Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

Optimization and Control of Power Flow in Distribution Networks

Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators.

Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory.

The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.

Processes controlling the quantities of biogenic materials in lakes and reservoirs subject to cultural eutrophication

The processes which control the growth, composition, succession and loss from suspension of phytoplankton algae are briefly reviewed, with special reference to function in eutrophic reservoir systems. The ecology of larger algal biomasses supported by high nutrient loading rates are more likely to be subject to physical (wash-out, underwater light penetration, thermal stability and mixing) than to chemical constraints. Sudden changes in the interactions between physical factors temporarily impair the growth of dominant algal species, and advance the succession. Certain algae may be cropped heavily, but selectively, by zooplankton feeding, but they are rarely the species which cause problems in waterworks practice. Grazing, however, does influence succession. A deeper understanding of the operation of loss control mechanism is urgently required. Potentially, manipulation of the physical environment provides an important means of alleviating day-to-day algal problems in eutrophic reservoirs; in terms of cost effectiveness these may prove to be more attractive than reducing nutrient loads at source.

Magnetic Cross-Linked Enzyme Aggregates (mCLEAs) of Candida antarctica Lipase: An Efficient and Stable Biocatalyst for Biodiesel Synthesis

Enzyme-catalyzed production of biodiesel is the object of extensive research due to the global shortage of fossil fuels and increased environmental concerns. Herein we report the preparation and main characteristics of a novel biocatalyst consisting of Cross-Linked Enzyme Aggregates (CLEAs) of Candida antarctica lipase B (CALB) which are covalently bound to magnetic nanoparticles, and tackle its use for the synthesis of biodiesel from non-edible vegetable and waste frying oils. For this purpose, insolubilized CALB was covalently cross-linked to magnetic nanoparticles of magnetite which the surface was functionalized with –NH2 groups. The resulting biocatalyst combines the relevant catalytic properties of CLEAs (as great stability and feasibility for their reutilization) and the magnetic character, and thus the final product (mCLEAs) are superparamagnetic particles of a robust catalyst which is more stable than the free enzyme, easily recoverable from the reaction medium and reusable for new catalytic cycles. We have studied the main properties of this biocatalyst and we have assessed its utility to catalyze transesterification reactions to obtain biodiesel from non-edible vegetable oils including unrefined soybean, jatropha and cameline, as well as waste frying oil. Using 1% mCLEAs (w/w of oil) conversions near 80% were routinely obtained at 30°C after 24 h of reaction, this value rising to 92% after 72 h. Moreover, the magnetic biocatalyst can be easily recovered from the reaction mixture and reused for at least ten consecutive cycles of 24 h without apparent loss of activity. The obtained results suggest that mCLEAs prepared from CALB can become a powerful biocatalyst for application at industrial scale with better performance than those currently available.

Marine fisheries, genetic effects and biodiversity

Preservation of marine biodiversity deserves serious consideration as almost 65% of the earth's organisms (excluding insects) are marine. There is little knowledge at present on the status of marine biodiversity. However, the seas are an important source of protein for human consumption and genetic diversity is a key factor in ecosystem functioning, stability and resilience. Overfishing and destructive practices may have unalterable impact on marine biodiversity. This paper discusses measures that can be adopted to protect the most productive areas of the marine ecosystem.

Experimentos numéricos para deposição de parafinas com modelo Multisólido

Este trabalho objetiva a construção de estruturas robustas e computacionalmente eficientes para a solução do problema de deposição de parafinas do ponto de vista do equilíbrio sólido-líquido. São avaliados diversos modelos termodinâmicos para a fase líquida: equação de estado de Peng-Robinson e os modelos de coeficiente de atividade de Solução Ideal, Wilson, UNIQUAC e UNIFAC. A fase sólida é caracterizada pelo modelo Multisólido. A previsão de formação de fase sólida é inicialmente prevista por um teste de estabilidade termodinâmica. Posteriormente, o sistema de equações não lineares que caracteriza o equilíbrio termodinâmico e as equações de balanço material é resolvido por três abordagens numéricas: método de Newton multivariável, método de Broyden e método Newton-Armijo. Diversos experimentos numéricos foram conduzidos de modo a avaliar os tempos de computação e a robustez frente a diversos cenários de estimativas iniciais dos métodos numéricos para os diferentes modelos e diferentes misturas. Os resultados indicam para a possibilidade de construção de arcabouços computacionais eficientes e robustos, que podem ser empregados acoplados a simuladores de escoamento em dutos, por exemplo.

