Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

The extended auxiliary the KdV equation with equation method for variable coefficients

This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.

A numerical method for determining the stuck point in extended reach drilling

A stuck drill string results in a major non-productive cost in extended reach drilling engineering. The first step is to determine the depth at which the sticking has occurred. Methods of measurement have been proved useful for determining the stuck points, but these operations take considerable time. As a result of the limitation with the current operational practices, calculation methods are still preferred to estimate the stuck point depth. Current analytical methods do not consider friction and are only valid for vertical rather than extended reach wells. The numerical method is established to take full account of down hole friction, tool joint, upset end of drill pipe, combination drill strings and tubular materials so that it is valid to determine the stuck point in extended reach wells. The pull test, torsion test and combined test of rotation and pulling can be used to determine the stuck point. The results show that down hole friction, tool joint, upset end of drill pipe, tubular sizes and materials have significant effects on the pull length and/or the twist angle of the stuck drill string.

Thermoelastic analysis of multiple defects with the extended finite element method

In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.

Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.

Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.

Interaction solutions for the second extended(3+1)-dimensional Jimbo–Miwa equation

Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.

Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method

Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.

Applying the New Extended Direct Algebraic Method to Solve the Equation of Obliquely Interacting Waves in Shallow Waters

In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.

Experimental Research on the Erosion Pattern and Protection Using the Extended Modelling Method

In the paper the extended modelling method with serial sands is used in an experimental research on the erosion patterns at the discharge outlet of a beach Hua-Neng power plant. The theoretical basis for the extended modelling method with serial sands is systematically presented in the paper and the method has been successfully employed in the sediment experiment of coastal works. According to the Froude Law, the model is designed to be a normal one with movable bed, the geometric scale lambda(L) = lambda(H) = 15, and three scales of sediment grain size are chosen, i.e., lambda(d1) = 0.207; lambda(d2) = 0.393; and lambda(d3) = 0.656. The median particle diameter of sea beach prototype sand d(50p) = 0.059 mm and the dis-changed water flow of the power plant is 21.7 m(3) / s. Three types of natural sea sands have been chosen as the serial modelling sands to extend the simulation of the prototype, thus replacing the conventional test in which artificial lightweight sands are used. As a result, this method can not only reduce the cost significantly, but also it is an advanced technique easy to use. Upon a series of tests, satisfactory results have been obtained.

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

Fabrication of the Sodium Ions Extended Gate Field Effect Transistor by Using the Entrapment Method

The sodium ion is necessary in physiological function and an important element in blood of human body,because the concentration of the sodium ion in the blood directly affects the functions of some organs or pathological feature,how to detect it is an important affair.In this paper,we measure the concentration of sodium ions by the extended gate field effect transistor (EGFET).We use three different substrates RuO_x/p-Si,ITO glass,SnO_2/ITO to fabricate EGFET,and we choose the optimum structure.The fabrication of device needed to use the entrapment method.

Determinants of Long Acting Reversible Contraception Method Use among Mothers in Extended Postpartum Period, Durame Town, Southern Ethiopia: A Cross Sectional Community Based Survey

Background: After a live birth, there is much unsatisfied interest in, and unmet family planning need for contraception. Waiting at least for 24 months before attempting the next pregnancy was recommended to reduce the risk of adverse maternal, perinatal and infant outcomes. The purpose of this study was to assess the determinants of long acting reversible contraception method use among mothers in extended postpartum period in Durame Town, Southern Ethiopia. Methods: A community based cross sectional study was conducted in Durame Town, Southern Ethiopia in December, 2014. Systematic random sampling technique was employed to recruit a total 460 study participants. Structured and pretested questioner was used to collect the data. Descriptive statistics was employed to characterize the study population using frequencies and proportions. Bivariate logistic regression analysis was conducted to identify all possible factors affecting utilization of LARC method. Multivariable logistic regression model was developed to control the confounding variables. Adjusted Odds Ratio (AOR) with 95% Confidence Interval (CI) was computed in identifying the real factors associated with use of LARC methods. Results: In this study we found that the prevalence of LARC method use among mothers during their extended postpartum period was 36.7% (95%CI: 32.2, 41.0). The unmet family planning need of mothers in the extended postpartum period was 123 (27.9%). The odds of using LARC by literate mother were four fold higher than their counterpart illiterate mothers (AOR 4.09 95%CI: 1.68, 9.58, P value < 0.001). The odds of mother who had pervious experiences of using LARC were up to eight folds higher than mother never used LARC methods (AOR 7.84 95% CI: 3.78, 16.23, P value< 0.001). Mother who received counseling service on LARC methods during delivery was up to three times more likely to utilize the services than not counseled (AOR 3.29 95% CI: 1.53, 7.03, P value < 0.001). And odds of mothers who received counseling service on LARC during immediate postpartum period were up to five fold more likely to opt method than never got the counseling service (AOR 4.55 95 % CI: 1.94, 10.66, P value < 0.001). Conclusions: In the study area, about one third of mothers utilized LARC methods during their extended postpartum period. Another one third of mother had unmet need for family planning. Participant’s education, previous history of using LARC methods, receiving counseling services on LARC during delivery and immediate postpartum periods were found major determinant for LARC use. Educating women, providing counseling service on LARC methods during antenatal, delivery and postnatal were recommended.

