Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Project, modelling and simulation of air stripping columns for the treatment of groundwater contaminated with volatile organic compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for the column design for any particular type of packing and contaminant avoiding the necessity of a pre-defined diameter used in the classical approach. It also renders unnecessary the employment of the graphical Eckert generalized correlation for pressure drop estimates. The hydraulic features are previously chosen as a project criterion and only afterwards the mass transfer phenomena are incorporated, in opposition to conventional approach. The design procedure was translated into a convenient algorithm using C++ as programming language. A column was built in order to test the models used either in the design or in the simulation of the column performance. The experiments were fulfilled using a solution of chloroform in distilled water. Another model was built to simulate the operational performance of the column, both in steady state and in transient conditions. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting system of ODE can be solved, allowing for the calculation of the concentration profile in both phases inside the column. In transient state the system of PDE was numerically solved by finite differences, after a previous linearization.

Multidimensional scaling visualization of earthquake phenomena

Earthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the Flinn–Engdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Space-time and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the non-uniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools, for understanding the global behavior of earthquakes.

Estudo da exposição profissional a formaldeído em laboratórios hospitalares de anatomia patológica

RESUMO - A exposição a formaldeído é reconhecidamente um dos mais importantes factores de risco presente nos laboratórios hospitalares de anatomia patológica. Neste contexto ocupacional, o formaldeído é utilizado em solução, designada comummente por formol. Trata-se de uma solução comercial de formaldeído, normalmente diluída a 10%, sendo pouco onerosa e, por esse motivo, a eleita para os trabalhos de rotina em anatomia patológica. A solução é utilizada como fixador e conservante do material biológico, pelo que as peças anatómicas a serem processadas são previamente impregnadas. No que concerne aos efeitos para a saúde do formaldeído, os efeitos locais parecem apresentar um papel mais importante comparativamente com os efeitos sistémicos, devido à sua reactividade e rápido metabolismo nas células da pele, tracto gastrointestinal e pulmões. Da mesma forma, a localização das lesões correspondem principalmente às zonas expostas às doses mais elevadas deste agente químico, ou seja, o desenvolvimento dos efeitos tóxicos dependerá mais da intensidade da dose externa do que da duração da exposição. O efeito do formaldeído no organismo humano mais facilmente detectável é a acção irritante, transitória e reversível sobre as mucosas dos olhos e aparelho respiratório superior (naso e orofaringe), o que acontece em geral para exposições frequentes e superiores a 1 ppm. Doses elevadas são citotóxicas e podem conduzir a degenerescência e necrose das mucosas e epitélios. No que concerne aos efeitos cancerígenos, a primeira avaliação efectuada pela International Agency for Research on Cancer data de 1981, actualizada em 1982, 1987, 1995 e 2004, considerando-o como um agente cancerígeno do grupo 2A (provavelmente carcinogénico). No entanto, a mais recente avaliação, em 2006, considera o formaldeído no Grupo 1 (agente carcinogénico) com base na evidência de que a exposição a este agente é susceptível de causar cancro nasofaríngeo em humanos. Constituiu objectivo principal deste estudo caracterizar a exposição profissional a formaldeído nos laboratórios hospitalares de anatomia patológica Portugueses. Pretendeu-se, ainda, descrever os fenómenos ambientais da contaminação ambiental por formaldeído e explorar eventuais associações entre variáveis. Considerou-se uma amostra de 10 laboratórios hospitalares de anatomia patológica, avaliada a exposição dos três grupos profissionais por comparação com os dois referenciais de exposição e, ainda, conhecidos os valores de concentração máxima em 83 actividades. Foram aplicados simultaneamente dois métodos distintos de avaliação ambiental: um dos métodos (Método 1) fez uso de um equipamento de leitura directa com o princípio de medição por Photo Ionization Detection, com uma lâmpada de 11,7 eV e, simultaneamente, realizou-se o registo da actividade. Este método disponibilizou dados para o referencial de exposição da concentração máxima; o outro método (Método 2) traduziu-se na aplicação do método NIOSH 2541, implicando o uso de bombas de amostragem eléctricas de baixo caudal e posterior processamento analítico das amostras por cromatografia gasosa. Este método, por sua vez, facultou dados para o referencial de exposição da concentração média ponderada. As estratégias de medição de cada um dos métodos e a definição dos grupos de exposição existentes neste contexto ocupacional, designadamente os Técnicos de Anatomia Patológica, os Médicos Anatomo-Patologistas e os Auxiliares, foram possíveis através da informação disponibilizada pelas técnicas de observação da actividade da análise (ergonómica) do trabalho. Estudaram-se diversas variáveis independentes, nomeadamente a temperatura ambiente e a humidade relativa, a solução de formaldeído utilizada, as condições de ventilação existentes e o número médio de peças processadas por dia em cada laboratório. Para a