Article
Mathematics, Applied
Antonio Gaudiello, Delfina Gomez, Maria-Eugenia Perez-Martinez
Summary: This article investigates a 3D multi-structure consisting of two thin films joined perpendicularly: a vertical film with small thickness h(n)(a) and a horizontal film with small thickness h(n)(b). The asymptotic behavior of an eigenvalue problem for the Laplacian on this multi-structure is studied as h(n)(a) and h(n)(b) approach zero. The limit problem is shown to depend on the value q = lim(n) h(n)(a/)h(n)(b), and three different limit regimes are identified based on the value of q belonging to ]0,+infinity 8[, q equal to +infinity, or q equal to 0. The limit problems are identified and H-1-strong convergence results are obtained.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Igor Pazanin
Summary: This paper presents the analytical results of the incompressible micropolar fluid flowing through a thin cylindrical pipe filled with porous medium, and performs asymptotic analysis in the critical case of strong coupling between velocity and microrotation. The error estimates are also derived to rigorously validate the proposed effective model.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Applied
Huanyuan Li
Summary: This paper focuses on the Cauchy problem of the three-dimensional nonhomogeneous incompressible micropolar fluid equations in the whole space. A weak Serrin-type blowup criterion for the strong solutions is established. It is proven that the strong solution exists globally for the Cauchy problem of the three-dimensional nonhomogeneous micropolar equations if the velocity satisfies the weak Serrin's condition, irrespective of the micro-rotational velocity. As an immediate application, it is further shown that the Cauchy problem of micropolar fluid equations has a unique global strong solution when the kinematic viscosity is sufficiently large, or the upper bound of initial density or initial kinetic energy is small enough.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Xin Zhong
Summary: The study focuses on the Cauchy problem of a nonhomogeneous magneto-micropolar fluid system with zero density at infinity in the entire space. It is proven that a unique local strong solution exists for the system, as long as the initial density and magnetic field decay not too slowly at infinity, without the need for any specific compatibility condition for the initial data.
ANALYSIS AND APPLICATIONS
(2021)
Article
Chemistry, Multidisciplinary
Kuniyuki Miwa, Souichi Sakamoto, Akihito Ishizaki
Summary: The energetic positions of molecular electronic states at molecule/electrode interfaces play a crucial role in determining the transport and optoelectronic properties of molecular junctions. A study investigates electroluminescence from single-molecule junctions where the molecule is strongly coupled with the vacuum electromagnetic field in a plasmonic nanocavity. It demonstrates an improvement in the electroluminescence efficiency by selectively controlling the formation of the lowest-energy excited state through strong light-matter coupling. The research findings contribute to manipulating optoelectronic conversion in molecular junctions and provide design principles for efficient molecular optoelectronic devices.
Article
Engineering, Mechanical
Michael P. Paidoussis
Summary: Early studies have revealed the fundamental dynamics of pipes conveying fluid, and subsequent research has focused on various variants of the system. The publication rate of related papers has exponentially increased over time.
JOURNAL OF FLUIDS AND STRUCTURES
(2022)
Article
Acoustics
Xiao-Ye Mao, Song Shu, Xin Fan, Hu Ding, Li-Qun Chen
Summary: An approximate method is proposed for the strong nonlinear and non-homogenous boundary value problem of a pipe conveying fluid, using modal correction and projection to treat the boundaries as generalized governing equations. The discussion on natural frequencies and harmonic convergence helps in judging the stability of the solution and the type of bifurcation, while revealing detailed information of the response. The proposed method shows advantages in dealing with strong boundaries compared to other existing methods.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Mathematics, Applied
Taras A. Mel'nyk, Arsen Klevtsovskiy
Summary: This article considers a steady-state convection-diffusion problem with a small diffusion factor in a thin three-dimensional graph-like junction composed of thin cylinders connected through a domain. The asymptotic expansion for the solution is constructed and justified using multiscale analysis. Asymptotic estimates in the norm of Sobolev space H-1 and the uniform norm are proved for the difference between the solution and proposed approximations, with a predetermined accuracy based on the level of the small parameter.
ASYMPTOTIC ANALYSIS
(2022)
Article
Mathematics, Applied
Michal Benes, Igor Pazanin, Marko Radulovic, Borja Rukavina
Summary: This paper studies the unsteady flow of a micropolar fluid through a thin pipe with a nonzero boundary condition for microrotation. The well-posedness of the corresponding initial-boundary value problem is first proved, and then a higher-order approximation of the solution is constructed using asymptotic analysis with respect to the pipe's thickness. A detailed study of the boundary layers near the ends of the pipe is provided, and a numerical example is presented to illustrate the behavior of the derived asymptotic solution.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Ping Hong, Xiaofeng Hou
Summary: In this paper, a new blowup criterion is established for the strong solution to the three-dimensional micropolar fluid equations with vacuum in a bounded domain. The blowup criterion is obtained in terms of BMOx norm of P and is independent of the velocity of rotation of the microscopic particles. The presence of vacuum is also allowed.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Chemistry, Multidisciplinary
Christoph P. Theurer, Florian Laible, Jia Tang, Katharina Broch, Monika Fleischer, Frank Schreiber
Summary: Utilizing strong light-matter coupling can modify the energy landscapes of excited states of organic semiconductors. This can be achieved by implementing them in optical microcavities, without the need for chemical modification. In this study, the strong coupling of Davydov transitions in polycrystalline pentacene thin films to surface lattice resonances supported by open cavities made of silver nanoparticle arrays was demonstrated. These thin films, together with the open architecture, are more suitable for device applications.