Global analysis of mRNA half-lives and de novo transcription in a dinoflagellate, Karenia brevis

Dinoflagellates possess many physiological processes that appear to be under post-transcriptional control. However, the extent to which their genes are regulated post-transcriptionally remains unresolved. To gain insight into the roles of differential mRNA stability and de novo transcription in dinoflagellates, we biosynthetically labeled RNA with 4-thiouracil to isolate newly transcribed and pre-existing RNA pools in Karenia brevis. These isolated fractions were then used for analysis of global mRNA stability and de novo transcription by hybridization to a K. brevis microarray. Global K. brevis mRNA half-lives were calculated from the ratio of newly transcribed to pre-existing RNA for 7086 array features using the online software HALO (Half-life Organizer). Overall, mRNA half-lives were substantially longer than reported in other organisms studied at the global level, ranging from 42 minutes to greater than 144 h, with a median of 33 hours. Consistent with well-documented trends observed in other organisms, housekeeping processes, including energy metabolism and transport, were significantly enriched in the most highly stable messages. Shorter-lived transcripts included a higher proportion of transcriptional regulation, stress response, and other response/regulatory processes. One such family of proteins involved in post-transcriptional regulation in chloroplasts and mitochondria, the pentatricopeptide repeat (PPR) proteins, had dramatically shorter half-lives when compared to the arrayed transcriptome. As transcript abundances for PPR proteins were previously observed to rapidly increase in response to nutrient addition, we queried the newly synthesized RNA pools at 1 and 4 h following nitrate addition to N-depleted cultures. Transcriptome-wide there was little evidence of increases in the rate of de novo transcription during the first 4 h, relative to that in N-depleted cells, and no evidence for increased PPR protein transcription. These results lend support to the growing consensus of post-transcriptional control of gene expression in dinoflagellates.

Novel architecture to facilitate disassembly and reuse of electronic components and sub-assemblies

This paper advances the proposition that in many electronic products, the partitioning scheme adopted and the interconnection system used to interconnect the sub-assemblies or components are intimately related to the economic benefits, and hence the attractiveness, of reuse of these items. An architecture has been developed in which the residual values of the connectors, components and sub-assemblies are maximized, and opportunities for take-back and reuse of redundant items are greatly enhanced. The system described also offers significant manufacturing cost benefits in terms of ease of assembly, compactness and robustness.

Dissecting Arabidopsis thaliana DICER function in small RNA processing, gene silencing and DNA methylation patterning.

Small RNAs have several important biological functions. MicroRNAs (miRNAs) and trans-acting small interfering RNAs (tasiRNAs) regulate mRNA stability and translation, and siRNAs cause post-transcriptional gene silencing of transposons, viruses and transgenes and are important in both the establishment and maintenance of cytosine DNA methylation. Here, we study the role of the four Arabidopsis thaliana DICER-LIKE genes (DCL1-DCL4) in these processes. Sequencing of small RNAs from a dcl2 dcl3 dcl4 triple mutant showed markedly reduced tasiRNA and siRNA production and indicated that DCL1, in addition to its role as the major enzyme for processing miRNAs, has a previously unknown role in the production of small RNAs from endogenous inverted repeats. DCL2, DCL3 and DCL4 showed functional redundancy in siRNA and tasiRNA production and in the establishment and maintenance of DNA methylation. Our studies also suggest that asymmetric DNA methylation can be maintained by pathways that do not require siRNAs.

Impedance control balances stability with metabolically costly muscle activation.

Humans are able to stabilize their movements in environments with unstable dynamics by selectively modifying arm impedance independently of force and torque. We further investigated adaptation to unstable dynamics to determine whether the CNS maintains a constant overall level of stability as the instability of the environmental dynamics is varied. Subjects performed reaching movements in unstable force fields of varying strength, generated by a robotic manipulator. Although the force fields disrupted the initial movements, subjects were able to adapt to the novel dynamics and learned to produce straight trajectories. After adaptation, the endpoint stiffness of the arm was measured at the midpoint of the movement. The stiffness had been selectively modified in the direction of the instability. The stiffness in the stable direction was relatively unchanged from that measured during movements in a null force field prior to exposure to the unstable force field. This impedance modification was achieved without changes in force and torque. The overall stiffness of the arm and environment in the direction of instability was adapted to the force field strength such that it remained equivalent to that of the null force field. This suggests that the CNS attempts both to maintain a minimum level of stability and minimize energy expenditure.

