Article
Thermodynamics
J. Finneran
Summary: This article introduces an improved method for evaluating gas phase fluid properties to predict the evaporation rate of liquid droplets more accurately. The new method reduces evaporation rate errors significantly and is theoretically based without the need for fitting parameters or empirical coefficients. It strikes a balance between computational speed and simplicity, while offering high accuracy comparable to variable fluid properties.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Mathematics, Applied
M. Vynnycky
Summary: In this paper, a one-dimensional Stefan-type model for swelling solvent sorption in a glassy polymer is revisited, focusing on the application of the boundary immobilization method. The initial behavior of the moving boundary is found to be parabolic-logarithmic, which differs from previous problems. A small-time analysis suggests a modification to the boundary immobilization formalism, and numerical experiments confirm the validity. The relevance of these findings to other moving boundary problems in the literature is also discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Phalguni Nanda, Gujji Murali Mohan Reddy
Summary: In this study, heuristic a posteriori error indicators are constructed for two-dimensional inverse problems with noisy data. The error due to discretization is controlled by two mean-driven double-filtering algorithms, resulting in effective numerical results.
STUDIES IN APPLIED MATHEMATICS
(2022)
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
Physics, Fluids & Plasmas
Mathieu Roule, Jean-Baptiste Fouvry, Christophe Pichon, Pierre-Henri Chavanis
Summary: In this study, we investigate the long-term relaxation of one-dimensional self-gravitating systems using both kinetic theory and N-body simulations. Our findings show that all combinations of thermal and Plummer equilibria, with or without collective effects, are consistent with the predictions of Balescu-Lenard and Landau for diffusion coefficients. Interestingly, collective effects reduce diffusion by a factor of about 10. The predicted flux for Plummer equilibrium matches the measured one, providing a remarkable validation of kinetic theory. We also observe a case of quasikinetic blocking for the same equilibrium.
Article
Thermodynamics
Jong Hyeon Son, Il Seouk Park
Summary: This study investigates numerical phase-change models that often approach phase changes from a volumetric perspective, overlooking the fact that phase change is an interfacial phenomenon. Comparisons of four numerical phase-change models applied to the 1D Stefan condensation problem reveal non-physical stepwise temperature changes over time in models based on a volumetric perspective.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2021)
Article
Chemistry, Multidisciplinary
Hongbo Xie, Junyuan Bai, Haiyan Ren, Shanshan Li, Hucheng Pan, Yuping Ren, Gaowu Qin
Summary: The Z phase is a basic unit in the F-K phases, rarely observed experimentally due to large volume ratios among constituents. However, a metastable two-dimensional F-K Z phase was discovered in a Mg-Sm-Zn system, showing that atomic shuffling can transform hexagonal close-packed structures to the topologically close-packed F-K Z phase, providing new insights into the formation mechanism and clustering behavior of F-K phases and quasicrystals.
Article
Engineering, Industrial
Caroline de Arruda Signorini, Silvio Alexandre de Araujo, Gislaine Mara Melega
Summary: This research examines the production planning of hollow-core slabs by proposing two mathematical models to solve the problem of minimizing production and inventory costs. Computational results demonstrate that the heuristic based on the compact model outperforms the one based on the extended model.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
(2022)
Article
Chemistry, Physical
Shun Sakamoto, Masaki Itatani, Kanta Tsukada, Hideki Nabika
Summary: The Liesegang phenomenon can be utilized in micro- and nanofabrication to induce periodic precipitation of diverse materials. Experimental results confirm that AgCl forms regular-type Liesegang patterns in gel medium, regardless of diffusion dimension, and adheres to the spacing law and the Matalon-Packter law.
Article
Computer Science, Interdisciplinary Applications
Tomas Fullana, Vincent Le Chenadec, Taraneh Sayadi
Summary: This study presents a range of optimization cases for two-dimensional Stefan problems using a tracking-type cost-functional. A level-set method and an immersed boundary method coupled with an implicit time-advancement scheme are used to capture the interface and solve the heat equation respectively. The numerical framework is validated and the gradient needed for the optimization algorithm is efficiently computed using an adjoint-based algorithm. Various control objectives are explored and the results demonstrate the effectiveness of parameterized boundary actuation in suppressing interfacial instabilities or maintaining desired crystal shapes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics
Alexander Sukhinov, Valentina Sidoryakina
Summary: The paper considers the initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems. A two-dimensional-one-dimensional splitting scheme has been proposed for operational suspension spread prediction in coastal systems. The accuracy and efficiency of the approach have been investigated, demonstrating its suitability for solving grid convection-diffusion equations in a parallel manner.
Article
Mathematics, Applied
Felix del Teso, Jorgen Endal, Juan Luis Vazquez
Summary: The study investigates the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in Double-struck capital R-N. We prove the existence of a continuous and bounded selfsimilar solution with a free boundary at the change-of-phase level. The study also provides well-posedness and basic properties of very weak solutions for general bounded data in several dimensions, and explores limits and connections with other diffusion problems.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
S. Nandi, Y. V. S. S. Sanyasiraju
Summary: This study introduces a front-tracking fixed grid method for solving the Stefan problem with moving phase change materials, and validates its effectiveness through numerical experiments. The research investigates the influence of various physical parameters on the rate of phase change and observes the movement of the interface under different conditions.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Byungjae Son, Inbo Sim
Summary: This study examines positive solutions to one-dimensional generalized double phase problems and the existence of positive radial solutions for high-dimensional generalized double phase problems using the Krasnoselskii-type fixed point theorem.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematics, Applied
P. Nanda, G. M. M. Reddy, M. Vynnycky
Summary: In this paper, a novel phase-wise sequential numerical approach based on the method of fundamental solutions (MFS) is developed for solving inverse two-phase nonlinear Stefan and Cauchy-Stefan problems in one dimension. By treating each phase independently, the complex problem is split into two single-phase inverse problems, allowing for the simultaneous reconstruction of boundary and initial data.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
