Physical nearest-neighbour models and non-linear time-series

1971 ◽  
Vol 8 (2) ◽  
pp. 222-232 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Equilibrium Distribution ◽  
Linear Models ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Non Linear

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

Physical nearest-neighbour models and non-linear time-series

1971 ◽  
Vol 8 (02) ◽  
pp. 222-232 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Equilibrium Distribution ◽  
Linear Models ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Non Linear

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

1972 ◽  
Vol 9 (01) ◽  
pp. 76-86
Author(s):  
M. S. Bartlett
Keyword(s):  
Time Series ◽  
Correlation Functions ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Correlations ◽  
Orthogonal Expansions ◽  
Non Linear ◽  
Time Series Approach

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed. Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Physical nearest-neighbour models and non-linear time-series. II Further discussion of approximate solutions and exact equations

1972 ◽  
Vol 9 (1) ◽  
pp. 76-86 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Time Series ◽  
Correlation Functions ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Correlations ◽  
Orthogonal Expansions ◽  
Non Linear ◽  
Time Series Approach

The approximate two- and three-dimensional solutions for spatial correlations, using the non-linear time-series approach for nearest-neighbour systems developed in my previous paper, are further discussed.Orthogonal expansions for the correlation functions are also developed which determine with this approach, though so far only in principle, the exact solutions.

Nearest-neighbour systems: a lemma with application to Bartlett's global solutions

1972 ◽  
Vol 9 (02) ◽  
pp. 418-421 ◽  
Author(s):  
J. E. Besag
Keyword(s):  
Markov Model ◽  
Equilibrium Distribution ◽  
Global Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice

Bartlett has proposed two alternative forms of spatial-temporal Markov model, each leading to the standard spatial equilibrium distribution for nearest-neighbour systems on a multi-dimensional lattice. The validity of one of these forms is discussed with the aid of a lemma.

Nearest-neighbour systems: a lemma with application to Bartlett's global solutions

1972 ◽  
Vol 9 (2) ◽  
pp. 418-421 ◽  
Author(s):  
J. E. Besag
Keyword(s):  
Markov Model ◽  
Equilibrium Distribution ◽  
Global Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice

Bartlett has proposed two alternative forms of spatial-temporal Markov model, each leading to the standard spatial equilibrium distribution for nearest-neighbour systems on a multi-dimensional lattice. The validity of one of these forms is discussed with the aid of a lemma.

scholarly journals Autoregressive Models of the Random fields—A Survey

2020 ◽  
pp. 1-9
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Estimation Methods ◽  
Suitable Model ◽  
Main Mode ◽  
One Dimensional ◽  
Non Linear ◽  
The Status ◽  
Ar Models ◽  
Shed Light

Autoregressive (AR) random fields are widely use to describe changes in the status of real-physical objects and implemented for analyzing linear & non-linear models. AR models are Markov processes with a higher order dependence for one-dimensional time series. Actually, various estimation methods were used in order to evaluate the autoregression parameters. Although in many applications background knowledge can often shed light on the search for a suitable model, but other applications lack this knowledge and often require the type of trial errors to choose a model. This article presents a brief survey of the literatures related to the linear and non-linear autoregression models, including several extensions of the main mode models and the models developed. The use of autoregression to describe such system requires that they be of sufficiently high orders which leads to increase the computational costs.

A Non-Linear Numerical Method for the Simulation of Parametric Roll Resonance in Regular Waves

2008 ◽  
Author(s):  
T. M. Ahmed ◽  
E. J. Ballard ◽  
D. A. Hudson ◽  
P. Temarel
Keyword(s):  
Numerical Method ◽  
Potential Flow ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Three Dimensional ◽  
Regular Waves ◽  
Time Step ◽  
Parametric Roll ◽  
Non Linear ◽  
Parametric Roll Resonance

In this paper, a non-linear time-domain method is used for the prediction of parametric roll resonance in regular waves, assuming the ship to be a system with three degrees of freedom in heave, pitch and roll. Coupled heave and pitch motions are obtained using a three-dimensional frequency-domain potential flow method which also provides the requisite hydrodynamic data of the ship in roll i.e. the potential flow based added inertia and damping. Periodic changes in the underwater hull geometry due to heave, pitch and the wave profile are calculated as a function of the instantaneous breadth. This is carried out using a two-dimensional approach i.e. for sections along the ship and at each time step. This formulation leads to a mathematical model that represents the roll equation of motion with third order non-linearities in the parametric excitation terms. Non-linearities in the roll damping and restoring terms are also accounted for. This method has been applied to two different hull forms, a post-Panamax C11 class containership and a transom stern Trawler, both travelling in regular waves. Special attention is focused on the influence of different operational aspects on parametric roll. Obtained results demonstrate that this numerical method succeeds in producing results similar to those available in the literature, both numerical and experimental.

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