Applied Mathematical Modelling

Journal: Applied Mathematical Modelling

Abbreviation

Appl. math. model.

Publisher

Elsevier

ISSN

0307-904X
1872-8480

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Publications 1 - 10 of 14

Experimental and numerical optimization modelling to reduce radiofrequency-induced risks of magnetic resonance examinations on leaded implants
Córcoles, Juan; Yao, Aiping; Kuster, Niels (2021)
Applied Mathematical Modelling
Convex formulations can be used to reduce the local specific absorption rate enhancement by active medical implants of radiofrequency fields in magnetic resonance examinations while minimizing the loss of image quality. This paper demonstrates that such an optimization methodology, previously presented for strictly computational models, can be extended to a hybrid scheme using experimentally determined implant models and pre-computed fields, which can enable quasi real-time exposure optimization. The methodology determines the optimum radiofrequency field shimming condition by considering both the reduction of specific absorption rate enhancement at the tip of the implant lead, created by the interaction of the radiofrequency fields tangential to the implant trajectory with the characteristic response of the implant, and the preservation of magnetic field homogeneity, which correlates to image quality. The inputs to this workflow are those required for each implant by standard ISO 10974 evaluation, namely the validated piece-wise transfer function of the implant, the clinical routing within the patient, and the pre-computed numerical estimation of patient exposure without the implant. Optimized incident field conditions were computed to meet a range of numerical targets for specific absorption rate reduction, stepping down percentagewise from the maximum field homogeneity to the minimum exposure enhancement, for a generic implant with a flexible wire in a standard benchtop radiofrequency coil and phantom. Measurements of the corresponding specific absorption rate enhancements validated the predictions from the optimization approach within the combined confidence interval.
An improved thermal model for SPH metal cutting simulations on GPU
Afrasiabi, Mamzi; Klippel, Hagen; Röthlin, Matthias; et al. (2021)
Applied Mathematical Modelling
This paper presents the first application of a higher-order Smoothed Particle Hydrodynamics (SPH) method to the thermal modeling of metal cutting problems. With this application, the heat transfer equation in the thermo-mechanical simulation of metal cutting is solved more accurately by addressing the consistency issue of standard SPH formulations. Furthermore, through a robust and effective surface-detection algorithm, this work enables the SPH cutting models to include heat loss thermal boundary conditions for the first time. Process forces, tool temperatures, and chip geometry are numerically investigated in machining a Ti6Al4V workpiece at two different cutting speeds. Several validation tests and sensitivity analyses are performed in high resolution, thanks to the runtime acceleration of SPH by parallel computing on Graphics Processing Units (GPUs). The results show that SPH simulations with the proposed thermal modeling approach achieve more realistic serrated chips in titanium cutting problems.
Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis
Sanchez-Linares, Carlos; de la Asunción, Marc; Castro, Manuel J.; et al. (2015)
Applied Mathematical Modelling
Two layer Savage–Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the resulting solution uncertainty (UQ) is a crucial task in geophysics. We propose a novel paradigm for UQ that combines the recently developed IFCP spatial discretizations with the recently developed Multi-level Monte Carlo (MLMC) statistical sampling method and provides a fast, accurate and computationally efficient framework to compute statistical quantities of interest. Numerical experiments, including realistic simulations of the Lituya Bay mega tsunami, are presented to illustrate the robustness of the proposed UQ algorithm.
Energy harvesting through arterial wall deformation
Pfenniger, Alois; Stahel, Andreas; Koch, Volker M.; et al. (2014)
Applied Mathematical Modelling
Hidden Markov model-based smith predictor for the mitigation of the impact of communication delays in wide-area power systems
Mo, Huadong; Sansavini, Giovanni (2021)
Applied Mathematical Modelling
