Article
Materials Science, Multidisciplinary
Md Abdul Kayum, Shamim Ara, M. S. Osman, M. Ali Akbar, Khaled A. Gepreel
Summary: Stable soliton solutions for the nonlinear Klein-Gordon equation have been established using the sine-Gordon expansion procedure, resulting in various new types of solitary wave solutions. The procedure is proven to be an efficient and straightforward mathematical tool for exact solitary wave solutions, with potential applications in optics, quantum mechanics, mathematical physics, and engineering.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
R. Carretero-Gonzalez, L. A. Cisneros-Ake, R. Decker, G. N. Koutsokostas, D. J. Frantzeskakis, P. G. Kevrekidis, D. J. Ratliff
Summary: The main objective of this work is to study quasi-one-dimensional kink-antikink stripes embedded in the two-dimensional sine-Gordon equation. By using variational techniques, we simplify the interaction dynamics between a kink and an antikink stripe, resulting in a reduced system of coupled equations that accurately describe the width and undulation dynamics. Additionally, we discuss the computational identification of the kink center and its numerical implications, as well as alternative approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
A. Paiva
Summary: The paper explores the interaction of Dirac delta-waves in models governed by the nonlinear Klein-Gordon equation, establishing that in certain cases they behave like classical solitons in the sine-Gordon equation. By examining the phi-four equation and the sine-Gordon equation, the study delves deeper into this phenomenon.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Optics
Yakup Yildirim, Anjan Biswas, Salam Khan, Padmaja Guggilla, Abdullah K. Alzahrani, Milivoj R. Belic
Summary: This study investigates solitons in fiber Bragg gratings with dispersive reflectivity, considering five forms of nonlinear refractive index structures. A full spectrum of single and straddled solitons is obtained using the integration scheme, the sine-Gordon equation method.
Article
Physics, Multidisciplinary
M. E. Akramov, J. R. Yusupov, I. N. Askerzade, D. U. Matrasulov
Summary: This study investigates the application of the discrete sine-Gordon equation on branched domains, providing both analytical solutions for special constraints and numerical solutions for unconstrained cases. Additionally, a simple model of a Josephson junction network is proposed based on the obtained results.
Article
Optics
Yakup Yildirim
Summary: This paper investigates optical solitons in birefringent fibers using the sine-Gordon equation scheme, obtaining solutions for dark solitons, singular solitons, bright solitons, and combo singular solitons. The coupled system derived from the Biswas-Arshed equation for birefringent fibers is analyzed, with four-wave mixing terms being neglected.
Article
Acoustics
Mengling Wu, Yongbin Ge, Zhi Wang
Summary: In this paper, an explicit compact difference method is developed for solving nonlinear hyperbolic equations with initial and three types of boundary conditions. A nonlinear explicit fourth-order compact difference scheme is derived using truncation error residual correction and the fourth-order Pade approximation. The stability of the corresponding scheme for linear hyperbolic equation is proven through Fourier analysis. To improve computational efficiency, the nonlinear scheme is linearized to obtain a linear explicit fourth-order compact difference scheme. Numerical experiments are conducted to validate the stability and accuracy of the proposed method.
Article
Engineering, Mechanical
Yakup Yildirim, Anjan Biswas, Asim Asiri
Summary: The concatenation model in polarization controlled fibers is reevaluated in this paper, and a complete range of 1-soliton solutions is identified using two integration methods. Several forms of straddled soliton solutions are displayed for the first time, and the conditions for soliton existence are presented as parameter constraints.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Yakup Yildirim, Anjan Biswas, Padmaja Guggilla, Salam Khan, Hashim M. Alshehri, Milivoj R. Belic
Summary: For the first time in the field of nonlinear optics, cubic-quartic solitons appearing in fibre Bragg gratings with dispersive reflectivity were addressed for four different cases of nonlinear refractive-index structures. A spectrum of single solitons and some straddled solitons emerged from the integration scheme adopted, using the sine-Gordon equation approach.
UKRAINIAN JOURNAL OF PHYSICAL OPTICS
(2021)
Article
Mathematics, Applied
Yibo Wang, Rui Du, Zhenhua Chai
Summary: In this paper, a lattice Boltzmann model with BGK operator (LBGK) is proposed for solving time-fractional nonlinear wave equations in Caputo sense. The model approximates the Caputo fractional derivative using a fast evolution algorithm and demonstrates second-order accuracy in space through numerical examples.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Physics, Particles & Fields
Jarah Evslin, Hengyuan Guo
Summary: This study focuses on the quantum harmonic oscillator Hamiltonians of quantum kinks, finding corrections beyond one loop to the quantum states and the energy cost of exciting the normal mode. A diagrammatic method for such calculations is also outlined.
