Search results for: boundary integral method

Authors: M. Kotobuki, M. Koishi

Abstract:

Li1.5Al0.5Ti1.5 (PO4)3(LATP) has received much attention as a solid electrolyte for lithium batteries. In this study, the LATP solid electrolyte is prepared by the co-precipitation method using Li3PO4 as a Li source. The LATP is successfully prepared and the Li ion conductivities of bulk (inner crystal) and total (inner crystal and grain boundary) are 1.1 × 10-3 and 1.1 × 10-4 S cm-1, respectively. These values are comparable to the reported values, in which Li2C2O4 is used as the Li source. It is conclude that the LATP solid electrolyte can be prepared by the co-precipitation method using Li3PO4 as the Li source and this procedure has an advantage in mass production over previous procedure using Li2C2O4 because Li3PO4 is lower price reagent compared with Li2C2O4.

Keywords: co-precipitation method, lithium battery, NASICON-type electrolyte, solid electrolyte

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Authors: C. F. Alegretti, F. R. Cunha, R. G. Gontijo

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This work investigates the effects of an applied magnetic field on the geometry-driven boundary layer detachment flow of a ferrofluid over a sudden expansion. Both constitutive equation and global magnetization equation for a ferrofluid are considered. Therefore, the proposed formulation consists in a coupled magnetic-hydrodynamic problem. Computational simulations are carried out in order to explore, not only the viability to control flow instabilities, but also to evaluate the consistency of theoretical aspects. The unidirectional sudden expansion in a ferrofluid flow is investigated numerically under the perspective of Ferrohydrodynamics in a two-dimensional domain using a Finite Differences Method. The boundary layer detachment induced by the sudden expansion results in a recirculating zone, which has been extensively studied in non-magnetic hydrodynamic problems for a wide range of Reynolds numbers. Similar investigations can be found in literature regarding the sudden expansion under the magnetohydrodynamics framework, but none considering a colloidal suspension of magnetic particles out of the superparamagnetic regime. The vorticity-stream function formulation is implemented and results in a clear coupling between the flow vorticity and its magnetization field. Our simulations indicate a systematic decay on the length of the recirculation zone as increasing physical parameters of the flow, such as the intensity of the applied field and the volume fraction of particles. The results all are discussed from a physical point of view in terms of the dynamical non-dimensional parameters. We argue that the decrease/reduction in the recirculation region of the flow is a direct consequence of the magnetic torque balancing the action of the torque produced by viscous and inertial forces of the flow. For the limit of small Reynolds and magnetic Reynolds parameters, the diffusion of vorticity balances the diffusion of the magnetic torque on the flow. These mechanics control the growth of the recirculation region.

Keywords: boundary layer detachment, ferrofluid, ferrohydrodynamics, magnetization, sudden expansion

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Authors: Anand Kishore Kola, G. Uday Bhaskar Babu, Kotturi Ajay Kumar

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The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV).

Keywords: modern dynamic systems, fractional order controllers, maximum-sensitivity, IMC-PID controllers, Smith predictor, IAE and TV

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Authors: Ebissa Gadissa Kedir, C. S. P. Ojha, K. S. Hari Prasad

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In the present study, the depth-averaged velocity and boundary shear stress in non-prismatic compound channels with three different converging floodplain angles ranging from 1.43ᶱ to 7.59ᶱ have been studied. The analytical solutions were derived by considering acting forces on the channel beds and walls. In the present study, five key parameters, i.e., non-dimensional coefficient, secondary flow term, secondary flow coefficient, friction factor, and dimensionless eddy viscosity, were considered and discussed. An expression for non-dimensional coefficient and integration constants was derived based on the boundary conditions. The model was applied to different data sets of the present experiments and experiments from other sources, respectively, to examine and analyse the influence of floodplain converging angles on depth-averaged velocity and boundary shear stress distributions. The results show that the non-dimensional parameter plays important in portraying the variation of depth-averaged velocity and boundary shear stress distributions with different floodplain converging angles. Thus, the variation of the non-dimensional coefficient needs attention since it affects the secondary flow term and secondary flow coefficient in both the main channel and floodplains. The analysis shows that the depth-averaged velocities are sensitive to a shear stress-dependent model parameter non-dimensional coefficient, and the analytical solutions are well agreed with experimental data when five parameters are included. It is inferred that the developed model may facilitate the interest of others in complex flow modeling.

