979 resultados para Oscillation


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本文给出由连续系统的S域,到离散领域?的转换的通式。并给出了离散传递函数W(?)的基本属性、离散振荡指标Md的基本概念、?变换的稳定判据、二阶无静差数字随动系统的动态综合、Md综合在海洋机器人航向控制中的应用。

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Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

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In this study, 172 mollusk assemblages from the Weinan loess section in the southeast of Loess Plateau, China, were identified quantitatively at relative high resolution. The results show: 1) the history and processes of paleoclimatic and paleoenvironmental changes in Weinan since the last 70 ka; 2) the characteristics of climatic changes during the period of the last glacial maximum (LGM); 3) the spatial pattern of paleoclimate variations at the south and middle parts of the Loess Plateau during the LGM period; 4) the timing of the last deglaciation and the return event of rapid climate change during the last deglaciation. The main conclusions are as follows: 1) 172 mollusk samples taken from the uppermost 9 m deposits cover the past 70 ka, which were sampled at the internals of 5 cm for S_0, 3 cm for L_(1-1) and L_(1-2), and 10 cm for L_(1-3), L_(1-4) and L_(1-5). Author analyzed quantitatively all individuals including broken pieces of snail shells, percentages of 15 species identified from 172 samples. Three main groups were determined according to the ecological requirement of each taxon. Based on the variations of three ecological groups and typical ecological species, The author intended to reconstruct the history of and processes of climate and environment since the last 70 ka in the Weinan region. The climate and environment in this region experienced the following changes: relative warm and humid stage from 67.5-20.3 cal. ka B.P., a period of forest-steppe or steppe developed; cold and arid stage from 20.3-15.5 cal. ka B.P., a dry steppe period, later wetter and colder; cold and humid period once time from 15.5 to 12.3 cal. ka B.P., a typical steppe or forest-steppe stage; cold and humid again from 12.3 cal. ka B.P. to 8.2 cal. ka B.P., a tropical steppe stage; warm and humid climate, a forest-steppe developed. 2) The climate during the period of the last glacial maximum (LGM) in Weinan was characterized by a general cold-humid condition, represented by occurrence of a number of the cool-humidiphilous mollusk species such as Gastocopta amigerella and Vallonia cf. pulchella in the section. 3) Comparison of the variations in abundance of Puncture orphana at Weinan with those at Luochuan and Changwu sections suggests that the summer monsoon intensity influenced differently at the three regions during the LGM period. The Weinan was weaker summer monsoon impact during all the period, the Luochuan was influenced occasionally, and Changwu was only a very short time affected, which indicated it might be located at the western margin of the summer monsoon influence during that period. 4) The ratio of thermo-humidiphilous mollusk group to cold-aridiphilous one shows an increase tendency at about 15 cal. ka B.P., reflecting the climate warming after the deglaciation in Weinan, which is approximately corresponding to the timing of warming period of the last deglaciation, found in the East Atlantic Ocean, the South China Sea and the Loess Plateau (indicated by the phytolith study). 5) A remarkable decrease in the number of thermo-humidiphilous and cool-humidiphilous mollusk species from 12.7 - 11.6 cal. ka B.P. indicates a cooling in climate and might be the reflection of the Younger Dryas event in Weinan. 6) Variations in the ratios of thermo-humidiphilous mollusk species to cold-aridiphilous ones reflect the climate instability in Holocene. There were four warm-humid periods (10-8.1 cal. ka B.P., 6.9-6.1 cal. ka B.P., 5.2-2.6cal. ka B.P., 1.6cal. ka B.P. to the present ) and three relative cold-arid periods (8.1-6.9 cal. ka B.P., 6.1-5.2 cal. ka B.P., 2.6-1.6 cal. ka B.P.), showing about a 1,000 year climatic oscillation.

