Article
Physics, Multidisciplinary
Vikas Chaurasiya, Rajneesh Kumar Chaudhary, Mohamed M. Awad, Jitendra Singh
Summary: This paper investigates a one-phase moving boundary problem with size-dependent thermal conductivity and moving phase change material. The problem is numerically solved using the heat balance integral method and the results are compared with an exact solution. The effects of various parameters on the temperature profile and the melting front tracking are discussed in detail. Additionally, a comparative study is conducted on different types of moving boundary problems, revealing the influence of problem type on the transition process.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Thermodynamics
Minghan Xu, Saad Akhtar, Mohammaderfan Mohit, Ahmad F. Zueter, Agus P. Sasmito
Summary: In this study, a two-phase Stefan problem with a convective or Robin boundary condition is formulated, without assuming that the interface moves instantaneously at time t = 0. A comprehensive asymptotic analysis is performed and the method of property averaging is employed. The developed asymptotic solution is verified and found to extend the valid range of the Stefan number compared to conventional techniques.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2024)
Article
Engineering, Multidisciplinary
S. L. Mitchell, N. P. McInerney, S. B. G. O'Brien
Summary: This study investigates a one-dimensional Stefan problem describing the sorption of swelling solvent in glassy polymer. By comparing formal asymptotic expansions and numerical schemes, the analysis of polymer state changes is carried out based on kinetic laws and control parameters.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Thermodynamics
E. P. Canzian, F. Santiago, A. V. Brito Lopes, M. R. Barbosa, A. G. Baranano
Summary: In this paper, we developed a double integral method to solve the solidification problem in spherical geometry with high Stefan and Biot numbers. The method outperformed the traditional simple integral method in terms of numerical accuracy. It also showed better performance than the single integral method in predicting solidification time for different conditions.
APPLIED THERMAL ENGINEERING
(2023)
Article
Thermodynamics
E. P. Canzian, F. Santiago, A. Brito Lopes, A. G. Baranano
Summary: In this study, simple and double integral methods were developed and applied to phase-change problems, specifically in the solidification process of spheres. The linear double integral method achieved better agreement with published data in terms of solidification time. The computational quadratic methods were found to be more accurate for higher Stefan and Biot numbers. This research validates the mathematical development using a linear temperature profile with the double integral method and suggests future extensions to different material solidification processes.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2022)
Article
Mathematics, Applied
Julieta Bollati, Adriana C. Briozzo, Maria F. Natale
Summary: This article discusses a non-classical one-phase Stefan problem with a specific control function, which depends on the evolution of temperature on the fixed face x = 0. It assumes Neumann boundary condition and an overspecified Robin condition on the fixed face. Under certain restrictions, an explicit similarity type solution is provided, and the free boundary and one or two unknown thermal coefficients are determined depending on whether the direct or inverse Stefan problem is considered.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Physics, Multidisciplinary
T. Dokoza, D. Pluemacher, M. Smuda, C. Jegust, M. Oberlack
Summary: In this paper, the one-dimensional two-phase Stefan problem is studied analytically using the unified transform method, leading to a system of non-linear Volterra-integral equations describing heat distribution. The position of the phase change can be solved numerically, followed by generating temperature distribution from their integral representation.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Mathematics, Applied
J. Bollati, D. A. Tarzia
Summary: This paper investigates various approximations for one-dimensional Stefan-like problems with space-dependent latent heat. By comparing and testing the accuracy of different approximation methods through numerical simulations, the optimal integral method is identified. Additionally, an approximate technique based on minimizing the least-squares error is proposed.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Dmitri V. Alexandrov, Peter K. Galenko
Summary: The analytical solution to the boundary integral equation is obtained for the growth of angled dendrites and arbitrary parabolic/paraboloidal solid/liquid interfaces in two and three dimensions. The undercooling of a binary melt and solute concentration at the phase transition boundary are determined. This theory potential can be useful in describing more complex growth shapes and interfaces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Automation & Control Systems
Rahel Bruegger, Helmut Harbrecht
Summary: This article discusses the multidimensional one-phase Stefan problem and suggests reformulating it as a shape optimization problem. The shape gradient of the objective functional is computed to apply gradient-based optimization algorithms. A numerical example is provided to justify the approach.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
John Lujano, Johannes Tausch
