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We propose a new prediction method for nonlinear time series based on the paradigm of deterministic chaos. Introducing a stochastically equivalent dynamical system to an original map, a prediction method is derived by minimizing a random term that defines intervals in which a good prediction performance is obtained. The use of the present method is illustrated for some chaotic systems with particular emphasis on issues of choices of variable time steps that are necessary when discretizing the stochastic differential equation. Applying to some systems, it is found that the present method works better than traditional chaotic methods. [ABSTRACT FROM AUTHOR]

A generalized information criterion is proposed to determine an embedding dimension and a delay time for delay coordinates of the reconstructed dynamics both for linear stochastic and nonlinear deterministic processes. While the standard maximum likelihood type method requires statistical parametric models such as autoregressive models, the generalized information criterion is constructed from the quantity in accordance with the second-order Renyi entropy in terms of the correlation integral for the finite number of data which is directly obtained from a time delay vector. It is found numerically that the present method works well when applied to chaotic and stochastic systems. [ABSTRACT FROM AUTHOR]

It has been reported that the chaos attractor generated from a differential equation containing a delay often attains a high dimension. When the high-dimensional time series data generated from a system containing a delay are analyzed, it is expected that the orbital reconstruction by the Takens embedding theorem is practically difficult. An approximate low-dimensional orbital reconstruction taking into account the delay is needed. However, when time series data containing a delay are treated, it is important to first estimate the delay accurately. Several methods have been proposed for estimating the delay. The previous methods are either those that cannot accurately estimate the delay while the existence of the delay can be recognized or those that can be applied only under the assumption that all state variables are observable. In this paper, a new embedding method and an algorithm are proposed for estimating the delay from an observed time series data set. By simulation, accurate estimation of the delay is confirmed. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(10): 10–16, 2000 [ABSTRACT FROM AUTHOR]

In the vicinity of the critical point of chaos as the accumulation point of period doubling bifurcations, the characteristic index is closely related to the bifurcation structure. Chaos is a typical nonlinear system, and hence its trajectory cannot be accurately reconstructed. However, qualitative evaluation is possible for the index that characterizes the vicinity of the critical point by a linear approximation model. In this paper, the lagged regression threshold model is used to quantitatively understand the characteristics of chaos, such as the Lyapunov index and the characteristic index. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(5): 1–9, 1999 [ABSTRACT FROM AUTHOR]

Earthquakes are complex, destructive phenomena and to model them is extremely difficult. Many mathematical models have been reported that take into account empirical rules known in connection with the frequency statistics of recent earthquakes. The cellular automaton is a model for critical phenomena that provide particles to a cell and it can be applied to the earthquake process. However, the cell configuration of the previously proposed model is extremely simple. In this paper, we propose a model in which the cells are arranged with the simulated fault diagram randomly distributed. Considering the dissipation of the strain energy of earthquake waves, the distributions of the particles in analogy to the earthquake are partially reduced. The results of applying this model to actual fault diagrams are reported. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(2): 20–27, 1999 [ABSTRACT FROM AUTHOR]

The parameter renormalization group method proposed in the previous papers is applied to the case where the system is described by two coupled one-dimensional maps to investigate the critical behavior of periodic-doubling. Particular attention is given to the asymmetric case where the maps have different bifurcation parameters. The first-order parameter renormalization equations are found to give qualitatively correct critical behaviors by comparing with numerical simulation. Furthermore, using the parameter reduction technique, it is found that critical behaviors of the coupled maps having a set of parameters on several critical lines are equivalent to those for the corresponding uncoupled maps. [ABSTRACT FROM AUTHOR]

This paper derives a renormalization formula defined on the parameter space where mapping behavior is preserved, together with the equivalent potential function. In contrast to the universal function given by Feigenbaum, the behavior near the critical point is governed by the potential function. There are several interesting features which are shared by Feigenbaum's universal function, such as the representation of the critical point in terms of the unstable fixed point of the potential function, but the mapping differs from the scaling. The one-dimensional mapping is considered as an example, and the critical point and the scaling, which are major constants characterizing chaos from the potential function, are calculated precisely. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 41–51, 1998 [ABSTRACT FROM AUTHOR]

Presents a systematic way for deriving the parameter renormalization group equation for one-dimensional maps. Investigation of critical behavior of periodic doubling; Asymptotic behavior of parameters for a period-2 orbit; Scaling of potential function and universal constants.