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Data on seawater carbon isotope in the Mesoproterozoic and Neoproterozoic is abundant. However, the sulfur isotopic age curve of seawater sulfates determined through the analysis of sulfur isotopic composition of marine evaporite is uncertain in the Mesoproterozoic and Neoproterozoic since evaporites are generally rare in Precambrian. The Mesoproterozoic and Neoproterozoic Carbonate Formations preserve not only the carbon isotopic records, but also the sulfur isotopic records of coeval seawater in the Huabei Platform and the Yangtze Platform, China. Sulfur isotopic composition can be determined by the extraction of trace sulfate from carbonate samples. Successive measurements of sulfur and carbon isotopic compositions of carbonate samples from the Mesoproterozoic and Neoproterozoic strata in the Huabei Platform and the Yangtze Platform was accomplished through the extracting of trace sulfate from carbonates. Sulfur and carbon isotopic compositions of coeval seawater were obtained from analytical results of sulfur and carbon isotopes of the same sample without diagenetic alteration. The high-resolution age curve of sulfur isotope given in this paper may reflect the trend of variations in sulfur isotope composition of seawater sulfates during the Mesoproterozoic and Neoproterozoic. It can be correlated with the characteristics of variation in age curve of carbon isotope of coeval seawater carbonates. The δ34S values of seawater varied from +10.3-37.0‰ during the Mesoproterozoic, which took on oscillated variation on the whole. The δ34S values took on high values in the Mesoproterozoic Chuanlinggou stage, Tuanshanzi stage Tieling stage and in Neoproterozoic Jing'eryu stage. The average of those was about +30‰. The sulfates have low δ34S values in the Mesoproterozoic Yangzhuang stage and Hongshuizhuang stage, The average of those was all lower than +20‰. There occured large-amplitude changs in δ34S values of seawater during the Mesoproterozoic. Large-amplitude oscillate of 534S values occured in the intervals of 1600~1400Ma and 1300~1200Ma. The δ13C values of seawater are mostly negative in Changcheng stage of late Paleoproterozoic, -0 ± 1‰ range in Jixian stage of Mesoproterozoic , and the positive 2±2‰ commonly in early Neoproterozoic Jing'eryu stage. From 1000 Ma to 900 Ma, about 108 years interval of oceanic 513C record is shortage. At the end of Paleoproterozoic (1700 - 1600 Ma), the oceanic 813C values change from -3‰ to 0‰, but strongly oscillate near 1600 Ma. Two larger variations of seawater 513C values occur in the Mesoproterozoic: one is a cycle of about 4%o happens at ca. 1400 Ma; another is rise from >2‰ to>5‰ at ca. 1250 Ma and then become stable at the near 1000 Ma. There appears a large positive excursion over +20‰ in 534S value of ancient seawater sulfates in the early Doushantuo stage. Simultaneously, 8 C values of ancient seawater occur a positive excursion reaching 10‰. These allow δ4S values and 513C values to reach high values of+51.7‰ and +6.9‰, respectively. The range of variation in 834S values of seawater is relatively narrow and 513C values are quite high in the middle Doushantuo stage. Then, δ34S values of seawater become oscillating, the same happens in δ13C values. Negative excursions in 834S values and 813C values occur simultaneously at the end of the Doushantuo stage, and the minimum of δ34S values and δ13C values dropped to -11.3‰ and -5.7‰, respectively. The ancient seawater in the Dengying stage has high δS values and δ13C values. Most of the δ34S values of the trace sulfate samples varied between +23.6‰ and +37.9‰ except two boundaries of the Dengying Formation, and the S13C values of the carbonate samples of the Dengying Formation varied between +0.5‰ and +5.0‰. There appeared large negative excursion in 834S values and δ13C values of ancient seawater at the bounder of Precambrian-Cambrian. The isotopic characteristics of sulfur and carbon implicated that the organic productivity and isotopic fractionation caused by biology were low and the palaeoceanic environment was quite unstable during the Mesoproterozoic. The increase and subsequent oscillation of seawater δ13C value occurred from 1700 to 1600 Ma and near 1300 Ma may be responsible to the two global tectonic events happened at coeval time. The characteristics of variation in sulfur and carbon isotopes of ancient seawater imply strong changes in oceanic environment, which became beneficial to inhabitation and propagation of organism. The organic production and the burial rate of organic carbon once reached a quite high level during the Doushantuo stage. However, the state of environment became unstable that means the global climate and the environment possibly were fluctuating and reiterating after the global glaciation. The negative excursions of S34S values and δ13C values occurring at the end of the Doushantuo stage represent a global event, which might be relative to the oxidation of deep seawater. The isotopic characteristics of sulfur and carbon implicated that there were a high organic productivity and a high burial rate of organic carbon in the Dengying stage. It is obvious that the palaeoceanic environment in Dengying stage was stable corresponding and beneficial for biology to inhabit and propagate except for the two boundaries. The tendency of sulfur and carbon isotopic variations maybe resulted from the gradual oxygenation of ocean environment during the Dengying stage. It has been reported that the secular variations of the sulfur isotopic compositions in seawater was negative correlated with that of carbon isotopic compositions. However, our results show that it is not the case. They were negatively correlated in some intervals and positively in some other intervals of the Mesoproterozoic and Neoproterozoic. The difference in correlation may be associated with the changes in conditions of redox in oceanic environment, e.g. sharp change of the oxidation-reduction interface. The strong changes in global environment may induce the abnormality to occur in the biogeo chemical S and C cycles in the ocean and accordingly sharp Variations in isotopic composition of seawater sulfur and carbon during the Mesoproterozoic and Neoproterozoic. Simultaneously, the global tectonism caused large changes of 87Sr/86Sr ratios. The leading factor that causes the variation in isotopic composition is different in the different intervals of the Mesoproterozoic and Neoproterozoic. Thus, there may exist different models of the biogeochemical S and C cycles in the ocean during the Mesoproterozoic and Neoproterozoic.

