Math. Comput. Appl., Volume 29, Issue 1 (February 2024) – 16 articles

Bioventing is an established technique extensively employed in the remediation of soil contaminated with petroleum hydrocarbons. In this study, the objective was to develop an improved foundational bioventing model that characterizes gas flow in vadose zones where aqueous and non-aqueous phase liquid (NAPL) are present and immobile, accounting for interphase mass transfer and first order biodegradation kinetics. By incorporating a correlation for the biodegradation rate constant, which is a function of soil properties including initial population of petroleum degrader microorganisms in soil, sand content, clay content, water content, and soil organic matter content, this model offers the ability to integrate a specific biodegradation rate constant tailored to the soil properties for each site. The governing equations were solved using the finite volume method in OpenFOAM employing the “porousMultiphaseFoam v2107” (PMF) toolbox. The equation describing gas flow in unsaturated soil was solved using a mixed pressure-saturation method, where calculated values were employed to solve the component transport equations. Calibration was done against a set of experimental data for a meso-scale reactor considering contaminant volatilization rate as the pre-calibration parameter and the mass transfer coefficient between aqueous and NAPL phase as the main calibration parameter. The calibrated model then was validated by simulating a large-scale reactor. The modelling results showed an error of 2.9% for calibrated case and 4.7% error for validation case which present the fitness to the experimental data, proving that the enhanced bioventing model holds the potential to improve predictions of bioventing and facilitate the development of efficient strategies to remediate soil contaminated with petroleum hydrocarbons. Full article

In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions—have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries. Full article

A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies. This computation traditionally relied on Vélu’s formulas, an approach with time complexity linear in the degree but which was further enhanced by Bernstein, De Feo, Leroux, and Smith to a square-root complexity. The improved square-root Vélu’s formulas exhibit a degree of parallelizability that has not been exploited in major implementations. In this study, we introduce a theoretical framework for parallelizing isogeny computations and provide a proof-of-concept implementation in C with OpenMP. While the parallelization effectiveness exhibits diminishing returns with the number of cores, we still obtain strong results when using a small number of cores. Concretely, our implementation shows that for large degrees it is easy to achieve speedup factors of up to $1.74$, $2.54$, and $3.44$ for two, four, and eight cores, respectively. Full article

Calcium (Ca²⁺) and magnesium (Mg²⁺) are essential for cellular function. The kidneys play an important role in maintaining the homeostasis of these cations. Their reabsorption along the nephron is dependent on distinct trans- and paracellular pathways and is coupled to the transport of other electrolytes. Notably, sodium (Na⁺) transport establishes an electrochemical gradient to drive Ca²⁺ and Mg²⁺ reabsorption. Consequently, alterations in renal Na⁺ handling, under pathophysiological conditions or pharmacological manipulations, can have major effects on Ca²⁺ and Mg²⁺ transport. One such condition is the administration of diuretics, which are used to treat a large range of clinical conditions, but most commonly for the management of blood pressure and fluid balance. While the pharmacological targets of diuretics typically directly mediate Na⁺ transport, they also indirectly affect renal Ca²⁺ and Mg²⁺ handling through alterations in the electrochemical gradient. To investigate renal Ca²⁺ and Mg² handling and how those processes are affected by diuretic treatment, we have developed computational models of electrolyte transport along the nephrons. Model simulations indicate that along the proximal tubule and thick ascending limb, the transport of Ca²⁺ and Mg²⁺ occurs in parallel with Na⁺, but those processes are dissociated along the distal convoluted tubule. We also simulated the effects of acute administration of loop, thiazide, and K-sparing diuretics. The model predicted significantly increased Ca²⁺ and Mg²⁺ excretions and significantly decreased Ca²⁺ and Mg²⁺ excretions on treatment with loop and K-sparing diuretics, respectively. Treatment with thiazide diuretics significantly decreased Ca²⁺ excretion, but there was no significant alteration in Mg²⁺ excretion. The present models can be used to conduct in silico studies on how the kidney adapts to alterations in Ca²⁺ and Mg²⁺ homeostasis during various physiological and pathophysiological conditions, such as pregnancy, diabetes, and chronic kidney disease. Full article

