939 resultados para optimal machining parameters


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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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This paper presents an inversion methodology through weighted least squares to obtain the electrical parameters for the soil of a typical mid-western region in Brazil using the model based in the formalism of the parabolic equations to calculate the electric field intensity received. To validate this methodology, the results of the radio signal measurement campaign conducted in six radial routes leaving the city of Brasilia, Federal District, where the transmitter was located, were used. The measurements were compared to computer simulations and, thus, the optimal values for the electric conductivity and relative permittivity for the soil of the region could be estimated. Finally, a quantitative analysis of these parameters was performed with the values found in the literature, which demonstrated the effectiveness of the proposed methodology.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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PREPARATION OF COATED MICROTOOLS FOR ELECTROCHEMICAL MACHINING APPLICATIONS Ajaya K. Swain, M.S. University of Nebraska, 2010 Advisor: K.P. Rajurkar Coated tools have improved the performance of both traditional and nontraditional machining processes and have resulted in higher material removal, better surface finish, and increased wear resistance. However, a study on the performance of coated tools in micromachining has not yet been adequately conducted. One possible reason is the difficulties associated with the preparation of coated microtools. Besides the technical requirement, economic and environmental aspects of the material and the coating technique used also play a significant role in coating microtools. This, in fact, restricts the range of coating materials and the type of coating process. Handling is another major issue in case of microtools purely because of their miniature size. This research focuses on the preparation of coated microtools for pulse electrochemical machining by electrodeposition. The motivation of this research is derived from the fact that although there were reports of improved machining by using insulating coatings on ECM tools, particularly in ECM drilling operations, not much literature was found relating to use of metallic coating materials in other ECM process types. An ideal ECM tool should be good thermal and electrical conductor, corrosion resistant, electrochemically stable, and stiff enough to withstand electrolyte pressure. Tungsten has almost all the properties desired in an ECM tool material except being electrochemically unstable. Tungsten can be oxidized during machining resulting in poor machining quality. Electrochemical stability of a tungsten ECM tool can be improved by electroplating it with nickel which has superior electrochemical resistance. Moreover, a tungsten tool can be coated in situ reducing the tool handling and breakage frequency. The tungsten microtool was electroplated with nickel with direct and pulse current. The effect of the various input parameters on the coating characteristics was studied and performance of the coated microtool was evaluated in pulse ECM. The coated tool removed more material (about 28%) than the uncoated tool under similar conditions and was more electrochemical stable. It was concluded that nickel coated tungsten microtool can improve the pulse ECM performance.

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Product miniaturization for applications in fields such as biotechnology, medical devices, aerospace, optics and communications has made the advancement of micromachining techniques essential. Machining of hard and brittle materials such as ceramics, glass and silicon is a formidable task. Rotary ultrasonic machining (RUM) is capable of machining these materials. RUM is a hybrid machining process which combines the mechanism of material removal of conventional grinding and ultrasonic machining. Downscaling of RUM for micro scale machining is essential to generate miniature features or parts from hard and brittle materials. The goal of this thesis is to conduct a feasibility study and to develop a knowledge base for micro rotary ultrasonic machining (MRUM). Positive outcome of the feasibility study led to a comprehensive investigation on the effect of process parameters. The effect of spindle speed, grit size, vibration amplitude, tool geometry, static load and coolant on the material removal rate (MRR) of MRUM was studied. In general, MRR was found to increase with increase in spindle speed, vibration amplitude and static load. MRR was also noted to depend upon the abrasive grit size and tool geometry. The behavior of the cutting forces was modeled using time series analysis. Being a vibration assisted machining process, heat generation in MRUM is low which is essential for bone machining. Capability of MRUM process for machining bone tissue was investigated. Finally, to estimate the MRR a predictive model was proposed. The experimental and the theoretical results exhibited a matching trend.

