Search results for: Einstein field equations

Authors: Takoua Soltani, Imen Soltani, Taoufik Aguili

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The communications' and radar systems' demands give rise to new developments in the domain of active integrated antennas (AIA) and arrays. The main advantages of AIA arrays are the simplicity of fabrication, low cost of manufacturing, and the combination between free space power and the scanner without a phase shifter. The integrated active antenna modeling is the coupling between the electromagnetic model and the transport model that will be affected in the high frequencies. Global modeling of active circuits is important for simulating EM coupling, interaction between active devices and the EM waves, and the effects of EM radiation on active and passive components. The current review focuses on the modeling of the active element which is a MESFET transistor immersed in a rectangular waveguide. The proposed EM analysis is based on the Method of Moments combined with the Generalised Equivalent Circuit method (MOM-GEC). The Method of Moments which is the most common and powerful software as numerical techniques have been used in resolving the electromagnetic problems. In the class of numerical techniques, MOM is the dominant technique in solving of Maxwell and Transport’s integral equations for an active integrated antenna. In this situation, the equivalent circuit is introduced to the development of an integral method formulation based on the transposition of field problems in a Generalised equivalent circuit that is simpler to treat. The method of Generalised Equivalent Circuit (MGEC) was suggested in order to represent integral equations circuits that describe the unknown electromagnetic boundary conditions. The equivalent circuit presents a true electric image of the studied structures for describing the discontinuity and its environment. The aim of our developed method is to investigate the antenna parameters such as the input impedance and the current density distribution and the electric field distribution. In this work, we propose a global EM modeling of the MESFET AsGa transistor using an integral method. We will begin by describing the modeling structure that allows defining an equivalent EM scheme translating the electromagnetic equations considered. Secondly, the projection of these equations on common-type test functions leads to a linear matrix equation where the unknown variable represents the amplitudes of the current density. Solving this equation resulted in providing the input impedance, the distribution of the current density and the electric field distribution. From electromagnetic calculations, we were able to present the convergence of input impedance for different test function number as a function of the guide mode numbers. This paper presents a pilot study to find the answer to map out the variation of the existing current evaluated by the MOM-GEC. The essential improvement of our method is reducing computing time and memory requirements in order to provide a sufficient global model of the MESFET transistor.

Keywords: active integrated antenna, current density, input impedance, MESFET transistor, MOM-GEC method

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: A. L. Qureshi, A. A. Mahessar, A. Baloch

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Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. However, it is difficult to find analytical solution of these complex non-linear equations. Hence, verification of the numerical model should be carried out against field data and numerical predictions. This paper presents the verification of developed finite element model applying for unsteady flow in the open channels. The results of a proposed model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29 km at both sites (15 km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400 km downstream from Sukkur barrage, which demonstrates accurate model predictions with observed daily discharges. Hence, this model may be utilized for predicting and issuing flood warnings about flood hazardous in advance.

Keywords: finite element method, Preissmann scheme, HEC-RAS, flood forecasting, Indus river

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Authors: Naseem Uddin

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Impinging jets are used in variety of engineering and industrial applications. This paper is based on numerical simulations of heat transfer by turbulent impinging jet with velocity field excitations using different Reynolds Averaged Navier-Stokes Equations models. Also Detached Eddy Simulations are conducted to investigate the differences in the prediction capabilities of these two simulation approaches. In this paper the excited jet is simulated in non-commercial CFD code OpenFOAM with the goal to understand the influence of dynamics of impinging jet on heat transfer. The jet’s frequencies are altered keeping in view the preferred mode of the jet. The Reynolds number based on mean velocity and diameter is 23,000 and jet’s outlet-to-target wall distance is 2. It is found that heat transfer at the target wall can be influenced by judicious selection of amplitude and frequencies.

Keywords: excitation, impinging jet, natural frequency, turbulence models

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Authors: Jurriaan Gillissen

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This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Hossein Shokouhmand, Masoomeh Shadab, Rohallah Torabi

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Turbulent flow inside the seal chamber of a pump operating at nearly high Reynolds number is investigated. A comparison of a 3-D computational model for flow and thermal analysis of a mechanical seal with experimental thermal results is presented. The computational model adequately predicts the flow field in the seal chamber and thermal characteristics with the rotating and stationary rings and the twister flow around the seal parts by solving N-S and energy equations in ANSYS-CFX software. The Reynolds stress model (RSM) is applied as a turbulence model for this purpose. Experimental work is discussed which quantifies the temperature of five different points of the working fluid in chamber, mass flow at inlet and the fluid pressure at inlet and outlet. Experimental measurements are combined with computational modeling to obtain local and average heat transfer characteristics. Numerical results of three cases including different flush rates are reported.

