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Item Open Access EFFECTS OF MELT TEMPERATURE AND NON-ISOTHERMAL FLOW IN DESIGN OF COAT HANGER DIES BASED ON FLOW NETWORK OF NON-NEWTONIAN FLUIDS(Polymers, 2022) Razeghiyadaki, Amin; Wei, Dongming; Perveen, Asma; Zhang, Dichuan; Wang, YanweiIn the design of coat hanger extrusion dies, the main objective is to provide a uniform flow rate at the die exit. Previously, a multi-rheology isothermal method model for coat hanger extrusion dies was developed to reach this objective. Polymer melts in extrusion dies commonly experience high shear rates. Viscous dissipation rooted by high shear rate may lead to significant temperature differences across the die. Due to temperature-dependency of viscosity, temperature differences may lead to nonuniform flow rates, which may significantly affect the flow rate at the die exit. As a result, a new design method is proposed to take into account the effects of temperature and viscous dissipation in the design of coat hanger dies. Although more non-Newtonian fluid rheology models can be adapted in the proposed study, as demonstration, temperature-dependent power-law and Carreau–Yasuda models are adapted in this study. Performances are compared with our isothermal method published earlier. In addition, the novel nonisothermal method is comprehensively examined where the effect of viscous dissipation is studied through Brinkman number of extrusion die. It is demonstrated that, for a low Brinkman number, both isothermal and nonisothermal design give similar flow uniformity level. However, for higher Brinkman numbers, the proposed nonisothermal method produces a design with more desirable velocity uniformity level along with a maximum improvement of 5.24% over the isothermal method. In addition, dependency of flow field on temperature, due to temperature-dependent viscosity, is studied, and it is demonstrated that fullydeveloped velocity profile changes as temperature increases along the flow channel. Moreover, the effect of the temperature sensitivity parameter in temperature-dependent non-Newtonian models is considered. It is demonstrated that the temperature boundary condition with the Biot number of 1.0 gives adequate results for lower values of the temperature sensitivity parameter.Item Open Access ANALYSIS OF LANDAU–LIFSHITZ AND NEO-HOOKEAN MODELS FOR STATIC AND DYNAMIC ACOUSTOELASTIC TESTING(Physica Scripta, 2022) Melnikov, Andrey; Malcolm, Alison E; Poduska, Kristin MA comparison of three different isotropic non-linear elastic models uncovers subtle but important differences in the acoustoelastic responses of a material slab that is subjected to dynamic deformations during a pump-probe experiment. The probe wave deformations are small and are superimposed on larger underlying deformations using three different models: Landau–Lifshitz (using itsfourth-order extension), compressible neo-Hookean model(properly accountingfor volumetric deformations), and an alternative neo-Hookeanmodel(fully decoupled energies due to distortional isochoric and volumetric deformations). The analyses yield elasticity tensors and respective expressionsfor the propagation speeds of P-wave and S-wave probesfor each model. Despite having many similarities, the different models give different predictions of which probe wave types will have speeds that are perturbed by different pump wave types. The analyses also show a conceptual inconsistency in the Landau–Lifshitz model, that a simple shear deformation induces a stress and a shear wave probe speed that depend on the second-order elastic constantλ, which controls resistance to volumetric changes and thus should not be present in the expressionsfor shear stress and shear wave probe speeds. Thus, even though the Landau–Lifshitz model is widely used, it may not always be the best option to model experimental data.Item Open Access ANALYSIS OF DEAD CORE FORMATION IN CATALYTIC REACTION AND DIFUSION PROCESSES WITH GENERALIZED DIFUSION FUX(Scientific Reports, 2022) Skrzypacz, Piotr; Kabduali, Bek; Kadyrbek, Alua; Szafert, Sławomir; Andreev, Vsevolod; Golman, BorisDead-core and non-dead-core solutions to the nonlinear diffusion–reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones where the reactant concentration vanishes is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fick’s diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick’s diffusion fluxes is established.Item Open Access SATURATED AND