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Abstract Background In areas with limited structure in place for microscopy diagnosis, rapid diagnostic tests (RDT) have been demonstrated to be effective. Method The cost-effectiveness of the Optimal® and thick smear microscopy was estimated and compared. Data were collected on remote areas of 12 municipalities in the Brazilian Amazon. Data sources included the National Malaria Control Programme of the Ministry of Health, the National Healthcare System reimbursement table, hospitalization records, primary data collected from the municipalities, and scientific literature. The perspective was that of the Brazilian public health system, the analytical horizon was from the start of fever until the diagnostic results provided to patient and the temporal reference was that of year 2006. The results were expressed in costs per adequately diagnosed cases in 2006 U.S. dollars. Sensitivity analysis was performed considering key model parameters. Results In the case base scenario, considering 92% and 95% sensitivity for thick smear microscopy to Plasmodium falciparum and Plasmodium vivax, respectively, and 100% specificity for both species, thick smear microscopy is more costly and more effective, with an incremental cost estimated at US$549.9 per adequately diagnosed case. In sensitivity analysis, when sensitivity and specificity of microscopy for P. vivax were 0.90 and 0.98, respectively, and when its sensitivity for P. falciparum was 0.83, the RDT was more cost-effective than microscopy. Conclusion Microscopy is more cost-effective than OptiMal® in these remote areas if high accuracy of microscopy is maintained in the field. Decision regarding use of rapid tests for diagnosis of malaria in these areas depends on current microscopy accuracy in the field.

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Recently high spectral resolution sensors have been developed, which allow new and more advanced applications in agriculture. Motivated by the increasing importance of hyperspectral remote sensing data, the need for research is important to define optimal wavebands to estimate biophysical parameters of crop. The use of narrow band vegetation indices (VI) derived from hyperspectral measurements acquired by a field spectrometer was evaluated to estimate bean (Phaseolus vulgaris L.) grain yield, plant height and leaf area index (LAI). Field canopy reflectance measurements were acquired at six bean growth stages over 48 plots with four water levels (179.5; 256.5; 357.5 and 406.2 mm) and tree nitrogen rates (0; 80 and 160 kg ha-1) and four replicates. The following VI was analyzed: OSNBR (optimum simple narrow-band reflectivity); NB_NDVI (narrow-band normalized difference vegetation index) and NDVI (normalized difference index). The vegetation indices investigated (OSNBR, NB_NDVI and NDVI) were efficient to estimate LAI, plant height and grain yield. During all crop development, the best correlations between biophysical variables and spectral variables were observed on V4 (the third trifoliolate leaves were unfolded in 50 % of plants) and R6 (plants developed first flowers in 50 % of plants) stages, according to the variable analyzed.

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The purpose of this study is to evaluate the influence of the cutting parameters of high-speed machining milling on the characteristics of the surface integrity of hardened AISI H13 steel. High-speed machining has been used intensively in the mold and dies industry. The cutting parameters used as input variables were cutting speed (v c), depth of cut (a p), working engagement (a e) and feed per tooth (f z ), while the output variables were three-dimensional (3D) workpiece roughness parameters, surface and cross section microhardness, residual stress and white layer thickness. The subsurface layers were examined by scanning electron and optical microscopy. Cross section hardness was measured with an instrumented microhardness tester. Residual stress was measured by the X-ray diffraction method. From a statistical standpoint (the main effects of the input parameters were evaluated by analysis of variance), working engagement (a e) was the cutting parameter that exerted the strongest effect on most of the 3D roughness parameters. Feed per tooth (f z ) was the most important cutting parameter in cavity formation. Cutting speed (v c) and depth of cut (a p) did not significantly affect the 3D roughness parameters. Cutting speed showed the strongest influence on residual stress, while depth of cut exerted the strongest effect on the formation of white layer and on the increase in surface hardness.