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To investigate the changes in the chemical weathering intensity of dust source region in Asia continent, ~(87)Sr/~(86)Sr ratios of acid-washed residues from the loess deposits in China and Tajikistan were analyzed, respectively. The results and conclusions are listed as below. 1. The oscillation of ~(87)Sr/~(86)Sr ratios of acid-insoluble residues in the Chinese Loess Plateau was mainly attributed to the chemical weathering intensity of the source region and the grain size. Counteracted the effect of particle size, the calibrated 87Sr/S6Sr ratio can be used as a proxy for the chemical weathering intensity of the source region. 2. The Sr/ Sr ratios of red clay-loess sequence from the Loess Plateau indicate that the chemical weathering intensity of the dust source region between 7.0 and 2.6 Ma is stronger than that in the Quaternary period. This also suggests a general decline in chemical weathering intensity of the source region from 2.6 Ma to the present. Such pattern is more remarkable since 1.0 Ma BP. 3. The ~(87)Sr/~(86)Sr ratios of the Tajik loess during 0.8-1.8 Ma is much more higher than those from 0.8 Ma to the present. This implies that the chemical weathering intensity of the source region in Central Asia is much stronger during 0.8-1.8 Ma than the period since 0.8 Ma. 4. The record of Sr isotope ratios from both sections shows an accelerating course of aridity of the Asian dust source region over the Quaternary period.

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The term black carbon is used to describe a relatively inert and ubiquitous form of carbon, comprising a range of materials from char and charcoal to element or graphite carbon produced by the incomplete combustion of fossil fuels and biomass. Due to its inertness, the BC in soils, lacustrine and marine sediments and ice can persist over a long period of time. So BC signatures in geological deposits can be used as evidence of natural fires happened in their surroundings. To study the temporal and spatial changes in paleofires over the Chinese Loess Plateau, black carbon concentrations were analyzed on the loess-paleosol samples from three sections including Lijiayuan, Lingtai and Weinan along a north-south transect. Using the orbitally-tuned time-scales of the sections, the black carbon sedimentation rates (BCSR) were calculated. Meanwhile, with objective to document fine resolution fire history during late Pleistocene and Holocene periods, we measured BC concentrations of loess-paleosol samples at dense sampling intervals since 28 ka BP. in Lijiayuan section. The BCSR of the samples were also calculated. In addition, we also conducted observation on black carbon morphologies to examine their sources. Based on the results, the following remarks can be concluded: 1. In the last two glacial cycles, the BCSR values in glacial periods are 2-3 times higher than in interglacial periods, and the BCSR variability has a relatively strong precession-associated 23 kyr period, suggesting that the glacial cold-dry climate conditions were apt to induce natural fires over the Loess Plateau, 2. Comparison of the BCSR records among the three loess sections demonstrates that natural fire occurrence was much more intensive and frequent in the northern and interglacial periods. 3. Pollen records and carbon isotope analyses of organic matter have shown that the Loess Plateau was covered by an Artemisia-dominated grassland vegetation both during glacial and interglacial periods, So grassland fires were the dominant fire types in the Plateau, which is also corroborated by the observation of black carbon morphology. In addition, statistics and comparison of BC particle sizes among the sections demonstrated that BC records probably reflected local fires. 4. According to previous studies about the effect of fires on vegetation changes, we considered that the fires might play an important role in the expansion of grassland during glacial periods, besides the control of climate changes. 5. The high resolution black carbon record in Lijiayuan section has shown that the BCSR series well documented Younger dryas (YD) and Heinrich (HI和H2) events, suggesting that natural fires in the northwestern part of Chinese Loess Plateau could regularly respond to the millennial scale climate oscillation.

