Basic Nonlinear Model Research Articles

A Fundamental Moving Boundary Problem of 1D Commingled Preferential Darcian Flow and Non-Darcian Flow Through Dual-Layered Porous Media

In consideration of vertical formation heterogeneity, a basic nonlinear model of 1D commingled preferential Darcian flow and non-Darcian flow with the threshold pressure gradient (TPG) in a dual-layered formation is presented. Non-Darcian flow in consideration of the TPG happens in the low-permeability tight layer, and the Darcian kinematic equation holds in the other high-permeability layer. The similarity transformation method is applied to analytically solve the model. Moreover, the existence and uniqueness of the analytical solution are proved strictly. Through analytical solution results, some significant conclusions are obtained. The existence of the TPG in the low-permeability tight layer can intensify the preferential Darcian flow in the high-permeability layer, and the intensity of the preferential Darcian flow is very sensitive to the dimensionless layer thickness ratio. The effect of the layer permeability ratio and layer elastic storage ratio on the production sub-rate is more sensitive than that of the layer thickness ratio. In addition, it is strictly demonstrated that moving boundary conditions caused by the TPG should be incorporated into the model. When the moving boundary is neglected, the preferential Darcian flow in the high-permeability layer will be exaggerated. Eventually, solid theoretical foundations are provided here, which are very significant for solving non-Darcian seepage flow problems in engineering by numerical simulation validation and physical experiment design. Furthermore, they are very helpful for better understanding the preferential flow behavior through the high-permeability paths (such as fractures) in the water flooding development of heterogeneous low-permeability reservoirs; then, the efficient profile control technology can be further developed to improve oil recovery.

A developed nonlinear model for the location-allocation and transportation problems in a cross-docking distribution network

The paper addresses the location-allocation and transportation problems in designing a cross-docking distribution network that consists of suppliers, cross-docks, and plants. A developed mixed-integer non-linear model is proposed for a post-distribution cross-docking strategy with multiple cross-docks and products that cross-docks can be connected. The objective function is to minimise the total cost comprising the cost of established cross-docks and transportation costs. To obtain this model, first, two models are introduced and compared (basic non-linear model 1 and non-linear model 2 with the possibility of connections between cross-docks). Results indicate that the total cost is decreased when the connection between cross-docks exists. So, model 2 is more efficient and suitable than model 1. Then, consolidation of plant orders is added to model 2, and the developed model is formulated. Finally, some problems with different sizes are generated randomly and solved by GAMS software to evaluate the model accuracy.

An adaptive robust control scheme for robot manipulators with unknown backlash nonlinearity in gears

This paper presents an adaptive robust control algorithm for the nonlinear dynamics of robot manipulators with unknown backlash in gears. The basic nonlinear model of a serial manipulator robot is used for the controller design, and this is combined with the nonlinear proposed dead zone model, based on the input and output torque. The main idea of providing this model is to achieve a dynamic model of the system considering the backlash of the robot joint gears, and having less complexity such that the developed controller does not need the inverse backlash model. The adaptive robust controller is developed, without using the inverse backlash model. The proposed controller is designed based on an unknown dead zone parameter and it guarantees the stability and path tracking of the robot trajectory with unknown dead zone parameter in the desired range. Numerical simulations are conducted to show the effectiveness of the proposed controller. Finally, the efficiency and capability of the proposed controller in dealing with the unknown backlash nonlinearities in gears of the manipulator are demonstrated by experimental results with a five-bar manipulator.

Optimal stabilization of small spacecraft angular motion in the process of deployment of an orbital tether system

The problem of stabilizing the motion of small spacecraft relative to the center of mass in the process of deploying an orbital tether system is presented in the paper. Stabilization is carried out with respect to the direction of the tether and is characterized by the classical Euler angles (precession, nutation and proper rotation). The proposed method of suboptimal control is based on the joint application of the principle of Bellman's dynamic programming and the averaging method. The integral quadratic optimality criterion that depends on operating deviations and low control inputs is used. Control synthesis is accomplished using the model of angular motion recorded for small angles of nutation. An example of calculating optimal control of an orbital tether system deployed for the purpose of de-orbiting small satellites to the Earth is given. The efficiency of the optimal control arrived at is confirmed by numerical calculations for the basic nonlinear model of motion of an orbital tether system.

Quantifying Changes in Structural Design Needed to Account for Aftershock Hazard

AbstractAftershocks have the potential to cause severe damage to buildings and threaten life following a major earthquake. However, their effect on seismic hazards is not explicitly accounted for in modern building design codes, nor in emerging methodologies such as performance-based seismic design. The objective of this study was to develop a methodology that can quantify the changes that would be needed in the structural design of a building to account for aftershock (AS) hazards and illustrate it using a basic nonlinear model of a building. In other words, what changes to a structural design would be needed such that the building has the same collapse probability for the combined mainshock and aftershock (MS + AS) hazard as the collapse probability for the original building, subjected to the mainshock (MS) only? The total collapse probability is computed using a combination of seismic fragility results convolved with the two types of hazard curves, namely, a typical hazard curve and an AS hazard curve....

A Parametric Analysis of the Basic Nonlinear Models of the Catalytic Reactions

A series of the simplest thermokinetic models, in which the kinetic subsystem corresponds to traditional catalytic mechanisms, such as the Eley–Rideal mono- and bimolecular mechanisms and the Langmuir–Hinshelwood mechanism, and autocatalytic mechanisms characterized by multiplicity of steady states and autooscillations in the kinetic region, were considered. The method of continuation along a parameter was used for studying these basic models of thermokinetics. The parametric analysis performed allowed us to identify parameter regions characterized by critical effects (multiplicity of steady states and autooscillations).

On the variational framework employing optimal control for biochemical thermodynamics

The maximum energy dissipation principle can be successfully applied to describe a range of basic nonlinear models. The application of the general variational framework [29–31] has been illustrated for basic linear schemes. The study presented in the paper shows how the kinetic processes at this level of the biomolecular and biophysical phenomena can be effectively described in terms of the maximum energy dissipation principle and its variational formulation. On the basis of this approach, a range of Lagrangians was proposed for basic nonlinear dissipative kinetic models. The results of this study show that the framework is in agreement with nonlinear equilibrium thermodynamics.

SLIM: a sliding linear model for estimating the proportion of true null hypotheses in datasets with dependence structures

The pre-estimate of the proportion of null hypotheses (π(0)) plays a critical role in controlling false discovery rate (FDR) in multiple hypothesis testing. However, hidden complex dependence structures of many genomics datasets distort the distribution of p-values, rendering existing π(0) estimators less effective. From the basic non-linear model of the q-value method, we developed a simple linear algorithm to probe local dependence blocks. We uncovered a non-static relationship between tests' p-values and their corresponding q-values that is influenced by data structure and π(0). Using an optimization framework, these findings were exploited to devise a Sliding Linear Model (SLIM) to more reliably estimate π(0) under dependence. When tested on a number of simulation datasets with varying data dependence structures and on microarray data, SLIM was found to be robust in estimating π(0) against dependence. The accuracy of its π(0) estimation suggests that SLIM can be used as a stand-alone tool for prediction of significant tests. The R code of the proposed method is available at http://aspendb.uga.edu/downloads for academic use.

On the derivation of macroscopic tissue equations from hybrid models of the kinetic theory of multicellular growing systems — The effect of global equilibrium

This paper deals with a new approach to the development of asymptotic methods for the derivation of biological tissue equations from the underlying description offered by models of the kinetic theory for active particles developed for multicellular systems. The basic nonlinear model is linked to a linear stochastic velocity-jump process used to describe the dynamics of velocity variations. Specifically, the method takes into account the effect of global equilibrium configurations on the derivation and structure of macroscopic, tissue level equations, and leads to the final objective reducing the a priori assumptions used in previous papers.

Modeling and Control of Distillation Column in a Petroleum Process

This paper introduces a calculation procedure for modeling and control simulation of a condensate distillation column based on the energy balance (L‐V) structure. In this control, the reflux rate L and the boilup rate V are used as the inputs to control the outputs of the purity of the distillate overhead and the impurity of the bottom products. The modeling simulation is important for process dynamic analysis and the plant initial design. In this paper, the modeling and simulation are accomplished over three phases: the basic nonlinear model of the plant, the full‐order linearised model, and the reduced‐order linear model. The reduced‐order linear model is then used as the reference model for a model‐reference adaptive control (MRAC) system to verify the applicable ability of a conventional adaptive controller for a distillation column dealing with the disturbance and the model‐plant mismatch as the influence of the plant feed disturbances.

A Novel Elastometer For Soft Tissue

A novel device has been designed to allow a surgeon to determine the medium strain (5-25%) compressive properties of highly extensible soft tissue during a surgical procedure. The motivation for the instrument is the need for accurate knowledge of the elastic properties of vaginal tissue in vivo during corrective surgery for incontinence in women. Studies have shown that a surgical technique that adjusts the elastic nature of vaginal tissue can reduce urge and stress incontinence symptoms. The success of the surgical technique would be greatly enhanced by the introduction of an objective measure of the stiffness of vaginal tissue. The compressive deformation is achieved by folding and pinching (indenting) the tissue between two circular cylinders. The applied load and indentation depth are used to estimate the elastic properties of the sampled tissue. A linear material model has been developed and tested against commercially available elastomers. The limits of application of the linear material model were determined using FEA and results from the experimental testing. A basic nonlinear model is also presented that can determine the Neo-Hookean constant of the material. The simple algorithms developed allow immediate inversion of measurements to give elastic properties, thereby permitting multiple readings to be made during a surgical procedure, an outcome that would not be possible if FEA or similar numerical methods were needed for interpretation of the readings. Experimental and numerical results are compared to the analytical models and a discussion of initial design ideas is presented. The device is shown to yield elastic modulus of test materials with an error of less than 10%.

Fluid Biaxial Banana Smectics: Symmetry at Work

Perhaps one of the most surprising results in the past 10 years was the prediction of Brand et al. [1] that fluid biaxial smectics made from comopunds without asymmetric carbons could, by symmetry, have a spontaneous polarization, P, in the layer plane. They called this construct, which can be either ferroelectric or antiferroelectric, smectic C9. Advances gained from their prediction include the development of highly efficient electrets for broad-band telecommunications [2, 3] as well as a basic non-linear model [4] for TLAFs, thresholdless antiferroelectrics [5], now seen in beatiful, CMOS compatible, active matrix liquid crystal displays [6] (figure 1).

Managing cattle grazing under degraded forests: An optimal control approach

In this paper aspects of knowledge generation and administration concerning management of a rural enterprise in the Argentine Chaco region are analyzed. The deterioration of natural resources and human living conditions show that forest-cattle interaction and the ecological economics of the system are poorly understood or not properly taken into account. A methodological solution to a typical decision-making problem is proposed here and illustrated by a worked example extracted from a real feasibility study. The introduction provides a summary of the natural history and of the human interventions in the region. Arguments on the roke of silvopastoral systems in reverting forest and soil degradation into sustainable productive undertakings are also exposed. The mathematical treatment of the problem follows a system theoretic approach. A basic nonlinear model for the dynamics is designed first. Its simplest version includes three state variables (livestock units, forest biomass and forage availability) and two manipulated variables (percentage of female calves sold each year and percentage of the cows that did not give birth during the past period and went for sale). States and controls are related by coupled differential-difference equations. Selected results from simulation are shown. Foundations are also laid for taking into account impulsional controls (selective and massive wood extractions, forage implantation, cattle additions and sales). The objective function reflects sustainable development principles. It evaluates the process in terms of usual economics and introduces ecological components of the management strategy. The total cost is expressed as the accumulation of net expenses made for a fixed number of years, minus the sale value of the firm at the end. Then a dynamic programming scheme is developed for finding optimal trajectories with respect to the basic setup. Shadow prices for the states are derived from the solution. Progress towards the building of a decision support system with the preceding elements is reported.

Surface‐Irrigation Nonlinear Optimization Models

Nonlinear optimization models are developed to design and manage furrow and border irrigation methods. The objective function of the basic nonlinear model is constructed on the basis of a profit relationship, while that of the expanded nonlinear model is constructed in terms of benefit and costs. The models are solved with the MINOS 5.0 package. The values of the design variables yielded by the nonlinear models are similar to those given by an existing linear optimization model. The expanded nonlinear model gives objective function (profit plus other costs) values that are greater than those of the basic nonlinear and linear models.