Keywords: depth-average velocity, converging floodplain angles, non-dimensional coefficient, non-prismatic compound channels

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Authors: Yang Zhong, Mei-Jie Xu

Abstract:

To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in the single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is an obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. Therefore, the dynamic change of parameter in asphalt mixture should be taken into consideration when the theoretical analysis is taken out.

Keywords: asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress

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Authors: Esmaeil Bahmyari

Abstract:

The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.

Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell

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Authors: Ali Kargar, Kamyar Mansour

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In this paper the boundary layer instability and transition on a rotating parabola which is sheathed shape on a rotating 30 degrees total apex angle cone have been study by smoke visualization. The rotating cone especially 30 degrees total apex angle is a well-established subject in some previous novel works and also in our previous works. But in this paper a stabilizing effect is detected by the bluntness of nose and also surface curvature. A parabola model which is satisfying those conditions (sheathed parabola of the 30 degrees cone) has been built and studied in the wind tunnel. The results are shown that the boundary layer transition occurs at higher rotational Reynolds number in comparison by the cone. The results are shown in the visualization pictures and also are compared graphically.

Keywords: transitional Reynolds number, wind tunnel, smoke visualization, rotating parabola

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

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This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation

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Authors: Zerroug Abdelhamid, Danielle Chassoux

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Various models are given to simulate homogeneous or heterogeneous cancerous tumors and extract in each case the boundary. The fractal dimension is then estimated by least squares method and compared to some previous methods.

Keywords: simulation, cancerous tumor, Markov fields, fractal dimension, extraction, recovering

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Authors: Chitsanzo Isaac

Abstract:

Across the world, the ongoing Covid-19 pandemic has challenged urban systems and policy frameworks, highlighting societal vulnerabilities and systemic inequities among many communities. Measures of confinement and social distancing to contain the Covid-19 virus have fragmented the physical and social fabric of cities. This has caused urban dwellers to reassess how they engage with their urban surroundings and maintain social ties. Urbanists have presented strategies that would allow communities to survive and even thrive, in extraordinary times of crisis like the pandemic. Tactical Urbanism, particularly the 15-Minute City, has gained popularity. It is considered a resilient approach in the global north, however, it’s transferability to the global south has been called into question. To this end, this paper poses the question: to what extent is the 15-Minute City framework integral sustainable design, and are there processes that make it adoptable by cities in the global south? This paper explores four issues using secondary quantitative data analysis and convergence analysis in the Paris and Blantyre urban regions. First, it questions how the 15-Minute City has been defined and measured, and how it impacts urban dwellers. Second, it examines the extent to which the 15-minute city performs under the lens of frameworks such as Wilber’s integral theory and Fleming’s integral sustainable design theory. Thirdly this work examines the processes that can be transferred to developing cities which foster community resilience through the perspectives of experience, behaviors, cultures, and systems. Finally, it reviews the principal ways in which a multi-perspective reality can be the basis for resilient community design and sustainable urban development. This work will shed a light on the importance of a multi-perspective reality as a means of achieving sustainable urban design goals in developing urban areas.

Keywords: 15-minute city, developing cities, global south, community resilience, integral sustainable design, systems thinking, complexity, tactical urbanism

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Authors: Zdeněk Veselý, Milan Honner, Jiří Mach

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The aim of the performed work is to establish the 2D and 3D model of direct unsteady task of sample heat treatment by moving source employing computer model on the basis of finite element method. The complex boundary condition on heat loaded sample surface is the essential feature of the task. Computer model describes heat treatment of the sample during heat source movement over the sample surface. It is started from the 2D task of sample cross section as a basic model. Possibilities of extension from 2D to 3D task are discussed. The effect of the addition of third model dimension on the temperature distribution in the sample is showed. Comparison of various model parameters on the sample temperatures is observed. Influence of heat source motion on the depth of material heat treatment is shown for several velocities of the movement. Presented computer model is prepared for the utilization in laser treatment of machine parts.

