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Packing problems with applications in additive manufacturing 在增材制造中的应用包装问题
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-08-12 DOI: 10.21136/AM.2026.0012-26
Andreas Fischer, Tetyana Romanova, Oleksandr Pankratov, Christian Berger, Uwe Scheithauer
{"title":"Packing problems with applications in additive manufacturing","authors":"Andreas Fischer,&nbsp;Tetyana Romanova,&nbsp;Oleksandr Pankratov,&nbsp;Christian Berger,&nbsp;Uwe Scheithauer","doi":"10.21136/AM.2026.0012-26","DOIUrl":"10.21136/AM.2026.0012-26","url":null,"abstract":"<div><p>Additive manufacturing is a very complex process. Hence, optimization models and methods play a central role for improving related technologies to save resources like material, time, and energy, and to protect the environment. We first provide existing principles for modeling corresponding tasks as problems of packing optimization, particularly the phi-function technique as a basic analytical tool. Due to the large number of items to pack, the mutual influence of items, and the resulting nonconvexity of the packing optimization problem, a practical solution may become extremely difficult. Therefore, in a generalized way, we present model-based algorithmic ideas to tackle such optimization problems. This includes a decomposition principle and heuristics for obtaining good feasible solutions. We discuss three main cases of packing optimization problems with significant relevance to additive manufacturing, where the general methodology is applied. In the first case we are concerned with the generation of void structures in components that should be printed. Those structures can save material, time, and energy. The second case deals with optimal placements of components in the build space of a 3D printer. In this way, production time can be saved. Finally, we study the problem of simulating the filling of a given 3D volume with particles of possibly different shapes. This may be employed for decreasing the porosity in printed parts, as well as for saving material.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 4","pages":"477 - 510"},"PeriodicalIF":0.6,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2026.0012-26.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A generalized optimal fourth-order iteration scheme for nonlinear systems 非线性系统的广义最优四阶迭代格式
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-08-12 DOI: 10.21136/AM.2026.0106-26
Moin-ud-Din Junjua, Rashid Ali, Khadijah M. Abualnaja
{"title":"A generalized optimal fourth-order iteration scheme for nonlinear systems","authors":"Moin-ud-Din Junjua,&nbsp;Rashid Ali,&nbsp;Khadijah M. Abualnaja","doi":"10.21136/AM.2026.0106-26","DOIUrl":"10.21136/AM.2026.0106-26","url":null,"abstract":"<div><p>We generalize an optimal fourth-order scalar method to solve systems of nonlinear equations. The proposed generalized scheme is optimal for solving systems of nonlinear equations. The fourth-order convergence of the proposed method is proved. The computational efficiency of the proposed iteration scheme is analysed and compared with several methods for nonlinear systems. To evaluate the numerical performance of the presented scheme, extensive numerical experiments are conducted and the results are compared with some existing fourth-order methods from the literature. The stability of the scheme is rigorously analysed through convergence planes, confirming its advantage over other fourth-order iteration techniques for systems of nonlinear equations.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 5","pages":"693 - 709"},"PeriodicalIF":0.6,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149219435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical modelling of plasma-assisted energy and fuel enhancement 等离子体辅助能量和燃料增强的数学建模
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-07-10 DOI: 10.21136/AM.2026.0016-26
Abhisek Kumar Singh, Punit Kumar
{"title":"Mathematical modelling of plasma-assisted energy and fuel enhancement","authors":"Abhisek Kumar Singh,&nbsp;Punit Kumar","doi":"10.21136/AM.2026.0016-26","DOIUrl":"10.21136/AM.2026.0016-26","url":null,"abstract":"<div><p>Plasma assisted energy and fuel enhancement has emerged as a promising interdisciplinary domain combining plasma physics, nonlinear dynamics, chemical kinetics, and applied mathematics to improve fuel efficiency, combustion stability, and emission reduction. Nonthermal plasmas provide highly energetic electrons capable of activating molecular species without significantly increasing bulk gas temperature, thereby enabling novel reaction pathways inaccessible through conventional thermal processes. This paper presents a comprehensive mathematical framework for modelling plasma-assisted fuel enhancement, emphasizing the coupling between plasma discharge physics, reactive species generation, transport phenomena, and fuel oxidizer chemistry. Governing equations based on fluid, kinetic, and quantum-informed approaches are formulated to describe electron energy distribution, ionization dynamics, radical formation, and plasma-fuel interactions. Reduced-order models, stability analysis, and scaling laws relevant to plasma-assisted combustion and fuel miscibility are discussed. The work highlights how mathematical modelling supports optimization of plasma parameters, predicts system performance, and enables translation of plasma-based fuel technologies toward sustainable energy applications.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 4","pages":"539 - 555"},"PeriodicalIF":0.6,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-scale mathematical models for plasma-liquid interactions 等离子体-液体相互作用的多尺度数学模型