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This work is structured as follows: In Section 1 we discuss the clinical problem of heart failure. In particular, we present the phenomenon known as ventricular mechanical dyssynchrony: its impact on cardiac function, the therapy for its treatment and the methods for its quantification. Specifically, we describe the conductance catheter and its use for the measurement of dyssynchrony. At the end of the Section 1, we propose a new set of indexes to quantify the dyssynchrony that are studied and validated thereafter. In Section 2 we describe the studies carried out in this work: we report the experimental protocols, we present and discuss the results obtained. Finally, we report the overall conclusions drawn from this work and we try to envisage future works and possible clinical applications of our results. Ancillary studies that were carried out during this work mainly to investigate several aspects of cardiac resynchronization therapy (CRT) are mentioned in Appendix. -------- Ventricular mechanical dyssynchrony plays a regulating role already in normal physiology but is especially important in pathological conditions, such as hypertrophy, ischemia, infarction, or heart failure (Chapter 1,2.). Several prospective randomized controlled trials supported the clinical efficacy and safety of cardiac resynchronization therapy (CRT) in patients with moderate or severe heart failure and ventricular dyssynchrony. CRT resynchronizes ventricular contraction by simultaneous pacing of both left and right ventricle (biventricular pacing) (Chapter 1.). Currently, the conductance catheter method has been used extensively to assess global systolic and diastolic ventricular function and, more recently, the ability of this instrument to pick-up multiple segmental volume signals has been used to quantify mechanical ventricular dyssynchrony. Specifically, novel indexes based on volume signals acquired with the conductance catheter were introduced to quantify dyssynchrony (Chapter 3,4.). Present work was aimed to describe the characteristics of the conductancevolume signals, to investigate the performance of the indexes of ventricular dyssynchrony described in literature and to introduce and validate improved dyssynchrony indexes. Morevoer, using the conductance catheter method and the new indexes, the clinical problem of the ventricular pacing site optimization was addressed and the measurement protocol to adopt for hemodynamic tests on cardiac pacing was investigated. In accordance to the aims of the work, in addition to the classical time-domain parameters, a new set of indexes has been extracted, based on coherent averaging procedure and on spectral and cross-spectral analysis (Chapter 4.). Our analyses were carried out on patients with indications for electrophysiologic study or device implantation (Chapter 5.). For the first time, besides patients with heart failure, indexes of mechanical dyssynchrony based on conductance catheter were extracted and studied in a population of patients with preserved ventricular function, providing information on the normal range of such a kind of values. By performing a frequency domain analysis and by applying an optimized coherent averaging procedure (Chapter 6.a.), we were able to describe some characteristics of the conductance-volume signals (Chapter 6.b.). We unmasked the presence of considerable beat-to-beat variations in dyssynchrony that seemed more frequent in patients with ventricular dysfunction and to play a role in discriminating patients. These non-recurrent mechanical ventricular non-uniformities are probably the expression of the substantial beat-to-beat hemodynamic variations, often associated with heart failure and due to cardiopulmonary interaction and conduction disturbances. We investigated how the coherent averaging procedure may affect or refine the conductance based indexes; in addition, we proposed and tested a new set of indexes which quantify the non-periodic components of the volume signals. Using the new set of indexes we studied the acute effects of the CRT and the right ventricular pacing, in patients with heart failure and patients with preserved ventricular function. In the overall population we observed a correlation between the hemodynamic changes induced by the pacing and the indexes of dyssynchrony, and this