Nonlinear Dispersive Model Research Articles

Some diagnostics in nonlinear reproductive dispersion models

This article discusses the problem of the detection of influential cases in nonlinear reproductive dispersion models (NRDM). A diagnostic based on case-deletion approach in estimating equations is proposed. The relationships between the generalized leverage defined by Wei et al. in 1998, statistical curvature, and the local influence of the response vector perturbations are investigated in NRDM. Two numerical examples are given to illustrate the results.

Dose‐Dependency in Local Disposition of 5‐Fluorouracil under Non‐Steady‐State Condition in Rat Liver

Dose‐dependency in local disposition of 5‐fluorouracil (5‐FU) was evaluated using the rat liver in the once‐through perfusion system under the non‐steady‐state condition. A curve‐fitting program based on Finite Element Method, MULTI(FEM), was adopted to evaluate the capacity‐limited elimination in the hepatic local disposition of 5‐FU, which is described by a nonlinear dispersion model with a pulse input. The dose of 5‐FU was increased from 10.4 to 208 μg for rat livers at five dose levels. Two nonlinear models, two‐compartment dispersion models with Michaelis–Menten elimination from the central compartment or from the peripheral compartment, were employed for comparison. The hepatic recovery ratio, FH, increased from 13.1% to 68.3% and the mean transit time, t-H, increased from 5.1 to 13.1s with an increase in the dose. It was found that the hepatic local disposition of 5‐FU was well represented by the peripheral elimination model. Vmax and Km in the model with peripheral Michaelis–Menten elimination were estimated to be 9.04 mg/h and 2.88 mg/L, respectively. Vmax estimated by the present investigation in situ was about seven times greater than that in vitro, whereas Kmin situ was close to that in vitro. This result suggests that the elimination activity by the hepatocytes in vitro may be lowered, compared with that in situ. © 2000 Wiley‐Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 89: 100–107, 2000

Comparative Analysis of Nonlinear Dispersive Shallow Water Models

The results of comparative analysis of some nonlinear dispersive models of shallow water are presented. The aim is to find their individual properties relevant for the numerical solution of some model problems of long wave transformation over submerged obstacles The study considers basic properties of the listed models and their numerical implementation. Computations are obtained compared with the analytical solution and experimental data. Attention is primarily focused on the models suggested by Peregrine (1967); Zheleznyak and Pelinovsky (1985); Kim, Reid, Whitakcr (1988): Fedotova and Pashkova (1997). Also classical equations of shallow water are considered in both linear and nonlinear approximations.

Influence diagnostics in nonlinear reproductive dispersion models

We extend some diagnostic methods studied by Pregibon (1981, Ann. Statist. 9, 705–724), Cook and Weisberg (1982, Residuals and Influence in Regression, Chapman & Hall, New York), and Wei (1998, Exponential Family Nonlinear Models, Springer, Singapore) to nonlinear reproductive dispersion models (NRDM, Jorgensen, 1997, The Theory of Dispersion Models, Chapman & Hall, London). The equivalency of case-deletion models and mean-shift outlier models in NRDM is investigated. Some of the diagnostic measures are illustrated with an example.

Numerical simulation of an obliquely incident solitary wave

Calculations using the finite-difference method with dynamically adaptive grids were performed within the framework of the Zheleznyak-Pelinovskii nonlinear-dispersion model and the three-dimensional potential flow model. The results are compared with calculations by other authors.

Analysis program based on finite element method, MULTI(FEM), for evaluation of dose‐dependent local disposition of drug in liver

A curve‐fitting program based on the Finite Element Method, MULTI(FEM), was developed to model nonlinear local disposition of a drug in the liver under non‐steady‐state conditions. The program was written in FORTRAN on an IBM‐compatible personal computer. The validity of MULTI(FEM) was confirmed by analyzing the outflow kinetics of oxacillin (a model drug) following a pulse input to isolated, perfused rat livers, according to both linear and nonlinear dispersion models. Four dose levels (300, 1000, 3000, and 5000 µg) of oxacillin were administered to observe the dose‐dependency in the hepatic local disposition. First, the individual outflow time‐profiles at the same dose were averaged, and the average time‐profile was analyzed by MULTI(FEM) based on linear dispersion models to yield a single curve fit. The fitted parameters at each dose level were compared with parameters estimated using MULTI(FILT), a program based on fast inverse Laplace transform, to analyze linear pharma‐cokinetics. The estimated parameters by MULTI(FEM) were in good agreement with those by MULTI(FILT). The apparent elimination rate constant (ke) decreased with an increase in dose, whereas other parameters showed no discernible dependency on an increase of dose. Second, the average outflow time‐profiles at the four dose levels were simultaneously analyzed by MULTI(FEM) based on dispersion models featuring Michaelis–Menten elimination. The outflow time‐profiles of oxacillin were well approximated by a two‐compartment dispersion model with central Michaelis–Menten elimination. The maximum elimination rate constant (Vmax) and the Michaelis constant (Km) were estimated to be 1520 µg/mL/min and 41.3 µg/mL, respectively. Thus, the capability of MULTI(FEM) was demonstrated in evaluating capacity‐limited local disposition in the liver.

Application of a non-linear dispersion model to analysis of the renal handling of p-aminohippurate in isolated perfused rat kidney.