ASYMMETRIC SATURATED IMPULSIVE CONTROL SYNCHRONIZATION OF COUPLED DELAYED INERTIAL NEURAL NETWORKS WITH TIME-VARYING DELAYS(Applied Mathematical Modelling, 2023) Udhayakumar, K.; Shanmugasundaram, S.; Kashkynbayev, Ardak; Janani, K.; Rakkiyappan, R.This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings.Item Open Access THE INFLUENCING FACTORS OF CO2 EMISSIONS AND THE ADOPTION OF ECO-INNOVATION ACROSS G-7 ECONOMIES: A NOVEL HYBRID MATHEMATICAL AND STATISTICAL APPROACH(Frontiers in Environmental Science, 2022-09-29) Rehman, Erum; Rehman, Shazia; Mumtaz, Ayesha; Jianglin, Zhang; Shahiman, Muhammad AliThe present study empirically analyzes the role of eco-innovation in plummeting carbon dioxide (CO2) emissions in conjunction with renewable energy usage, foreign direct investment, and trade openness for the states in G-7 from 1990 to 2019 in a mathematical and statistical context. Under the dynamical framework, the estimates of mathematical grey relational analyses indicate that eco-innovation holds a stronger degree of association with CO2 emissions. Further, the estimates demonstrate that, compared to the other G-7 states, Japan is the country where eco-innovation is a more striking variable. However, renewable energy utilization seems weaker in Japan, which necessitates adopting renewable energy to curb carbon emissions in the region. Statistically, the odds ratio illustrates a similar pattern, demonstrating that the odds of occurrence for eco-innovation are much stronger in reducing the rising levels of carbon emissions within the G-7 states. Moreover, trade openness and foreign direct investment were revealed to be the leading contributors to carbon emissions in Germany and Canada, respectively, whilst appearing to be significant variables in lowering emissions in the United States and the United Kingdom. The outcomes of this investigation offer significant perspectives for policymakers in formulating holistic and environmentally friendly policies by embracing eco-innovation as a potentially significant component for sustainable economic expansion and environmental health.Item Open Access MUTUAL INTERDEPENDENCE OF THE PHYSICAL PARAMETERS GOVERNING THE BOUNDARY-LAYER FLOW OF NON-NEWTONIAN FLUIDS(Applied Sciences, 2022-05-23) Al-Ashhab, Samer; Wei, Dongming; Alyami, Salem A.; Azad, AKM; Moni, Mohammad AliWe consider non-Newtonian boundary-layer fluid flow, governed by a power-law OstwalddeWaele rheology. Boundary-layer flows of non-Newtonian fluids have far-reaching applications, and are very frequently encountered in physical, as well as, engineering and industrial processes. A similarity transformation results in a BVP consisting of an ODE and some boundary conditions. Our aim is to derive highly accurate analytical relationships between the physical and mathematical parameters associated with the BVP and boundary-layer flow problem. Mathematical analyses are employed, where the results are verified at the numerical computational level, illustrating the accuracy of the derived relations. A set of “Crocco variables” is used to transform the problem, and, where appropriate, techniques are used to deal with the resulting singularities in order to establish an efficient computational setting. The resulting computational setting provides an alternative, which is different from those previously used in the literature. We employ it to carry out our numerical computations.Item Open Access DYNAMICS OF FRACTIONAL-ORDER EPIDEMIC MODELS WITH GENERAL NONLINEAR INCIDENCE RATE AND TIME-DELAY(Mathematics, 2021-08-03) Kashkynbayev, Ardak; Rihan, Fathalla A.In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if R0 < 1, the disease-free steady-state is locally and globally asymptotically stable. However, for R0 > 1, there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical resultsItem Open Access OSCILLATION CRITERIA FOR LINEAR DIFFERENCE EQUATIONS WITH SEVERAL VARIABLE DELAYS(Opuscula Mathematica, 2021) Benekas, Vasileios; Garab, Abel; Kashkynbayev, Ardak; Stavroulakis, Ioannis P.We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.Item Open Access ON THE CAUCHY PROBLEM FOR A NONLOCAL NONLINEAR SCHRÖDINGER EQUATION(Discrete and Continuous Dynamical Systems, 2022-12) Wang, Hongwei; Esfahani, AminThis paper considers the one-dimensional Schrödinger equation with nonlocal nonlinearity that describes the interactions of nonlinear dispersive waves. We obtain some the local well-posedness and ill-posedness result associated