EUROPEAN PHYSICAL JOURNAL C
(2021)
Article
Mathematics, Applied
Abdullahi Yusuf, Tukur A. Sulaiman, Mustafa Inc, Sayed Abdel-Khalek, K. H. Mahmoud
Summary: This study investigates the nonlinear Hamiltonian amplitude equation using two analytical techniques and successfully constructs important wave solutions, depicting the clear dynamical behavior of the results. All acquired solutions satisfy the original equation.
Article
Automation & Control Systems
Anthony Hastir, Joseph J. Winkin, Denis Dochain
Summary: An adaptive funnel control method is proposed to regulate the output of a class of nonlinear infinite-dimensional systems. The funnel controller achieves the control goal under assumptions on the nonlinear system dynamics. The theory is applied to regulate the temperature in a chemical reactor and validated through numerical simulations.
Article
Mathematics
Jiong Weng, Xiaojing Liu, Youhe Zhou, Jizeng Wang
Summary: The proposed method converts nonlinear wave equations into a system of ODEs and achieves a complete decoupling between spatial and temporal discretization. Numerical solutions to benchmark problems show that the wavelet algorithm has higher accuracy and faster convergence compared to existing methods. The accuracy of the method remains consistent across different equations and nonlinearities, indicating independence from equation order and nonlinearity.
Article
Multidisciplinary Sciences
Belal Batiha
Summary: In this article, the Daftardar-Gejji and Jafari method (DJM) is utilized to approximate an analytical solution for the sine-Gordon equation. By solving examples, the accuracy of DJM is demonstrated, and a comparison study between DJM, the variational iteration method (VIM), and the exact solution is presented. The comparison of the symmetrical results from this study with existing literature is satisfactory.
Article
Thermodynamics
Pranay P. Nagrani, Federico Municchi, Amy M. Marconnet, Ivan C. Christov
Summary: In this study, a two-fluid model is developed to investigate heat transfer in dense non-Brownian suspensions. The model is calibrated using experimental data to determine closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase. It is found that both shear and thermal gradients contribute to particle migration, and a thermo-rheological migration force is identified to explain this phenomenon.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Review
Physics, Condensed Matter
Ivan C. Christov
Summary: Microfluidic devices manufactured from soft polymeric materials have become popular in chemical and biological analysis due to their cheap and disposable nature. This review focuses on the physics of these systems and summarizes recent progress in understanding the interaction between non-Newtonian fluid flows and deformable boundaries. The review also explores key experimental results and relevant applications, along with the fundamental principles for physics-based modeling.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2022)
Article
Cardiac & Cardiovascular Systems
Kimberly A. Stevens Boster, Tanmay C. Shidhore, Aaron A. Cohen-Gadol, Ivan C. Christov, Vitaliy L. Rayz
Summary: This study discusses the challenges of patient-specific modeling of aneurysms in the presence of AVMs and explores the relationship between distal resistance and aneurysmal wall shear stress using physiologically realistic estimates. The results show that the presence of an AVM can significantly alter aneurysmal wall shear stress and that patient-specific flow measurements are necessary for meaningful predictions.
CARDIOVASCULAR ENGINEERING AND TECHNOLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
Tanmay C. Shidhore, Hannah L. Cebull, Megan C. Madden, Ivan C. Christov, Vitaliy L. Rayz, Craig J. Goergen
Summary: Modeling fluid-structure interactions in cardiovascular systems plays a crucial role in obtaining realistic computational models. However, determining the appropriate boundary conditions is challenging due to a lack of information on the contact between the arterial wall and surrounding tissue. This study presents a method to calibrate external tissue support parameters using 4D ultrasound data, and demonstrates that the same tissue support parameter estimates can be used for modeling healthy and diseased states of the vessel.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mechanics
Xiaojia Wang, Ivan C. Christov
Summary: Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. This study proposes a one-dimensional model to investigate the effect of fluid-structure interactions (FSIs) on the global instability of microchannels. The proposed model qualitatively agrees with experimental observations and captures key effects.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Physics, Fluids & Plasmas
Evgeniy Boyko, Howard A. Stone, Ivan C. Christov
Summary: This article introduces a closed-form expression for the flow rate-pressure drop relation in deformable microchannels, bypassing the detailed calculation of the fluid-structure interaction problem. The theoretical study shows a trade-off between the compliance of the deforming top wall and the drag due to sidewalls in the flow-rate-controlled situation.