Keywords: mechanical seal, CFD_CFX, reynolds stress model, flow field, heat transfer analysis, stream line, heat transfer coefficient, heat flux, nusselt

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Authors: Thana Ananacha

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This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered namely 400 and 800 W.m-2 the corresponding initial condition temperatures were to 30.5 and 38.5 ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: thermal simulation, Double Glass Wall, velocity field, finite element method (FEM)

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: S. Obregon-Cano, R. Moreno-Rojas, E. Cartea-Gonzalez, A. De Haro-Bailon

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The potential of near-infrared spectroscopy (NIRS) for screening the total glucosinolate (t-GSL) content, and also, the aliphatic glucosinolates gluconapin (GNA), progoitrin (PRO) and glucobrassicanapin (GBN) in turnip greens and turnip tops was assessed. This crop is grown for edible leaves and stems for human consumption. The reference values for glucosinolates, as they were obtained by high performance liquid chromatography on the vegetable samples, were regressed against different spectral transformations by modified partial least-squares (MPLS) regression (calibration set of samples n= 350). The resulting models were satisfactory, with calibration coefficient values from 0.72 (GBN) to 0.98 (tGSL). The predictive ability of the equations obtained was tested using a set of samples (n=70) independent of the calibration set. The determination coefficients and prediction errors (SEP) obtained in the external validation were: GNA=0.94 (SEP=3.49); PRO=0.41 (SEP=1.08); GBN=0.55 (SEP=0.60); tGSL=0.96 (SEP=3.28). These results show that the equations developed for total glucosinolates, as well as for gluconapin can be used for screening these compounds in the leaves and stems of this species. In addition, the progoitrin and glucobrassicanapin equations obtained can be used to identify those samples with high, medium and low contents. The calibration equations obtained were accurate enough for a fast, non-destructive and reliable analysis of the content in GNA and tGSL directly from NIR spectra. The equations for PRO and GBN can be employed to identify samples with high, medium and low contents.

Keywords: brassica rapa, glucosinolates, gluconapin, NIRS, turnip greens

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Authors: Rama Bhargava, Mania Goyal

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The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.

Keywords: viscoelastic nanofluid, partial slip, stretching sheet, heat generation/absorption, MHD flow, FEM

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Tasawar Hayat, Madiha Rashid, Maria Imtiaz, Ahmed Alsaedi

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This problem is about the study of flow of viscous fluid due to rotating disk in nanofluid. Effects of magnetic field, slip boundary conditions and thermal radiations are encountered. An incompressible fluid soaked the porous medium. In this model, nanoparticles of Cu is considered with water as the base fluid. For Copper-water nanofluid, graphical results are presented to describe the influences of nanoparticles volume fraction (φ) on velocity and temperature fields for the slip boundary conditions. The governing differential equations are transformed to a system of nonlinear ordinary differential equations by suitable transformations. Convergent solution of the nonlinear system is developed. The obtained results are analyzed through graphical illustrations for different parameters. Moreover, the features of the flow and heat transfer characteristics are analyzed. It is found that the skin friction coefficient and heat transfer rate at the surface are highest in copper-water nanofluid.

Keywords: MHD nanofluid, porous medium, rotating disk, slip effect

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Fatemeh Shahi, Mehdi Sharifian, Laia Shahrassai, Elham Eskandari A.

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A new mechanism is reported here for magnetic field generation in laser-plasma interaction by means of nonlinear ponderomotive force. The plasma considered here is unmagnetized inhomogeneous plasma with an exponentially decreasing profile. A damped periodic magnetic field with a relatively lower frequency is obtained using the ponderomotive force exerted on plasma electrons. Finally, with an electric field and by using Faraday’s law, the magnetic field profile in the plasma has been obtained. Because of the negative exponential density profile, the generated magnetic field is relatively slowly oscillating and damped through the plasma.

Keywords: magnetic field generation, laser-plasma interaction, ponderomotive force, inhomogeneous plasma

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Authors: Lukas Vierus, Thomas Schuster

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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

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The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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Authors: Behzad Ali Khan, M. Zubair Akbar Qureshi

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The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.