This paper proposes the D2Q5 Lattice Boltzmann method (LBM) method, in two dimensions with five discrete lattice velocities, for simulating linear sound wave propagation in closed rooms. A second-order linear acoustic equation obtained from the LBM method was used as the model equation. Boundary conditions at the domain boundary use the bounce-back scheme. The LBM numerical calculation algorithm in this paper is relatively simpler and easy to implement. Parallelization with the GPU CUDA was implemented to speed up the execution time. The calculation results show that the use of parallel GPU CUDA programming can accelerate the proposed simulation 27.47 times faster than serial CPU programming. The simulation results are validated with analytical solutions for acoustic pulse reflected by the flat and oblique walls, the comparisons show very good concordance, and the D2Q5 LBM has second-order accuracy. In addition, the simulation results in the form of wavefront propagation images in complicated shaped rooms are also compared with experimental photographs, and the comparison also shows excellent concordance. The numerical results of the D2Q5 LBM are promising and also demonstrate the great capability of the D2Q5 LBM for investigating room acoustics in various complexities. Full article

In this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theorem. The obtained solutions have the form of infinite non-harmonic Fourier series. The main advantage of the proposed approach is the closed-form of the solutions, which are capable of accurately evaluating the solution at any time. Moreover, it allows one to study the asymptotic behavior of the solutions. A remarkable discovery, which to the best of our knowledge has never been presented in the literature, is that there are some particular linear systems of both retarded and neutral delay differential equations for which the solution asymptotically approaches a limit cycle. The well-known method of steps in many cases is unable to obtain the asymptotic behavior of the solution and would most likely fail to detect such cycles. Examples illustrating the Laplace transform method for linear systems of DDEs are presented and discussed. These examples are designed to facilitate a discussion on how the spectral properties of the matrices determine the manner in which one proceeds and how they impact the behavior of the solution. Comparisons with the exact solution provided by the method of steps are presented. Finally, we should mention that the solutions generated by the Laplace transform are, in most instances, extremely accurate even when the truncated series is limited to only a handful of terms and in many cases become more accurate as the independent variable increases. Full article

Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz’s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. Full article

Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the generalization accuracy of a CTESN surrogate is the method of projecting the reservoir state to the output. This paper shows that of the two common projection methods (linear and nonlinear), the surrogates developed via the nonlinear projection consistently outperform those developed via the linear method. CTESN surrogates are developed for several challenging benchmark cases governed by stiff ODEs, and for each case, the performance of the linear and nonlinear projections is compared. The results of this paper demonstrate the applicability of CTESNs to a variety of problems while serving as a reference for important algorithmic and hyper-parameter choices for CTESNs. Full article

Electromyography (EMG) is a widely used method for estimating muscle activity and could help in understanding how muscles interact with each other and affect human movement control. To detect muscle interactions during elbow flexion and extension, a recently developed InterCriteria Analysis (ICrA) based on the mathematical formalisms of index matrices and intuitionistic fuzzy sets is applied. ICrA has had numerous implementations in different fields, including biomedicine and quality of life; however, this is the first time the approach has been used for establishing muscle interactions. Six human upper arm large surface muscles or parts of muscles responsible for flexion and extension in shoulder and elbow joints were selected. Surface EMG signals were recorded from four one-joint (pars clavicularis and pars spinata of m. deltoideus [DELcla and DELspi, respectively], m. brachialis [BRA], and m. anconeus [ANC]) and two two-joint (m. biceps brachii [BIC] and m. triceps brachii-caput longum [TRI]) muscles. The outcomes from ten healthy subjects performing flexion and extension movements in the sagittal plane at four speeds with and without additional load are implemented in this study. When ICrA was applied to examine the two different movements, the BIC–BRA muscle interaction was distinguished during flexion. On the other hand, when the ten subjects were observed, four interacting muscle pairs, namely DELcla-DELspi, BIC-TRI, BIC-BRA, and TRI-BRA, were detected. The results obtained after the ICrA application confirmed the expectations that the investigated muscles contribute differently to the human upper arm movements when the flexion and extension velocities are changed, or a load is added. Full article