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Sediment cores DH99a and DH99b recovered in the central part of Daihai Lake in north-central China were analysed at 2- to 4-crn intervals for grain-size distribution. Grain-size distributions of the lake sediments are inferred to be a proxy for past changes in East Asian monsoon precipitation, such that greater silt-size percentage and higher median grain size reflect increased monsoonal precipitation rates. The grain-size record of Daihai Lake sediments spanning the last ca 11,000 yr indicates that the monsoonal precipitation in the lake region can be divided into three stages: the Early, Middle and Late Holocene. During the Early Holocene before ca 7900 cal yr BP, the median grain size (Md) and the silt-fraction content were relatively low and constant, suggesting relatively low precipitation over the lake region. The Middle Holocene between ca 7900 and 3100 cal yr BP was marked by intensified and highly variable monsoonal precipitation, as indicated by high and variable Md values and silt contents of the lake sediments. During this period, average precipitation rate gradually increased from ca 7900 to 6900 cal yr BP, displayed intense oscillations between ca 6900 and 4400 cal yr BP, and exhibited a decreasing trend while fluctuating from ca 4400 to 3100 cal yr BP Although generally high during the Middle Holocene, both the Md and the silt content assumed distinctly low values at the short intervals of ca 6500-6400, 6000-5900, 5700-5600, 4400-4200 cal yr BP, implying that monsoonal precipitation might have been significantly reduced during these intervals. During the Late Holocene since ca 3100 cal yr BP, grain-size values suggest that precipitation decreased. However, during the Late Holocene, relatively higher Md values and silt contents occurring between ca 1700 to 1000 cal yr BP may denote an intensification of hydrological cycles in the lake area. Changes in the East Asian monsoonal precipitation were not only directly linked with the changing seasonality of solar insolation resulting from progressive changes in the Earth's orbital parameters, but also may have been closely related to variations in the temperature and size of the Western Pacific Warm Pool, in the intensity of the El Nino-Southern Oscillation, and in the path and strength of the North Equatorial Current in the western Pacific.

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From the perspective of a polymer solution, the rheological properties of the popular polyethersulfone (PES)/N-methyl-2-pyrrolidone (NMP)/nonsolvent (NS) membrane-forming system were investigated thoroughly with a controlled stress rheometer (HAAKE RS75, Germany). The scope of the study included measurements of the controlled-stress flow curve, creep recovery, and dynamic oscillation. H2O, 1-butanol, ethylene glycol, and diethylene glycol were used as NS additives. The effects of the polymer concentration and the quality of the solvent mixture, as characterized by the approaching ratio, on the rheological behavior of the dopes were studied. Up to 38 wt % PES and extremely adjacent to the phase separation (i.e., the approaching ratio of the dope was 0.95), the viscous property dominated all the dopes, which behaved as Newtonian fluids. Moreover, all the membrane-forming dopes investigated were in the crossover regime in the semidilute region, in which the chains were overlapping but unentangled. (C) 2001 John Wiley & Sons, Inc.

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Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height, either through altering the frequency or altering the acceleration amplitude. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape, and such changes can be effected through modifying the horizontal oscillation amplitude and phase. Changing the slope at this zero crossing controls writing slant; this slope depends on the horizontal and vertical velocity zero amplitudes and on the relative phase difference. Letter height modulation is also best applied at the vertical velocity zero crossing to preserve an even baseline. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. Under these constraints interletter separation is not an independent parameter. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal, rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical sources; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory. It is shown that the minimum energy movement for the spring muscle is bang-coast-bang. For certain parameter values a singular arc solution can be shown to be minimizing. Experimental measurements however indicate that handwriting is not a minimum energy movement.