Keywords: computer simulation, unsteady model, heat treatment, complex boundary condition, moving heat source

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Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

Abstract:

A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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Authors: Wen-Bao Qiao, Jean-Charles Créput

Abstract:

To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: parallel 2-opt, double links, large scale TSP, GPU

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

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In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied. The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length. To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed. Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition. The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work. The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: buckling, finite strip, different sides support, plates on foundation

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Authors: Vassilis C. Moulianitis, Evgenios Scourboutis, Ilias Katsanis, Paraskevas Papanikos, Nikolas Zacharopoulos

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This paper presents the conceptual design of an automated biomethane potential measurement system. First, the design specifications for the BMP system and the basic components of the system will be presented. Three concepts that meet the design specifications will be presented. The basic characteristics of each concept will be analyzed in detail. The concepts will be evaluated using a set of design criteria that includes flexibility, cost, size, complexity, aesthetics, and accessibility in order to determine the best solution. The evaluation will be based on the discrete Choquet integral.

Keywords: automated biomethane test, conceptual mechatronics design, concept evaluation, Choquet integral

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Authors: Ali Mortazavi

Abstract:

The main objective of this research project is to delve into a multitude of geomechanical risks associated with various mining methods employed within the underground mining industry. Controlling geotechnical design parameters and operational factors affecting the selection of suitable mining techniques for a given underground mining condition will be considered from a risk assessment point of view. Important geomechanical challenges will be investigated as appropriate and relevant to the commonly used underground mining methods. Given the complicated nature of rock mass in-situ and complicated boundary conditions and operational complexities associated with various underground mining methods, the selection of a safe and economic mining operation is of paramount significance. Rock failure at varying scales within the underground mining openings is always a threat to mining operations and causes human and capital losses worldwide. Geotechnical design is a major design component of all underground mines and basically dominates the safety of an underground mine. With regard to uncertainties that exist in rock characterization prior to mine development, there are always risks associated with inappropriate design as a function of mining conditions and the selected mining method. Uncertainty often results from the inherent variability of rock masse, which in turn is a function of both geological materials and rock mass in-situ conditions. The focus of this research is on developing a methodology which enables a geomechanical risk assessment of given underground mining conditions. The outcome of this research is a geotechnical risk analysis algorithm, which can be used as an aid in selecting the appropriate mining method as a function of mine design parameters (e.g., rock in-situ properties, design method, governing boundary conditions such as in-situ stress and groundwater, etc.).

Keywords: geomechanical risk assessment, rock mechanics, underground mining, rock engineering

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Authors: Win-Jin Chang, Haw-Long Lee, Yu-Ching Yang

Abstract:

Atomic finite element simulation is applied to investigate the vibration frequency of a single-layer gamma graphyne with an attached mass for the CCCC, SSSS, CFCF, SFSF boundary conditions using the commercial code ANSYS. The fundamental frequencies of the graphyne sheet are compared with the results of the previous study. The results of the comparison are very good in all considered cases. The attached mass causes a shift in the resonant frequency of the graphyne. The frequencies of the single-layer gamma graphyne with an attached mass for different boundary conditions are obtained, and the order based on the boundary condition is CCCC >SSSS > CFCF> SFSF. The highest frequency shift is obtained when the attached mass is located at the center of the graphyne sheet. This is useful for the design of a highly sensitive graphyne-based mass sensor.

Keywords: graphyne, finite element analysis, vibration analysis, frequency shift

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Authors: Nicolas Thiers, Romain Gers, Olivier Skurtys

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In this work, we study numerically the effect of a thermal perturbation on the heat transfer in a rectangular differentially heated cavity of aspect ratio 4, filled by air. In order to maintain the center symmetry, the thermal perturbation is imposed by a square wave at both active walls, at the same relative position of the hot or cold boundary layers. The influences of the amplitude and the vertical location of the perturbation are investigated. The air flow is calculated solving the unsteady Boussinesq-Navier-Stokes equations using the PN - PN-2 Spectral Element Method (SEM) programmed in the Nek5000 opencode, at RaH= 9x107, just before the first bifurcation which leads to periodical flow. The results show that the perturbation has a major impact for the highest amplitude, and at about three quarters of the cavity height, upstream, in both hot and cold boundary layers.