recolha de informação sobre estas variáveis foi preenchida, durante a permanência nos laboratórios estudados, uma Grelha de Observação e Registo. Como variáveis dependentes seleccionaram-se três indicadores de contaminação ambiental, designadamente o valor médio das concentrações superiores a 0,3 ppm em cada laboratório, a Concentração Média Ponderada obtida para cada grupo de exposição e o Índice do Tempo de Regeneração de cada laboratório. Os indicadores foram calculados e definidos através dos dados obtidos pelos dois métodos de avaliação ambiental aplicados. Baseada no delineado pela Universidade de Queensland, foi ainda aplicada uma metodologia de avaliação do risco de cancro nasofaríngeo nas 83 actividades estudadas de modo a definir níveis semi-quantitativos de estimação do risco. Para o nível de Gravidade considerou-se a informação disponível em literatura científica que define eventos biológicos adversos, relacionados com o modo de acção do agente químico e os associa com concentrações ambientais de formaldeído. Para o nível da Probabilidade utilizou-se a informação disponibilizada pela análise (ergonómica) de trabalho que permitiu conhecer a frequência de realização de cada uma das actividades estudadas. A aplicação simultânea dos dois métodos de avaliação ambiental resultou na obtenção de resultados distintos, mas não contraditórios, no que concerne à avaliação da exposição profissional a formaldeído. Para as actividades estudadas (n=83) verificou-se que cerca de 93% dos valores são superiores ao valor limite de exposição definido para a concentração máxima (VLE-CM=0,3 ppm). O “exame macroscópico” foi a actividade mais estudada e onde se verificou a maior prevalência de resultados superiores ao valor limite (92,8%). O valor médio mais elevado da concentração máxima (2,04 ppm) verificou-se no grupo de exposição dos Técnicos de Anatomia Patológica. No entanto, a maior amplitude de resultados observou-se no grupo dos Médicos Anatomo-Patologistas (0,21 ppm a 5,02 ppm). No que respeita ao referencial da Concentração Média Ponderada, todos os valores obtidos nos 10 laboratórios estudados para os três grupos de exposição foram inferiores ao valor limite de exposição definido pela Occupational Safety and Health Administration (TLV-TWA=0,75 ppm). Verificou-se associação estatisticamente significativa entre o número médio de peças processadas por laboratório e dois dos três indicadores de contaminação ambiental utilizados, designadamente o valor médio das concentrações superiores a 0,3 ppm (p=0,009) e o Índice do Tempo de Regeneração (p=0,001). Relativamente à temperatura ambiente não se observou associação estatisticamente significativa com nenhum dos indicadores de contaminação ambiental utilizados. A humidade relativa apresentou uma associação estatisticamente significativa apenas com o indicador de contaminação ambiental da Concentração Média Ponderada de dois grupos de exposição, nomeadamente com os Médicos Anatomo-Patologistas (p=0,02) e os Técnicos de Anatomia Patológica (p=0,04). A aplicação da metodologia de avaliação do risco nas 83 actividades estudadas permitiu verificar que, em cerca de dois terços (35%), o risco foi classificado como (pelo menos) elevado e, ainda, constatar que 70% dos laboratórios apresentou pelo menos 1 actividade com a classificação de risco elevado. Da aplicação dos dois métodos de avaliação ambiental e das informações obtidas para os dois referenciais de exposição pode concluir-se que o referencial mais adequado é a Concentração Máxima por estar associado ao modo de actuação do agente químico. Acresce, ainda, que um método de avaliação ambiental, como o Método 1, que permite o estudo das concentrações de formaldeído e simultaneamente a realização do registo da actividade, disponibiliza informações pertinentes para a intervenção preventiva da exposição por permitir identificar as actividades com a exposição mais elevada, bem como as variáveis que a condicionam. As peças anatómicas apresentaram-se como a principal fonte de contaminação ambiental por formaldeído neste contexto ocupacional. Aspecto de particular interesse, na medida que a actividade desenvolvida neste contexto ocupacional e, em particular na sala de entradas, é centrada no processamento das peças anatómicas. Dado não se perspectivar a curto prazo a eliminação do formaldeído, devido ao grande número de actividades que envolvem ainda a utilização da sua solução comercial (formol), pode concluir-se que a exposição a este agente neste contexto ocupacional específico é preocupante, carecendo de uma intervenção rápida com o objectivo de minimizar a exposição e prevenir os potenciais efeitos para a saúde dos trabalhadores expostos. ---------------- ABSTRACT - Exposure to formaldehyde is recognized as one of the most important risk factors present in anatomy and pathology laboratories from hospital settings. In this occupational setting, formaldehyde is used in solution, typically diluted to 10%, and is an inexpensive product. Because of that, is used in routine work in anatomy and pathology laboratories. The solution is applied as a fixative and preservative of biological material. Regarding formaldehyde health effects, local effects appear to have a more important role compared with systemic effects, due to his reactivity and rapid metabolism in skin, gastrointestinal tract and lungs cells. Likewise, lesions location correspond mainly to areas exposed to higher doses and toxic effects development depend more on external dose intensity than exposure duration. Human body formaldehyde effect more easily detectable is the irritating action, transient and reversible on eyes and upper respiratory tract (nasal and throat) membranes, which happen