Application Of Nonlinear Analysis Research Articles

Chaos, Continuous EEG, and Cognitive Mechanisms: a Future for Clinical Neurophysiology

ABSTRACT.With the advent of the modern theory of nonlinear dynamic systems (chaos theory), new concepts and analytical tools have become available to extract more information from complex signals such as the EEG. This paper gives a brief introduction to the main ideas and basic principles of chaos theory. Additionally, application of nonlinear analysis to EEG is illustrated with examples from twofields: 1) prediction and detection of epileptic seizures; 2) characterization of functional interactions between brain regions in normal and disturbed cognition.While the prediction of seizures with nonlinear EEG analysis is currently the cause of much excitement, there are still many controversies. The more modest goal of detecting seizures in patients in neonatal and adult intensive care wards, however, has been shown to be much closer to practical clinical implementation. Nonlinear analysis of functional interactions between brain regions with the synchronization likelihood shows how optimal information processing may depend upon a delicate balance between coupling and uncoupling. Finally it is suggested how the notion of synchronization between dynamic systems can be used toformulate a general concept (“fragile binding”) of normal and abnormal brain function.

Limit-State Analysis and Design of Cable-Tensioned Structures

This paper deals with application of nonlinear analysis to study the system's limit state behaviour of cable-tensioned steel structures. The cable tendon is modelled as an equivalent truss element with initial pretensioned force applied either as self-equilibrating axial load or as an equivalent thermal load. The modulus of elasticity of the cable material can be modified to account for the constructional stretch and sagging effects in the cables. Pin-jointed space truss systems are modelled using a plastic-hinge nonlinear formulation, which implicitly satisfies the design specifications for ultimate strength of axially loaded members. Rigid space frame systems are modelled using an elasto-plastic nonlinear frame analysis program. The effectiveness of providing pretensioned cables in improving the limit state behaviour of pin-and rigid-connected space frames is demonstrated through several examples.

Application of Non-linear Analysis to Intensity Oscillations of the Chromospheric Bright Points

We have applied several nonlinear techniques to the intensity oscillations of the chromospheric bright points observed at the Vacuum Tower Telescope (VTT) of the Sacramento Peak Observatory. A 35-min time sequence obtained in the Ca ii H line over a quiet region at the center of the solar disk under high spatial, spectral, and temporal resolution has been used. A relatively new approach is used to detect the hidden periodicity and to extract the associated periodic component(s) from an apparently irregular time series. The unique feature of this approach is that the constituent component(s) can be non-sinusoidal in nature. The periodicity analysis shows that time series of intensity oscillations of most of the bright points can be composed of two non-sinusoidal periodic components with periodicity varying between 2.4 min and 5.8 min. With the help of a multivariate embedding technique, globally significant spatial nonlinear correlation is found. The identification of the nonlinear interaction between bright points is performed by using the methods of dynamical phase synchronization and the similarity index. The analysis indicates that bright points are interconnected in the sense that some bright points are more active and can influence the other relatively passive bright points.

The use of non-linear analysis for differentiating the biomagnetic activity in ovarian lesions

In this study we investigated the biomagnetic activity measured with the superconducting quantum interference device (SQUID) in benign and malignant ovarian lesions using non-linear analysis. We used a single channel biomagnetometer SQUID in order to measure the magnetic field emitted from benign and malignant ovarian lesions. We can differentiate such biomagnetic activities using non-linear analysis. Using the application of non-linear analysis in the ovarian lesions together with the use of dimensional calculations we have observed a clear saturation value for the dimension of malignant ovarian lesions and non-saturation for benign ovarian lesions. The biomagnetic measurements with the SQUID and the application of non-linear analysis in benign and malignant ovarian lesions, is a promising procedure in assessing and differentiating ovarian tumours.

The chaos theory for differentiating fetal biomagnetic brain activity in normal and pre-eclamptic pregnancies

In this study we investigated the fetalbiomagnetic brainactivity obtained in normal and pre-eclamptic pregnancies using a non-linear analysis. Measurements were performed using a single channel biomagnetometer superconducting quantum interference device (SQUID) in an electrically shielded room of low magnetic noise. Using the application of non-linear analysis and dimensionality calculations we have observeda clear saturation for the dimension of the fetal biomagnetic brain activity from pre-eclamptic pregnancies and no saturationfor fetalbrain activity in normal pregnancies. Thus, the biomagnetic measurements with the SQUID and the application of non-linear analysis, is a promising procedure in assessing and differentiating fetal biomagnetic brain activity in normal and pre-eclamptic pregnancies.

Stability of ψ‐additive mappings: applications to nonlinear analysis

The Hyers‐Ulam stability of mappings is in development and several authors have remarked interesting applications of this theory to various mathematical problems. In this paper some applications in nonlinear analysis are presented, especially in fixed point theory. These kinds of applications seem not to have ever been remarked before by other authors.

Research on General Instability of Cylindrical Shells Reinforced by Ring Stiffeners under Uniform Pressure (2nd Report)

General instability is one of the most important subjects of cylindrical shells reinforced by ring stiffeners under uniform pressure. Recently, based on the application of nonlinear analysis using the finite element method, and more reliable collapse tests using models manufactured with high fabrication technique and of uniform material characteristics, the study to review the design procedure, which were based on the experimental works of collapse tests using a number of scale models, has been carried out.Since pressure hulls of deep diving submersibles are usually welded structures, the welding distortion is inevitable, which might have a large influence on collapse strength. The authors have presented the elasto-plastic analysis using three dimensional finite element in the first report to estimate collapse pressure reduction of general instability by initial imperfection.To investigate the infuence of initial imperfection of complex mode and that on the overall structure, however, more effective mothod is required instead of the three dimensional analysis.In the present paper, the authors propose the elasto-plastic analysis using the quasiaxisymmetric finite element, which represents the deformation of stiffened shells by Fourier series. The analytical results compared with those obtained from the current full three-dimensional analysis show a good agreement. Futhermore, the authors investigate the influence of initial imperfection on the collapse strength of scale models, which are machined or welded, by comparing the results of the theoretical analysis and those of experimental test.

Research on General Instability of Cylindrical Shells Reinforced by Ring Stiffners under Uniform Pressure (1st Report)

General instability is one of the most important subjects of cylindrical shells reinforced by ring stiffeners under uniform pressure. Recently, based on the application of nonlinear analysis using the finite element method, and more reliable collapse tests using models manufactured with high fabrication technique and of uniform material characteristics, the study to review the design procedure, which were based on the experimental works of collapse tests using a number of scale models, has been carried out.Since pressure hulls of deep diving submersibles are usually welded structures, the welding distortion is inevitable, which might have a large influence on collapse strength. The authors have presented the elasto-plastic analysis using three dimensional finite element in the first report to estimate collapse pressure reduction of general instability by initial imperfection.To investigate the infuence of initial imperfection of complex mode and that on the overall structure, however, more effective mothod is required instead of the three dimensional analysis.In the present paper, the authors propose the elasto-plastic analysis using the quasiaxisymmetric finite element, which represents the deformation of stiffened shells by Fourier series. The analytical results compared with those obtained from the current full three-dimensional analysis show a good agreement. Futhermore, the authors investigate the influence of initial imperfection on the collapse strength of scale models, which are machined or welded, by comparing the results of the theoretical analysis and those of experimental test.