Journal of Mathematics in Industry

Abstract In this paper, we explore the effectiveness of strategies for mitigating urban warming from a numerical simulation standpoint. To achieve this, a reinterpretation of porosity on an urban context allows us to identify the urban surface covered by streets, and the urban surface covered by buildings as the fluid and solid phases of an urban-porous media, respectively. Using a Gaussian distribution we define the urban porosity at all points within an urban zone. Once the urban porosity is defined, a Darcy-Brinkman-Forchheimer type model is coupled with a thermal exchange model to obtain the wind field, and the air temperature. The convective nature of the model, and the porosity gradients lead us to use stabilized finite element methods in order to avoid the appearance of spurious oscillations in numerical solutions: we use a pressure stabilizer for the Darcy-Brinkman-Forchheimer model and a least-squares stabilizer for the thermal exchange model. Numerical experiments were conducted on a domain modeled after the Metropolitan Zone of Guadalajara City, Mexico, to evaluate strategies such as white roofs, concrete-paved streets instead of asphalt, and large urban parks. The results reveal significant differences in urban temperatures, which in turn helps to alleviate thermal stress for city inhabitants.

Néstor García-Chan

Juan A. Licea-Salazar

Luis G. Gutierrez-Ibarra

Numerical evaluation of urban-warming mitigation strategies in an urban-porous media. An application of stabilized finite elements methods

城市多孔介质中城市增温缓解策略的数值评估。稳定有限元方法的应用

Abstract Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional (2D) freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging optics and optimize them to obtain a system that produces minimal aberrations. This is done by minimizing a merit function that quantifies aberrations and is dependent on the energy distributions at the source and target of an optical system, which are input parameters essential for inverse freeform design. The proposed method is tested for two configurations: a single-reflector system and a double-reflector system. Classical designs consisting of aspheric elements are well-known for their ability to minimize aberrations. We compare the performance of our freeform optical elements with classical designs. The optimized freeform designs outperform the classical designs in both configurations.

Sanjana Verma

Martijn J. H. Anthonissen

Jan H. M. ten Thije Boonkkamp

Wilbert L. IJzerman

Design of two-dimensional reflective imaging systems: an approach based on inverse methods

二维反射成像系统设计：基于逆方法的途径

Abstract Introduction It is well known that social contact patterns differ from country to country. This variation coincides with significant socioeconomic heterogeneity that complicates the design of effective nonpharmaceutical interventions. This study examined how socioeconomic heterogeneity in selected African countries might be factored in to explain better patterns of social contact mix between countries. Methods We used a standardized contact matrix for 32 African countries, estimated in (Prem et al. in PLoS Comput Biol 17(7):e1009098, 2021). We scaled the matrices using an epidemic model from (Röst et al. in Viruses 12(7):708, 2020). We also analyzed aggregated data from the World Bank country website. The data includes 28 variables; social, economic, environmental, institutional, governance, health and well-being, education, gender inequality, and other development-related indicators that describe countries. Principal component analysis was used to visualize socioeconomic similarities between countries and identify the indicators for maximum variation. The $(2D)^{2} PCA$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>P</mml:mi> <mml:mi>C</mml:mi> <mml:mi>A</mml:mi> </mml:math> approach was used to reduce the dimension of synthetic contact matrices for each country to avoid the dimensionality curse. Then, hierarchical aggregate clustering was used to identify groups of countries with similar social patterns, taking into account the country’s socioeconomic performance. Results Our model yielded four meaningful clusters, each with a few distinguishing features. Social contacts varied between groups, but were generally similar within each set. The socioeconomic performance of the country influenced the clusters. Conclusions Our results suggest that integrating socioeconomic factors into social contacts can better explain infectious disease transmission dynamics and that similar interventions can be implemented in countries within the cluster

Evans Kiptoo Korir

Zsolt Vizi

Clusters of African countries based on the social contacts and associated socioeconomic indicators relevant to the spread of the epidemic

基于社会接触及相关社会经济指标的非洲国家集群与疫情传播

Abstract A stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.

Hidekazu Yoshioka

Yuta Yaegashi

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

随机脉冲控制模型中不完全干预的数学与数值分析

The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

Jonas Bundschuh

Laura A. M. D’Angelo

Herbert De Gersem

Quasi-3-D spectral wavelet method for a thermal quench simulation

准三维谱小波方法用于热淬火模拟

Abstract Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from eight subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, was carried out. In particular, a system of ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations was proposed and used to extract more informative inferences from the patients’ data. For this work, Matlab and R programs were used to find the most appropriate values of the parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) for each patient. Fitting was carried out by Particle Swarm Optimization to minimize the ordinary least squares error between the observed CGM data and the data from the ODE model. Goodness of fit tests were made in order to assess which probability distribution was best suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.

Giulia Elena Aliffi

Giovanni Nastasi

Vittorio Romano

Dario Pitocco

Alessandro Rizzi

Elvin J. Moore

Andrea De Gaetano

A system of ODEs for representing trends of CGM signals

表示CGM信号趋势的ODE系统

Abstract While interactive simulations have been mostly limited to Computer Graphics applications, new generations of Graphics Processing Units (GPUs) allow the realization of industrial-grade interactive 3D physics simulations. By combining an immersed boundary method with efficient GPU-based MINRES and CG solvers using a GPU-based geometric multigrid preconditioner, we demonstrate a fast industrial 3D computational mechanics solver. The various implementation aspects - specifically how they differ from similar concepts used in the Computer Graphics community - are discussed in detail. The proposed concept opens up new classes of industrial simulation applications allowing a democratization beyond today’s expert users, from designer centric simulation to operational and service decisions based on 3D simulations. To support this, we provide various benchmark cases including a real-world study of a simulation-based service decision for a damaged gear-box mount.

Abbreviation	J.Math.Industry
Journal Impact	1.19
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q3)

ISSN	2190-5983
h-index	17

Publication Information	Publisher: Springer Verlag，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2011，Proportion of original research papers: 100.00%，Self Citation Rate:8.30%， Gold OA Rate: 100.00%
Journal Fees	$1490Details
Average review cycle	网友分享经验：13 Weeks

Journal of Mathematics in Industry

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Numerical evaluation of urban-warming mitigation strategies in an urban-porous media. An application of stabilized finite elements methods

Design of two-dimensional reflective imaging systems: an approach based on inverse methods

Clusters of African countries based on the social contacts and associated socioeconomic indicators relevant to the spread of the epidemic

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Quasi-3-D spectral wavelet method for a thermal quench simulation

Numerical evaluation of urban-warming mitigation strategies in an urban-porous media. An application of stabilized finite elements methods

Design of two-dimensional reflective imaging systems: an approach based on inverse methods

Clusters of African countries based on the social contacts and associated socioeconomic indicators relevant to the spread of the epidemic

A system of ODEs for representing trends of CGM signals

Fast 3D solvers for interactive computational mechanics