with this equation in the Sobolev spaces. Moreover, we prove the existence of standing waves of this equation. As corollary, we derive the conditions under which the solutions are uniformly bounded in the energy space.Item Open Access ALMOST PERIODIC SOLUTIONS OF FUZZY SHUNTING INHIBITORY CNNS WITH DELAYS(AIMS Mathematics, 2022) Kashkynbayev, Ardak; Koptileuova, Moldir; Issakhanov, Alfarabi; Cao, JindeIn the present paper, we prove the existence of unique almost periodic solutions to fuzzy shunting inhibitory cellular neural networks (FSICNN) with several delays. Further, by means of Halanay inequality we analyze the global exponential stability of these solutions and obtain corresponding convergence rate. The results of this paper are new, and they are concluded with numerical simulations confirming them.Item Open Access ON THE PERSISTENCE OF SPATIAL ANALYTICITY FOR THE BEAM EQUATION(Journal of Mathematical Analysis and Applications, 2022) Dufera, Tamirat T.; Mebrate, Sileshi; Tesfahun, AchenefPersistence of spatial analyticity is studied for solution of the beam equation utt + (m + Δ2) u + |u| p−1u = 0 on Rn × R. In particular, for a class of analytic initial data with a uniform radius of analyticity σ0, we obtain an asymptotic lower bound σ(t) c/√t on the uniform radius of analyticity σ(t) of solution u(·,t), as t → ∞. © 2022 Elsevier Inc. All rights reservedItem Open Access ROLE OF MEDIA IN ADDRESSING THE SOCIALIZATION PROBLEMS OF THE YOUNGER GENERATION: THE CASE OF KAZAKHSTAN(Media Watch, 2020) KUTYM, BEGIM K.; YESSENBEKOVA, ULBOSSYN M.; TURZHAN, ONGAIGUL I.; KOSHANOVA, KULNASH A.; YEGEMBERDIYEV, ISKAKH D.The article examines the cultural and educational mission of modern media related to the spiritual and cultural education of youth in Kazakhstan. Over the past two decades, the socialization problems of Kazakh youth have been removed from the state’s social policy agenda. Methods of comparative and complex analysis were applied in this study. To define acute youth problems, the study analyzed television projects and printed materials related to different periods of media activity in Kazakhstan. Several sociological measurements were used to reveal the needs of the television audience. The study defined the key socialization factors and institutions of young people. The article describes the role of media in establishing social standards of behavior, communication, and activity that directly affect the process of socialization. The study analyzes the activities of TV channels performing a cultural and educational function. The need to strengthen the editorial policy of media resources, focusing on socially significant issues with priority given to social and educational broadcasting, became an essential conclusion of the study. The results of the study allowed to compile an average portrait of the young generation, as well as to identify the key characteristics for the correction of life strategies.Item Open Access PERIODICALLY FORCED NONLINEAR OSCILLATORS WITH HYSTERETIC DAMPING(arxiv, 2020) Bountis, Anastasios; Kaloudis, Konstantinos; Spitas, ChristosWe perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as t → ∞. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop’s model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid [2], which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.Item Open Access Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process(arxiv, 2020) LEE, EunghyunWe find the formulas of the transition probabilities of the N-particle multi species asymmetric simple exclusion processes (ASEP), and show that the transition prob abilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.Item Open Access COMPLEX DYNAMICS AND STATISTICS OF 1-D HAMILTONIAN LATTICES: LONG RANGE INTERACTIONS AND SUPRATRANSMISSION(Nonlinear Phenomena in Complex Systems, 2019) Bountis, AnastasiosIn this paper, I review a number of results that my co-workers and I have obtained in the field of 1–Dimensional (1D) Hamiltonian lattices. This field has grown in recent years, due to its importance in revealing many phenomena that concern the occurrence of chaotic behavior in conservative physical systems with a high number of degrees of freedom. After the establishment of the Kolomogorov–Arnol’d–Moser (KAM) theory in the 1960s, a wealth of results were obtained about such systems as small perturbations of completely integrable N degree-of-freedom Hamiltonians, where ordered motion is dominant in the form