CL(active)) are transfer kinetic modeling parameters. Influx clearance is assumed to be equal to CL(diff), and efflux clearance is the sum of CL(diff), CL(active), and bulk flow clearance (CL(bulk)). The average influx clearance for the population was 0.0055 ml/min (interindividual variability, 17%). Passive diffusion clearance was greater in rabbits receiving grepafloxacin at 15 mg/kg than in those treated with higher doses (0.0088 versus 0.0034 ml/min). Assuming a CL(bulk) of 0.01 ml/min, CL(active) was estimated to be 0.017 ml/min (11%), and clearance by total efflux was estimated to be 0.032 ml/min. The population kinetic model allows not only to quantify in vivo efflux and influx mechanisms at the serum-CSF barrier but also to analyze the effects of different dose regimens on transfer kinetic parameters in the rabbit meningitis model. The modeling-based approach also provides a tool for the simulation and prediction of various outcomes in which researchers might be interested, which is of great potential in designing dose-finding trials.

Altered hypertrophic chondrocyte kinetics in GDF-5 deficient murine tibial growth plates

The growth/differentiation factors (GDFs) are a subgroup of the bone morphogenetic proteins best known for their role in joint formation and chondrogenesis. Mice deficient in one of these signaling proteins, GDF-5, exhibit numerous skeletal abnormalities, including shortened limb bones. The primary aim of this study was determine whether GDF-5 deficiency would alter the growth rate in growth plates from the long bones in mice and, if so, how this is achieved. Stereologic and cell kinetic parameters in proximal tibial growth plates from 5-week-old female GDF-5 -/- mice and control littermates were examined. GDF-5 deficiency resulted in a statistically significant reduction in growth rate (-14%, p=0.03). The effect of genotype on growth rate was associated with an altered hypertrophic phase duration, with hypertrophic cells from GDF-5 deficient mice exhibiting a significantly longer phase duration compared to control littermates (+25%, p=0.006). These data suggest that one way in which GDF-5 might modulate the rate of endochondral bone growth could be by affecting the duration of the hypertrophic phase in growth plate chondrocytes.

Stability and kinetics of nucleic acid triplexes with chimaeric DNA/RNA third strands

A series of chimaeric DNA/RNA triplex-forming oligonucleotides (TFOs) with identical base-sequence but varying sequential composition of the sugar residues were prepared. The structural, kinetic and thermodynamic properties of triplex formation with their corresponding double-helical DNA target were investigated by spectroscopic methods. Kinetic and thermodynamic data were obtained from analysis of non-equilibrium UV-melting- and annealing curves in the range of pH 5.1 to 6.7 in a 10 mM citrate/phosphate buffer containing 0.1M NaCl and 1 mM EDTA. It was found that already single substitutions of ribo- for deoxyribonucleotides in the TFOs greatly affect stability and kinetics of triplex formation in a strongly sequence dependent manner. Within the sequence context investigated, triplex stability was found to increase when deoxyribonucleotides were present at the 5'-side and ribonucleotides in the center of the TFO. Especially the substitution of thymidines for uridines in the TFO was found to accelerate both, the association and dissociation process, in a strongly position-dependent way. Differential structural information on triplexes and TFO single-strands was obtained from CD-spectroscopy and gel mobility experiments. Only minor changes were observed in the CD spectra of the triplexes at all pH values investigated, and the electrophoretic mobility was nearly identical in all cases, indicating a high degree of structural similarity. In contrast, the single-stranded TFOs showed high structural variability as determined in the same way. The results are discussed in the context of the design of TFOs for therapeutic or biochemical applications.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Evaluation of the bioaccumulation kinetics of gold nanorods in vital mammalian organs by mean of TXRF spectrometry

This work presents the first application of total-reflection X-ray fluorescence (TXRF) spectrometry, a new and powerful alternative analytical method, to evaluation of the bioaccumulation kinetics of gold nanorods (GNRs) in various tissues upon intravenous administration in mice. The analytical parameters for developed methodology by TXRF were evaluated by means of the parallel analysis of bovine liver certified reference material samples (BCR-185R) doped with 10 μg/g gold. The average values (n = 5) achieved for gold measurements in lyophilized tissue weight were as follows: recovery 99.7%, expanded uncertainty (k = 2) 7%, repeatability 1.7%, detection limit 112 ng/g, and quantification limit 370 ng/g. The GNR bioaccumulation kinetics was analyzed in several vital mammalian organs such as liver, spleen, brain, and lung at different times. Additionally, urine samples were analyzed to study the kinetics of elimination of the GNRs by this excretion route. The main achievement was clearly differentiating two kinds of behaviors. GNRs were quickly bioaccumulated by highly vascular filtration organs such as liver and spleen, while GNRs do not show a bioaccumulation rates in brain and lung for the period of time investigated. In parallel, urine also shows a lack of GNR accumulation. TXRF has proven to be a powerful, versatile, and precise analytical technique for the evaluation of GNRs content in biological systems and, in a more general way, for any kind of metallic nanoparticles.