Nonlinear reaction‐diffusion models of self‐organization and deterministic chaos: Theory and possible applications to description of electrical cardiac activity and cardiovascular circulation

Kardashov, V.; Einav, Sh.; Okrent, Ya. N.; Kardashov, T.

doi:10.1155/ddns/2006/98959

Cited by 11 publications

(11 citation statements)

References 17 publications

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“…Rosenau-Hyman (RH) equation (1) was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops [1], being also proposed in the analysis of patterns on liquid surfaces [3]. Equations with compacton solutions have also found applications such as the lubrication approximation for thin viscous films [4], semiclassical models for Bose-Einstein condensates [5], long nonlinear surface waves in a rotating ocean when the high-frequency dispersion is null [6], the pulse propagation in ventricle-aorta system [7], dispersive models for magma dynamics [8], or, even, particle wavefunctions in nonlinear quantum mechanics [9]. RH equation is also the continuous limit of the discrete equations of a nonlinear lattice [1].…”

Section: Introductionmentioning

confidence: 99%

Self-similar radiation from numerical Rosenau–Hyman compactons

Rus

Villatoro

2007

Journal of Computational Physics

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The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the RosenauHyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.

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Section: Introductionmentioning

confidence: 99%

Self-similar radiation from numerical Rosenau–Hyman compactons

Rus

Villatoro

2007

Journal of Computational Physics

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“…Often, in RD systems, diffusion is guided by a unique diffusion coefficient for each element in the system. However, the diffusion coefficient can be replaced by diffusion functions as done in [KEOK06]. This is usually done to induce movement in a specific direction or set of directions.…”

Section: Modelmentioning

confidence: 99%

Synthesis of Human Skin Pigmentation Disorders

Barros

Walter

2016

Computer Graphics Forum

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Changes in the human pigmentary system can lead to imbalances in the distribution of melanin in the skin resulting in artefacts known as pigmented lesions. Our work takes as departing point biological data regarding human skin, the pigmentary system and the melanocytes life cycle and presents a reaction–diffusion model for the simulation of the shape features of human‐pigmented lesions. The simulation of such disorders has many applications in dermatology, for instance, to assist dermatologists in diagnosis and training related to pigmentation disorders. Our study focuses, however, on applications related to computer graphics. Thus, we also present a method to seamless blend the results of our simulation model in images of healthy human skin. In this context, our model contributes to the generation of more realistic skin textures and therefore more realistic human models. In order to assess the quality of our results, we measured and compared the characteristics of the shape of real and synthesized pigmented lesions. We show that synthesized and real lesions have no statistically significant differences in their shape features. Visually, our results also compare favourably with images of real lesions, being virtually indistinguishable from real images.

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“…Authors do not propose to replace current approaches to theory generation by one based on chaos theory, rather authors suggest extending current theory by introducing a chaos layer. Kardashov et al 104 proposed a unit analytical approach that could be associated with real ECG and pressure pulses signal processing. Results shows that analytical dynamic models coupled with the available signal processing methods could be used for describing the self-organization and chaos degree in the heartbeats propagation and pressure pulses in ventricular at ejection phase.…”

Section: Reasoning Classification and Learningmentioning

confidence: 99%

Artificial Intelligence in Civil Engineering

Chen

Zheng

2012

Mathematical Problems in Engineering

155

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Artificial intelligence is a branch of computer science, involved in the research, design, and application of intelligent computer. Traditional methods for modeling and optimizing complex structure systems require huge amounts of computing resources, and artificial-intelligence-based solutions can often provide valuable alternatives for efficiently solving problems in the civil engineering. This paper summarizes recently developed methods and theories in the developing direction for applications of artificial intelligence in civil engineering, including evolutionary computation, neural networks, fuzzy systems, expert system, reasoning, classification, and learning, as well as others like chaos theory, cuckoo search, firefly algorithm, knowledge-based engineering, and simulated annealing. The main research trends are also pointed out in the end. The paper provides an overview of the advances of artificial intelligence applied in civil engineering. of different forms in civil engineering. Bassuoni and Nehdi 6 developed neuro-fuzzy based prediction of the durability of self-consolidating concrete to various sodium sulfate exposure regimes. Prasad et al. 7 presented an artificial neural network ANN to predict a 28day compressive strength of a normal and high strength self-compacting concrete SCC and high performance concrete HPC with high volume fly ash. Lee et al. 8 used an artificial intelligence technique of back-propagation neural networks to assess the slope failure. The numerical results demonstrate the effectiveness of artificial neural networks in the evaluation of slope failure potential. Shaheen et al. 9 presented a proposed methodology for extracting the information from experts to develop the fuzzy expert system rules, and a tunneling case study was used to illustrate the features of the integrated system. Das et al. 10 described two artificial intelligence techniques for prediction of maximum dry density MDD and unconfined compressive strength UCS of cement stabilized soil. Forcael et al. 11 presented the results of a study that incorporates computer simulations in teaching linear scheduling concepts and techniques, in a civil engineering course "Construction Planning and Scheduling." To assess the effect of incorporating computer simulation in teaching linear scheduling, the students' evaluations and answers to the questionnaire were statistically compared. Krcaronemen and Kouba 12 proposed a methodology for designing ontologybacked software applications that make the ontology possible to evolve while being exploited by one or more applications at the same time. The methodology relies on a contract between the ontology and the application that is formally expressed in terms of integrity constraints. In addition, a reference Java implementation of the methodology and the proof-of-concept application in the civil engineering domain was introduced.Due to a lot of uncertain factors, complicated influence factors in civil engineering, each project has its individual character and generality; function of expe...

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Nonlinear reaction‐diffusion models of self‐organization and deterministic chaos: Theory and possible applications to description of electrical cardiac activity and cardiovascular circulation

Cited by 11 publications

References 17 publications

Self-similar radiation from numerical Rosenau–Hyman compactons

Self-similar radiation from numerical Rosenau–Hyman compactons

Synthesis of Human Skin Pigmentation Disorders

Artificial Intelligence in Civil Engineering

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