In this paper, we propose an extended credit migration model with asymmetric fixed boundaries and multiple ratings, for a more precise depiction of credit changes in the real world. A model with three ratings is established and analyzed as an example, and then the results are generalized to a general multirating form model. We prepare the model meaningfully by arranging the asymmetric boundaries in a suitable order. A PDE system problem is deduced, and the existence and uniqueness of the solution for the problem are obtained using PDE techniques, which further ensure the rationality of the model. Due to the flexible configuration of asymmetric boundaries, the multirating model has various types of structures in the buffer zones where the credit rating keeps its original state. For instance, the two buffers in the three-rating model may be separated, connected, or intersected, as presented in the numerical results for different boundary parameters. Full article

In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method. Full article

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time. Full article

Small-scale photovoltaic (PV) systems are essential for the local energy supply. The most commonly known PV cell is configured as a large-area p–n junction made from silicon, but PV systems today include PV cells of various manufactures and origins. The dependence relationship between current and voltage is nonlinear, known as the current–voltage characteristic. The values of the characteristic equation’s parameters define the working regime of the PV cell. In the present work, the parameter values are iteratively obtained by nonlinear regression for an explicit model. The acceleration of the convergence of these values is studied for an approximation simplifying the iterative calculation in the case of perpendicular offsets. The new estimations of parameters allow for a much faster estimate of the maximum power point of the PV system. Full article

It is frequently observed that adult members of prey species sometimes use their predation mechanism on juvenile members of predator species. Ecological literature describes this phenomenon as prey–predator role reversal dynamics.Numerous authors have observed and described the biological development behind this feeding behaviour. However, the dynamics of this role reversal have hardly been illustrated in the literature in a precise way. In this regard, we formulated an ecological model using the standard prey–predator interactions, allowing for a reverse feeding mechanism. The mathematical model consisted of a three-species food-web structure comprising the common prey, intermediate predator, and top predator. Note that a role-reversal mechanism was observed between the intermediate and top predators based on the scarcity of the prey population. However, we observed the most critical parameters had a significant effect on this reverse feeding behaviour. The bifurcation analysis is the primary criterion for this identification. The proposed deterministic model is then extended to its stochastic analogue by allowing for environmental influences on the tri-trophic food web structure. The conditional moment approach is applied to obtain the equilibrium distribution of populations and their conditional moments in the system. The stochastic setup analysis also supports the stability of this food chain structure, with some restricted conditions. Finally, to facilitate the interpretation of our mathematical results, we investigated it using numerical simulations. Full article

In this paper, we develop a finite difference method for solving the wave equation with fractional damping in 1D and 2D cases, where the fractional damping is given based on the Caputo fractional derivative. Firstly, based on the weighted method, we propose a new numerical approximation for the Caputo fractional derivative and apply it for the 1D case to obtain a time-stepping method. We then develop an alternating direction implicit (ADI) scheme for the 2D case. Using the discrete energy method, we prove that the proposed difference schemes are unconditionally stable and convergent in both 1D and 2D cases. Finally, several numerical examples are given to verify the theoretical results. Full article

Simulation and modeling of thermal recuperative incinerators may play an important role in enhancing efficiency and ensuring compliance with environmental regulations. In this context, the primary objective of this study is to simulate and comprehensively understand the operation of a geometrically complex thermal recuperative incinerator with an integrated preheater featuring varying levels of heat recovery. To achieve this objective, a simple yet effective 0D model was developed. This modeling approach allows for a holistic evaluation of the performance of the incinerator, enabling the assessment of key parameters, such as temperatures and heat transfer rates, under varying operating conditions. Successful validation of the model is established by comparing its results with measurements from an industrial thermal recuperative incinerator in operation at a vehicle assembly plant, with maximum relative differences of around 9%. Simulations for different percentages of flue gases bypassing the preheater were conducted, indicating a good compromise between heat transfer and pressure drop and a 22% heat recovery at around 50%. The model presented in this paper provides a robust foundation for comprehensively assessing and optimizing the performance of thermal recuperative incinerators and systems that comprise thermal recuperative incinerators, with implications for waste management and sustainable energy recovery systems. Full article