In previous papers by Awrejcewicz in 1986 and Narayanan and Jayaraman in 1991, it was claimed that the nonlinear oscillator with dry friction exhibited chaos for several forcing frequencies. The chaos determination was achieved using the characteristic exponent of Lyapunov which requires the right-hand side of the differential equation to be differentiable. With the addition of the dry friction term, the right-hand side of the equation of motion is not continuous and therefore not differentiable. Thus this approach cannot be used. The Filippov definition must be employed to handle the discontinuity in the spatial variable. The behavior of the nonlinear oscillator with dry friction is studied using a numerical solver which produces the Filippov solution. The results show that the system is not chaotic; rather it has a stable periodic limit cycle for at least one forcing frequency. Other forcing frequencies produce results that do not clearly indicate the presence of chaotic motion. / Graduation date: 2002

Control of machines that exhibit flexibility becomes important when designers attempt to push the state of the art with faster, lighter machines. Three steps are necessary for the control of a flexible planet. First, a good model of the plant must exist. Second, a good controller must be designed. Third, inputs to the controller must be constructed using knowledge of the system dynamic response. There is a great deal of literature pertaining to modeling and control but little dealing with the shaping of system inputs. Chapter 2 examines two input shaping techniques based on frequency domain analysis. The first involves the use of the first deriviate of a gaussian exponential as a driving function template. The second, acasual filtering, involves removal of energy from the driving functions at the resonant frequencies of the system. Chapter 3 presents a linear programming technique for generating vibration-reducing driving functions for systems. Chapter 4 extends the results of the previous chapter by developing a direct solution to the new class of driving functions. A detailed analysis of the new technique is presented from five different perspectives and several extensions are presented. Chapter 5 verifies the theories of the previous two chapters with hardware experiments. Because the new technique resembles common signal filtering, chapter 6 compares the new approach to eleven standard filters. The new technique will be shown to result in less residual vibrations, have better robustness to system parameter uncertainty, and require less computation than other currently used shaping techniques.

A class of hippocampal interneurons in CA1, bordering the lacunosum-moleculare and radiatum hippocampal layers (the LM/R cell), has been shown to exhibit membrane potential oscillations (MPOs) subthreshold to action potential generation. MPOs occur at theta frequency (4-12 Hz) and are of interest because of their putative role in promoting network level theta activity. MPOs arise without synaptic input suggesting that they originate through interactions in the cell’s repertoire of currents. To investigate the generation of MPOs we develop a single compartment model of the cell based on the physiological characterization of its currents. The model includes both deterministic current models and white noise. Our analysis allows for a complete characterization of the cell’s dynamics over the subthreshold range and shows that MPOs arise through the interaction between current dynamics and system noise. We find that MPOs show a particular dependency on the A-type potassium and persistent sodium current magnitudes.

A class of hippocampal interneurons in CA1, bordering the lacunosum-moleculare and radiatum hippocampal layers (the LM/R cell), has been shown to exhibit membrane potential oscillations (MPOs) subthreshold to action potential generation. MPOs occur at theta frequency (4-12 Hz) and are of interest because of their putative role in promoting network level theta activity. MPOs arise without synaptic input suggesting that they originate through interactions in the cell’s repertoire of currents. To investigate the generation of MPOs we develop a single compartment model of the cell based on the physiological characterization of its currents. The model includes both deterministic current models and white noise. Our analysis allows for a complete characterization of the cell’s dynamics over the subthreshold range and shows that MPOs arise through the interaction between current dynamics and system noise. We find that MPOs show a particular dependency on the A-type potassium and persistent sodium current magnitudes.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Integrative Neuroscience." Includes bibliographical references (p. 124-148).

This work deals with the subject of global solar oscillations. These oscillations are observed as fluctuations in the diameter of the sun. A diameter is determined by a mathematical solar edge definition at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA) instrument. The oscillations have periods ranging from a few minutes to several hours and have amplitudes measured in millionths of a solar radius. These small amplitudes are observable only due to the unique properties of the edge definition. The properties of the observed solar oscillations are determined from the data; their statistical significance and repeatability are then tested. The possibility of using the observed oscillations as a seismic tool for understanding the solar interior and its motions is explored.

Information is transmitted from the cell surface to various specific targets in the cell via several cellular signaling pathways. Cytosolic free calcium (Ca2+)is one of the most versatile and ubiquitous intracellular messengers since it is able to regulate diverse number of functions such as proliferation, secretion, fertilization, metabolism, learning and memory. In the last couple of years, evidence has been accumulating that Ca2+ ion is able to integrate information from multiple signaling pathways and convert this information into a code which regulates events ranging from contraction to modification of gene expression (Berridge et al. 1998). It was shown that Ca2+ concentration displays oscillatory behavior in response to agonist stimulation in a variety of cells(Goldbeter 1996) and the frequency of these oscillations increases with the concentration of agonist, a behavior called frequency encoding which has led to the concept that many Ca2+-regulated processes are controlled by these codes(Berridge 1998). Although the presence of Ca2+ oscillations and the sources of Ca2+ pools involved is known in many cell types, it is yet not known how the various frequencies of Ca2+ oscillations are converted into codes that regulate the numerous cellular events. Recently a number of cellular targets that decode Ca2+ signals and are tuned to the frequency of Ca2+ oscillations have been identified. Prominent among them are calcium-calmodulin kinase II (CAM II) and protein kinase C (PKC). The objective of this work is to study and mathematically model the oxytocin and vasopressin-induced Ca2+ oscillations in cells of normal rat liver (Clone 9) and cells of pregnant human myometrium. The proposed model accounts for the receptor-controlled Ca2+ oscillations involving positive feedback leading to activation of phospholipase C (PLC) and negative feedback from PKC onto G-proteins which simulates many of the features of observed intracellular Ca2+. The model also incorporates the concept that coordinated Ca2+ signals in a group of hepatocytes require both effective gap junctions and the presence of agonist at each cell surface. Another objective of this research is to understand the relevance of frequency-encoded signals by performing an analysis of frequencies of Ca2+ oscillations using the Fast Fourier Transform and the Wavelet Transform. The validity of the model was confirmed by using statistical tests to check if the frequencies and amplitudes of the experimental Ca2+ oscillations match with those of the modelled oscillations.

The production of charmed particles and a limit to tau lepton production have been measured using a hybrid emulsion spectrometer in the Fermilab wide-band neutrino beam. / The relative cross section for charged current charmed particle production is / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / and the energy dependence of the cross section and the kinematic distributions of the charm events are given. One event with charm pair production was observed. A limit of (sigma)((nu)(--->)(mu)cc)/(sigma)((nu)(--->)(mu)c) < 0.06 (90%C.L.) is set to the ratio of charged current pair and single charm production. The relative rates of D(DEGREES), D('+), F('+), and (LAMDA)(,c)('+) production have been measured--the fraction of D mesons is / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / Momentum, transverse momentum, Feynman X, and fragmentation (Z) distributions are presented. The mean Z for charmed hadrons is 0.59 (+OR-) 0.03((+OR-) 0.03). / No tau leptons were observed, and an upper limit to the (nu)(,(mu))-(tau) coupling of 0.0063 (90%C.L.) is set. For (nu)(,(mu))-(nu)(,(tau)) oscillations this implies / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / for maximum mixing.

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