Numerical Solutions Of Nonlinear Equations Research Articles

Dispersal kernel of green rice leafhopper estimated from truncated data

AbstractCharacterizing dispersal kernels from truncated data is important for managing and predicting population dynamics. We used mark‐recapture data from 10 previously published replicated experiments at three host plant development stages (seedling, tillering, and heading) to estimate parameters of the normal and exponential dispersal kernels for green rice leafhopper,Nephotettix cincticeps(Uhler). We compared classic statistical methods for estimating untruncated distribution parameters from truncated data with maximum likelihood (MLE) and the method of statistical moments for simulated and empirical data. Simulations showed that both methods provided accurate parameter estimates with similar precision. The method of moments is algebraically complex, but simple to calculate, while the MLE methods require numerical solutions of nonlinear equations. Simulations also showed that accurate, precise estimates of the parameters of the untruncated distributions could be attained even under severe truncation with sufficient numbers of recaptures. Both diffusivity and the exponential mean were higher with later plant growth stage, showing that insects moved farther and faster at the heading stage. Precision of the estimates was not strongly related to percent capture, size of the experimental field, or the number of leafhoppers captured. The leptokurtic exponential kernel fit the data better than the normal kernel for all the experiments. These results support an alternative explanation for the strong density‐dependent population regulation of this species at the heading stage. Instead of leafhopper density per se, the increase in movement at this stage could integrate the populations in the separate fields, leveling densities throughout the landscape.

An Accurate and Fast Computational Algorithm Based on Hybrid Methods

The numerical solutions of nonlinear equation for a single diode equivalent circuit of a solar cell are introduced. Four numerically algorithms, which include newton's; Predictor-Corrector Hally and Accelerated Predictor-Corrector Hally methods are described and compared in the present work. These algorithms are applied to calculate the voltage; current; power of a solar cell with the different values of load resistance programmed by Matlab language. The results showed that the proposed algorithm is the most efficient compare with other three algorithms.

Constructing multi-looped surfaces by loop joining

The objective of this research is to develop a surface joining method for constructing multi-looped surfaces. Based on this method, surfaces can be self-joined or inter-joined on loops to construct multi-looped surfaces. A loop is a continuous and closed boundary on a surface. By constructing one or several single-looped B-spline surfaces, multi-looped surfaces are constructed through loop joining of boundary curve segments. Loop joining is completed by merging the control points on the surface boundaries of B-spline surfaces. With the merging of data structures simultaneously, the consistencies of geometry and topology are kept in the surface model. The proposed method for constructing multi-looped surfaces has the advantages that it is conceptually explicit, simple for user understanding and easy for system programming, and there is no computation of surface/surface intersections involved, thus no numerical solutions for nonlinear equations are required.

Dynamo theory for the interface between the convection zone and the radiative interior of a star part

Abstract We discuss numerical solutions of nonlinear equations that model magnetic field generation in a thin layer beneath the convection zone of a late type star. The model equations were derived previously in Paper I (DeLuca and Gilman, 1986b). Three main results are found: first, the oscillating, dynamo wave solutions discussed in DeLuca and Gilman (1986a) are shown to be a result of the severe truncation used in those calculations; second, the induced velocity feld is shown to have an important role in determining the spatial structure of the magnetic field solutions; time dependent solutions have been found. These are not wave-like solutions, rather the amplitude of different horizontal wave modes vary in time. Further, we show that the exact solutions found in Paper I are generally unstable, with the exception of those that are independent of ŷ (latitude in our Cartesian geometry), which are stable if the transient induced velocity field remains small. We conclude that the induced velocity fields are an important ingredient in any model of dynamo action below the solar convection zone.

Relaxation of Distortions in a Nematic Thin Film with Weak Anchoring Condition

Abstract Dynamical properties of a nematic thin film are investigated under the weak anchoring condition on the boundaries. By solving the equations for small distortions, their asymptotic behaviors are found. Numerical solutions of nonlinear equations for the director field are obtained both in case of small and large distortions around the lower and upper threshold fields. The asymptotic behaviors of these solutions are compared with the analytical results. It is concluded that the dynamics around the upper critical field is governed by the boundaries and strongly space dependent.

Meanders and Detached Eddies of a Strong Eastward-Flowing Jet Using a Two-Layer Quasi-Geostrophic Model

The process of meander growth on and eddy detachment from an eastward flowing oceanic jet, which is modeled after the Gulf Stream east of Cape Hatteras, is studied using numerical solutions of nonlinear equations. The equations express potential-vorticity conservation in a two-layer quasi-geostrophic model with a weak planetary β effect. Solutions are restricted to a spatially periodic, temporally growing case. Initially, small-amplitude meanders are given, being superimposed on the jet. The solutions describe a process in which the meanders grow increasingly larger, the larger meanders are cut off, and cyclonic and anticyclonic eddies are detached southward and northward, respectively. Concurrent with the eddy detachment, an eastward flow is restored in the upper layer, and the lower layer develops an eastward flow under the restored jet and two westward flows north and south of it. A baroclinic instability is very effective in meander growth, while a weak β effect is necessary for eddy detachment; i.e., the meander grows large enough for the detachment by taking potential energy from the basic flow, and the β effect then cuts off the large-amplitude meander. This two-layer weak planetary β case is contrasted with a one-layer case when meander amplitude is much smaller, as well as a two-layer zero β case when no eddy is detached in spite of large-amplitude meanders. A topographic β effect is examined, when southward increase of depth is introduced instead of latitudinal gradient of the Coriolis parameter. In a weak topographic β case, flow patterns are very similar to those of a weak planetary, β case. In a strong topographic β case, no eddy is detached. The results are compared with Gulf Stream meanders and detached eddies.

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

One parameter operator imbedding to modify Newton method for solution of nonlinear equations

Numerical solutions of nonlinear equations for shells of revolution.

Numerical solutions of nonlinear equations for shells of revolution.