The Smoothing Newton Method for Solving the Extended Linear Complementarity Problem

The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.

Extended (G'/G) Method Applied to the Modified Non-Linear Schrodinger Equation in the Case of Ocean Rogue Waves

The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments show exactly that rogue waves occur in deep and shallow water. To study the behavior of freak waves in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems, we derive a modified nonlinear Schr&oumldinger equation modeling the propagation of rogue waves in deep water in order to seek analytic solutions of this nonlinear partial differential equation by using generalized extended G'/G-expansion method with the aid of mathematica. Particular attentions have been paid to the behavior of rogue wave’s amplitude which highlights rogue wave’s destructive power.

Diagnostic Validity of Cica Beta Test 1 for the Detection of Extended Spectrum Beta-Lactamase (ESBL) Producing Gram Negative Bacteria by Comparing with Phenotypic Method

Background: Detection of extended spectrum beta lactamase producing bacteria is an important issue in the clinical settings. Objective: The purpose of the present study was to validate the Cica Beta Test 1 for detection of extended spectrum beta-lactamase (ESBL) producing bacteria. Method: This analytical type of cross-sectional study was carried out in the Department of Microbiology and Immunology at Bangabandhu Sheikh Mujib Medical University (BSMMU), Dhaka from January 2006 to December 2006 for a period of one (01) year. All the patients presented with the clinical features of urinary tract infection and surgical as well as burn wound infection at any age with both sexes were selected as study population. All bacteria were isolated and identified by their colony morphology, staining characters, pigment production, motility and other relevant biochemical tests. Phenotypic confirmation of ESBLs producing isolates were done by inhibitor potentiated disc diffusion test according to CLSI recommendation. The Cica Beta Test 1 was performed according to the manufacturer’s instructions. Result: A total number of 288 Gram negative bacteria were isolated. Among these isolates Cica Beta test 1 was positive in 97 strains and phenotypic confirmatory test was positive in 89 strains. The test sensitivity of Cica Beta Test 1 was 100% (95% CI 95.9% to 100.0%). Specificity of the test was 96.0% (95% CI 92.2% to 98.2%). The positive predictive value (PPV) and negative predictive value (NPV) were 92.7% (95% CI 84.5% to 95.7%) and 100.0% (95% CI 98.0% to 100.0%) respectively. The accuracy of the test was 97.2% (95% CI 95.1% to 99.1%). Area under ROC curve = 0.980 (95% CI 0.964 to 0.996);p value 0.0001. Conclusion: In conclusion, Cica Beta Test 1 is very high sensitivity and specificity for the detection of ESBL from Gram negative bacteria.

The Extended Tanh Method for Compactons and Solitons Solutions for the CH(<i>n</i>,2<i>n</i>– 1,2<i>n</i>,–<i>n</i>) Equations

In this paper, by using the sine-cosine method, the extended tanh-method, and the rational hyperbolic functions method, we study a class of nonlinear equations which derived from a fourth order analogue of generalized Camassa-Holm equation. It is shown that this class gives compactons, solitary wave solutions, solitons, and periodic wave solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.

Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum

The 6061-T651 aluminium alloy is one of the most common aluminium alloys for marine components and general structures. The stress intensity factor (SIF) is an important parameter for estimating the life of the cracked structure. In this paper, the stress intensity factors of a slant-cracked plate, which is made of 6061-T651 aluminum, have been calculated using extended finite element method (XFEM) and finite element method (FEM) in ABAQUS software and the results were compared with theoretical values. Numerical values obtained from these two methods were close to the theoretical values. In simulations of crack growth at different crack angles, the crack propagation angle values were closer to the theoretical values in XFEM method. Also, the accuracy and validity of fatigue crack growth curve were much closer to the theoretical graph in XFEM than the FEM. Therefore, in this paper the capabilities of XFEM were realized in analyzing issues such as cracks.