Keywords: direct numerical simulation, heat transfer enhancement, localized thermal perturbations, natural convection, rectangular differentially-heated cavity

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Roland Lachmayer, Mahtab Afsari

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Research is the cornerstone for advancement of human communities. So that it is one of the indexes for evaluating advancement of countries. Research projects are usually cost and time-consuming and do not end in result in short term. Project scheduling is one of the integral parts of project management. The present article offers a new method by using C# and Matlab software to solve Fuzzy GERT networks for Exclusive-OR kind of nodes to schedule the network. In this article we concentrate on flowcharts that we used in Matlab to show how we apply Matlab to schedule Exclusive-OR nodes.

Keywords: research projects, fuzzy GERT, fuzzy CPM, CPM, α-cuts, scheduling

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Authors: Kshitish Ch. Mistri, Abhishek Kumar Singh

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The effect of undulatory boundary surface of a medium as well as the degree of bonding between two consecutive mediums, on the propagation of surface waves is an unavoidable matter of fact. Therefore, this paper investigates the propagation of Rayleigh-type wave in a corrugated fibre-reinforced layer overlying an initially stressed orthotropic half-space under gravity. Also, the two mediums are assumed to be loosely (or imperfectly) bonded. Numerical computation of the obtained frequency equation has been carried out which aids to analyze the influence of corrugation, loose bonding, initial stress and gravity on the phase velocity of Rayleigh-type wave. Moreover, the presence and absence of corrugation, loose bonding and initial stress are also discussed in a comparative manner.

Keywords: corrugated boundary surface, fibre-reinforced layer, initial stress, loose bonding, orthotropic half-space, Rayleigh-type wave

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Authors: Anna Bykalyuk, Frédéric Kuznik, Kévyn Johannes

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In this paper, the influence of a vertical plate’s thermal capacity is numerically investigated in order to evaluate the evolution of the thermal boundary layer structure, as well as the convective heat transfer coefficient and the velocity and temperature profiles. Whereas the heat flux of the heated vertical plate is evaluated under time depending boundary conditions. The main important feature of this problem is the unsteadiness of the physical phenomena. A 2D CFD model is developed with the Ansys Fluent 14.0 environment and is validated using unsteady data obtained for plasterboard studied under a dynamic temperature evolution. All the phenomena produced in the vicinity of the thermal conductive vertical plate (plasterboard) are analyzed and discussed. This work is the first stage of a holistic research on transient free convection that aims, in the future, to study the natural convection in the vicinity of a vertical plate containing Phase Change Materials (PCM).

Keywords: CFD modeling, natural convection, thermal conductive plate, time-depending boundary conditions

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Authors: Devinder Singh, Rajneesh Kumar, Arvind Kumar

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The present investigation deals with the deformation of micropolar generalized thermoelastic solid subjected to thermo-mechanical loading due to a thermal laser pulse. Laplace transform and Fourier transform techniques are used to solve the problem. Thermo-mechanical laser interactions are taken as distributed sources to describe the application of the approach. The closed form expressions of normal stress, tangential stress, coupled stress and temperature are obtained in the domain. Numerical inversion technique of Laplace transform and Fourier transform has been implied to obtain the resulting quantities in the physical domain after developing a computer program. The normal stress, tangential stress, coupled stress and temperature are depicted graphically to show the effect of relaxation times. Some particular cases of interest are deduced from the present investigation.

