Plants absorb CO2 through pores in their leaves called stomata, which are known to open and close in response to myriad environmental and physiological triggers. We demonstrate that blue light inhibits stomatal aperture oscillations in both the guard cells and surrounding tissue layers, whereas these oscillations continue under the influence of red light. This observation of blue light behavior agrees with recent research and suggests another physiological pathway for oscillations.

Abstract not available

Thesis (Ph. D. in electrical engineering)--Washington State University, December 2007. / Includes bibliographical references (p. 135-146).

Paul Chorney. / "May 26, 1958." Issued also as a thesis, M.I.T. Dept. of Electrical Engineering, May, 1958. / Bibliography: leaf 81. / Army Signal Corps Contract DA36-039-sc-64637. Dept. of the Army Task 3-99-06-108 and Project 3-99-00-100.

No description available.

Considerable interest in oscillating reactions has been generated by the large number of such processes observed in biological systems. Thus the existence of oscillating chemical reactions is well known. However, very few homogeneous chemical systems are known to either exhibit temporal oscillations or to develop spatial structure; that is, one which changes with respect to time and position within the reaction vessel. The only reaction presently known to exhibit both temporal and spatial oscillatory structures is the cerium ion catalyzed oxidation of malonic acid by bromate in a sulfuric acid medium.Temporal oscillations in [ce(IV)]/[ce(III)] were first reported by Belousov in 1959 and development of spatial structure by Zhabotinskii in 1967. The actual oscillations, both temporal and spatial are exhibited with the reagents oscillating from a bright blue to red. The colors whichindicate the variations in the chemical concentrations can be changed by the use of different reagents.Chemical oscillation has several physical and biological significances, particularly biochemical-oscillations at the intracellular level, which permit the organism to adapt in a flexible way to external conditions. The BelousovZhavotinskii reaction, however, is primarily an inorganic redose reaction but is important because, when coupled with the process of diffusion, it is possible to obtain spatial patterns and this can be a foundation for a biochemical theory of morphogenesis. A study of this particular reaction will also enable investigators to better understand and develop a precise theory of chemical oscillation.Several investigations have already been done on this reaction, but have all been primarily chemical in nature. The purpose of this paper therefore is primarily a mathematical analysis of the Belousov-Zhabotinskii reaction. Conditions for stability of the equilibrium solutions and the existence of oscillation will be discussed.Ball State UniversityMuncie, IN 47306

