941 resultados para Period-doubling bifurcation
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The proportion of torpedograss tissue exposed to glyphosate at application rates of 0.28, 0.56, 1.12, 2.24, and 4.48 kg/ha affected control as measured by regrowth. The effect of tissue exposure was more pronounced as application rate decreased. This study suggests that higher rates of glyphosate need to be used during higher water levels, when less torpedograss tissue is exposed to herbicide spray and lower rates may be used during periods of low water levels. Addition of the water conditioning agent Quest (R) (0.25% v/v) to glyphosate spray mixtures diminished the influence of simulated rain events following glyphosate application. Twelve other adjuvants did not influence the effect of simulated rain events.
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An overview on the onset of thermocapillary oscillatory convection in a floating half zone is provided, and it is a typical subject in the microgravity sciences related to the space materials science, especially the floating zone processing, and also to the microgravity fluid physics. The main interests are focused around the process for onset of oscillatory thermocapillary convection, which is known also as the bifurcation transition from quasi-steady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, such as the Marangoni number, Prandtl number, geometrical parameters, and heat transfer parameters. Recent studies show that, there exists the bifurcation transition from steady and axial symmetric convection to the steady and axial non-symmetric convection before the onset of oscillation in cases of small Prandtl number fluids and in cases of larger Prandtl number fluids of fat liquid bridge with small aspect ratio. The transition process is a strong non-linear process because the velocity deviation has the same order of magnitude as that of an average flow after the onset of oscillation, and unsteady 3-D numerical simulation is suitable to do in depth analysis on strong non-linear process, and leads generally to a better comparison with the experimental results.
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The bifurcation and nonlinear stability properties of the Meinhardt-Gierer model for biochemical pattern formation are studied. Analyses are carried out in parameter ranges where the linearized system about a trivial solution loses stability through one to three eigenfunctions, yielding both time independent and periodic final states. Solution branches are obtained that exhibit secondary bifurcation and imperfection sensitivity and that appear, disappear, or detach themselves from other branches.
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I. Existence and Structure of Bifurcation Branches
The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.
II. Constructive Techniques for the Generation of Solution Branches
A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.
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The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.
The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.
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The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.
The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.
The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.
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It is known that the larvae of Chironomidae in the first stages of life after leaving the egg case, swim for a long time in a body of water. Positive reaction in light, the capability of directed swimming and passive floating in suspension allow the larvae to temporarily carry out a planktonic way of life. This study describes the behaviour of Chironomus dorsalis larvae after leaving the egg case. The feeding of chironomid larvae in the first stages of development was also described.
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Temperature and stress tunabilities of long-period Bragg gratings imprinted in Panda fiber are presented in this letter. It is shown that the temperature and strain response of the resonance peaks for fast and slow axes are different not only in their magnitudes but also in the signs of the slope. Furthermore, the characteristics for different order modes are different both in magnitudes and signs. The complicated phenomena are discussed by using a simplified model.
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Based on the Mach-Zehnder effect between the core mode and the cladding modes, the interference fringes are formed by a pair of cascaded long-period fiber gratings (CLPFGs). Theoretical analyses show that the spectral spacing and the wavelength of these fringes are functions of the waveguide dispersion factor gamma, which is a characterizing parameter to LPFG and with theoretical and applicational significance. By measuring the characteristics of the transmission spectra of CLPFGs, the absolute value of gamma can be obtained. At the same time, the thermo-optic coefficient of effective refractive index difference between core and cladding modes, p, can also be obtained by measured the temperature sensitivity of these fringes. In the experiments, \gamma\ and mu were measured by this method to be 0.874 and 4.08 x 10(-5) degreesC(-1), respectively, for LPFGs with period of 450 mum and with a HE14 resonant peak at 1554 nm. (C) 2004 Elsevier B.V. All rights reserved.