may have practical implications for hemodynamic-guided device implantation. The optimal ventricular pacing site for patients with conventional indications for pacing remains controversial. The majority of them do not meet current clinical indications for CRT pacing. Thus, we carried out an analysis to compare the impact of several ventricular pacing sites on global and regional ventricular function and dyssynchrony (Chapter 6.c.). We observed that right ventricular pacing worsens cardiac function in patients with and without ventricular dysfunction unless the pacing site is optimized. CRT preserves left ventricular function in patients with normal ejection fraction and improves function in patients with poor ejection fraction despite no clinical indication for CRT. Moreover, the analysis of the results obtained using new indexes of regional dyssynchrony, suggests that pacing site may influence overall global ventricular function depending on its relative effects on regional function and synchrony. Another clinical problem that has been investigated in this work is the optimal right ventricular lead location for CRT (Chapter 6.d.). Similarly to the previous analysis, using novel parameters describing local synchrony and efficiency, we tested the hypothesis and we demonstrated that biventricular pacing with alternative right ventricular pacing sites produces acute improvement of ventricular systolic function and improves mechanical synchrony when compared to standard right ventricular pacing. Although no specific right ventricular location was shown to be superior during CRT, the right ventricular pacing site that produced the optimal acute hemodynamic response varied between patients. Acute hemodynamic effects of cardiac pacing are conventionally evaluated after stabilization episodes. The applied duration of stabilization periods in most cardiac pacing studies varied considerably. With an ad hoc protocol (Chapter 6.e.) and indexes of mechanical dyssynchrony derived by conductance catheter we demonstrated that the usage of stabilization periods during evaluation of cardiac pacing may mask early changes in systolic and diastolic intra-ventricular dyssynchrony. In fact, at the onset of ventricular pacing, the main dyssynchrony and ventricular performance changes occur within a 10s time span, initiated by the changes in ventricular mechanical dyssynchrony induced by aberrant conduction and followed by a partial or even complete recovery. It was already demonstrated in normal animals that ventricular mechanical dyssynchrony may act as a physiologic modulator of cardiac performance together with heart rate, contractile state, preload and afterload. The present observation, which shows the compensatory mechanism of mechanical dyssynchrony, suggests that ventricular dyssynchrony may be regarded as an intrinsic cardiac property, with baseline dyssynchrony at increased level in heart failure patients. To make available an independent system for cardiac output estimation, in order to confirm the results obtained with conductance volume method, we developed and validated a novel technique to apply the Modelflow method (a method that derives an aortic flow waveform from arterial pressure by simulation of a non-linear three-element aortic input impedance model, Wesseling et al. 1993) to the left ventricular pressure signal, instead of the arterial pressure used in the classical approach (Chapter 7.). The results confirmed that in patients without valve abnormalities, undergoing conductance catheter evaluations, the continuous monitoring of cardiac output using the intra-ventricular pressure signal is reliable. Thus, cardiac output can be monitored quantitatively and continuously with a simple and low-cost method. During this work, additional studies were carried out to investigate several areas of uncertainty of CRT. The results of these studies are briefly presented in Appendix: the long-term survival in patients treated with CRT in clinical practice, the effects of CRT in patients with mild symptoms of heart failure and in very old patients, the limited thoracotomy as a second choice alternative to transvenous implant for CRT delivery, the evolution and prognostic significance of diastolic filling pattern in CRT, the selection of candidates to CRT with echocardiographic criteria and the prediction of response to the therapy.

