Search results for: weakly solving

Authors: Alexander Mikkelsen, Khobaib Khobaib, Zbigniew Rozynek

Abstract:

Drops covered by particles have found important uses in various fields, ranging from stabilization of emulsions to production of new advanced materials. Particles at drop interfaces can be interlocked to form solid capsules with properties tailored for a myriad of applications. Despite the huge potential of particle-laden drops and capsules, the knowledge of their deformation and stability are limited. In this regard, we contribute with experimental studies on the deformation and manipulation of silicone oil drops covered with micrometer-sized particles subjected to electric fields. A mixture of silicone oil and particles were immersed in castor oil using a mechanical pipette, forming millimeter sized drops. The particles moved and adsorbed at the drop interfaces by sedimentation, and were structured at the interface by electric field-induced electrohydrodynamic flows. When applying a direct current electric field, free charges accumulated at the drop interfaces, yielding electric stress that deformed the drops. In our experiments, we investigated how particle properties affected drop deformation, break-up, and particle structuring. We found that by increasing the size of weakly-conductive clay particles, the drop shape can go from compressed to stretched out in the direction of the electric field. Increasing the particle size and electrical properties were also found to weaken electrohydrodynamic flows, induce break-up of drops at weaker electric field strengths and structure particles in chains. These particle parameters determine the dipolar force between the interfacial particles, which can yield particle chaining. We conclude that the balance between particle chaining and electrohydrodynamic flows governs the observed drop mechanics.

Keywords: drop deformation, electric field induced stress, electrohydrodynamic flows, particle structuring at drop interfaces

Procedia PDF Downloads 203

Authors: Odoh Dickson Akpegi

Abstract:

The paper is about the need for an indigenous language in order to meaningfully harness both our human and material resources for the nation’s integration. It then examines the notty issue of the national language question and advocates a piece meal approach in solving the problem. This approach allows for the development and use of local languages in minority areas, especially in Benue State, as a way of preparing them for consideration as possible replacement for English language as Nigeria’s national or official language. Finally, an arrangement to follow to prepare the languages for such competition at the national level is presented.

Keywords: indigenous language, English language, official language, National integration

Procedia PDF Downloads 558

Authors: Said Algarni

Abstract:

The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

Procedia PDF Downloads 296

Authors: G. W. Greubel, A. Kalam

Abstract:

This paper provides a review of the technical problems facing the South African electricity system and discusses a hypothetical ‘virtual grid’ concept that may assist in solving the problems. The proposed solution has potential application across emerging markets with constrained power infrastructure or for companies who wish to be entirely powered by renewable energy. South Africa finds itself at a confluence of forces where the national electricity supply system is constrained with under-supply primarily from old and failing coal-fired power stations and congested and inadequate transmission and distribution systems. Simultaneously, the country attempts to meet carbon reduction targets driven by both an alignment with international goals and a consumer-driven requirement. The constrained electricity system is an aspect of an economy characterized by very low economic growth, high unemployment, and frequent and significant load shedding. The fiscus does not have the funding to build new generation capacity or strengthen the grid. The under-supply is increasingly alleviated by the penetration of wind and solar generation capacity and embedded roof-top solar. However, this increased penetration results in less inertia, less synchronous generation, and less capability for fast frequency response, with resultant instability. The renewable energy facilities assist in solving the under-supply issues but merely ‘kick the can down the road’ by not contributing to grid stability or by substituting the lost inertia, thus creating an expanding issue for the grid to manage. By technically balancing its electricity demand and supply a company with facilities located across the country can be protected from the effects of load shedding, and thus ensure financial and production performance, protect jobs, and contribute meaningfully to the economy. By treating the company’s load (across the country) and its various distributed generation facilities as a ‘virtual grid’, which by design will provide ancillary services to the grid one is able to create a win-win situation for both the company and the grid.

Keywords: load shedding, renewable energy integration, smart grid, virtual grid, virtual power plant

Procedia PDF Downloads 56

Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

Abstract:

Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty

Procedia PDF Downloads 555

Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

Procedia PDF Downloads 503

Authors: S. Aditya, K. T. Nideesh, N. Guruprasad

Abstract:

Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost.