Keywords: pulse laser, integral transform, thermoelastic, boundary value problem

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Authors: Yilei Song, Linlin Tian, Ning Zhao

Abstract:

Turbulence energetics and structures in the wake of large-scale wind turbines under the stably-stratified atmospheric boundary layer (SABL) can be complicated due to the presence of low-level jets (LLJs), a region of higher wind speeds than the geostrophic wind speed. With a modified one-k-equation, eddy viscosity model specified for atmospheric flows as the sub-grid scale (SGS) model, a realistic atmospheric state of the stable ABL is well reproduced by large-eddy simulation (LES) techniques. Corresponding to the precursor stably stratification, the detailed wake properties of a standard 5-MW wind turbine represented as an actuator line model are provided. An engineering model is proposed for wake prediction based on the simulation statistics and gets validated. Results confirm that the proposed wake model can provide good predictions for wind turbines under the SABL.

Keywords: large-eddy simulation, stably-stratified atmospheric boundary layer, wake model, wind turbine wake

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Authors: Adrian W. Egger, Savvas P. Triantafyllou, Eleni N. Chatzi

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The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which introduces a scaling center in each element’s domain, thus transitioning from a Cartesian reference frame to one resembling polar coordinates. Consequently, an analytical solution is achieved in radial direction, implying that only the boundary need be discretized. The only limitation imposed on the resulting polygonal elements is that they remain star-convex. Further arbitrary p- or h-refinement may be applied locally in a mesh. The polygonal nature of SBFEM elements has been exploited in quadtree meshes to alleviate all issues conventionally associated with hanging nodes. Furthermore, since in 2D this results in only 16 possible cell configurations, these are precomputed in order to accelerate the forward analysis significantly. Any cells, which are clipped to accommodate the domain geometry, must be computed conventionally. However, since SBFEM permits polygonal elements, significantly coarser meshes at comparable accuracy levels are obtained when compared with conventional quadtree analysis, further increasing the computational efficiency of this scheme. The generalized stress intensity factors (gSIFs) are computed by exploiting the semi-analytical solution in radial direction. This is initiated by placing the scaling center of the element containing the crack at the crack tip. Taking an analytical limit of this element’s stress field as it approaches the crack tip, delivers an expression for the singular stress field. By applying the problem specific boundary conditions, the geometry correction factor is obtained, and the gSIFs are then evaluated based on their formal definition. Since the SBFEM solution is constructed as a power series, not unlike mode superposition in FEM, the two modes contributing to the singular response of the element can be easily identified in post-processing. Compared to the extended finite element method (XFEM) this approach is highly convenient, since neither enrichment terms nor a priori knowledge of the singularity is required. Computation of the gSIFs by SBFEM permits exceptional accuracy, however, when combined with hybrid quadtrees employing linear elements, this does not always hold. Nevertheless, it has been shown that crack propagation schemes are highly effective even given very coarse discretization since they only rely on the ratio of mode one to mode two gSIFs. The absolute values of the gSIFs may still be subject to large errors. Hence, we propose a post-processing scheme, which minimizes the error resulting from the approximation space of the cracked element, thus limiting the error in the gSIFs to the discretization error of the quadtree mesh. This is achieved by h- and/or p-refinement of the cracked element, which elevates the amount of modes present in the solution. The resulting numerical description of the element is highly accurate, with the main error source now stemming from its boundary displacement solution. Numerical examples show that this post-processing procedure can significantly improve the accuracy of the computed gSIFs with negligible computational cost even on coarse meshes resulting from hybrid quadtrees.

Keywords: linear elastic fracture mechanics, generalized stress intensity factors, scaled finite element method, hybrid quadtrees

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Olga I. Moskalenko, Maksim O. Zhuravlev, Alexey A. Koronovskii, Alexander E. Hramov

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Intermittent behavior near the boundary of phase synchronization in the presence of noise is studied. In certain range of the coupling parameter and noise intensity the intermittency of eyelet and ring intermittencies is shown to take place. Main results are illustrated using the example of two unidirectionally coupled Rössler systems. Similar behavior is shown to take place in two hydrodynamical models of Pierce diode coupled unidirectionally.

Keywords: chaotic oscillators, phase synchronization, noise, intermittency of intermittencies

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator 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 Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. 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 analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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