The water stability of shrimp diets with various polysaccharides as a binding agent

The water stability of shrimp (Penaeus monodon) diets with various polysaccharides as binding agents were tested without steaming. The diet with alginate showed the best water stability and did not completely disintegrate in 24 hours. However, the use of alginate is dependent on cost and availability, so alternate choices may be a combination of sago palm starch and wheat flour or glutinous rice flour.

Breathers and thermal relaxation as a temporal process: A possible way to detect breathers in experimental situations

Breather stability and longevity in thermally relaxing nonlinear arrays is investigated under the scrutiny of the analysis and tools employed for time series and state reconstruction of a dynamical system. We briefly review the methods used in the analysis and characterize a breather in terms of the results obtained with such methods. Our present work focuses on spontaneously appearing breathers in thermal Fermi-Pasta-Ulam arrays but we believe that the conclusions are general enough to describe many other related situations; the particular case described in detail is presented as another example of systems where three incommensurable frequencies dominate their chaotic dynamics (reminiscent of the Ruelle-Takens scenario for the appearance of chaotic behavior in nonlinear systems). This characterization may also be of great help for the discovery of breathers in experimental situations where the temporal evolution of a local variable (like the site energy) is the only available/measured data. © 2005 American Institute of Physics.

Structural and functional properties of the hemoglobin components from the Caspian Sea Acipenser persicus and Acipenser stellatus

Hemoglobin (Hb) variability is a commonly used index of phylogenetic differentiation and molecular adaptation in fish. In the current study, the structural and functional characteristics of Hbs from two Sturgeon species of the Southern Caspian Sea Basin were investigated. After extraction and separation of hemoglobin from whole blood , the polyacrylamide gel electrophoresis (SDSPAGE), native-PAGE and isoelectric focusing (IEF) were used to confirm Hb variability in these fishes. Ion-exchange on CM-cellulose chromatography was used for purification of the dominant Hbs from these fishes. The accuracy of the methods was confirmed by IEF and SDS-PAGE. Spectral studies using fluorescence spectrophotometery, circular dichroism spectropolarimetry (CD) analysis and UV–vis spectrophotometery. Oxygen affinities of these Hbs were compared using Hb-oxygen dissociation curves. Also, the dominant Hbs from these blood fishes were utilized for further experiments. The behavior of Hbs during the denaturation process by n-dodecyl trimethylammonium bromide (DTAB) is investigated by UV–vis spectrophotometer and circular dichroism spectropolarimetry. The thermal denaturation properties of the Hbs wereinvestigated by differential scanning calorimetry (DSC) and Hbs aggregation performed chemically in the presence of dithiotreitol (DTT) by UV–vis spectrophotometer and chemometric study. The results demonstrate a significant relationship between stability of fish hemoglobins and the ability of fish for entering to deeper depths. The UV–Vis absorption spectra identified species of hemoglobin and showed the concentration of oxyHb and metHb decreases and deoxyHb increases upon interaction with DTAB. Besides the UV–vis spectrophotometry, the interaction of DTAB with hemoglobins has been studied using circular dichroism spectropolarimetry analysis. This experiment was utilized to measure the unfolding mechanism and compared alpha-helix secondary structure under different conditions for Hbs. The results reveal that the Acipenser stellatus Hb in comparison with Acipenser persicus Hb has more stability and more structural compactness. Besides, the results confirm the hypothesis that there is a meaningful relation between average habitat depth, partial oxygen pressure, oxygen affinity, structural compactness of Hb, and its stability.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behavior of casing grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading, and the near-casing flow field is then investigated using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. © 2011 American Society of Mechanical Engineers.

Enhancing the stability of subsonic compressors using casing grooves

Casing grooves are known to increase the stable operating range of axial compressors. The mechanism by which this stability enhancement occurs is poorly understood. This paper develops a better understanding of the behaviour of grooves through analysis of new data. An experimental parametric study is used to demonstrate the effect of varying the axial location of a single casing groove on the stability and efficiency of the compressor. The effect that the groove has on rotor outflow blockage, blade loading and the near-casing flow field is then studied using both experimental and computational methods. It is found that the interaction of the groove with the flow field is different when the groove is positioned forward or aft relative to the blade. The interaction of the groove with the flow in the tip region in both of these positions is presented in detail. Finally, the implications of these findings for the design of casing grooves of different depths are discussed. Copyright © 2009 Rolls-Royce plc.