Summary: In this study, the one-dimensional Stefan problem is reformulated as a shape optimization problem, where the position of the phase transition is optimized with respect to time. By minimizing the mismatch of the Dirichlet to Neumann map at the moving interface, the minimizer is shown to be the only stationary point of the shape functional. A gradient-based optimization method is derived using shape calculus and the heat equation's state and adjoint equations are solved with integral equation techniques to avoid domain discretization. The Nystrom quadrature method is analyzed and numerical results are presented, demonstrating the effectiveness of the approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Samat A. Kassabek, Durvudkhan Suragan
Summary: In this paper, the heat polynomials method (HPM) proposed by the authors for one-dimensional one-phase inverse Stefan problem is extended to the two-phase case. The solution of the problem is presented in the form of a linear combination of heat polynomials. The coefficients of this combination can be determined by satisfying the initial and boundary conditions or by the least square method for the boundary of a domain. The regularization is taken into account due to the ill-posed nature of the inverse problem. Our numerical results show good accuracy when compared with results obtained by another method.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Vikas Chaurasiya, Rajneesh Kumar Chaudhary, Abderrahim Wakif, Jitendra Singh
Summary: This paper analyzes a one-phase moving boundary problem involving size-dependent thermal conductivity and a moving phase change material under generalized boundary conditions. The numerical solution is obtained using the heat balance integral method with an approximation of the quadratic temperature profile. The study shows the effects of dimensionless problem parameters on temperature profile and moving melting interface.
WAVES IN RANDOM AND COMPLEX MEDIA
(2022)
Article
Mathematics, Applied
Borjan Geshkovski, Debayan Maity
Summary: In this paper, the authors study the one-phase Stefan problem with surface tension in a two-dimensional strip-like geometry. They prove the local null-controllability of the system in any positive time with control supported within an arbitrary open and non-empty subset. They also consider a family of one-dimensional systems and prove observability results that are uniform with respect to the Fourier frequency parameter.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
A. Elsaid, S. M. Helal
Summary: This paper proposes a modified form of Taylor series, known as the moving Taylor series. The coefficients and time-derivatives of the proposed series are formulated and the new power series is applied to solve the one-dimensional one phase Stefan problem. Examples are provided to demonstrate the steps of the proposed technique and the results show its efficiency compared to other semi-analytic techniques.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Thermodynamics
V. Cregan, J. Williams, T. G. Myers
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2020)
Article
Thermodynamics
Marc Calvo-Schwarzwalder, Timothy G. Myers, Matthew G. Hennessy
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2020)
Article
Thermodynamics
T. G. Myers, F. Font
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2020)
Article
Thermodynamics
C. Fanelli, V Cregan, F. Font, T. G. Myers
Summary: A mathematical model is generalized for growth of multiple nanocrystals, with comparisons showing good agreement among different approximation levels. The N particle model and analytical solution exhibit excellent fit with experimental data, providing insights into crystal growth processes and parameters. The analytical solution can be used to represent multi-stage growth processes and optimize crystal growth.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Thermodynamics
Timothy G. Myers, Abel Valverde, Maria Aguareles, Marc Calvo-Schwarzwalder, Francesc Font
Summary: This study develops a mathematical model for the erosion or leaching process of a solid material by a flowing fluid in a column. The model combines an advection-diffusion equation with a linear kinetic reaction to describe the mass transfer between the solid and fluid. Two specific cases are analyzed, and perturbation and numerical solutions are used to verify the model. The model is also validated using experimental data, showing excellent agreement in estimating the extracted fraction.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Engineering, Multidisciplinary
Maria Aguareles, Marc Calvo-Schwarzwalder, Francesc Font, Timothy G. Myers
Summary: A simple mathematical model is developed to estimate the energy stored in a green roof. Analytical solutions are derived for both shallow and deep substrates. The results show that the energy and surface temperature vary linearly with fractional leaf coverage, albedo, and irradiance, while the effect of evaporation rate and convective heat transfer is non-linear. It is found that a typical green roof is significantly cooler and stores less energy than a concrete roof, even with a high albedo coating.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Nanoscience & Nanotechnology
Claudia Fanelli, Katerina Kaouri, Timothy N. Phillips, Timothy G. Myers, Francesc Font
Summary: This study developed a mathematical model to investigate the transport of drug nanocarriers in the bloodstream under the influence of an external magnetic field. The results showed the importance of considering the non-Newtonian behavior of blood flow when modeling drug delivery. The study also evaluated the particle concentration at the vessel wall and the evolution of particle flux, providing valuable insights for transferring magnetic nanoparticle drug delivery to clinical applications.