To analyze the renal handling of therapeutic compounds observed as a non-linear process with a diffusion phenomenon, we employed a non-linear dispersion model described with a partial differential equation and solved it by using the finite difference method with an implicit scheme in a model dependent analysis. In this study, the renal handling of p-aminohippurate (PAH) was investigated in isolated perfused rat kidney, in which a 50 microl bolus of injection solution containing [3H]PAH and [14C]inulin was administered rapidly into the renal artery. The venous outflows were then collected for 15 min with a fraction collector. The renal extraction ratio of PAH was decreased from 65% to 18% as the PAH concentration in the injection solution was increased from 2 microM to 10 mM. The PAH outflow profile changed as the extraction process became saturated. With the non-linear dispersion model, the Michaelis-Menten parameters for the PAH extraction process were estimated by a model fitting calculation. The calculated values were 0.83 micromol/min/kidney for Vmax and 89 microM for Km. It was demonstrated that the model dependent analysis with a non-linear dispersion model is a useful approach to characterize renal drug handling, and is probably applicable for examining other non-linear processes which involve a diffusion phenomenon.

Nonlinear-dispersive Shallow-water Models of High Order Approximation

The class of nonlinear-dispersive (NLD) models of hydrodynamics was considered, the comparison of a series of hydrodynamic models was performed, and the selection of the most satisfactory model for carrying out economical and effective finite-difference schemes adequately modeling a wide class of natural wave processes was made.

Numerical Simulation of Wave Transformation by Two Nonlinear-dispersive Models

Finite-difference schemes for one- and two-dimensional variants of nonlinear-dispersive models of shallow water are considered. Dissipative and dispersive properties are analyzed, and the results of numerical calculations given.

Asymptotic dynamics of short waves in nonlinear dispersive models

Multiple-scale perturbation theory, well known for long waves, is extended to the study of the far-field behavior of short waves, commonly called ripples. It is proved that the Benjamin--Bona--Mahony--Peregrine equation can support the propagation of short waves. This result contradicts the Benjamin hypothesis that short waves do not propagate in this model and closes a part of the old controversy over different solutions for the Korteweg--de Vries and Benjamin--Bona--Mahony--Peregrine equations. We have shown that, in a short-wave analysis, a nonlinear (quadratic) Klein-Gordon--type equation replaces the ubiquitous Korteweg--de Vries equation of the long-wave approach. Moreover, the kink solutions of ${\ensuremath{\varphi}}^{4}$ and sine-Gordon equations are understood as an asymptotic behavior of short waves to all orders. It is proved that the antikink solution oF the ${\ensuremath{\varphi}}^{4}$ model, which was never obtained perturbatively, occurs as a perturbation expansion in the wave number $k$ in the short-wave limit.

WAVE AND CURRENT FIELDS AROUND GAPPED SUBMERGED BREAKWATERS

非線形分散波理論にづく数値モデルを用いて, 幅広透過潜堤周辺の波浪場と流速場の変形解析を行った. 平面水槽を用いた透過潜堤の実験を行い, モデルの妥当性を確認した. 数値計算から潜堤を通過する波は, 潜堤の天端及び不連続部背後面において極大値をとることが明らかとなった. また, 流れは天端面端部の周りで増大し, 平均水位の分布がその推進力となっていることが確認された. これらの特性に関して, 潜堤の空隙特性との関係が検討された.

On the algorithm for one nonlinear dispersive shallow-water model

Article On the algorithm for one nonlinear dispersive shallow-water model was published on January 1, 1997 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 12, issue 4).

Analysis of the numerical algorithms for nonlinear dispersive shallow-water models

Analysis of the numerical algorithms for nonlinear dispersive shallow-water models

Methods of construction and the analysis of difference schemes for nonlinear dispersive models of wave hydrodynamics

Article Methods of construction and the analysis of difference schemes for nonlinear dispersive models of wave hydrodynamics was published on January 1, 1997 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 12, issue 2).

Analysis of difference algorithms for nonlinear dispersive shallow water models

Analysis of difference algorithms for nonlinear dispersive shallow water models

Asymptotic behaviour of nonlinear dispersive models with variable coefficients

We consider mathematical models of evolution which are conservative and include in the simplest case, an equation describing the unidirectional propagation of weakly nonlinear, dispersive long waves suffering disturbances due to the possible unevennes of the botton surface. Our main result gives rates of decay of the amplitude in terms of the «alterations» of the bottom surface.

Global Existence of Solutions of a Nonlinear Dispersive Model

Global Existence of Solutions of a Nonlinear Dispersive Model

Discrete nonlinear-dispersion shallow-water model

Discrete nonlinear-dispersion shallow-water model

On the Initial Value Problem for a Class of Nonlinear Dispersive Models

On the Initial Value Problem for a Class of Nonlinear Dispersive Models

Two-Dimensional Nonlinear Dispersive Wave-Current and Three-Dimensional Beach Deformation Model

ABSTRACTA numerical wave model based on the Boussinesq equations were extended to the computation of a two-dimensional wave-current field including diffraction, refraction and wave breaking. The energy dissipation due to wave breaking was modeled with a momentum mixing term using eddy viscosity. Beach evolution around a coastal structure was simulated on the basis of the computed velocity field. Applicability of the model was confirmed through laboratory experiments.