Pub Date : 2025-11-01Epub Date: 2025-09-29DOI: 10.1016/j.rinam.2025.100632
Ben Mansour Dia , Guy Olivier Ngongang Ndjawa
High-capacity batteries that employ lithium-metal anodes experience filamentary dendrite growth at the anode/electrolyte interface, which significantly impacts battery performance and safety. In this study, we introduce a constrained phase-field approach to model dendrite-free electro-deposition by incorporating an optimal control mechanism into the phase-field evolution. Specifically, dendrite formation is mitigated by introducing an energy functional that penalizes the formation of interfaces with high-curvature protrusions. We develop a coupled multiphysics model comprising a nonconserved Allen–Cahn equation for the metal electrode interface, a reaction–diffusion (Cahn–Hilliard-type) equation for ionic transport, and electrostatic charge conservation with Butler–Volmer boundary kinetics. The model is solved under a variational framework, yielding modified phase-field evolution equations that steers deposition away from dendritic pathways. Our findings suggest a novel paradigm for designing charging protocols and interface modifications that could enable safer dendrite-free lithium-metal batteries.
{"title":"Enabling dendrite-free lithium metal batteries through a constrained phase-field model","authors":"Ben Mansour Dia , Guy Olivier Ngongang Ndjawa","doi":"10.1016/j.rinam.2025.100632","DOIUrl":"10.1016/j.rinam.2025.100632","url":null,"abstract":"<div><div>High-capacity batteries that employ lithium-metal anodes experience filamentary dendrite growth at the anode/electrolyte interface, which significantly impacts battery performance and safety. In this study, we introduce a constrained phase-field approach to model dendrite-free electro-deposition by incorporating an optimal control mechanism into the phase-field evolution. Specifically, dendrite formation is mitigated by introducing an energy functional that penalizes the formation of interfaces with high-curvature protrusions. We develop a coupled multiphysics model comprising a nonconserved Allen–Cahn equation for the metal electrode interface, a reaction–diffusion (Cahn–Hilliard-type) equation for ionic transport, and electrostatic charge conservation with Butler–Volmer boundary kinetics. The model is solved under a variational framework, yielding modified phase-field evolution equations that steers deposition away from dendritic pathways. Our findings suggest a novel paradigm for designing charging protocols and interface modifications that could enable safer dendrite-free lithium-metal batteries.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100632"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-15DOI: 10.1016/j.rinam.2025.100638
Junjie Zhang, Lina Niu
We proved an optimal local Calderón–Zygmund type estimate with a variable power in weighted Lorentz spaces for the weak solution of non-uniformly elliptic two-sided obstacle problems. It is mainly assumed that the nonlinearity satisfies the -growth condition and -BMO condition, while the exponents are strong -Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.
{"title":"Weighted Lorentz estimates with a variable power for non-uniformly elliptic two-sided obstacle problems","authors":"Junjie Zhang, Lina Niu","doi":"10.1016/j.rinam.2025.100638","DOIUrl":"10.1016/j.rinam.2025.100638","url":null,"abstract":"<div><div>We proved an optimal local Calderón–Zygmund type estimate with a variable power in weighted Lorentz spaces for the weak solution of non-uniformly elliptic two-sided obstacle problems. It is mainly assumed that the nonlinearity satisfies the <span><math><mrow><mo>(</mo><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span>-growth condition and <span><math><mrow><mo>(</mo><mi>δ</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math></span>-BMO condition, while the exponents <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> are strong <span><math><mo>log</mo></math></span>-Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100638"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-01DOI: 10.1016/j.rinam.2025.100649
Zhongxiang Wang , Cai Chang
In this paper, we focus on the existence of ground state solution with prescribed -norm for the following modified Kirchhoff problem: where , are constants, , if , and if . By employing a novel scaling method, we establish the existence of ground state normalized solutions for the above problem. Our result is new for the mass supercritical case , notably for the case .