Article
Mathematics
Haibo Cui, Junpei Gao, Lei Yao
Summary: This paper studies the large time behavior of the solution for one-dimensional compressible micropolar fluid model with large initial data. The model describes micro-rotational motions and spin inertia commonly found in suspensions, animal blood, and liquid crystal. The study obtains uniform positive lower and upper bounds of density and temperature independent of space and time, and the asymptotic behavior of the micro-rotation velocity.
ELECTRONIC RESEARCH ARCHIVE
(2021)
Article
Astronomy & Astrophysics
Shingo Akama, Shinichi Hirano
Summary: In this paper, the authors investigate whether the models of Galilean Genesis without the strong coupling problem can explain the statistical properties of the observed cosmic microwave background fluctuations based on two unified frameworks of Galilean Genesis. They show that the models avoiding strong coupling and allowing a slightly red-tilted scalar power spectrum suffer from an overproduction of a scalar non-Gaussianity.
Article
Engineering, Multidisciplinary
Andrei G. Shvarts, Julien Vignollet, Vladislav A. Yastrebov
Summary: A computational framework was developed to simulate thin fluid flow in narrow interfaces between solids, exploring the complex coupling between fluid and solid mechanics equations as well as the effects of contact surface properties. The framework's robustness was demonstrated through simulation experiments, showcasing the application of two-way coupling methods in fluid flow interfaces.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Electrical & Electronic
Luke Smith, Zhichao Li, Steve Dixon
Summary: Clamp-on ultrasonic transit time difference flow meters provide a solution for metering without cutting into existing pipelines. By considering design features such as a curved contact face and a scattering surface, unwanted ultrasonic modes can be minimized. However, minimizing these modes does not offer any advantage for transit time difference measurement.
IEEE SENSORS JOURNAL
(2022)
Article
Mathematics, Applied
Michal Benes, Igor Pazanin
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics, Applied
Michal Benes, Igor Pazanin, Marko Radulovic
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2020)
Article
Mathematics, Applied
Michal Benes
Summary: This paper investigates the global existence, uniqueness, and homogenization of degenerate partial differential equations with integral conditions arising from coupled transport processes and chemical reactions in three-dimensional highly heterogeneous porous media. Global weak solutions of the microscale problem are proven through semidiscretization in time, showing two-scale convergence as the scale parameter approaches zero. Emphasis is placed on the contribution of first order correctors in periodic homogenization and the uniqueness of solutions to the homogenized problem under additional assumptions.
ACTA APPLICANDAE MATHEMATICAE
(2021)
Article
Mathematics
Michal Benes, Petr Kucera, Petra Vackova
Summary: This paper proves the local in time existence and uniqueness of a solution for the initial velocity in the 2D Navier-Stokes system with three types of boundary conditions, including the so called do-nothing boundary condition. The solution can belong to a class of functions that can be at least a little stronger than L-2(Omega).
JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS
(2021)
Article
Mathematics, Applied
Michal Benes
Summary: This paper discusses a degenerate fully nonlinear parabolic system that models coupled two-phase flow and heat transport through porous media. By reformulating the mathematical model using the characteristics of the global pressure and the capillary pressure potential, we prove the existence of a weak solution on any physically relevant time interval.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Michal Benes, Igor Pazanin, Marko Radulovic
Summary: This paper focuses on the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions, specifically Navier's slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The paper aims to prove the existence, regularity and uniqueness of the solution in distribution spaces.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Michal Benes, Igor Pazanin, Marko Radulovic, Borja Rukavina
Summary: This paper studies the unsteady flow of a micropolar fluid through a thin pipe with a nonzero boundary condition for microrotation. The well-posedness of the corresponding initial-boundary value problem is first proved, and then a higher-order approximation of the solution is constructed using asymptotic analysis with respect to the pipe's thickness. A detailed study of the boundary layers near the ends of the pipe is provided, and a numerical example is presented to illustrate the behavior of the derived asymptotic solution.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Michal Benes
Summary: This study considers a fully nonlinear degenerate parabolic system that describes the three-dimensional variable-density Darcian flow of a heat conducting fluid through porous media. The research establishes the global existence of weak solutions to the relevant initial-boundary value problems in nonsmooth domains under physically reasonable hypotheses on the data and mixed boundary conditions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Michal Benes
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2020)
Article
Engineering, Multidisciplinary
Michal Benes, Radek Stefan
Proceedings Paper
Mathematics, Applied
Michal Benes, Lukas Krupika
PROGRAMS AND ALGORITHMS OF NUMERICAL MATHEMATICS 19
(2019)
Proceedings Paper
Mathematics, Applied
Michal Benes, Radek Stefan
INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM-2018)
(2019)
Proceedings Paper
Mathematics, Applied
Michal Benes, Lukas Krupicka
7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2018)
(2018)
Proceedings Paper
Mathematics, Applied
Michal Benes
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)
(2018)
Proceedings Paper
Mathematics, Applied
Michal Benes, Lukas Krupicka
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)
(2018)