MICROFLUIDICS AND NANOFLUIDICS
(2022)
Article
Mathematics, Applied
S. L. Mitchell, T. G. Myers
Summary: In this paper, the thermal evolution in a one-dimensional bagasse stockpile is investigated. The mathematical model involves four unknowns: temperature, oxygen content, liquid water content, and water vapor content. The model is first nondimensionalized to identify dominant terms and simplify the system. Solutions for the approximate and full system are then calculated. It is shown that spontaneous combustion can occur under certain conditions. Importantly, the study demonstrates that sequential building can effectively avoid spontaneous combustion, providing a practical solution for preventing accidents in stockpile management.
Article
Thermodynamics
Timothy G. Myers, Alba Cabrera-Codony, Abel Valverde
Summary: This paper investigates the standard one-dimensional model for adsorption in a packed column. The study compares different mass sink models and their accuracy in predicting the adsorption behavior of different contaminants. The results indicate that a Sips sink model provides excellent agreement with experimental data.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Mathematics, Applied
M. Aguareles, E. Barrabes, T. Myers, A. Valverde
Summary: In this study, the dynamics of a contaminated fluid flowing through an adsorption column are investigated. A one-dimensional advection-diffusion equation coupled to a sink term is derived to account for contaminant adsorption. The adsorption rate is modelled by the Sips equation, and the order of the exponents is determined through analyzing the chemical reaction. By applying a travelling wave substitution, the governing equations are reduced to two coupled ordinary differential equations.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Thermodynamics
Abel Valverde, Alba Cabrera-Codony, Marc Calvo-Schwarzwalder, Timothy G. Myers
Summary: Experimental data shows that the breakthrough curves of column adsorption are influenced by the size of the adsorbent particles. In this paper, a new formulation is proposed to incorporate the diffusion of the adsorbate, and approximate analytical solutions are derived for two kinetic models. The accuracy of the analytical solutions is validated through comparison with numerical solutions and experimental data, which suggests that the new analytical solutions perform better than previous models. However, there are still cases where neither model can predict the behavior accurately.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2024)
Proceedings Paper
Engineering, Multidisciplinary
Marc Calvo-Schwarzwalder, Abel Valverde, Francesc Font, Maria Aguareles, Timothy G. Myers
Summary: In this article, a mathematical model for filtration in a cylindrical column packed with a porous material is developed. The model is applicable for the removal of trace and significant quantities of substances, and is validated against experimental data for the removal of CO2 from gas and antibiotics from water. Additionally, a modification is proposed to handle extraction processes involving the removal of material from a porous matrix.
PROGRESS IN INDUSTRIAL MATHEMATICS AT ECMI
(2022)
Article
Critical Care Medicine
Jaume Mesquida, A. Caballer, L. Cortese, C. Vila, U. Karadeniz, M. Pagliazzi, M. Zanoletti, A. Perez Pacheco, P. Castro, M. Garcia-de-Acilu, R. C. Mesquita, D. R. Busch, T. Durduran
Summary: This study aims to characterize microvascular reactivity in peripheral skeletal muscle of severe COVID-19 patients and found significant impairments in dynamic vascular occlusion test-derived parameters, indicating lower metabolic rate and diminished endothelial reactivity in COVID-19 patients. Baseline oxygen saturation and deoxygenation rate were negatively correlated with the severity of ARDS in COVID-19 patients.
Article
Energy & Fuels
T. G. Myers, F. Font, M. G. Hennessy
Article
Materials Science, Multidisciplinary
A. Beardo, M. G. Hennessy, L. Sendra, J. Camacho, T. G. Myers, J. Bafaluy, F. X. Alvarez
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)