Results 31 to 40 of about 1,675 (248)

Non-autonomous scalar discontinuous ordinary differential equation

Journal of Mathematical Analysis and Applications, 2005
A scalar differential equation is considered. The right-hand side of the equation represents a sum of a discontinuous function \(f(x)\) and a function \(h(t)\). The functions \(f\) and \(h\) are nonnegative, \(f\) is finite a.e. and \(1/f\) and \(h\) are Lebesgue integrable. The existence of a local absolutely continuous solution is proved. The authors
Pikuta, Piotr, Rzymowski, Witold
openaire   +2 more sources

Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations

Моделирование и анализ информационных систем, 2015
The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied.
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov   +2 more
doaj   +1 more source

Solution Continuation on a Discontinuity Set

Моделирование и анализ информационных систем, 2016
The movement of an object characterized by ordinary differential equations (ODE) with discontinuous right-hand sides along the surface of a gap is called a sliding mode. It is required to find the connection of the right-slip characteristics of the system (
A. M. Tsirlin
doaj   +1 more source

A Workflow to Accelerate Microstructure‐Sensitive Fatigue Life Predictions

Advanced Engineering Materials, EarlyView.
This study introduces a workflow to accelerate predictions of microstructure‐sensitive fatigue life. Results from frameworks with varying levels of simplification are benchmarked against published reference results. The analysis reveals a trade‐off between accuracy and model complexity, offering researchers a practical guide for selecting the optimal ...
Luca Loiodice, Krzysztof S. Stopka, Michael D. Sangid   +2 more
wiley   +1 more source

A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations

Journal of Applied Mathematics, 2013
Nonsmooth mechanical systems, which are mechanical systems involving dry friction and rigid unilateral contact, are usually described as differential inclusions (DIs), that is, differential equations involving discontinuities.
Xiaogang Xiong, Ryo Kikuuwe, Motoji Yamamoto   +2 more
doaj   +1 more source

Non-Classical Relaxation Oscillations in Neurodynamics

Моделирование и анализ информационных систем, 2014
A modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one.
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov   +2 more
doaj   +1 more source

ON THE CONVERGENCE OF MULTISTEP METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH DISCONTINUITIES

Demonstratio Mathematica, 1983
This paper is concerned with the solution of an initial value problem on some interval, where the solution satisfies the initial condition and the differential equation almost everywhere on that interval, by quasilinear multistep methods. (Such methods include the family of linear multistep methods as a special case.) Sufficient conditions for the ...
openaire   +2 more sources

Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading

Advanced Engineering Materials, EarlyView.
The approach by Amor and the approach by Miehe and Zhang for asymmetric damage behavior in the phase field method for fracture are compared regarding their fitness for microcrack‐based failure modeling. The comparison is performed for the case of a dual‐phase microstructure with a brittle and a ductile constituent.
Jakob Huber, Jan Torgersen, Ewald Werner
wiley   +1 more source

Karl Popper and the Mechanisms of Hydrogen Embrittlement

Advanced Engineering Materials, EarlyView.
Representation of the beginning of loss of ductility rather than embrittlement. Small concentrations of hydrogen in a diffusible form within iron are well‐established to harm the mechanical integrity of steels. There are theories that attempt to explain the pernicious role of hydrogen.
H. K. D. H. Bhadeshia
wiley   +1 more source

Energy-optimal electrical-stimulation pulses shaped by the Least-Action Principle. [PDF]

PLoS ONE, 2014
Electrical stimulation (ES) devices interact with excitable neural tissue toward eliciting action potentials (AP's) by specific current patterns. Low-energy ES prevents tissue damage and loss of specificity.
Nedialko I Krouchev, Simon M Danner, Alain Vinet, Frank Rattay, Mohamad Sawan   +4 more
doaj   +1 more source