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In Deutschland wird zur oralen Vitamin-K-Antagonistentherapie überwiegend der Wirkstoff Phenprocoumon (PPC) eingesetzt und die meisten Patienten werden durch ihren Hausarzt betreut. In einer deskriptiven, nicht-interventionellen Studie wurde die Ist-Situation der Versorgung von PPC-Patienten im ambulanten Sektor untersucht. Ziel war es, die Qualität und Effektivität der bisherigen Standardtherapie zu evaluieren. In Anbetracht der Einführung der neuen oralen Antikoagulantien (NOAC) ist die Untersuchung der PPC-Therapie von besonderem Interesse. Dem „Throughput-Modell“ folgend sollten „Input“- und „Outcome“-Parameter analysiert werden. rnIn einer klinischen Studie wurden 50 ambulant behandelte Patienten mit PPC-Therapie jeweils über einen Zeitraum von 3 Jahren retrospektiv beobachtet. In 5 niedergelassenen Arztpraxen in Rheinland-Pfalz wurden dazu 10 Patienten pro Praxis rekrutiert. Anhand der Patientenakte wurde eine Dokumentenanalyse durchgeführt. Die Selbstmedikation wurde mit einem eigens erstellten Fragebogen erfasst. rnIm Studienkollektiv wurden im Median 3 Comorbiditäten ermittelt. Die mediane Wochendosis betrug 4,0 Tabletten à 3 mg PPC. Die Patienten wurden im Median mit weiteren 15 verschiedenen Wirkstoffen therapiert, einer davon wurde in Selbstmedikation eingenommen. Im gesamten Beobachtungszeitraum fanden pro Patient im Median 57 Arztbesuche statt, die durch die Phenprocoumon-Therapie bedingt waren. INR (International normalized ratio)-Messungen (Median 47) waren der häufigste Grund für die Arztbesuche, so dass ein 3-Wochen-Rhythmus vom Gesamtkollektiv zu 97% erreicht wurde. Die „stabile“ INR-Einstellung wurde im Median nach 94 Tagen erreicht. Die prozentuale Rate (INR (%)) für die Einhaltung des INR-Zielbereiches (ZSB) erreichte internationale Benchmark-Werte, was auf eine gute Versorgungsqualität hindeutete. Die genauere Analyse ergab jedoch große interindividuelle Schwankungen. Während der „stabilen“ INR-Einstellung wurden bessere Ergebnisse als im Gesamtbeobachtungszeitraum erzielt. Drei Patienten (6%) erreichten die „stabile“ INR-Einstellung innerhalb von 3 Jahren nie. Die Auswertung für den erweiterten ZSB (ZSB ± 0,2) ergab bessere INR (%)-Ergebnisse als für den ZSB. Die Zeit im INR-ZSB (TTR (%)) erreichte mit 75% höhere Werte als INR (%) im ZSB mit 70%. Tendenziell war das Patientenkollektiv eher unter- als übertherapiert (Median „Under-INR“ 18% bzw. „Over-INR“ 8%). Erkrankungen und Impfungen stellten die wichtigsten der zahlreichen Einflussfaktoren für INR-Shifts hin zu Werten außerhalb des ZSB dar. Patienten, die Comedikation mit hohem Interaktionspotential einnahmen, erreichten in den INR-Qualitätsindikatoren schlechtere Ergebnisse als Patienten ohne potentiell interagierende Comedikation (Mann-Whitney-U-Test; p-Wert=0,003 für TTR (%), p=0,008 für INR (%)). In Zeitintervallen der „stabilen“ INR-Einstellung war der Unterschied nur für TTR (%) auffällig (Mann-Whitney-U-Test; p=0,015). Für den erweiterten ZSB waren die Unterschiede bezüglich beider INR-Qualitätsindikatoren nicht auffällig. Insgesamt wurden 41 unerwünschte Ereignisse (UAW) beobachtet, davon 24 (59%) in der Phase der „stabilen“ INR-Einstellung (21 leichte Blutungen, 1 schwere Blutung, 2 thromboembolische Ereignisse (TE)). Je 4 leichte Blutungen (19%) wurden in einen möglichen bzw. sicheren kausalen Zusammenhang mit der VKA-Therapie gebracht, wenn ein Zeitintervall von 3 Tagen zwischen der INR-Messung und Auftreten der UAW geprüft wurde. Ein TE wurde als sicher kausal gewertet. Von insgesamt 5 Krankenhausaufenthalten waren 3 bzw. 2 durch Blutungen bzw. TE veranlasst. Des Weiteren wurde im 3-Tage-Zeitintervall für 4 INR-Shifts hin zu Werten außerhalb des ZSB eine Interaktion mit verordneter CM als in sicherem oder möglichem kausalen Zusammenhang bewertet. Bei 49% der beobachteten Grippeimpfungen wurde ein INR-Shift festgestellt, der in ca. 60% der Fälle zu einem subtherapeutischen INR-Wert führte. Insgesamt war das klinische Ergebnis nicht optimal. rnDas „Outcome“ in Form der gesundheitsbezogenen Lebensqualität (LQ) wurde retrospektiv-prospektiv mittels SF-36-Fragebogen ermittelt. Die Patienten zeigten gegenüber der Normalbevölkerung einen Verlust an LQ auf körperlicher Ebene bzw. einen Gewinn auf psychischer Ebene. Das humanistische Ergebnis erfüllte bzw. übertraf damit die Erwartungen. rnInsgesamt wiesen die Ergebnisse darauf hin, dass Qualität und Effektivität der Antikoagulationstherapie mit PPC im ambulanten Sektor weiterer Optimierung bedürfen. Mit intensivierten Betreuungsmodellen lässt sich ein besseres Outcome erzielen. rn