En aquesta tesi es té en compte un model no lineal de creixement de població de cèl·lules que s'estructuren pel seu contingut de ciclina i cinases depenents de ciclina (CDK). Aquest model condueix a un sistema no lineal d'equacions en derivades parcials de primer ordre amb termes no locals. Per estudiar aquest sistema utilitzem la teoria de semigrups lineals positius i la formulació semilineal, que són eines molt poderoses per fer front a l'anàlisi d'aquest tipus de models, tant des del punt de vista del problema de valor inicial, com de l'existència i l'estabilitat d'estats estacionaris. El model que es considera a la tesi descriu la següent situació biològica: les cèl·lules s'estructuren en relació amb el contingut d'un determinat grup de proteïnes anomenades ciclines i CDK i es divideixen en dos tipus: proliferants i quiescents. Les cèl·lules proliferants creixen i es divideixen, donant a lloc al final del cicle cel·lular a noves cèl·lules, o bé van cap al compartiment de les quiescents, mentre que les cèl·lules quiescents no envelleixen ni es divideixen, ni canvien el seu contingut de ciclina, però o tornen cap al compartiment de proliferació o bé romanen en l’estat de repòs. D'altra banda, tant les cèl·lules proliferants com les quiescents poden experimentar l'apoptosi, la mort cel·lular programada. L'únic terme no lineal en el model és un terme de reclutament de cèl·lules quiescents cap a la fase de proliferació. En aquest treball demostrem l'existència global, unicitat i positivitat de les solucions del problema de valor inicial. Reescrivint el nostre sistema en una forma abstracta podem demostrar que un cert operador lineal és el generador infinitesimal d'un semigrup positiu fortament continu. D'altra banda s'utilitza la formulació semilineal estàndard per a l’equació no lineal abstracta i obtenim una única solució global positiva per a qualsevol condició inicial positiva a L1. També es prova l'existència i unicitat d'un estat estacionari no trivial del nostre sistema sota hipòtesis adequades. Com es fa sovint en situacions similars, el problema és relacionat amb provar l'existència (i unicitat) d'un vector propi positiu normalitzat. Això correspon als vectors propis del valor propi dominant d'un determinat operador lineal positiu parametritzat pel valor de la variable de feedback. L'existència tant del valor propi dominant i de (l’únic) vector propi positiu està donat per una versió del teorema de Perron- Frobenius en dimensió infinita. També s’inclouen simulacions numèriques basades en la integració al llarg de les línies característiques. Amb l'ajuda d'aquestes simulacions numèriques trobem inestabilitat de l'estat estacionari per a valors de paràmetres compatibles amb els que donen inestabilitat en el model de dimensió finita. També s'inclou la demostració de l'existència de solucions independents del contingut de ciclina per a una elecció molt particular dels valors dels paràmetres i funcions que defineixen el model. Finalment s'utilitza la formulació anomenada cumulativa (o en retard) de la dinàmica de poblacións estructurades. En particular s'ha considerat una versió diferent del model estudiat abans, on es suposa que el pas de proliferants a quiescents només pot ocórrer una sola vegada, enfocament oposat al primer model on aquestes transicions poden ocórrer infinites vegades. A més a més, també suposem que hi ha un valor particular x del contingut de ciclina que separa les cèl·lules que encara no es poden dividir de les altres que sí que poden dividir-se. L'equació del model resulta ser una equació amb retard que relaciona els valors actuals d'aquestes variables amb la seva història (el seu valor en el passat). Fent servir aquest enfocament, es pot provar l'existència i unicitat de solucions del problema de valor inicial, i el principi d'estabilitat lineal a través d'una formulació semilineal en el marc dels semigrups duals. / In this thesis we consider a nonlinear cell population model where cells are structured with respect to the content of cyclin and cyclin dependent kinases (CDK). This model leads to a first order nonlinear partial differential equations system with non local terms. To study this system we use the theory of positive linear semigroups and the semilinear formulation, which are very powerful tools to deal with the analysis of this kind of models, both from the point of view of the initial value problem as well as the existence and stability of steady states. The model considered in the thesis describes the following biological situation: cells are structured with respect to the content of a certain group of proteins called cyclin and CDK and are distributed into two types: proliferating and quiescent cells. The proliferating cells grow and divide, giving birth at the end of the cell cycle to new cells, or else transit to the quiescent compartment, whereas quiescent cells do not age nor divide nor change their cyclin content but either transit back to the proliferating compartment or else stay in the quiescent compartment. Moreover, both proliferating and quiescent cells may experiment apoptosis, i.e. programmed cell death. The only nonlinear term is a recruitment term of quiescent cells going back to the proliferating phase. In this work we start proving global existence, uniqueness and positiveness of the solutions of the initial value problem. We rewrite our system in an abstract form and show that some linear operator is the infinitesimal generator of a positive strongly continuous semigroup. On the other hand we use the standard semilinear formulation for the nonlinear (abstract) equation and obtain a unique global positive solution for any positive initial condition in L1. We also prove the existence and uniqueness of a nontrivial steady state of our system under suitable hypotheses. As it is often done in similar situations, the problem is related to proving the existence (and uniqueness) of a positive normalized eigenvector. This eigenvector corresponds to the dominant eigenvalue of a certain positive linear operator parameterized by the value of the (one dimensional) feedback variable G. The existence of both dominant eigenvalue and (unique) positive eigenvector is given by a version of the infinite dimensional Perron-Frobenius theorem. We include numerical simulations based on the integration along characteristic lines. With the help of these numerical simulations we find instability of the steady state for parameter values compatible with the ones which give instability in the finite dimensional model. We also include a computation showing the existence of cyclin-independent solutions for a very particular choice of the parameter values and functions defining the model. Finally we use the so-called cumulative or delayed formulation of the structured population dynamics. In particular we have considered a different version of the model studied before, where one assumes that proliferating cells can become quiescent only once opposed to the other approach where these transitions can occur infinitely many times and moreover, we also assume that there is a particular value x of the cyclin content that separates cells which still cannot divide from the others which are able to divide. The model equation turns out to be a delay equation relating the current values of these variables with their history (their value in the past). Using this approach, one can prove existence and uniqueness of solutions of the initial value problem, and the linear stability principle by means of a semi-linear formulation in the framework of dual semigroups.