Keywords: NW method, optimum utilization, transportation problem, Vogel’s approximation method

Procedia PDF Downloads 436

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

Abstract:

In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

Procedia PDF Downloads 331

Authors: Fatima Zohra Mahi, Luca Varani

Abstract:

We present an analytical model for the calculation of the sensitivity, the spectral current noise and the detectivity for an optically illuminated In0.53Ga0.47As n+nn+ diode. The photocurrent due to the excess carrier is obtained by solving the continuity equation. Moreover, the current noise level is evaluated at room temperature and under a constant voltage applied between the diode terminals. The analytical calculation of the current noise in the n+nn+ structure is developed. The responsivity and the detectivity are discussed as functions of the doping concentrations and the emitter layer thickness in one-dimensional homogeneous n+nn+ structure.

Keywords: detectivity, photodetectors, continuity equation, current noise

Procedia PDF Downloads 642

Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

Abstract:

This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

Procedia PDF Downloads 201

Authors: Osman Ali, Jeanne Kriek

Abstract:

Introduction: The current instructional approach entrenched in memorizing does not assist conceptual understanding in science. Instructional approaches that encourage research, investigation, and experimentation, which depict how scientists work, should be encouraged. One such teaching strategy is problem-based learning (PBL). PBL has many advantages; enhanced self-directed learning and improved problem-solving and critical thinking skills. However, despite many advantages, PBL has challenges. Research confirmed is time-consuming and difficult to formulate ill-structured questions. Professional development interventions are needed for in-service educators to adopt the PBL strategy. The purposively selected educators had to implement PBL in their classrooms after the intervention to develop their practice and then reflect on the implementation. They had to indicate their achievements and challenges. This study differs from previous studies as the rural educators were subjected to implementing PBL in their classrooms and reflected on their experiences, beliefs, and attitudes regarding PBL. Theoretical Framework: The study reinforced Vygotskian sociocultural theory. According to Vygotsky, the development of a child's cognitive is sustained by the interaction between the child and more able peers in his immediate environment. The theory suggests that social interactions in small groups create an opportunity for learners to form concepts and skills on their own better than working individually. PBL emphasized learning in small groups. Research Methodology: An exploratory case study was employed. The reason is that the study was not necessarily for specific conclusive evidence. Non-probability purposive sampling was adopted to choose eight schools from 89 rural public schools. In each school, two educators were approached, teaching physical sciences in grades 10 and 11 (N = 16). The research instruments were questionnaires, interviews, and lesson observation protocol. Two open-ended questionnaires were developed before and after intervention and analyzed thematically. Three themes were identified. The semi-structured interviews and responses were coded and transcribed into three themes. Subsequently, the Reform Teaching Observation Protocol (RTOP) was adopted for lesson observation and was analyzed using five constructs. Results: Evidence from analyzing the questionnaires before and after the intervention shows that participants knew better what was required to develop an ill-structured problem during the implementation. Furthermore, indications from the interviews are that participants had positive views about the PBL strategy. They stated that they only act as facilitators, and learners’ problem-solving and critical thinking skills are enhanced. They suggested a change in curriculum to adopt the PBL strategy. However, most participants may not continue to apply the PBL strategy stating that it is time-consuming and difficult to complete the Annual Teaching Plan (ATP). They complained about materials and equipment and learners' readiness to work. Evidence from RTOP shows that after the intervention, participants learn to encourage exploration and use learners' questions and comments to determine the direction and focus of classroom discussions.