of invariant tori. Since the 1980s, however, and particularly in the last two decades, there has been great progress in understanding the properties of Hamiltonian 1D lattices far from the KAM regime, where "weak" and "strong" forms of chaos begin to play an increasingly significant role. It is the purpose of this review to address and highlight some of these advances, in which the author has made several contributions concerning the dynamics and statistics of these latticesItem Open Access FOURIER NEURAL NETWORKS: A COMPARATIVE STUDY(arxiv, 2019) Zhumekenov, Abylay; Uteuliyeva, Malika; Takhanov, Rustem; Assylbekov, Zhenisbek; Castro, Alejandro J.We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them outperforms the standard neural network with sigmoid activation function in the real-world tasks. All neural networks, both Fourier and the standard one, empirically demonstrate lower approximation error than the truncated Fourier series when it comes to approximation of a known function of multiple variables.Item Open Access GLOBAL ANALYTIC SOLUTIONS FOR THE NONLINEAR SCHRODINGER EQUATION(arxiv, 2019) BIYAR, MAGZHAN; DA SILVA, DANIEL OLIVEIRAWe prove the existence of global analytic solutions to the nonlinear Schr¨odinger equation in one dimension for a certain type of analytic initial data in L2Item Open Access STABILITY PROPERTIES OF 1-DIMENSIONAL HAMILTONIAN LATTICES WITH NON-ANALYTIC POTENTIALS(arxiv, 2020) Bountis, Anastasios; Kaloudis, Konstantinos; Oikonomou, Thomas; Manda, Bertin Many; Skokos, CharalamposWe investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from non-analytic potentials. In particular, we study the dynamics of a model governed by a “graphene-type” force law and one inspired by Hollomon’s law describing “work-hardening” effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of non-analytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles N and the total energy E are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for larg e N, it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.Item Open Access SERSNET: SURFACE-ENHANCED RAMAN SPECTROSCOPY BASED BIOMOLECULE DETECTION USING DEEP NEURAL NETWORK(MDPI AG, 2021-11-30) Park, Seongyong; Lee, Jaeseok; Khan, Shujaat; Wahab, Abdul; Kim, MinseokSurface-Enhanced Raman Spectroscopy (SERS)-based biomolecule detection has been a challenge due to large variations in signal intensity, spectral profile, and nonlinearity. Recent advances in machine learning offer great opportunities to address these issues. However, welldocumented procedures for model development and evaluation, as well as benchmark datasets, are lacking. Towards this end, we provide the SERS spectral benchmark dataset of Rhodamine 6G (R6G) for a molecule detection task and evaluate the classification performance of several machine learning models. We also perform a comparative study to find the best combination between the preprocessing methods and the machine learning models. Our best model, coined as the SERSNet, robustly identifies R6G molecule with excellent independent test performance. In particular, SERSNet shows 95.9% balanced accuracy for the cross-batch testing task. Keywords: Surface Enhanced Raman Spectroscopy; molecule detection; machine learning; deep learningItem Open Access LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS AND MITTAG-LEFFLER KERNELS(Alexandria Engineering Journal, 2021-10-27) Fernandez, Arran; Restrepo, Joel E.; Suragan, DurvudkhanFractional differential equations with constant coefficients can be readily handled by a number of methods, but those with variable coefficients are much more challenging. Recently, a method has appeared in the literature for solving fractional differential equations with variable coefficients, the solution being in the form of an infinite series of iterated fractional integrals. In the current work, we consider fractional differential equations with Atangana–Baleanu integro- differential operators and continuous variable coefficients, and establish analytical solutions for such equations. The representation of the solution is given by a uniformly convergent infinite series involving Atangana–Baleanu operators. To the best of our knowledge, this is the first time that explicit analytical solutions have been given for such general Atangana–Baleanu differential equa- tions with variable coefficients. The corresponding results for fractional differential equations with constant coefficients are also given