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Delay Terms (delay + term)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Identification of chaos in a regenerative cutting process by the 0-1 test

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Grzegorz Litak
We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Stability analysis for real-time pseudodynamic and hybrid pseudodynamic testing with multiple sources of delay

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2008
Oya Mercan
Abstract Real-time pseudodynamic (PSD) and hybrid PSD test methods are experimental techniques to obtain the response of structures, where restoring force feedback is used by an integration algorithm to generate command displacements. Time delays in the restoring force feedback from the physical test structure and/or the analytical substructure cause inaccuracies and can potentially destabilize the system. In this paper a method for investigating the stability of structural systems involved in real-time PSD and hybrid PSD tests with multiple sources of delay is presented. The method involves the use of the pseudodelay technique to perform an exact mapping of fixed delay terms to determine the stability boundary. The approach described here is intended to be a practical one that enables the requirements for a real-time testing system to be established in terms of system parameters when multiple sources of delay exist. Several real-time testing scenarios with delay that include single degree of freedom (SDOF) and multi-degree of freedom (MDOF) real-time PSD/hybrid PSD tests are analyzed to illustrate the method. From the stability analysis of the real-time hybrid testing of an SDOF test structure, delay-independent stability with respect to either experimental or analytical substructure delay is shown to exist. The conditions that the structural properties must satisfy in order for delay-independent stability to exist are derived. Real-time hybrid PSD testing of an MDOF structure equipped with a passive damper is also investigated, where observations from six different cases related to the stability plane behavior are summarized. Throughout this study, root locus plots are used to provide insight and explanation of the behavior of the stability boundaries. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On a class of PDEs with nonlinear distributed in space and time state-dependent delay terms

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2008
Alexander V. Rezounenko
Abstract A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss advantages of this class. Local and long-time asymptotic properties, including the existence of global attractor and a principle of linearized stability, are studied. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Modelling the progress of light leaf spot (Pyrenopeziza brassicae) on winter oilseed rape (Brassica napus) in relation to leaf wetness and temperature

PLANT PATHOLOGY, Issue 2 2001
K. Papastamati
A compartmental model was developed to describe the progress with time of light leaf spot (Pyrenopeziza brassicae) on leaves of winter oilseed rape (Brassica napus) during the autumn in the UK. Differential equations described the transition between the four compartments: healthy susceptible leaves, infected symptomless leaves, sporulating symptomless leaves and leaves with necrotic light leaf spot lesions, respectively. The model was fitted to data on the progress of light leaf spot on winter oilseed rape at a single site during the autumn of the 1990,1991 season. Model parameters were used to describe rates of leaf appearance, leaf death, infection by airborne ascospores (primary inoculum) and infection by splash-dispersed conidiospores (secondary inoculum). Infection was dependent on sufficient leaf wetness duration. The model also included delay terms for the latent period between infection and sporulation and the incubation period between infection and the appearance of necrotic light leaf spot lesions. This modified SEIR model formulation gave a reasonable fit to the experimental data. Sensitivity analysis showed that varying the parameter accounting for the rate of infection by ascospores affected the magnitude of the curves after the start of the epidemic, whilst including a parameter for conidiospore infection improved the fit to the data. Use of ascospore counts from different sites and different years showed variation in spore release patterns sufficient to affect model predictions. [source]