Keywords: darcy forcheimer, hybrid ferro fluid, porous medium, porous channel

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Authors: Jaan Lellep, Shahid Mubasshar

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A numerical solution is developed for simply supported nanoarches based on the non-local theory of elasticity. The nanoarch under consideration has a step-wise variable cross-section and is weakened by crack-like defects. It is assumed that the cracks are stationary and the mechanical behaviour of the nanoarch can be modeled by Eringen’s non-local theory of elasticity. The physical and thermal properties are sensitive with respect to changes of dimensions in the nano level. The classical theory of elasticity is unable to describe such changes in material properties. This is because, during the development of the classical theory of elasticity, the speculation of molecular objects was avoided. Therefore, the non-local theory of elasticity is applied to study the vibration of nanostructures and it has been accepted by many researchers. In the non-local theory of elasticity, it is assumed that the stress state of the body at a given point depends on the stress state of each point of the structure. However, within the classical theory of elasticity, the stress state of the body depends only on the given point. The system of main equations consists of equilibrium equations, geometrical relations and constitutive equations with boundary and intermediate conditions. The system of equations is solved by using the method of separation of variables. Consequently, the governing differential equations are converted into a system of algebraic equations whose solution exists if the determinant of the coefficients of the matrix vanishes. The influence of cracks and steps on the natural vibration of the nanoarches is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigenfrequencies of the nanoarches is developed with the help of computer software. The effects of various physical and geometrical parameters are recorded and drawn graphically.

Keywords: crack, nanoarches, natural frequency, step

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

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A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, Nonlocal Strain Gradient Theory, velocity gradient

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Mustapha Rilwan Adewale, Salau Ayobami Muhammed

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This study focuses on the heat transfer analysis of magneto-hydrodynamics (MHD) squeezing flow between parallel disks, considering a viscous incompressible fluid. The upper disk exhibits both upward and downward motion, while the lower disk remains stationary but permeable. By employing similarity transformations, a system of nonlinear ordinary differential equations is derived to describe the flow behavior. To solve this system, a numerical approach, namely the Chebyshev collocation method, is utilized. The study investigates the influence of flow parameters and compares the obtained results with existing literature. The significance of this research lies in understanding the heat transfer characteristics of MHD squeezing flow, which has practical implications in various engineering and industrial applications. By employing the similarity transformations, the complex governing equations are simplified into a system of nonlinear ordinary differential equations, facilitating the analysis of the flow behavior. To obtain numerical solutions for the system, the Chebyshev collocation method is implemented. This approach provides accurate approximations for the nonlinear equations, enabling efficient computations of the heat transfer properties. The obtained results are compared with existing literature, establishing the validity and consistency of the numerical approach. The study's major findings shed light on the influence of flow parameters on the heat transfer characteristics of the squeezing flow. The analysis reveals the impact of parameters such as magnetic field strength, disk motion amplitude, fluid viscosity on the heat transfer rate between the disks, the squeeze number(S), suction/injection parameter(A), Hartman number(M), Prandtl number(Pr), modified Eckert number(Ec), and the dimensionless length(δ). These findings contribute to a comprehensive understanding of the system's behavior and provide insights for optimizing heat transfer processes in similar configurations. In conclusion, this study presents a thorough heat transfer analysis of magneto-hydrodynamics squeezing flow between parallel disks. The numerical solutions obtained through the Chebyshev collocation method demonstrate the feasibility and accuracy of the approach. The investigation of flow parameters highlights their influence on heat transfer, contributing to the existing knowledge in this field. The agreement of the results with previous literature further strengthens the reliability of the findings. These outcomes have practical implications for engineering applications and pave the way for further research in related areas.

Keywords: squeezing flow, magneto-hydro-dynamics (MHD), chebyshev collocation method(CCA), parallel manifolds, finite difference method (FDM)

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Tun Myat Aung, Ni Ni Hla

Abstract:

This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: discrete logarithm problem, general attacks, elliptic curve, prime field, binary field

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Authors: Yunzhe Tong, Jun Fan, Bin Wang

Abstract:

The vibroacoustic behavior of an immersed infinite cylindrical shell with periodic lengthwise ribs has been studied in this paper. The motions of the shell are described by the Donnell equations. Each lengthwise rib is modeled as an elastic beam. The motions of the bulkheads are decomposed into the longitudinal motions and flexural motions. The analytical expressions of the shell motions can be obtained through circumferential mode expansion, Fourier Transform and periodic boundary condition in the circumferential direction. Furthermore, the far-field radiated pressure has been obtained using the stationary phase. The analysis of wavenumber domain shows that periodic lengthwise stiffeners in the circumferential direction can produce flexural Bloch waves. The dominant feature in far-field pressure amplitude is the resonance of the supersonic components of the flexural Bloch waves in the circumferential direction.

Keywords: flexural Bloch wave, stiffened shell, vibroacoustics, wavenumber analysis

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

Abstract:

We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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