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Differentiable simulators enable gradient-based optimization of soft robots over material parameters, control, and morphology, but accurately modeling real systems remains challenging due to the sim-to-real gap. This issue becomes more…
The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep,…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
Understanding the visocoelastic properties of soft biological tissues is important for progress in the field of human healthcare. This study analyzes the viscoelastic properties of soft biological tissues using a fractional dynamics model.…
Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body…
Traumatic axonal injury occurs when loads experienced on the tissue-scale are transferred to the individual axons. Mechanical characterization of axon deformation especially under dynamic loads however is extremely difficult owing to their…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of…
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…
Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs which are liable to anomalous…
Hemodynamics in the aorta from computational fluid dynamics (CFD) simulations can provide a comprehensive analysis of relevant cardiovascular diseases. Coupling the three-element Windkessel model with the patient-specific CFD simulation to…
The goal of this paper is to establish a general framework for dynamic behaviors of coupled fractional-order stochastic dynamic systems of particles by using star-coupled models. In particular, the general mechanics on the dynamic behaviors…
We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based…
Memristive associative learning has gained significant attention for its ability to mimic fundamental biological learning mechanisms while maintaining system simplicity. In this work, we introduce a high-order memristive associative…
Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…
Constraining the parameters of physical models with $>5-10$ parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
With the rising complexity of numerous novel applications that serve our modern society comes the strong need to design efficient computing platforms. Designing efficient hardware is, however, a complex multi-objective problem that deals…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…