in general for frequent exposure to concentrations higher than 1 ppm. High doses are cytotoxic and can lead to degeneration, and also to mucous membranes and epithelia necrosis. With regard to carcinogenic effects, first assessment performed by International Agency for Research on Cancer in 1981, updated in 1982, 1987, 1995 and 2004, classified formaldehyde in Group 2A (probably carcinogenic). However, most recent evaluation in 2006, classifies formaldehyde carcinogenic (Group 1), based on evidence that exposure to this agent is likely to cause nasopharyngeal cancer in humans. This study principal objective was to characterize occupational exposure to formaldehyde in anatomy and pathology hospital laboratories, as well to describe formaldehyde environmental contamination phenomena and explore possible associations between variables. It was considered a sample of 10 hospital pathology laboratories, assessed exposure of three professional groups for comparison with two exposure metrics, and also knows ceiling concentrations in 83 activities. Were applied, simultaneously, two different environmental assessment methods: one method (Method 1) using direct reading equipment that perform measure by Photo Ionization Detection, with 11,7 eV lamps and, simultaneously, make activity description and film. This method provided data for ceiling concentrations for each activity study (TLV-C). In the other applied method (Method 2), air sampling and formaldehyde analysis were performed according to NIOSH method (2541). This method provided data average exposure concentration (TLV-TWA). Measuring and sampling strategies of each methods and exposure groups definition (Technicians, Pathologists and Assistants) was possible by information provided by activities (ergonomic) analysis. Several independent variables were studied, including temperature and relative humidity, formaldehyde solution used, ventilation conditions, and also anatomic pieces mean value processed per day in each laboratory. To register information about these variables was completed an Observation and Registration Grid. Three environmental contamination indicators were selected has dependent variables namely: mean value from concentrations exceeding 0,3 ppm in each laboratory, weighted average concentration obtained for each exposure group, as well each laboratory Time Regeneration Index. These indicators were calculated and determined through data obtained by the two environmental assessment methods. Based on Queensland University proposal, was also applied a methodology for assessing nasopharyngeal cancer risk in 83 activities studied in order to obtain risk levels (semi-quantitative estimation). For Severity level was considered available information in scientific literature that defines biological adverse events related to the chemical agent action mode, and associated with environment formaldehyde concentrations. For Probability level was used information provided by (ergonomic) work analysis that helped identifies activity frequency. Environmental assessment methods provide different results, but not contradictory, regarding formaldehyde occupational exposure evaluation. In the studied activities (n=83), about 93% of the values were above exposure limit value set for ceiling concentration in Portugal (VLE-CM = 0,3 ppm). "Macroscopic exam" was the most studied activity, and obtained the higher prevalence of results superior than 0,3 ppm (92,8%). The highest ceiling concentration mean value (2,04 ppm) was obtain in Technicians exposure group, but a result wider range was observed in Pathologists group (0,21 ppm to 5,02 ppm). Concerning Method 2, results from the three exposure groups, were all lower than limit value set by Occupational Safety and Health Administration (TLV-TWA=0,75ppm). There was a statistically significant association between anatomic pieces mean value processed by each laboratory per day, and two of the three environmental contamination indicators used, namely average concentrations exceeding 0,3 ppm (p=0,009) and Time Regeneration Index (p=0,001). Temperature was not statistically associated with any environmental contamination used indicators. Relative humidity had a statistically significant association only with one environmental contamination indicator, namely weighted average concentration, particularly with Pathologists group (p=0,02) and Technicians group (p=0,04). Risk assessment performed in the 83 studied activities showed that around two thirds (35%) were classified as (at least) high, and also noted that 70% of laboratories had at least 1 activity with high risk rating. The two environmental assessment methods application, as well information obtained from two exposure metrics, allowed to conclude that most appropriate exposure metric is ceiling concentration, because is associated with formaldehyde action mode. Moreover, an environmental method, like Method 1, which allows study formaldehyde concentrations and relates them with activity, provides relevant information for preventive information, since identifies the activity with higher exposure, as well variables that promote exposure. Anatomic pieces represent formaldehyde contamination main source in this occupational setting, and this is of particular interest because all activities are focused on anatomic pieces processing. Since there is no prospect, in short term, for formaldehyde use elimination due to large number of activities that still involve solution use, it can be concluded that exposure to this agent, in this particular occupational setting, is preoccupant, requiring an rapid intervention in order to minimize exposure and prevent potential health effects in exposed workers.