{"title":"The existence of ground state normalized solution for mass supercritical modified Kirchhoff equation","authors":"Zhongxiang Wang , Cai Chang","doi":"10.1016/j.rinam.2025.100649","DOIUrl":"10.1016/j.rinam.2025.100649","url":null,"abstract":"<div><div>In this paper, we focus on the existence of ground state solution with prescribed <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm for the following modified Kirchhoff problem: <span><span><span><math><mrow><mo>−</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>u</mi><mi>Δ</mi><mrow><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>−</mo><mi>λ</mi><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span> are constants, <span><math><mrow><mi>p</mi><mo>∈</mo><mfenced><mrow><mn>4</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></mfenced></mrow></math></span>, <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mn>6</mn></mrow></math></span> if <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn></mrow></math></span>, and <span><math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mo>+</mo><mi>∞</mi></mrow></math></span> if <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>. By employing a novel scaling method, we establish the existence of ground state normalized solutions for the above problem. Our result is new for the mass supercritical case <span><math><mrow><mn>4</mn><mo>+</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo><</mo><mi>p</mi><mo>≤</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, notably for the case <span><math><mrow><mi>p</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100649"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-15DOI: 10.1016/j.rinam.2025.100653
Baoyan Han , Bo Zhu
In this paper, we consider a class of mixed type Hilfer fractional differential equations with noninstantaneous impulses, nonlocal conditions and time delay. We discuss the existence results, Ulam–Hyers stability, generalized Ulam–Hyers stability and Ulam–Hyers–Rassias stability via Sadovskii’s fixed point theorem, fractional calculus and theory of operators.
{"title":"Existence and stability of mixed type Hilfer fractional differential equations with impulses and time delay","authors":"Baoyan Han , Bo Zhu","doi":"10.1016/j.rinam.2025.100653","DOIUrl":"10.1016/j.rinam.2025.100653","url":null,"abstract":"<div><div>In this paper, we consider a class of mixed type Hilfer fractional differential equations with noninstantaneous impulses, nonlocal conditions and time delay. We discuss the existence results, Ulam–Hyers stability, generalized Ulam–Hyers stability and Ulam–Hyers–Rassias stability via Sadovskii’s fixed point theorem, fractional calculus and theory of operators.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100653"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-06DOI: 10.1016/j.rinam.2025.100652
Targyn A. Nauryz , Stanislav N. Kharin
This paper presents a mathematical model and analytical study of the thermal dynamics in an electrical contact bridge under the influence of the Thomson effect and Joule heat generation. The model considers a bridge structure adjacent to a vapor zone, in which temperature evolution is governed by a nonlinear heat equation, featuring temperature-dependent thermal and thermoelectric coefficients, as well as an internal Joule heat source. The analysis introduces dimensionless variables and employs a self-similar transformation to reduce the problem to a boundary value problem for nonlinear ordinary differential and integral equations. The existence and uniqueness of the similarity solution are established via fixed point theory under appropriate conditions on the nonlinear coefficients. Analytical results are obtained for the case of constant coefficients, while the general nonlinear case is treated with an integral approach. Additionally, special cases such as linearly temperature-dependent Thomson and thermal coefficients are examined to illustrate parameter sensitivity. The results describe how variations in the Thomson effect, Joule heating, and material properties influence the temperature field, bridge opening, and boiling front propagation, providing a deeper understanding of coupled thermoelectric and phase-change processes in electrical contacts. The findings provide a rigorous mathematical basis for simulating temperature fields in electrical contacts with moving boundaries and for understanding the influence of thermoelectric effects in current-carrying devices.
{"title":"Mathematical modeling and analysis of thermal dynamics in an electrical contact bridge with nonlinear Stefan problem including thermoelectric effect and internal heat source","authors":"Targyn A. Nauryz , Stanislav N. Kharin","doi":"10.1016/j.rinam.2025.100652","DOIUrl":"10.1016/j.rinam.2025.100652","url":null,"abstract":"<div><div>This paper presents a mathematical model and analytical study of the thermal dynamics in an electrical contact bridge under the influence of the Thomson effect and Joule heat generation. The model considers a bridge structure adjacent to a vapor zone, in which temperature evolution is governed by a nonlinear heat equation, featuring temperature-dependent thermal and thermoelectric coefficients, as well as an internal Joule heat source. The analysis introduces dimensionless variables and employs a self-similar transformation to reduce the problem to a boundary value problem for nonlinear ordinary differential and integral equations. The existence and uniqueness of the similarity solution are established via fixed point theory under appropriate conditions on the nonlinear coefficients. Analytical results are obtained for the case of constant coefficients, while the general nonlinear case is treated with an integral approach. Additionally, special cases such as linearly temperature-dependent Thomson and thermal coefficients are examined to illustrate parameter sensitivity. The results describe how variations in the Thomson effect, Joule heating, and material properties influence the temperature field, bridge opening, and boiling front propagation, providing a deeper understanding of coupled thermoelectric and phase-change processes in electrical contacts. The findings provide a rigorous mathematical basis for simulating temperature fields in electrical contacts with moving boundaries and for understanding the influence of thermoelectric effects in current-carrying devices.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100652"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-11-25DOI: 10.1016/j.rinam.2025.100673
Elyas Shivanian , Ahmad Jafarabadi , Mousa J. Huntul
This study focuses on retrieving a time-dependent source term in the heat equation governed by two distinct nonlocal boundary conditions. The inverse problem is structured with an interior energy over-specification constraint. The proposed computational framework combines the partition of unity approach for spatial discretization with the finite difference scheme for temporal advancement. Through energy analysis, the semi-discrete time-stepping formulation is proven to be unconditionally stable and convergent at a rate of . Despite being linear and uniquely solvable, the problem is inherently ill-posed, as slight disturbances in input data can induce significant errors in the reconstructed solution. To counteract this instability, Tikhonov regularization is implemented, yielding a stable approximation even under noisy data conditions. Moreover, a novel parameter selection strategy for the regularization is introduced, which surpasses standard methods by delivering substantially improved results. Numerical simulations corroborate the scheme’s robustness, demonstrating its accuracy with noise-free inputs and its resilience when handling contaminated measurements.