The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm generation and modulation in this structure is an important step in understanding its function. In this thesis, these phenomena are studied via mathematical models of networks of hippocampal interneurons. The two types of neural networks considered here are homogenous and heterogenous networks. In homogenous networks, the input current to each neuron is equal, while in heterogenous networks, this assumption is relaxed and there is a specified degree of heterogeneity in the input stimuli. A phase reduction technique is applied to the neural network model of the hippocampal interneurons and attempts are made to understand the implications of heterogeneity to the existence and stability of the synchronized oscillations. The Existence of a critical level of heterogeneity above which the synchronized rhythms are not stable is established, and linear analysis is applied to derive expressions for estimating the perturbations in the network frequency and timing of the neural spikes. The mathematical techniques developed in this thesis are general enough to be applied to models describing other types of neurons not considered here. Possible biological implications include the application of high frequency local stimulation to alleviate the synchronous neural oscillations in pathological conditions such as epilepsy and Parkinson's disease and the possible role of heterogeneity in controlling the rhythm frequency and switching between various cognitive states.

In this thesis it has been investigated if LQG control could be used to mitigate torsional oscillations in a variable speed, fixed pitch wind turbine. The wind turbine is a vertical axis wind turbine with a 40 m tall axis that is connected to a generator. The power extracted by the turbine is delivered to the grid via a passive rectifier and an inverter. By controlling the grid side inverter the current is controlled and hence the rotational speed can be controlled. A state space model was developed for the LQG controller. The model includes both the dynamics of the electrical system as swell as the two mass system, consisting of the turbine and the generator connected with a flexible shaft. The controller was designed to minimize a quadratic criterion that punishes both torsional oscillations, command following and input signal magnitude. Integral action was added to the controller to handle the nonlinear aerodynamic torque. The controller was compared to the existing control system that uses a PI controller to control the speed, and tested usingMATLAB Simulink. Simulations show that the LQG controller is just as good as the PI controller in controlling the speed of the turbine, and has the advantage that it can be tuned such that the occurrence of torsional oscillations is mitigated. The study also concluded that some external method of dampening torsional oscillations should be implemented to mitigate torsional oscillations in case of a grid fault or loss of PWM signal.

The GARVEE Transportation Program started by the Idaho Transportation Department has improved parts of I-84 in Boise, Idaho. These desired improvements led to the widening of a bridge over the New York Canal (NYC) in 2009. To support the wider road, additional bridge columns were installed. The new bridge columns had a larger diameter than the existing columns and raised the number of columns from 28 to 60. Construction was completed just before the irrigation season began. During the first irrigation season it was observed that waves and oscillations were occurring within the canal immediately adjacent to the bridge structure. Throughout the irrigation season, it was observed that the intensity of the oscillations would vary. It was also observed that the wave oscillations propagated upstream and downstream from the bridge structure. Both longitudinal and transverse waves were observed. The waves appeared to originate in the section of the canal that was under the I-84 Bridge. A physical model was built in 2010 at Utah State University's (USU) Utah Water Research Laboratory (UWRL) in an attempt to simulate the oscillation phenomenon and to develop potential solutions to the problem. During the original modeling work, a thorough investigation to the causes of this phenomenon was not accomplished due to time constraints. The objective of the follow-up research presented in this thesis was to qualitatively determine the causes of the oscillations. Laboratory tests were performed using the original physical model used in the original 2010 testing.