相关论文: A Symbolic Method for the Analysis of a Nonlinear …
We study a topological physics in a one-dimensional nonlinear system by taking an instance of a mechanical rotator model with alternating spring constants. This nonlinear model is smoothly connected to an acoustic model described by the…
The hypothesis of molecular chaos plays the central role in kinetic theory, which provides a closure leading to the Boltzmann equation for quantitative description of classic fluids. Yet how to properly extend it to active systems is still…
This study introduces a novel approach for deriving the governing equations of the musculoskeletal system in the human body. The proposed formalism offers a framework to effectively incorporate the kinematic characteristics of biological…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
Strong-motion duration and number of cycles of motion are the well-known parameters with which earthquake engineers currently use to take into account the influence of motion duration for the dynamic analysis of structures. In addition to…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
This paper investigates the nonlinear dynamics of stepping flexible frames under seismic excitation. The conventional iterative method of solution of peak quasi-dynamic displacement of stepping frames is not guaranteed to converge. To…
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this…
This paper develops a conceptual extension of the Kinetic Theory of Active Particles, building upon the framework introduced in [2]. Living systems cannot be adequately described within classical single-scale paradigms, even when refined.…
A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is…
Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used…
In this paper, a model is presented to extract statistical summaries to characterize the repetition of a cyclic body action, for instance a gym exercise, for the purpose of checking the compliance of the observed action to a template one…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
Life mechanics, an emerging field, focuses on the self-organizing forces and motions within living systems. This study introduces the novel concept of active force, generated by mind-body interactions, as an essential element in…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
Kinetic theory frameworks are widely used for modeling stochastic interacting systems, where the evolution primarily depends on binary interactions. Recently, in this framework the action of the external force field has been introduction in…
Motivated by the need to predict dangerous scenarios, this article introduces a non-linear dynamic model for motorcycles consisting of four rigid bodies. Using Jourdain's principle, the model incorporates both longitudinal and lateral…