{"title":"A local meshless technique for recovering dual forms of time-varying sources in the nonlocal inverse heat equation","authors":"Elyas Shivanian , Ahmad Jafarabadi , Mousa J. Huntul","doi":"10.1016/j.rinam.2025.100673","DOIUrl":"10.1016/j.rinam.2025.100673","url":null,"abstract":"<div><div>This study focuses on retrieving a time-dependent source term in the heat equation governed by two distinct nonlocal boundary conditions. The inverse problem is structured with an interior energy over-specification constraint. The proposed computational framework combines the partition of unity approach for spatial discretization with the finite difference scheme for temporal advancement. Through energy analysis, the semi-discrete time-stepping formulation is proven to be unconditionally stable and convergent at a rate of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>δ</mi><mi>t</mi><mo>)</mo></mrow></mrow></math></span>. Despite being linear and uniquely solvable, the problem is inherently ill-posed, as slight disturbances in input data can induce significant errors in the reconstructed solution. To counteract this instability, Tikhonov regularization is implemented, yielding a stable approximation even under noisy data conditions. Moreover, a novel parameter selection strategy for the regularization is introduced, which surpasses standard methods by delivering substantially improved results. Numerical simulations corroborate the scheme’s robustness, demonstrating its accuracy with noise-free inputs and its resilience when handling contaminated measurements.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100673"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145614874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-11-10DOI: 10.1016/j.rinam.2025.100665
Jingwei Chen
This paper develops an -parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs). The analysis accommodates time–space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of , establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and facilitates applications in finance, physics and biology where time-changed Lévy models are prevalent.
{"title":"α-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity","authors":"Jingwei Chen","doi":"10.1016/j.rinam.2025.100665","DOIUrl":"10.1016/j.rinam.2025.100665","url":null,"abstract":"<div><div>This paper develops an <span><math><mi>α</mi></math></span>-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs). The analysis accommodates time–space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator <span><math><mi>E</mi></math></span> are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of <span><math><mrow><mo>min</mo><mrow><mo>{</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mi>α</mi><mo>/</mo><mn>2</mn><mo>}</mo></mrow></mrow></math></span>, establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and facilitates applications in finance, physics and biology where time-changed Lévy models are prevalent.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100665"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145519625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-10-23DOI: 10.1016/j.rinam.2025.100659
Saman Bagherbana, Jafar Biazar, Hossein Aminikhah
We present a reliable numerical method for solving multidimensional partial Volterra integro-differential equations (PVIDEs). This comprehensive approach integrates techniques from product integration, the Nyström method, and spectral collocation, all founded on ultraspherical polynomials. The primary objective of our methodology is to employ variable and function transformations to reformulate the equations into a novel class of PVIDEs. Subsequently, the ultraspherical product integration-spectral collocation approach is applied to derive equivalent algebraic equations. Newton’s iterative method is then utilized to simultaneously compute the numerical solution and the first-order partial derivative. We rigorously analyze the error bounds of the proposed method in both - and -norms. Our results demonstrate that the errors in the numerical solution, as well as in the numerical first-order partial derivative, decay exponentially. Numerical examples are provided to validate reliability and efficiency of the ultraspherical product integration-spectral collocation approach.