Keywords: problem-solving, self-directed, critical thinking, intervention

Procedia PDF Downloads 119

Authors: Laroussi Chaabane, Amel El Ghali, Emmanuel Beyou, Mohamed Hassen V. Baouab

Abstract:

In this research, the functionalization of graphene oxide sheets by ethylenediamine (EDA) was accomplished and followed by the grafting of bis(2-pyridylmethyl) amino group (BPED) onto the activated graphene oxide sheets in the presence of chloroacetylchloride (CAC) and then combined with magnetic nanoparticles (Fe₃O₄NPs) to produce a magnetic graphene-based composite [(Go-EDA-CAC)@Fe₃O₄NPs-BPED]. The physicochemical properties of [(Go-EDA-CAC)@Fe₃O₄NPs-BPED] composites were investigated by Fourier transform infrared (FT-IR), scanning electron microscopy (SEM), X-ray diffraction (XRD), thermogravimetric analysis (TGA). Additionally, the catalysts can be easily recycled within ten seconds by using an external magnetic field. Moreover, [(Go-EDA-CAC)@Fe₃O₄NPs-BPED] was used for removing Cu(II) ions from aqueous solutions using a batch process. The effect of pH, contact time and temperature on the metal ions adsorption were investigated, however weakly dependent on ionic strength. The maximum adsorption capacity values of Cu(II) on the [(Go-EDA-CAC)@Fe₃O₄NPs-BPED] at the pH of 6 is 3.46 mmol.g⁻¹. To examine the underlying mechanism of the adsorption process, pseudo-first, pseudo-second-order, and intraparticle diffusion models were fitted to experimental kinetic data. Results showed that the pseudo-second-order equation was appropriate to describe the Cu (II) adsorption by [(Go-EDA-CAC)@Fe₃O₄NPs-BPED]. Adsorption data were further analyzed by the Langmuir, Freundlich, and Jossens adsorption approaches. Additionally, the adsorption properties of the [(Go-EDA-CAC)@Fe₃O₄NPs-BPED], their reusability (more than 6 cycles) and durability in the aqueous solutions open the path to removal of Cu(II) from water solution. Based on the results obtained, we report the activity of Cu(II) supported on [(Go-EDA-CAC)@Fe₃O₄NPs-BPED] as a catalyst for the cross-coupling of symmetric alkynes.

Keywords: graphene, magnetic nanoparticles, adsorption kinetics/isotherms, cross coupling

Procedia PDF Downloads 138

Authors: Paolo Sassi, Jorge Freiria, Gabriel Usera

Abstract:

In this work, a finite volume fluid flow solver is coupled with a discrete element method module for the simulation of the dynamics of free and elastic bodies in interaction with the fluid and between themselves. The open source fluid flow solver, caffa3d.MBRi, includes the capability to work with nested overlapping grids in order to easily refine the grid in the region where the bodies are moving. To do so, it is necessary to implement a recognition function able to identify the specific mesh block in which the device is moving in. The set of overlapping finer grids might be displaced along with the set of bodies being simulated. The interaction between the bodies and the fluid is computed through a two-way coupling. The velocity field of the fluid is first interpolated to determine the drag force on each object. After solving the objects displacements, subject to the elastic bonding among them, the force is applied back onto the fluid through a Gaussian smoothing considering the cells near the position of each object. The fishnet is represented as lumped masses connected by elastic lines. The internal forces are derived from the elasticity of these lines, and the external forces are due to drag, gravity, buoyancy and the load acting on each element of the system. When solving the ordinary differential equations system, that represents the motion of the elastic and flexible bodies, it was found that the Runge Kutta solver of fourth order is the best tool in terms of performance, but requires a finer grid than the fluid solver to make the system converge, which demands greater computing power. The coupled solver is demonstrated by simulating the interaction between the fluid, an elastic fishnet and a set of free bodies being captured by the net as they are dragged by the fluid. The deformation of the net, as well as the wake produced in the fluid stream are well captured by the method, without requiring the fluid solver mesh to adapt for the evolving geometry. Application of the same strategy to the simulation of elastic structures subject to the action of wind is also possible with the method presented, and one such application is currently under development.