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A small investigation of the ecology of the river Lambourn was carried out during 1967-70. During this period it became clear that detailed and reliable information could only be obtained by a much larger investigation. The present study was planned to meet the minimum requirements. No pumping is expected during this period and, since the pumping carried out during the pilot scheme was on a small scale, it is reasonable to assume that the river is still relatively unaffected by pumping.The present investigation has two main objectives both of which depend on obtaining a detailed picture of the ecology of the river at the present time. First, it will provide basic information on the state of the river prior to the development of the pumping scheme which will be available for comparison at any later date. Secondly, it may be possible to use some of the data to predict the ecological changes which may occur if the flow of the river is altered by the pumping scheme. This report is part of a series of fives studies on the River Lambourn which were undertaken between 1970 and 1979. [PDF contains 83 pages]
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Few detailed studies have been made on the ecology of the chalk streams. A complex community of plants and animals is present and much more information is required to achieve an understanding of the requirements and interactions of all the species. It is important that the rivers affected by this scheme should be studied and kept under continued observation so that any effects produced by the scheme can be detected. This need has been recognised by the Thames Conservancy and the Water Resources Board who jointly sponsored this investigation on one of the chalk streams involved in the scheme. The present investigation has two main objectives both of which depend on obtaining a detailed picture of the ecology of the river at the present time. First, it will provide basic information on the state of the river prior to the development of the pumping scheme which will be available for comparison at any later date. Secondly, it may be possible to use some of the data to predict the ecological changes which may occur if the flow of the river is altered by the pumping scheme. The study covers suspended solids, invertebrates, fish.This report is part of a series of fives studies on the River Lambourn which were undertaken between 1970 and 1979. [PDF contains 24 pages]
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The investigations described in this report were carried out to fulfill three distinct but interrelated objectives. In 1973 the Thames Conservancy were making plans for a second stage of their groundwater scheme which would take water from the chalk aquifers in the valley of the Kennet and they wanted basic information on the ecological state of this river and its upper tributaries. Little appeared to be known about limestone streams and a preliminary study of one of the streams in this area was desirable as a basis for planning more detailed studies if these were needed later. At a progress meeting held in March 1976 the problems and opportunities presented by the developing drought conditions were considered. It was concluded that the ecological effects of the exceptionally low natural flows should be studied and that it would be important to assess the ecological impact of the groundwater scheme if it was brought into operation that year. This could only be done on the Lambourn and the Winterbourne and it was decided that considerable effort should be diverted there for this purpose and that the field observations should be extended to cover any recovery period after the end of the drought. To make this possible it was agreed that the studies of invertebrates and detritus on the Kennet should be reduced considerably and that the proposed study of the limestone stream should be abandoned. The revised objectives were as follows: A detailed ecological study of several sites on the Kennet and its tributaries above Kintbury, extending over at least two years and involving observations on wate r weeds , invertebrates, fish, detritus and the trophic relationships within the river community. Quantitativ e and qualitative sampling of water weeds and invertebrates during one year at a number of sites on several chalk streams to determine whether the patterns and relationships found in the Lambourn are also found at the other sites. Observations on the Lambourn at Bagnor were to continue for most of the period to look for long-term fluctuations and to enable these sites to act as controls with which the other sites could be compared. Further detailed studies on the Lambourn and the Winterbourne to assess the impact of low flows, trial pumping and the operation of the groundwater scheme.
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The objective of this short project progress report is to investigate, in a catchment on which earlier nitrate data are available for comparison, seasonality and budgets, in relation to land use, of nitrate inputs, concentrations and loads. Sampling was undertaken from 1984-87 in the River Frome catchment and data on nitrate concentrations analysed.
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The objective of this short project progress report is to investigate the possible water quality implications of modern watercress growing practices. Chalk receiving watercourses are usually of high supply, amenity, game fishing and fish farming value. Any headwater pollution load, therefore, needs characterising and quantifying. Two sites of watercress farming were studied in 1986-87 and nutrient levels examined. Different approaches of watercress farmers in Dorset and Hampshire are summarised.