Researchers from Department of Mathematics Engineering investigated nonlinear SH waves in an elastic layered half space with a more ealistic material inhomogenity model.
The study titled “SH Waves in a weakly inhomogenous half space with a nonlinear thin layer coating” was published in Zeitschrift Für Angewandte Mathematik Und Physik (ZAMP) by ITU Mathematics Engineering faculty members Prof. Dr. Semra Ahmetolan, Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayse Peker-Dobie, and Dr. Neşe Özdemir.
In this study, the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer was investigated. It was assumed that the constituent material of the layer is nonlinear, homogeneous, isotropic, compressible, and hyperelastic, whereas for the half-space, it is nonlinear, heterogeneous, compressible and a different hyperelastic material. By employing the nonlinear thin layer approximation, the problem of wave propagation in a layered half-space is reduced to the one for a nonlinear heterogeneous half-space with a modified nonlinear homogeneous boundary condition on the top surface. This new problem is analyzed by a relevant perturbation method, and a nonlinear Schrödinger (NLS) equation defining the self-modulation of waves asymptotically is obtained. The dispersion relation is derived for different heterogeneous properties of the half-space and the thin layer. Then the results of the thin layer approximation are compared with the ones for the finite layer. The solitary solutions of the derived NLS equation are obtained for selected real material models. It has been discussed how these solutions are influenced by the heterogeneity of the semi-infinite space.
https://doi.org/10.1007/s00033-024-02213-y
Alternative Solution Methods to Shapley Iteration for the Solution of Stochastic Matrix Games
The research titled " Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games", conducted by Assoc. Prof. Dr. Burhaneddin İzgi, faculty member of the Department of Mathematics Engineering and Assoc. Prof. Dr. Nazım Kemal Üre, faculty member of the Department of Artificial Intelligence and Data Engineering, was published in Applied Mathematics and Computation. In this novel research, Murat Özkaya (Ph.D. student of Izgi) and Professor Matjaz Perc from the University of Maribor are also coauthors of the paper.
In this paper, they present four alternative solution methods to Shapley iteration for the solution of stochastic matrix games. They first combine the extended matrix norm method for stochastic matrix games with Shapley iteration and then state and prove the weak and strong hybrid versions of Shapley iterations. Then, they present the semi-extended matrix norm and iterative semi-extended matrix norm methods, which are analytic-solution-free methods, for finding the approximate solution of stochastic matrix games without determining the strategy sets. They illustrate comparisons between the Shapley iteration, weak and strong hybrid Shapley iterations, semi-extended matrix norm method, and iterative semi-extended matrix norm method with several examples. The results reveal that the strong and weak hybrid Shapley iterations improve the Shapley iteration and decrease the number of iterations, and the strong hybrid Shapley iteration outperforms all the other proposed methods. Finally, they compare these methods and present their performance analyses for large-scale stochastic matrix games as well.
https://doi.org/10.1016/j.amc.2024.128638
A Work on Stabilization of Self-Steepening Optical Solitons in a Periodic PT-Symmetric Potential
The study titled “Stabilization of Self-Steepening Optical Solitons in a Periodic PT-Symmetric Potential” was published in Chaos, Solitons & Fractals by İTÜ Mathematics Engineering faculty members Prof. Dr. Nalan Antar and Research Assistant Eril Güray Çelik.
In this study, they have made significant progress in controlling self-steepening solitons governed by the modified nonlinear Schrödinger (MNLS) equation. These solitons are crucial for fiber optic communication, but they undergo both a position shift and an amplitude increase during their propagation. This inherent instability hinders their effectiveness in practical applications. The study demonstrates that incorporating a periodic PT-symmetric potential into the MNLS equation significantly improves soliton behavior. This approach effectively suppresses both the position shift and amplitude increase, leading to more stable soliton propagation. This breakthrough paves the way for enhanced performance in fiber optic communication systems, relying on these robust solitons for clearer and more reliable data transmission.
https://doi.org/10.1016/j.chaos.2024.115125
A Study Focusing on Singularly Perturbative Behaviour of Nonlinear Advection–Diffusion-Reaction Processes
The study titled “Singularly perturbative behaviour of nonlinear advection–diffusion-reaction processes” led by İTÜ Department of Mathematics Engineering member Prof. Dr. Murat Sarı was published in “The European Physical Journal Plus”.