Lettuce (Lactuca sativa L.) leaf-proteome profiles after exposure to cylindrospermopsin and a microcystin-LR/cylindrospermopsin mixture: A concentration-dependent response

The intensification of agricultural productivity is an important challenge worldwide. However, environmental stressors can provide challenges to this intensification. The progressive occurrence of the cyanotoxins cylindrospermopsin (CYN) and microcystin-LR (MC-LR) as a potential consequence of eutrophication and climate change is of increasing concern in the agricultural sector because it has been reported that these cyanotoxins exert harmful effects in crop plants. A proteomic-based approach has been shown to be a suitable tool for the detection and identification of the primary responses of organisms exposed to cyanotoxins. The aim of this study was to compare the leaf-proteome profiles of lettuce plants exposed to environmentally relevant concentrations of CYN and a MC-LR/CYN mixture. Lettuce plants were exposed to 1, 10, and 100 lg/l CYN and a MC-LR/CYN mixture for five days. The proteins of lettuce leaves were separated by twodimensional electrophoresis (2-DE), and those that were differentially abundant were then identified by matrix-assisted laser desorption/ionization time of flight-mass spectrometry (MALDI-TOF/TOF MS). The biological functions of the proteins that were most represented in both experiments were photosynthesis and carbon metabolism and stress/defense response. Proteins involved in protein synthesis and signal transduction were also highly observed in the MC-LR/CYN experiment. Although distinct protein abundance patterns were observed in both experiments, the effects appear to be concentration-dependent, and the effects of the mixture were clearly stronger than those of CYN alone. The obtained results highlight the putative tolerance of lettuce to CYN at concentrations up to 100 lg/l. Furthermore, the combination of CYN with MC-LR at low concentrations (1 lg/l) stimulated a significant increase in the fresh weight (fr. wt) of lettuce leaves and at the proteomic level resulted in the increase in abundance of a high number of proteins. In contrast, many proteins exhibited a decrease in abundance or were absent in the gels of the simultaneous exposure to 10 and 100 lg/l MC-LR/CYN. In the latter, also a significant decrease in the fr. wt of lettuce leaves was obtained. These findings provide important insights into the molecular mechanisms of the lettuce response to CYN and MC-LR/CYN and may contribute to the identification of potential protein markers of exposure and proteins that may confer tolerance to CYN and MC-LR/CYN. Furthermore, because lettuce is an important crop worldwide, this study may improve our understanding of the potential impact of these cyanotoxins on its quality traits (e.g., presence of allergenic proteins).