{"title":"An ultraspherical product integration-spectral collocation method for multidimensional partial Volterra integro-differential equations and its convergence analysis","authors":"Saman Bagherbana, Jafar Biazar, Hossein Aminikhah","doi":"10.1016/j.rinam.2025.100659","DOIUrl":"10.1016/j.rinam.2025.100659","url":null,"abstract":"<div><div>We present a reliable numerical method for solving multidimensional partial Volterra integro-differential equations (PVIDEs). This comprehensive approach integrates techniques from product integration, the Nyström method, and spectral collocation, all founded on ultraspherical polynomials. The primary objective of our methodology is to employ variable and function transformations to reformulate the equations into a novel class of PVIDEs. Subsequently, the ultraspherical product integration-spectral collocation approach is applied to derive equivalent algebraic equations. Newton’s iterative method is then utilized to simultaneously compute the numerical solution and the first-order partial derivative. We rigorously analyze the error bounds of the proposed method in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>- and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norms. Our results demonstrate that the errors in the numerical solution, as well as in the numerical first-order partial derivative, decay exponentially. Numerical examples are provided to validate reliability and efficiency of the ultraspherical product integration-spectral collocation approach.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100659"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the valuation of commodity options within the context of a Wishart stochastic volatility model that is equipped with a jump process. To achieve this, we propose a semi-analytical solution for pricing European options on commodity futures by introducing the characteristic function of the proposed model. The unique challenges posed by this model underscore the necessity for effective calibration techniques. To address this, we utilize an Artificial Neural Network (ANN) designed to improve the precision and efficiency of the calibration process. To optimize the presented ANN model, we use the flower pollination (FP) algorithm. Empirical studies suggest that the Wishart stochastic volatility model incorporating a jump factor enhances calibration accuracy compared to common models in the literature. Moreover, applying the FP-optimized ANN to calibration leads to a marked improvement in accuracy, as demonstrated by both in-sample and out-of-sample data.
{"title":"Commodity options pricing under Wishart stochastic volatility model equipped with jump process: Model calibration by an optimized neural network","authors":"Abdelouahed Hamdi , Maryam Noorani , Farshid Mehrdoust","doi":"10.1016/j.rinam.2025.100661","DOIUrl":"10.1016/j.rinam.2025.100661","url":null,"abstract":"<div><div>This paper presents the valuation of commodity options within the context of a Wishart stochastic volatility model that is equipped with a jump process. To achieve this, we propose a semi-analytical solution for pricing European options on commodity futures by introducing the characteristic function of the proposed model. The unique challenges posed by this model underscore the necessity for effective calibration techniques. To address this, we utilize an Artificial Neural Network (ANN) designed to improve the precision and efficiency of the calibration process. To optimize the presented ANN model, we use the flower pollination (FP) algorithm. Empirical studies suggest that the Wishart stochastic volatility model incorporating a jump factor enhances calibration accuracy compared to common models in the literature. Moreover, applying the FP-optimized ANN to calibration leads to a marked improvement in accuracy, as demonstrated by both in-sample and out-of-sample data.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100661"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze pattern formation in a two-component system within an isotropically growing or shrinking domain. By studying the evolution of a Lyapunov-like function, we derive time-dependent Turing bifurcation conditions through a stability analysis of linear perturbations across all Fourier modes. This general framework enables explicit characterization of pattern formation dynamics. Numerically, we consider two cases: a steady base state (exponential growth) and a time-dependent state (linear growth). First, we validate our approach by recovering the well-known conditions for fixed domains. Then, we simulate the Brusselator reaction system in dynamic domains, obtaining excellent agreement with our model’s predictions. These simulations highlight key pattern features, including evolution, amplitude growth, and wavenumber inertia. Our findings provide a novel energetic and geometrical perspective on the Turing bifurcation.
{"title":"Turing conditions for a two-component isotropic growing system from a potential function","authors":"Aldo Ledesma-Durán, Consuelo García-Alcántara, Iván Santamaría-Holek","doi":"10.1016/j.rinam.2025.100664","DOIUrl":"10.1016/j.rinam.2025.100664","url":null,"abstract":"<div><div>We analyze pattern formation in a two-component system within an isotropically growing or shrinking domain. By studying the evolution of a Lyapunov-like function, we derive time-dependent Turing bifurcation conditions through a stability analysis of linear perturbations across all Fourier modes. This general framework enables explicit characterization of pattern formation dynamics. Numerically, we consider two cases: a steady base state (exponential growth) and a time-dependent state (linear growth). First, we validate our approach by recovering the well-known conditions for fixed domains. Then, we simulate the Brusselator reaction system in dynamic domains, obtaining excellent agreement with our model’s predictions. These simulations highlight key pattern features, including evolution, amplitude growth, and wavenumber inertia. Our findings provide a novel energetic and geometrical perspective on the Turing bifurcation.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100664"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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