The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.
https://doi.org/10.1140/epjp/s13360-024-04894-w
Mathematical Modelling of Antibiotic Interaction on Evolution of Antibiotic Resistance: An Analytical Approach
The study titled “Mathematical modelling of antibiotic interaction on evolution of antibiotic resistance: an analytical approach” led by İTÜ Department of Mathematics Engineering member Prof. Dr. Murat Sarı was published in “PeerJ”.
The emergence and spread of antibiotic-resistant pathogens have led to the exploration of antibiotic combinations to enhance clinical effectiveness and counter resistance development. Synergistic and antagonistic interactions between antibiotics can intensify or diminish the combined therapy’s impact and evolve as bacteria transition from wildtype to mutant (resistant) strains. Experimental studies have shown that the antagonistically interacting antibiotics against wildtype bacteria slow down the evolution of resistance. Interestingly, other studies have shown that antibiotics that interact antagonistically against mutants accelerate resistance. However, it is unclear if the beneficial effect of antagonism in the wildtype bacteria is more critical than the detrimental effect of antagonism in the mutants. This study aims to illuminate the importance of antibiotic interactions against wildtype bacteria and mutants on the deacceleration of antimicrobial resistance.
To address this, a mathematical model that explores the population dynamics of wildtype and mutant bacteria under the influence of interacting antibiotics is developed and analyzed. The model investigates the relationship between synergistic and antagonistic antibiotic interactions with respect to the growth rate of mutant bacteria acquiring resistance.
https://doi.org/10.7717/peerj.16917
Researchers from the Department of Mathematical Engineering investigated 3D Plate Dynamics in the Framework of Space-Fractional Generalized Thermoelasticity – Theory and Validation.
The study titled “3D Plate Dynamics in the Framework of Space-Fractional Generalized Thermoelasticity – Theory and Validation” is published in American Institute of Aeronautics and Astronautics (AIAA) and authered by Assoc. Prof Dr. Soner Aydınlık, Prof. Ahmet Kiris and Prof. Dr. Wojciech Sumelka. The first author (SA) has been supported by The Scientific and Research Council of Turkey (TÜBİTAK) to conduct this research under TÜBİTAK-2219-International Postdoctoral Research Fellowship Program for Turkish Citizens. The support is gratefully acknowledged.
This study aims to examine the dynamics of 3D plates under uniform and non-uniform temperature distributions within the framework of the Fractional Generalized Thermoelasticity approach. The following crucial outcomes reflect the completeness of the proposed model:
• The variations of natural frequencies and mode shapes versus temperature are compared with the experimental results of the NASA report. It is observed that these are both fundamental for identifying the fractional material properties and the thermal and elastic ones.
• The nonlocal approach using fractional calculus gives more consistent results with the experimental one than the classical local theory.
• In the model, the effects connected with thermoelastic damping result in the quadratic eigenvalue problem where complex frequencies and modes are obtained.
• The complex frequency spectrum and mode shapes of the 3D plate with free ends under two different temperature distributions are considered for different values of the fractional continua order and the length scale parameter .
• The fractional solution closest to the experimental results and the classical modes are compared for the first four frequencies. Moreover, the absolute differences between them are also presented with contour plots.
• For the uniform temperature distribution, a mode shifting is observed between the modes corresponding to the 4th and 5th frequencies, while this is not kept for the non-uniform temperature distribution.
• For the non-uniform temperature distribution, mode shape analysis is performed, assuming that elasticity modulus, thermal expansion, and specific heat parameters are functions of temperature.
• The frequencies close to the experimental values are obtained at smaller values of fractional order while temperature increases for the fixed length scale parameter.
• It is observed that the peak point of the out-of-plane displacement is shifted toward the warm zone under the non-uniform temperature distribution. This investigation shows a good agreement with the experimental observations.
These novelties indicate that combining fractional mechanics and Generalized thermoelasticity can establish a more accurate model for complex materials under thermal loading.
https://doi.org/10.2514/1.J063310