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Abstract A wide range of mechanical systems have gaps, cracks, intermittent contact or other geometrical discontinuities while simultaneously experiencing Coulomb friction. A piecewise linear model with discontinuous force elements is discussed in this paper that has the capability to accurately emulate the behavior of such mechanical assemblies. The mathematical formulation of the model is standardized via a universal differential inclusion and its behavior, in different scenarios, is studied. In addition to the compatibility of the proposed model with numerous industrial systems, the model also bears significant scientific value since it can demonstrate a wide spectrum of motions, ranging from periodic to chaotic. Furthermore, it is demonstrated that this class of models can generate a rare type of motion, called weakly chaotic motion. After their detailed introduction and analysis, an efficient hybrid symbolic-numeric computational method is introduced that can accurately obtain the arbitrary response of this class of nonlinear models. The proposed method is capable of treating high dimensional systems and its proposition omits the need for utilizing model reduction techniques for a wide range of problems. In contrast to the existing literature focused on improving the computational performance when analyzing these systems when there is a periodic response, this method is able to capture transient and nonstationary dynamics and is not restricted to only steady-state periodic responses.
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A 10-year prospectus for mathematical epidemiology
There is little significant work at the intersection of mathematical and computational epidemiology and detailed psychological processes, representations, and mechanisms. This is true despite general agreement in the scientific community and the general public that human behavior in its seemingly infinite variation and heterogeneity, susceptibility to bias, context, and habit is an integral if not fundamental component of what drives the dynamics of infectious disease. The COVID-19 pandemic serves as a close and poignant reminder. We offer a 10-year prospectus of kinds that centers around an unprecedented scientific approach: the integration of detailed psychological models into rigorous mathematical and computational epidemiological frameworks in a way that pushes the boundaries of both psychological science and population models of behavior.
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- Award ID(s):
- 2200112
- PAR ID:
- 10434183
- Date Published:
- Journal Name:
- Frontiers in Psychology
- Volume:
- 14
- ISSN:
- 1664-1078
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fpsyg.2023.986289