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-07-08 DOI: 10.21136/AM.2026.0017-26
Abhisek Kumar Singh, Punit Kumar
{"title":"Multi-scale mathematical models for plasma-liquid interactions","authors":"Abhisek Kumar Singh,&nbsp;Punit Kumar","doi":"10.21136/AM.2026.0017-26","DOIUrl":"10.21136/AM.2026.0017-26","url":null,"abstract":"<div><p>Plasma-liquid interactions (PLIs) occur in a wide range of natural and engineered systems including biomedical sterilization, wastewater treatment, materials synthesis, and electrochemical processing. These interactions span multiple spatial and temporal scales, coupling complex plasma dynamics with liquid phase transport and chemistry. Developing tractable mathematical models that capture the essential physics across scales is crucial to enable predictive simulations, optimize applications, and guide experimental design. This paper reviews the fundamental mathematical frameworks used in modelling PLI systems, with emphasis on multi-scale coupling strategies. We discuss kinetic and fluid descriptions of plasma, continuum models for liquids, interface conditions, and numerical methods for tackling stiff, heterogeneous problems. We synthesize approaches including asymptotic analysis, continuum kinetic hybrid methods, reduced models, and scale separation techniques. Representative case studies illustrate the interplay between disparate scales and highlight challenges such as non-equilibrium effects, interface charge dynamics, and strongly coupled reaction transport phenomena. The review concludes with a discussion of open mathematical problems, emerging multi-physics challenges, and potential directions for future research, particularly in model reduction, rigorous analysis of interface dynamics, and uncertainty quantification.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 4","pages":"557 - 573"},"PeriodicalIF":0.6,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148965368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetry-based characterizations of the exponential distribution 基于对称的指数分布特征
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-06-30 DOI: 10.21136/AM.2026.0289-25
Jafar Ahmadi, Massoumeh Fashandi
{"title":"Symmetry-based characterizations of the exponential distribution","authors":"Jafar Ahmadi,&nbsp;Massoumeh Fashandi","doi":"10.21136/AM.2026.0289-25","DOIUrl":"10.21136/AM.2026.0289-25","url":null,"abstract":"<div><p>The exponential distribution is one of the most widely used continuous distributions in reliability theory, failure time analysis, Poisson processes, and survival analysis. In this paper, we establish new characterizations of the exponential distribution based on the probability integral transformation. Characterizations derived from both distributional relationships and moment properties of certain functions of the underlying variables are presented. Furthermore, analogous results for distributional relationships are obtained for functions of order statistics and <i>k</i>-record statistics. Using the completeness properties of the sequences of functions {(1 − <i>u</i>)<sup><i>i</i>−1</sup><i>u</i><sup><i>n</i>−<i>i</i></sup>, 0 &lt; <i>u</i> &lt; 1, <i>n</i> ⩾ <i>i</i> ⩾ 1} and {(− log <i>u</i>)<sup><i>n</i>−1</sup>, 0 &lt; <i>u</i> &lt; 1, <i>n</i> ⩾ 1}, moment-based characterization results are also established for functions of order statistics and <i>k</i>-record statistics, respectively. Since ordinary record values are special cases of <i>k</i>-records, the corresponding results hold for usual records as well.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"455 - 470"},"PeriodicalIF":0.6,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homogenization of stochastic convective Brinkman-Forchheimer equations 随机对流Brinkman-Forchheimer方程的均匀化
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-06-24 DOI: 10.21136/AM.2026.0263-24
Aurelien Fouetio
{"title":"Homogenization of stochastic convective Brinkman-Forchheimer equations","authors":"Aurelien Fouetio","doi":"10.21136/AM.2026.0263-24","DOIUrl":"10.21136/AM.2026.0263-24","url":null,"abstract":"<div><p>We study the homogenization of stochastic convective Brinkman-Forchheimer equations (SCBFE) or the tamed Navier-Stokes equations which describe the motion of incompressible fluid flows in satured porous medium. We combine some compactness arguments such as Prokhorov’s and Skorokhod’s probabilistic compactness results with the sigma-convergence method to prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized stochastic problem with constant coefficients.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"427 - 453"},"PeriodicalIF":0.6,"publicationDate":"2026-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability estimates for polyharmonic operator from partial boundary measurements 从部分边界测量估计多谐算子的稳定性
