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With the popularity of electric vehicles, the demand for lithium-ion batteries is increasing. Temperature significantly influences the performance and safety of batteries. Battery thermal management systems can effectively control the…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal}…
In this work, we develop a numerical fitting routine to extract multiple thermal parameters using frequency-domain thermoreflectance (FDTR) for materials having non-standard, non-semi-infinite geometries. The numerical fitting routine is…
On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our…
We derive and validate a partition function for low-dimensional systems interacting with a heat bath, addressing the general issue of thermodynamic modeling of nanoscale systems. In contrast to bulk systems in the canonical (NVT) ensemble…
Low lattice thermal conductivity is essential for high thermoelectric performance of a material. Lattice thermal conductivity is often computed using density functional theory (DFT), typically at a high computational cost. Training machine…
We show by microscopic calculation that thermodynamics of the multicomponent Sutherland model is equivalent to that of a free particle system with fractional exclusion statistics at all temperatures. The parameters for exclusion statistics…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
Identification of fractional order systems is considered from an algebraic point of view. It allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
Systems at finite temperature make up the vast majority of realistic physical scenarios. Indeed, although zero temperature is often accompanied by simpler mathematics, the richness in physical results is evident when one considers the…
The zero-temperature XX chain is studied with emphasis on the properties of a block of $L$ spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using…
We introduce a fractional Bessel process with constant negative drift, defined as a time-changed Bessel process via the inverse of a stable subordinator, independent of the base process. This construction yields a model capable of capturing…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are…