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Item Open Access Adaptive numerical homogenization for upscaling single phase flow and transport(ELSEVIER, 2019-03-05) Amanbek, Yerlan; Singh, Gurpreet; Wheeler, Mary F.; Duijn, HansvanWe propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.Item Open Access Adoption of e-Government in the Republic of Kazakhstan(MDPI, 2020-07-09) Amanbek, Yerlan; Balgayev, Ilyas; Batyrkhanov, Kanat; Tan, MargaretInformation and Communication Technology has been gaining importance in the economy of Kazakhstan, the largest landlocked country. In this paper, we investigate the factors that influence Kazakhstan’s e-Government portal use at the informational stage and describe the challenges encountered by citizens while using the portal. Statistical analysis is performed on a web-based questionnaire survey targeted at citizens of Kazakhstan. The technology acceptance model is used as a methodology to measure attitude towards portal usage. This paper also discusses the barriers that can restrict the successful adoption of e-Government services. The results show that awareness among citizens is high and they perceive the portal to be useful, but only a limited percentage of citizens actually use it regularly. The results of this paper could be used to help the IT managers of the portal to improve the management of informational content and maintain more effective adoption among citizens.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 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 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 Analytical and numerical investigations of thecollapse of blood vessels with nonlinear wallmaterial embedded in nonlinear soft tissues(Alexandria Engineering Journal, 2018-11-22) Ghazy, Mohammed; Elgindi, Mohamed B.; Wei, DongmingIn this paper, shapes of nonlinear blood vessels, surrounded by nonlinear soft tissues,and buckled due to radial pressure are solved for analytically and numerically. The blood flow ratesthrough the bucked shapes are then computed numerically. A Fung-type isotropic hyperelasticstress-strain constitutive equation is used to establish a nonlinear mathematical model for radialbuckling of blood vessels...Item Open Access APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS(John Wiley and Sons Inc, 2021-03-23) Zhumekenov, Abylay; Takhanov, Rustem; Castro, Alejandro J.; Assylbekov, ZhenisbekThe paper investigates approximation error of two-layer feedforward Fourier Neural Networks (FNNs). Such networks are motivated by the approximation properties of Fourier series. Several implementations of FNNs were proposed since 1980s: by Gallant and White, Silvescu, Tan, Zuo and Cai, and Liu. The main focus of our work is Silvescu's FNN, because its activation function does not fit into the category of networks, where the linearly transformed input is exposed to activation. The latter ones were extensively described by Hornik. In regard to non-trivial Silvescu's FNN, its convergence rate is proven to be of order O(1/n). The paper continues investigating classes of functions approximated by Silvescu FNN, which appeared to be from Schwartz space and space of positive definite functions.Item Open Access BENIGN OVERFITTING WITH RETRIEVAL AUGMENTED MODELS(Nazarbayev University School of Sciences and Humanities, 2022) Assylbekov, Zhenisbek; Tezekbayev, Maxat; Nikoulina, Vassilina; Gallé, MatthiasDespite the fact that modern deep neural networks have the ability to memorize (almost) the entire training set they generalize well to unseen data, contradicting traditional learning theory. This phenomenon --- dubbed benign overfitting --- has been theoretically studied so far in simplified settings only. At the same time, ML practitioners (especially in NLP) figured out how to exploit this feature for more efficient training: retrieval-augmented models (e.g., kNN-LM, RETRO) explicitly store (part of) the training sample in the storage and thus try to (partially) remove a load of memorization from the neural network. In this paper we link these apparently separate threads of research, and propose several possible research directions regarding benign overfitting in retrieval-augmented models.Item Open Access Classifying equivalence relations in the Ershov hierarchy(Springer, 2020-02-13) Mustafa, Manat; Bazhenov, Nikolay; Mauro, Luca San; Sorbi, Andrea; Yamaleev, MarsComputably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽c. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ02 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽c on the Σ−1a∖Π−1a equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.Item Open Access A COMPARISON OF MACHINE LEARNING ALGORITHMS IN PREDICTING LITHOFACIES: CASE STUDIES FROM NORWAY AND KAZAKHSTAN(MDPI AG, 2021-03-29) Merembayev, Timur; Kurmangaliyev, Darkhan; Bekbauov, Bakhbergen; Amanbek, YerlanDefining distinctive areas of the physical properties of rocks plays an important role in reservoir evaluation and hydrocarbon production as core data are challenging to obtain from all wells. In this work, we study the evaluation of lithofacies values using the machine learning algorithms in the determination of classification from various well log data of Kazakhstan and Norway. We also use the wavelet-transformed data in machine learning algorithms to identify geological properties from the well log data. Numerical results are presented for the multiple oil and gas reservoir data which contain more than 90 released wells from Norway and 10 wells from the Kazakhstan field. We have compared the the machine learning algorithms including KNN, Decision Tree, Random Forest, XGBoost, and LightGBM. The evaluation of the model score is conducted by using metrics such as accuracy, Hamming loss, and penalty matrix. In addition, the influence of the dataset features on the prediction is investigated using the machine learning algorithms. The result of research shows that the Random Forest model has the best score among considered algorithms. In addition, the results are consistent with outcome of the SHapley Additive exPlanations (SHAP) framework.