A control scheme to achieve wafer-to-wafer temperature uniformity in the reaction tube used for oxidation, diffusion, or annealing during semiconductor processes is proposed. In the analytical model, self-radiation loss, radiation between neighboring wafers, radiation from the tube wall, and thermal diffusion on a wafer surface are taken into account. The temperature monitoring points were the inlet, middle, and outlet of the reaction tube. The analysis indicates that if the tube wall temperatures at the inlet and outlet are 6 percent higher than that at the center of the tube, the wafer-to-wafer temperature becomes uniform. In the experiment, taking the silica tube temperature as the tube wall temperature, the increase in the temperatures at the inlet and outlet must be 5.6 percent to achieve wafer-to-wafer temperature uniformity, while it should be 6.9 percent if the temperature of the secondary tube is considered to be the tube wall temperature. Experiment results verify the effectiveness of the model. At the same time, the tube wall temperature is assumed to be influenced not only by the temperature of the silica tube but also by that of the secondary tube. The model predicts that the wafer temperature increased by 1°C if the tube wall temperature is increased as described in the foregoing. However, in the experiment, the wafer temperature increases by 1.6°C at most [ABSTRACT FROM AUTHOR]

In the high-temperature process of semiconductors, the temperature distribution on the wafer surface during the procedures of the wafer insertion into the removal from the oxidation or diffusion furnace is important in determining the density of the dislocation due to the thermal stress and the uniformities of both the oxide thickness and the diffusion depth. As the size of a wafer and the density of integration increase, the analysis of the thermal transient characteristics becomes more important. This paper analyzes the model of the temperature transient characteristics proposed previously and describes the transient characteristics on a wafer by measuring the temperature distribution on a wafer in a furnace using an infrared radiometer. The simulation for a case where a wafer of 150 mm in diameter is inserted into furnace at a speed of 20 cm/min indicates that the temperature variation on a wafer at every moment is as high as 150°C. This result agrees with the experimental result within an accuracy of 25°C. When the insertion speed is 100 cm/min, the temperature variation increases by 20 to 30 percent and is maintained until the wafer reaches the high-temperature zone. This is caused by the increase in the rate of temperature change with time due to the radiation from the tube wall which is the external heat source. This tendency is more noticeable for wafers located at the middle row. [ABSTRACT FROM AUTHOR]

The nonuniform temperatures that develop over silicon wafers on insertion and removal from the furnaces used in the oxidation and diffusion processes of semiconductor fabrication are one factor in reduced yields. For example, because of temperature differences in the oxidation process there are thermal stresses and differing thermal hystereses over the wafer surface which degrade the uniformity of the oxide layer formed. The most pronounced temperature differences, occurring when the wafers are inserted into the furnace, develop mainly because of the effect of the boat μg which supports the wafers. Since the heat capacity of the boat is much greater than that of the wafers, during the slower rise in the boat temperature radiant heat exchange with the wafer bottoms keeps the temperature of the bottoms lower than the temperature of the wafer tops, which are almost unaffected by the boat. This transient in the wafer temperature depends on such process parameters as the boat insertion speed, the ratio between the wafer and furnace reactor tube diameters, and the wafer spacing. In order to analyze this temperature characteristic the process is modelled and the results of numerical simulation are compared with experiment. The model for the wafer temperatures inside the furnace is a system of coupled partial differential equations for the mostly radiant heat fluxes of the boat and wafers. With an insertion speed of 2 m/sec, both the experimental data and the model give a maximum temperature difference over the wafer surface of 230°C near the end of insertion, thus confirming the model. [ABSTRACT FROM AUTHOR]

In semiconductor fabrication it is difficult to form channels with precisely controlled lengths, even when using plasma etching which itself is highly precise. This is because of fluctuations in the processes preceding the etching, as, for example, in the developed resist dimensions. This paper proposes a method for controlling channel lengths which relies on an optimized over-etching, the extra etching time after the normal etch completion depending on the variation in resist dimension, etc. In the method a phenomenological model is set up for the rate of change of channel length as a function of the resist dimension and etching cross section, and the polysilicon layer thickness and Its phosphorus doping density as determined by sheet resistance. The model coefficients are estimated by a Kalman filter on wafer and lot measurement data. The results of production line experiments with the present method show a reduction in channel length variation by one-half compared with the previous uncontrolled method. [ABSTRACT FROM AUTHOR]

The 1/f spectra that appear in electroencephalogram data are among the characteristics that appear in the wide range of self-organizing phenomena encompassing both physical and sociological phenomena. The fact that they appear across the various objects suggests that the underlying cause of the 1/f spectra can be elucidated by using a simplified model that does not depend on the detailed structure of the objects. This paper, treating the electroencephalogram as a macro-quantity of neuron activities, demonstrates the existence of a self-similar solution through the spatial-temporal coarse-graining of a neural network, which is a simplified model of the brain. The self-similar solution in fact leads to the derivation of a 1/f spectrum. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 72–81, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10016 [ABSTRACT FROM AUTHOR]