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Treatment with growth hormone (GH) has become standard practice for replacement in GH-deficient children or pharmacotherapy in a variety of disorders with short stature. However, even today, the reported adult heights achieved often remain below the normal range. In addition, the treatment is expensive and may be associated with long-term risks. Thus, a discussion of the factors relevant for achieving an optimal individual outcome in terms of growth, costs, and risks is required. In the present review, the heterogenous approaches of treatment with GH are discussed, considering the parameters available for an evaluation of the short- and long-term outcomes at different stages of treatment. This discourse introduces the potential of the newly emerging prediction algorithms in comparison to other more conventional approaches for the planning and evaluation of the response to GH. In rare disorders such as those with short stature, treatment decisions cannot easily be deduced from personal experience. An interactive approach utilizing the derived experience from large cohorts for the evaluation of the individual patient and the required decision-making may facilitate the use of GH. Such an approach should also lead to avoiding unnecessary long-term treatment in unresponsive individuals.

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Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.

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OBJECTIVES: The aim of this phantom study was to evaluate the contrast-to-noise ratio (CNR) in pulmonary computed tomography (CT)-angiography for 300 and 400 mg iodine/mL contrast media using variable x-ray tube parameters and patient sizes. We also analyzed the possible strategies of dose reduction in patients with different sizes. MATERIALS AND METHODS: The segmental pulmonary arteries were simulated by plastic tubes filled with 1:30 diluted solutions of 300 and 400 mg iodine/mL contrast media in a chest phantom mimicking thick, intermediate, and thin patients. Volume scanning was done with a CT scanner at 80, 100, 120, and 140 kVp. Tube current-time products (mAs) varied between 50 and 120% of the optimal value given by the built-in automatic dose optimization protocol. Attenuation values and CNR for both contrast media were evaluated and compared with the volume CT dose index (CTDI(vol)). Figure of merit, calculated as CNR/CTDIvol, was used to quantify image quality improvement per exposure risk to the patient. RESULTS: Attenuation of iodinated contrast media increased both with decreasing tube voltage and patient size. A CTDIvol reduction by 44% was achieved in the thin phantom with the use of 80 instead of 140 kVp without deterioration of CNR. Figure of merit correlated with kVp in the thin phantom (r = -0.897 to -0.999; P < 0.05) but not in the intermediate and thick phantoms (P = 0.09-0.71), reflecting a decreasing benefit of tube voltage reduction on image quality as the thickness of the phantom increased. Compared with the 300 mg iodine/mL concentration, the same CNR for 400 mg iodine/mL contrast medium was achieved at a lower CTDIvol by 18 to 40%, depending on phantom size and applied tube voltage. CONCLUSIONS: Low kVp protocols for pulmonary embolism are potentially advantageous especially in thin and, to a lesser extent, in intermediate patients. Thin patients profit from low voltage protocols preserving a good CNR at a lower exposure. The use of 80 kVp in obese patients may be problematic because of the limitation of the tube current available, reduced CNR, and high skin dose. The high CNR of the 400 mg iodine/mL contrast medium together with lower tube energy and/or current can be used for exposure reduction.

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This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.

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We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.