© 2020 Elsevier Inc. The use of an open communication network in a wide-area power system (WAPS) introduces random delays into the transmission of frequency measurements and control signals, which can deteriorate the load frequency control (LFC) performance. Current studies are focusing on developing a suitable delay margin controller to maintain the stability of the WAPS. This paper introduces a new Smith predictor (SP) with tools to accurately predict the input time delays and consequently mitigate the LFC performance loss caused by unreliable communication. The time delays are predicted via the discrete hidden Markov model (DHMM) and the exponentially weighted moving average (EWMA) model. The predicted delays are then input to the SP. The DHMM adopts two different scalar quantization methods, i.e., the uniform technique and the K-means clustering technique. It then maps the time delays on to a discrete observational space. To validate the findings for practical applications, we conduct a case study on a test platform, namely a single-area WAPS with Ethernet, which is implemented via the Truetime simulator. The results indicate that the SP is more effective in eliminating load disturbances and enhancing the robustness against time delays than existing delay-margin-based controllers. The K-means DHMM-based SP achieved better LFC performance than the one with the EWMA. The stability of the LFC system with time-varying delay is discussed using a Lyapunov–Krasovskii-based delay-dependent criterion and the small gain theorem.
Analytical solutions of curvilinear nano-beams: An application to nano-circular ring problems and gradient initial stresses
Özer, Teoman; Kröger, Martin (2026)
Applied Mathematical Modelling
This study investigates the analytical solutions for homogeneous, not only isotropic but also anisotropic curved nano-beams with axial symmetry and extends classical elasticity (CE) to gradient elasticity (GE). The stress fields are determined using a gradient Airy stress function, which corresponds to the classical Airy stress potential. For both cases, the gradient Airy stress functions are derived from analytical solutions of the governing differential equations, which are written in the form of the (classical) Airy stress function. The corresponding stress in GE is determined for different cases with displacement fields derived from CE. The analytical solutions show that GE stresses and displacement fields contain expressions with Bessel and hypergeometric functions. These solutions make it possible to compare the CE and GE stress and displacement fields. As an application, the stress and displacement fields for a nano-circular ring representing a multiply connected body are solved analytically for classical and nano-scale cases. In addition, the initial stresses are extended to GE for nested rings, where the GE initial stresses are introduced. Finally, it is shown analytically and numerically that the GE solutions for all derived stress and displacement fields, including the gradient Airy stress functions, approach CE when the gradient coefficient c converges to zero.
Theoretical Analysis of a SIRD Model with Constant Amount of Alive Population and COVID–19 Applications
Babaei, Navid Amiri; Kröger, Martin; Özer, Teoman (2024)
Applied Mathematical Modelling
This study deals with a theoretical analysis of the integrability properties and analytical solutions of an initial-value problem for a SIRD model with a constant amount of alive population (SIRD-CAAP), which is in the form of a fourth-dimensional and first-order coupled system of nonlinear ordinary differential equations, by using the partial Hamiltonian method. This research represents a COVID-19 study as a real-world problem by using the analytical results obtained in the study. The first integrals and the associated exact analytical solutions are investigated of the model with respect to algebraic relations among the model parameters. Then, for both cases, the dynamical behaviors of the model based on the analytical solutions are analyzed, and the graphical representations of the closed-form solutions are demonstrated and compared. In addition, it is shown that the SIRD-CAAP model can be decoupled based on its first integrals for all cases from the mathematical perspective point of view. Furthermore, the periodicity properties and the classification of the regimes of the solutions with respect to the model parameter constraints are discussed. Finally, the COVID-19 applications are given using the data related to the different countries.
Application of time reverse modeling on ultrasonic non-destructive testing of concrete
Saenger, Erik H.; Kocur, Georg Karl; Jud, Roman; et al. (2011)
Applied Mathematical Modelling
Modeling and simulation of air-assist atomizers with applications to food sprays
Tanner, Franz X.; Feigl, Kathleen; Kaario, Ossi; et al. (2016)
Applied Mathematical Modelling
Analytical solution to a growth problem with two moving boundaries
Braun, A; Wokaun, Alexander; Hermanns, H.-G. (2003)
Applied Mathematical Modelling

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