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 Context Vectors Are Reflections of Word Vectors in Half the Dimensions(AI ACCESS FOUNDATION, 2019-09) Assylbekov, Zhenisbek; Takhanov, RustemThis paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec. We start from basic probabilistic assumptions on the nature of word vectors, context vectors, and text generation. These assumptions are supported either empirically or theoretically by the existing literature. Next, we show that under these assumptions the widely-used word-word PMI matrix is approximately a random symmetric Gaussian ensemble. This, in turn, implies that context vectors are reflections of word vectors in approximately half the dimensions. As a direct application of our result, we suggest a theoretically grounded way of tying weights in the SGNS model.Item Open Access CRITICAL HARDY INEQUALITIES(SUOMALAINEN TIEDEAKATEMIA, 2019) Ruzhansky, Michael; Suragan, DurvudkhanWe prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical Hardy inequality and prove Hardy-Sobolev type inequalities. Most of the obtained estimates are new already for the case of R-n. For example, for any f is an element of C-0(infinity) (R-n \ { 0 }) we obtain the range of critical Hardy inequalities of the formItem Open Access Dead-Core Solutions to Simple Catalytic Reaction Problems in Chemical Engineering(The Institute of Combustion Problems, 2019-02-20) Sabit, F.; Shakipov, Mansur; Skrzypacz, Piotr; Golman, BorisThe catalytic chemical reaction is usually carried out in a pellet where the catalyst is distributed throughout its porous structure. The selectivity, yield and productivity of the catalytic reactor often depend on the rates of chemical reactions and the rates of diffusion of species involved in the reactions in the pellet porous space. In such systems, the fast reaction can lead to the consumption of reactants close to the external pellet surface and creation of the dead core where no reaction occurs. This will result in an inefficient use of expensive catalyst. In the discussed simplified diffusion-reaction problems a nonlinear reaction term is of power-law type with a small positive reaction exponent. Such reaction term represents the kinetics of catalytic reaction accompanied by a strong adsorption of the reactant. The ways to calculate the exact solutions possessing dead cores are presented. It was also proved analytically that the exact solution of the nonlinear two-point boundary value problem satisfies physical a-priori bounds. Furthermore, the approximate solutions were obtained using the orthogonal collocation method for pellets of planar, spherical and cylindrical geometries. Numerical results confirmed that the length of the dead core increases for the more active catalysts due to the larger values of the reaction rate constant. The dead core length also depends on the pellet geometry.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 DYNAMICS OF FRACTIONAL-ORDER EPIDEMIC MODELS WITH GENERAL NONLINEAR INCIDENCE RATE AND TIME-DELAY(MDPI AG, 2021-08-03) Kashkynbayev, Ardak; Rihan, Fathalla A.Abstract: 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 results. Keywords: epidemic model; fractional calculus; global stability; lyapunov functionals; time-delayItem 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 Efficient and secure business model for content centric network using elliptic curve cryptography(International Journal of Communication Systems, 2018-10-25) Adhikari, Sharmistha; Ray, Sangram; Biswas, Gosta P.; Obaidat, Mohammad S.Initially, Internet has evolved as a resource sharing model where resources are identified by IP addresses. However, with rapid technological advancement, resources/hardware has become cheap and thus, the need of sharing hardware over Internet is reduced. Moreover, people are using Internet mainly for information exchange and hence, Internet has gradually shifted from resource sharing to information sharing model. To meet the recent growing demand of information exchange, Content Centric Network (CCN) is envisaged as a clean‐slate future network architecture which is specially destined for smooth content distribution over Internet. In CCN, content is easily made available using network caching mechanism which is misaligned with the existing business policy of content providers/publishers in IP‐based Internet. Hence, the transition from contemporary IP‐based Internet to CCN demands attention for redesigning the business policy of the content publishers/providers. In this paper, we have proposed efficient and secure communication protocols for flexible CCN business model to protect the existing business policies of the content publisher while maintaining the salient CCN features like in‐network content caching and Interest packet aggregation. To enhance the efficiency and security, the Elliptic Curve Cryptography (ECC) is used. The proposed ECC‐based scheme is analyzed to show that it is resilient to relevant existing cryptographic attacks. The performance analysis in terms of less computation and communication overheads and increased efficiency is given. Moreover, a formal security verification of the proposed scheme is done using widely used AVISPA simulator and BAN logic that shows our scheme is well secured.Item Open Access Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials(Mathematics in Engineering, 2019-04-03) Mac´ıas-D´ıaz, Jorge E.; Bountis, Anastasios; Christodoulidi, HelenWe consider a family of 1-dimensional Hamiltonian systems consisting of a large number of particles with on-site potentials and global (long range) interactions. The particles are initially at rest at the equilibrium position, and are perturbed sinusoidally at one end using Dirichlet data, while at the other end we place an absorbing boundary to simulate a semi-infinite medium. Using such a lattice with quadratic particle interactions and Klein-Gordon type on-site potential, we use a parameter 0 ≤ α < ∞as a measure of the “length” of interactions, and show that there is a sharp threshold above which energy is transmitted in the form of large amplitude nonlinear modes, as long as driving frequencies Ω lie in the forbidden band-gap of the system. This process is called nonlinear supratransmission and is investigated here numerically to show that it occurs at higher amplitudes the longer the range of interactions, reaching a maximum at a value α = αmax . 1.5 that depends on Ω. Below this αmax supratransmission thresholds decrease sharply to values lower than the nearest neighbor α = ∞ limit. We give a plausible argument for this phenomenon and conjecture that similar results are present in related systems such as the sine-Gordon, the nonlinear Klein-Gordon and the double sine-Gordon type.Item Open Access Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups(Springer, 2020-06-10) Ruzhansky, Michael; Suragan, Durvudkhan; Yessirkegenov, NurgissaIn this paper we describe the Euler semigroup {e−tE∗E}t>0 on homogeneous Lie groups, which allows us to obtain various types of the Hardy–Sobolev and Gagliardo–Nirenberg type inequalities for the Euler operator E. Moreover, the sharp remainder terms of the Sobolev type inequality, maximal Hardy inequality and |⋅|-radial weighted Hardy–Sobolev type inequality are established.