Effects of storage, processing and proteolytic digestion on microcystin-LR concentration in edible clams

Accumulation of microcystin-LR (MC-LR) in edible aquatic organisms, particularly in bivalves, is widely documented. In this study, the effects of food storage and processing conditions on the free MC-LR concentration in clams (Corbicula fluminea) fed MC-LR-producing Microcystisaeruginosa (1 × 105 cell/mL) for four days, and the bioaccessibility of MC-LR after in vitro proteolytic digestion were investigated. The concentration of free MC-LR in clams decreased sequentially over the time with unrefrigerated and refrigerated storage and increased with freezing storage. Overall, cooking for short periods of time resulted in a significantly higher concentration (P < 0.05) of free MC-LR in clams, specifically microwave (MW) radiation treatment for 0.5 (57.5%) and 1 min (59%) and boiling treatment for 5 (163.4%) and 15 min (213.4%). The bioaccessibility of MC-LR after proteolytic digestion was reduced to 83%, potentially because of MC-LR degradation by pancreatic enzymes. Our results suggest that risk assessment based on direct comparison between MC-LR concentrations determined in raw food products and the tolerable daily intake (TDI) value set for the MC-LR might not be representative of true human exposure.

Early physiological and biochemical responses of rice seedlings to low concentration of microcystin-LR

Microcystin-leucine and arginine (microcystin- LR) is a cyanotoxin produced by cyanobacteria like Microcystis aeruginosa, and it’s considered a threat to water quality, agriculture, and human health. Rice (Oryzasativa) is a plant of great importance in human food consumption and economy, with extensive use around the world. It is therefore important to assess the possible effects of using water contaminated with microcystin-LR to irrigate rice crops, in order to ensure a safe, high quality product to consumers. In this study, 12 and 20-day-old plants were exposed during 2 or 7 days to a M. aeruginosa extract containing environmentally relevant microcystin-LR concentrations, 0.26–78 lg/L. Fresh and dry weight of roots and leaves, chlorophyll fluorescence, glutathione S-transferase and glutathione peroxidase activities, and protein identification by mass spectrometry through two-dimensional gel electrophoresis from root and leaf tissues, were evaluated in order to gauge the plant’s physiological condition and biochemical response after toxin exposure. Results obtained from plant biomass, chlorophyll fluorescence, and enzyme activity assays showed no significant differences between control and treatment groups. How- ever, proteomics data indicates that plants respond to M. aeruginosa extract containing environmentally relevant microcystin-LR concentrations by changing their metabolism, responding differently to different toxin concentrations. Biological processes most affected were related to protein folding and stress response, protein biosynthesis, cell signalling and gene expression regulation, and energy and carbohydrate metabolism which may denote a toxic effect induced by M. aeruginosa extract and microcystin- LR. Theimplications of the metabolic alterations in plant physiology and growth require further elucidation.

Measurement of lead concentration in biological tissues by atomic spectroscopy techniques

Dissertation for the degree of Doctor of Philosophy in Physics

Evaluation of the formalin-Tween concentration technique for parasitic detection

The formalin-Tween sedimentation method was compared with the formalin-ether sedimentation for parasitic detection. Of a total 297 fecal specimens examined, 72.1% were positive. The formalin-tween technique was effective for ascertaining helminths, particularly Ascaris lumbricoides, Trichuris trichiura and hookworm eggs; however it has less capability for protozoa detection. This method is simple, inexpensive, less time consuming and highly sensitive when detecting the parasitic infection, particularly when focusing on helminth eggs.

Distributed Sensing of Fluid Dynamic Phenomena with the XDense Sensor Grid Network

IEEE International Conference on Cyber Physical Systems, Networks and Applications (CPSNA'15), Hong Kong, China.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Chaotic Phenomena and Performance Optimization in the Trajectory Control of Redundant Manipulators

Redundant manipulators have some advantages when compared with classical arms because they allow the trajectory optimization, both on the free space and on the presence of abstacles, and the resolution of singularities. For this type of manipulators, several kinetic algorithms adopt generalized inverse matrices. In this line of thought, the generalized inverse control scheme is tested through several experiments that reveal the difficulties that often arise. Motivated by theseproblems this paper presents a new method that ptimizes the manipulability through a least squre polynomialapproximation to determine the joints positions. Moreover, the article studies influence on the dynamics, when controlling redundant and hyper-redundant manipulators. The experiment confirm the superior performance of the proposed algorithm for redundant and hyper-redundant manipulators, revealing several fundamental properties of the chaotic phenomena, and gives a deeper insight towards the future development of superior trajectory control algorithms.