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-06-23 DOI: 10.21136/AM.2026.0194-24
Yanjun Ma
{"title":"Stability estimates for polyharmonic operator from partial boundary measurements","authors":"Yanjun Ma","doi":"10.21136/AM.2026.0194-24","DOIUrl":"10.21136/AM.2026.0194-24","url":null,"abstract":"<div><p>We establish a ln-ln-type estimate for the electric potential associated to the zeroth order perturbation of the polyharmonic operator when the Dirichlet-to-Neumann map is taken only on a subset.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"409 - 426"},"PeriodicalIF":0.6,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On one-parameter generalization of Fibonacci and Leonardo elliptic quaternions 斐波那契和列奥纳多椭圆四元数的单参数推广
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-06-15 DOI: 10.21136/AM.2026.0120-26
Dorota Bród, Anetta Szynal-Liana
{"title":"On one-parameter generalization of Fibonacci and Leonardo elliptic quaternions","authors":"Dorota Bród,&nbsp;Anetta Szynal-Liana","doi":"10.21136/AM.2026.0120-26","DOIUrl":"10.21136/AM.2026.0120-26","url":null,"abstract":"<div><p>The motion of a point on an ellipsoid can be interpreted using the generation of elliptical rotations. An elliptical rotation can be defined using elliptic quaternions. The Fibonacci sequence, defined by the second-order linear relation, is a famous sequence used in mathematics, physics, computer science, technical analysis and others. In this paper, we introduce and study generalized Fibonacci-Leonardo elliptic quaternions, which generalize the Fibonacci elliptic quaternions and Leonardo elliptic quaternions, simultaneously. We give the ordinary generating functions, the Binet-type formulas, general bilinear index-reduction formulas, and the sum of the finite, finite odd, and finite even terms of these quaternions.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"353 - 364"},"PeriodicalIF":0.6,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping 结合干摩擦和hessian驱动阻尼的连续二阶动力学结构单调包涵
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-05-29 DOI: 10.21136/AM.2026.0178-25
Yan Tang, Yanqin Huang
{"title":"On the structural monotone inclusion of continuous second-order dynamics combining dry friction and Hessian-driven damping","authors":"Yan Tang,&nbsp;Yanqin Huang","doi":"10.21136/AM.2026.0178-25","DOIUrl":"10.21136/AM.2026.0178-25","url":null,"abstract":"<div><p>To obtain the null point of the sum for a maximally monotone operator <i>A</i> and a cocoercive operator <i>B</i>, this article is concerned with the asymptotic properties of the trajectories to a second-order continuous damped autonomous dynamical systems with dry friction, which plays a crucial role for achieving stability within a finite time. Additionally, Hessian-driven damping is incorporated, which helps mitigating oscillations for inertial effects. The combination of dry friction and Hessian-driven damping in the context of split monotone inclusions represents a novel contribution, as it simultaneously ensures finite-time convergence and suppresses oscillatory behavior. The existence and uniqueness of global solutions, as well as the convergence of system trajectories are analyzed, the performance of the iterative algorithm generated by the second-order dynamic system discretely are also verified through several numerical experiments.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"299 - 326"},"PeriodicalIF":0.6,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounded penalty method for the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity 带非局部库仑摩擦的修正sigorini接触问题的有界惩罚法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2026-05-26 DOI: 10.21136/AM.2026.0261-25
El-Hassan Benkhira, Ilham El Ouardy, Youssef Mandyly, Rachid Fakhar
{"title":"Bounded penalty method for the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity","authors":"El-Hassan Benkhira,&nbsp;Ilham El Ouardy,&nbsp;Youssef Mandyly,&nbsp;Rachid Fakhar","doi":"10.21136/AM.2026.0261-25","DOIUrl":"10.21136/AM.2026.0261-25","url":null,"abstract":"<div><p>We consider the bounded penalty method to solve the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity studied in I. El Ouardy, Y. Mandyly, H. Benkhira, and R. Fakhar (2024). We formulate a regularized variational problem and prove the existence and uniqueness of its solution using elliptic quasi-variational inequalities, strongly monotone operators, and Schauder’s fixed point theorem. We also derive error estimates that depend on the penalty parameter ϵ, establishing a convergence rate of <span>(O(sqrt{epsilon}))</span>. Finally, we propose an iterative method to numerically solve the regularized problem and prove its convergence.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"365 - 392"},"PeriodicalIF":0.6,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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