PHYSICAL REVIEW FLUIDS
(2022)
Article
Biophysics
Tanmay C. Shidhore, Aaron A. Cohen-Gadol, Vitaliy L. Rayz, Ivan C. Christov
Summary: Cerebral aneurysm progression is influenced by both biomechanical and clinical risk factors, with areas of low shear and high oscillatory stress identified as potential indicators of aneurysmal growth. Comparative computational analysis of stable and growing aneurysm models revealed higher values of low shear and median peak systolic arterial wall displacement in growing aneurysms. Additionally, a novel metric called the oscillatory stress index (OStI) identified regions of combined low wall shear and high oscillatory stress in growing aneurysms, possibly associated with collagen degradation and remodeling.
JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME
(2023)
Article
Mechanics
Xiaojia Wang, Shrihari D. Pande, Ivan C. Christov
Summary: This paper investigates the fluid-structure interaction in two novel geometric configurations in microfluidics experiments. The mathematical theory for the flow rate-pressure drop relation is derived, and the predicted displacement field is validated against numerical simulations. The results show good agreement between theory and simulations, and weak flow inertia can be easily incorporated to improve the accuracy.
MECHANICS RESEARCH COMMUNICATIONS
(2022)
Article
Mechanics
Evgeniy Boyko, Ivan C. Christov
Summary: We analyze the fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. We provide a theoretical framework for calculating the effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and channel deformation. By identifying characteristic scales and dimensionless parameters, and using the lubrication approximation and perturbation expansion, we derive an expression for the pressure as a function of the channel's non-uniform shape in the weakly viscoelastic limit. We show the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure, deformation, and flow rate-pressure drop relation.
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
(2023)
Article
Mathematics, Applied
Ivan C. Christov, Isanka Garli Hevage, Akif Ibraguimov, Rahnuma Islam
Summary: We generalize Einstein's random walk model to derive a class of degenerate nonlinear parabolic equations in nondivergence form. These equations have diffusion coefficients that depend on the dependent variable and its gradient and vanish when either one of the latter does. We prove the finite speed of propagation property of solutions using a De Giorgi-Ladyzhenskaya iteration procedure and establish a mapping theorem for the divergence-form version of the governing equation in one spatial dimension. Numerical results demonstrate the main mathematical results for this special case, and we provide an explicit construction of the one-dimensional self-similar solution with finite speed of propagation function.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mechanics
Ivan C. Christov, Howard A. Stone
Summary: This study provides new concepts for understanding the transport phenomena in granular material flows by introducing a non-Fickian macroscopic model of axial diffusion in a cylindrical tumbler. The model considers diffusion induced by particle collisions only in a thin surface flowing layer due to shear localization. All model parameters are linked to measurable quantities in the granular flow. The proposed model is shown to be a specific case of linear constitutive relations with memory. An exact solution for the spreading of a finite-width pulse initial condition under the non-Fickian model is derived and compared to the solution of the Fickian model.
MECHANICS RESEARCH COMMUNICATIONS
(2023)
Article
Mechanics
Daihui Lu, Ivan C. Christov
Summary: In this study, the physics-informed neural network (PINN) approach is applied to extend the applicability of phenomenological models for particle migration in shear flow. The PINN is trained using a physics-based model for shear-induced particle migration in suspensions, which provides better fidelity to experimental data and a novel understanding of migration fluxes. The PINN approach is validated for radial particle migration in a non-Brownian suspension in an annular Couette flow and then applied to analyze experiments on particle migration in Poiseuille slot flow.
INTERNATIONAL JOURNAL OF MULTIPHASE FLOW
(2023)
Article
Mechanics
Pranay P. Nagrani, Ritwik V. Kulkarni, Parth U. Kelkar, Ria D. Corder, Kendra A. Erk, Amy M. Marconnet, Ivan C. Christov
Summary: Thermal greases, complex paste-like materials used for enhancing heat transfer, exhibit complex rheological behavior that can be characterized using specific rheological models.
JOURNAL OF RHEOLOGY
(2023)
Article
Physics, Fluids & Plasmas
Zongxin Yu, Ivan C. Christov
Summary: In this study, the geometrical equivalence between the deformed ferrofluid droplet in a Hele-Shaw cell and a spinning gear under crossed magnetic fields is revealed using center manifold reduction. The dynamics and time-dependent behavior of the interface are investigated, and a slowly time-varying magnetic field is designed to control the timing and emergence of the interfacial traveling wave. The results contribute to understanding the mechanisms of dynamic bifurcation and delayed instability.
Article
Mechanics
George Zhang, Ivan C. Christov, Aminur Rahman
Summary: Discrete dynamical models of walking droplets reveal quantum statistics and related behaviors in classical hydrodynamic systems, as well as n-bounce resonances. Numerical experiments show a fractal structure of resonances in the velocity in-velocity out diagram. Further theoretical analysis and experimental realizations will enhance our understanding of this model.
MECHANICS RESEARCH COMMUNICATIONS
(2023)
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.