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Reasoning with fuzzy sets can be achieved through measures such as similarity and distance. However, these measures can often give misleading results when considered independently, for example giving the same value for two different pairs…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
In this paper we propose an extension of the Cahn method to binary mixtures and study the problem of wetting near a two-phase critical point without any assumption on the form of intermolecular potentials. A comparison between Cahn's method…
The concept of chemical bonding can ultimately be seen as a rationalization of the recurring structural patterns observed in molecules and solids. Chemical intuition is nothing but the ability to recognize and predict such patterns, and how…
The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary. Direct generalization of MBO-type methods…
We present a numerical stability analysis of the immersed boundary(IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier…
This paper treats the problem of the merging of formations, where the underlying model of a formation is graphical. We first analyze the rigidity and persistence of meta-formations, which are formations obtained by connecting several rigid…
In this work, we present a novel type of molecular dynamics simulation that aims at discovering, in a blind way, new metastable states. Using only data coming from an initial unbiased simulation, and with the help of an appropriately…
In this work, the nonlinear dynamics of a fully three-dimensional multicomponent vesicle in shear flow are explored. Using a volume- and area-conserving projection method coupled to a gradient-augmented level set and surface phase method,…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
We apply the proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analyis mainly focuses on the question…
The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only)…
Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most…
Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine…
Environmental perception with the multi-modal fusion of radar and camera is crucial in autonomous driving to increase accuracy, completeness, and robustness. This paper focuses on utilizing millimeter-wave (MMW) radar and camera sensor…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
The monogamous nature of entanglement has been illustrated by the derivation of entanglement sharing inequalities - bounds on the amount of entanglement that can be shared amongst the various parts of a multipartite system. Motivated by…