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De-excited dynamics of p-chlorotoluene and p-dichlorobenzene have been investigated by the femtosecond pump-probe method in a supersonic molecular beam. The yields of the parent ion and daughter ion are examined as a function of the delay time between the pump and probe laser pulses. The lifetime constants of excited p-chlorotoluene and p-dichlorobenzene are determined. Possible de-excitation mechanisms are suggested that the initially excited S-1 state is predissociative via the repulsive triplet state. The substituent effects of additional chlorine atom and methyl group are discussed. Moreover, for the first time, we observe a novel quantum beat oscillation in p-dichlorobenzene. (c) 2005 Elsevier B.V. All rights reserved.

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The influence of laser-field parameters, such as intensity and pulse width, on the population of molecular excited state is investigated by using the time-dependent wavepacket method. For a two-state system in intense laser fields, the populations in the upper and lower states are given by the wavefunctions obtained by solving the Schrodinger equation through split-operator scheme. The calculation shows that both the laser intensity and the pulse width have a strong effect on the population in molecular excited state, and that as the common feature of light-matter interaction (LMI), the periodic changing of the population with the evolution time in each state can be interpreted by Rabi oscillation and area-theorem. The results illustrate that by controlling these two parameters, the needed population in excited state of interest can be obtained, which provides the foundation of light manipulation of molecular processes. (C) 2005 Elsevier B.V. All rights reserved.

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Schrijver, C.J. and Brown, D.S., 2000, Oscillations in the magnetic field of the solar corona in response to flares near the photosphere, Astrophysical Journal, 537, L69-L72. Sponsorship: PPARC

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Douglas B. Murray, Manfred Beckmann, and Hiroaki Kitano. (2007). Regulation of yeast oscillatory dynamics. Proceedings of the National Academy of Sciences of the USA, 104 (7), 2241-2246 Sponsorship: Solution-Oriented Research for Science and Technology Agency to the Systems Biology Institute /21st Century Center of Excellence Program and Special Coordination Program of the Ministry of Education, Sports, Culture, Science, and Technology to Keio University RAE2008

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Projeto de Pós-Graduação/Dissertação apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Mestre em Medicina Dentária

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1) A large body of behavioral data conceming animal and human gaits and gait transitions is simulated as emergent properties of a central pattern generator (CPG) model. The CPG model incorporates neurons obeying Hodgkin-Huxley type dynamics that interact via an on-center off-surround anatomy whose excitatory signals operate on a faster time scale than their inhibitory signals. A descending cornmand or arousal signal called a GO signal activates the gaits and controL their transitions. The GO signal and the CPG model are compared with neural data from globus pallidus and spinal cord, among other brain structures. 2) Data from human bimanual finger coordination tasks are simulated in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed both at low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases. When driven by environmental patterns with intermediate phase relationships, the model's output exhibits a tendency to slip toward purely in-phase and anti-phase relationships as observed in humans subjects. 3) Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop) and the pronk are simulated. Rapid gait transitions are simulated in the order--walk, trot, pace, and gallop--that occurs in the cat, along with the observed increase in oscillation frequency. 4) Precise control of quadruped gait switching is achieved in the model by using GO-dependent modulation of the model's inhibitory interactions. This generates a different functional connectivity in a single CPG at different arousal levels. Such task-specific modulation of functional connectivity in neural pattern generators has been experimentally reported in invertebrates. Phase-dependent modulation of reflex gain has been observed in cats. A role for state-dependent modulation is herein predicted to occur in vertebrates for precise control of phase transitions from one gait to another. 5) The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are sirnulated. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The CPG model simulates the walk and the run by generating oscillations which exhibit the same phase relationships. but qualitatively different waveform shapes, at different GO signal levels. The fraction of each cycle that activity is above threshold quantitatively distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run. 6) A key model properly concerns the ability of a single model CPG, that obeys a fixed set of opponent processing equations to generate both in-phase and anti-phase oscillations at different arousal levels. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases.