A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increases monotonically, with bath upper and lower asymptotes. Like the Ric...
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A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increases monotonically, with bath upper and lower asymptotes. Like the Richards growth equation, it can have its maximum slope at any value between its minimum and maximum. The new sigmoid equation is unique because it always tends towards exponential growth at small sizes or low densities, unlike the Richards equation, which only has this characteristic in part of its range. The new sigmoid equation is therefore uniquely suitable for circumstances in which growth at small sizes or low densities is expected to be approximately exponential, and the maximum slope of the growth curve can be at any value. Eleven widely different sigmoid curves were constructed with an exponential form at low values, using an independent algorithm. Sets of 100 variations of sequences of 20 points along each curve were created by adding random errors. In general, the new sigmoid equation fitted the sequences of points as closely as the original curves that they were generated from. The new sigmoid equation always gave closer fits and more accurate estimates of the characteristics of the 11 original sigmoid curves than the Richards equation. The Richards equation could not estimate the maximum intrinsic rate of increase (relative growth rate) of several of the curves. Both equations tended to estimate that points of inflexion were closer to half the maximum size than was actually the case;the Richards equation underestimated asymmetry by more than the new sigmoid equation. When the two equations were compared by fitting to the example dataset that was used in the original presentation of the Richards growth equation, both equations gave good fits. The Richards equation is sometimes suitable for growth processes that may or may not be close to exponential during initial growth. The new sigmoid is more suitable when initial growth is believed to be ge
Modeling and numerical solutions of vapor phase epitaxy are limited because of convergence ability and a large number of iterations. To overcome these limitations, for the first time two Newton-like methods have been ...
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Modeling and numerical solutions of vapor phase epitaxy are limited because of convergence ability and a large number of iterations. To overcome these limitations, for the first time two Newton-like methods have been applied to models of vapor phase epitaxy for GaAs and InxGa1-xP: The Newton-Raphson method (NRM) and the power-law formalism method (PLFM). We compare the performances of the two methods In terms of the ability of convergence and the iteration numbers. The results indicate that PLFM is always significantly superior to NRM. All calculations by PLFM successfully converge from a rough estimated initial values for equilibrium partial pressures, where NRM can not. These results suggest that the Limitation in the numerical calculations of the vapor growth epitaxy can be widely extended by the application of PLFM.
The ''partly coupled'' algorithm and numerical schemes are developed to solve a coupled model of air-sea-wave interaction, using the matrix and simple pivotal-condensation methods. The ''partly...
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The ''partly coupled'' algorithm and numerical schemes are developed to solve a coupled model of air-sea-wave interaction, using the matrix and simple pivotal-condensation methods. The ''partly coupled'' algorithm is used to handle boundary conditions at the air-sea interface to allow for solving systems of the atmospheric and oceanic equations, as two separate systems. This ''partly coupled'' algorithm is simpler, more effective, and requires less computing efforts to solve an air-sea-wave coupled model compared to the ''fully coupled'' algorithm developed by Ly [1] for solving a coupled model of the baroclinic atmospheric and oceanic boundary layers. In the numerical schemes, the buoyancy terms of dissipation and TKE budget equations are used as conditions for rearranging equation coefficient vectors to satisfy stability conditions. The mathematical coupled model of the air-sea-wave system is also presented. The model equations are written in the same form for both atmospheric and oceanic boundary layers, and include equations for momentum, the k-epsilon turbulence scheme, and stratification in the atmospheric and oceanic boundary layers. In the model, ocean wind-induced wave effects are modeled by using boundary conditions for the turbulent energy dissipation at the interface in a k-epsilon turbulence closure of the coupled model. numerical experiments are designed for various geostrophic winds, wave heights, and wave ages under neutral atmospheric stratification to demonstrate an example in solving a coupled model of the air-sea-wave system. The numerical simulations show that surface wind-induced waves have strong effects on the basic physical characteristics of the air-sea system.
Three-dimensional (3-D) digital images and patterns under transformations are facilitated by the splitting- shooting method (SSM) and the splitting- integration method (SIM), The combination (CSIM) of using both SSM a...
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Three-dimensional (3-D) digital images and patterns under transformations are facilitated by the splitting- shooting method (SSM) and the splitting- integration method (SIM), The combination (CSIM) of using both SSM and SIM and two combinations (CIIM) of using SIM only are proposed for a cycle conversion T-1T, where T is a nonlinear transformation, and T-1 is its inverse transformation. This paper focuses on exploitation of accuracy of obtained image greyness. In our discrete algorithms, letting a 3-D pixel be split into N-3 subpixels, the convergence rates, O(1/N), O(1/N-2), and O(1/N-3);of sequential error can be achieved by the three combinations respectively. High convergence rates indicate less CPU time needed. Both error bounds and computation of pixel greyness have shown the significance of the proposed new algorithms.
Here we investigate the optimal harvesting problem for some periodic age-dependent population dynamics;namely, we consider the linear Lotka-McKendrick model with periodic vital rates and a periodic forcing term that s...
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Here we investigate the optimal harvesting problem for some periodic age-dependent population dynamics;namely, we consider the linear Lotka-McKendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. Existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established. We also state necessary optimality conditions. A numerical algorithm is developed to approximate the optimal control and the optimal harvest. Some numerical results are presented.
Computation of an ARMA covariance function is a common ingredient in analysis and synthesis of various problems in stochastic control, estimation, and signal processing, Several approaches can be used for this purpose...
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Computation of an ARMA covariance function is a common ingredient in analysis and synthesis of various problems in stochastic control, estimation, and signal processing, Several approaches can be used for this purpose. In this paper, we present an algorithm based on simple polynomial calculations. Compared with alternative strategies, it has small computational load, shows good numerical robustness, and can be extended to handle multivariable ARMA processes, even with complex-valued coefficients.
A robust second order Newton iteration scheme is proposed for solving the nonlinear algebraic equations. Potential applications include the projection of the initial guess to the solution when the parameters in the eq...
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A robust second order Newton iteration scheme is proposed for solving the nonlinear algebraic equations. Potential applications include the projection of the initial guess to the solution when the parameters in the equations are changed. The mathematical derivation leading to the scheme is given and pros and cons of the method are discussed. As an example, the method has been applied to the evaluation of charge-sheet model for MOS as used in the circuit simulation.
In this paper we study numerical computations of oxygen diffusion problems with a moving oxidation front on unbounded domains of planar, cylindrical and spherical geometrical shapes. A new domain transformation techni...
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In this paper we study numerical computations of oxygen diffusion problems with a moving oxidation front on unbounded domains of planar, cylindrical and spherical geometrical shapes. A new domain transformation technique of space variables and time variable is introduced in the application of the variable grid method for numerical computation of these problems. Some upper bound estimates of oxidation fronts are obtained. A numerical algorithm is proposed and discussed. (C) 1998 John Wiley & Sons, Ltd.
We describe a method for computing interactions among spherical particles embedded in an elastic matrix. The interfaces between the particles and the matrix may or may not be perfect. The method is applied to the prob...
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We describe a method for computing interactions among spherical particles embedded in an elastic matrix. The interfaces between the particles and the matrix may or may not be perfect. The method is applied to the problem of determining the effective elastic moduli of composites when the interfaces satisfy a linear law. The effective properties are computed as functions of the volume fraction of the particles, the ratio of shear moduli, the Poisson ratios, and two parameters describing the linear interfacial characteristics of the inclusion-matrix interface. The results for the effective elastic properties for a wide range of these parameters are compared with effective-medium approximations and an agreement to within 30% is observed for the special case of hard-sphere random arrays considered in the study. We also consider a case of a three-phase composite material containing equal amounts of rigid inclusions and voids. The results for this case are compared with the predictions of a modified effective-medium approximation theory, and once again a similar level of agreement is found between the two. (C) 1997 Elsevier Science Ltd.
The first version of PSCAN program (Personal Superconductor Circuit ANalyzer) was introduced in 1991. The program is a general purpose superconductor circuit simulator with an emphasis on the design of Rapid Single-Fl...
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The first version of PSCAN program (Personal Superconductor Circuit ANalyzer) was introduced in 1991. The program is a general purpose superconductor circuit simulator with an emphasis on the design of Rapid Single-Flux-Quantum (RSFQ) circuits. In the intervening years a number of new features were gradually added to the program. In particular, verification of the correct circuit behavior was enhanced using a special hierarchical Single-Flux-Quantum Hardware Description Language (SFQHDL). Next, a fast heuristic algorithm for margin optimization was introduced, which increased the number of parameters that can be simultaneously optimized in reasonable CPU times. Finally, recently we improved the numerical algorithm used for the simulation by using sparse symmetric positive definite matrices (instead of general structure band matrices as before). As a result, simulation speed has increased almost tenfold. Now it takes about 30 seconds of a CPU time on HP715/100 workstation to run a 2,000-ps simulation of a 120-Josephson-junction circuit, and about a week to optimize all parameters of a two hundred Josephson junction circuit. We have merged all these improvements in a new version of our simulator, PSCAN'96, which will be released by the time of this conference.
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