Keywords: computational fluid dynamics, discrete element method, fishnets, nested overlapping grids

Procedia PDF Downloads 416

Authors: Mohan Bilikallahalli Sannathimmappa, Vinod Nambiar, Rajeev Aravindakshan

Abstract:

Background: Image-based teaching-learning module is innovative student-centered andragogy. The objective of our study was to explore medical students’ perception of effectiveness of image-based learning strategy in promoting their lifelong learning skills and evaluate its impact on improving students’ exam grades. Methods: A prospective single-cohort study was conducted on undergraduate medical students of the academic year 2021-22. The image-based teaching-learning module was assessed through pretest, posttest, and exam grades. Students’ feedback was collected through a predesigned questionnaire on a 3-point Likert Scale. The reliability of the questionnaire was assessed using Cronbach’s alpha coefficient test. In-Course Exam-4 results were compared with In-Course Exams 1, 2, and 3. Correlation coefficients were worked out wherever relevant to find the impact of the exercise on grades. Data were collected, entered into Microsoft Excel, and statistically analyzed using SPSS version 22. Results: In total, 127 students were included in the study. The posttest scores of the students were significantly high (24.75±) as compared to pretest scores (8.25±). Students’ opinion towards the effectiveness of image-based learning in promoting their lifelong learning skills was overwhelmingly positive (Cronbach’s alpha for all items was 0.756). More than 80% of the students indicated image-based learning was interesting, encouraged peer discussion, and helped them to identify, explore, and revise key information and knowledge improvement. Nearly 70% expressed image-based learning enhanced their critical thinking and problem-solving skills. Nine out of ten students recommended image-based learning module for future topics. Conclusion: Overall, Image-based learning was found to be effective in achieving undergraduate medical students learning outcomes. The results of the study are in favor of the implementation of Image-based learning in Microbiology courses. However, multicentric studies are required to authenticate our study findings.

Keywords: active learning, knowledge, medical education, microbes, problem solving

Procedia PDF Downloads 69

Authors: Diego Luján Villarreal

Abstract:

Visual prostheses are designed to repair some eyesight in patients blinded by photoreceptor diseases, such as retinitis pigmentosa (RP) and age-related macular degeneration (AMD). Electrode-to-cell proximity has drawn attention due to its implications on secure single-localized stimulation. Yet, few techniques are available for understanding the relationship between the number of cells activated and the current injection. We propose an answering technique by solving the governing equation for time-dependent electrical currents using finite element discretization to obtain the volume of stimulation.

Keywords: visual prosthetic devices, volume for stimulation, FEM discretization, 3D simulation

Procedia PDF Downloads 71

Authors: Harshit Garg, Shakshi Gupta

Abstract:

One of the major problems in today’s world is the growing pollution. The cause for all environmental problems is the increasing pollution rate. Looking upon the statistics, one can find out that most of the pollution is caused by the vehicular pollution which is more than 70 % of the total pollution, effecting the environment as well as human health proportionally. One is aware of the fact that vehicles run on roads so why not having the roads which could adsorb that pollution, not only once but a number of times. Every problem has a solution which can be solved by the state of art of technology, that is one can use the innovative ideas and thoughts to make technology as a solution to the problem of vehicular pollution on roads. Solving the problem up to a certain limit/ percentage can be formulated into a new term called ECO ROADS.

Keywords: environment, pollution, roads, sustainibility

Procedia PDF Downloads 554

Authors: Rachid Ziteuni, Selt Omar

Abstract:

In this paper, we propose a new polynomial metaheuristic elaboration (tabu search) for solving scheduling problems. This method allows us to solve the scheduling problem of n tasks on m identical parallel machines with unavailability periods. This problem is NP-complete in the strong sens and finding an optimal solution appears unlikely. Note that all data in this problem are integer and deterministic. The performance criterion to optimize in this problem which we denote Pm/N-c/summs of (wjCj) is the weighted sum of the end dates of tasks.

Keywords: scheduling, parallel identical machines, unavailability periods, metaheuristic, tabu search

Procedia PDF Downloads 329

Authors: Leila Maleki, Ezatollah Ahmadi

Abstract:

The aim of this study was to investigate the effectiveness of memory training exercise on cognitive flexibility. The method of this study was experimental. The statistical population selected 40 students 14 years old, samples were chosen by available sampling method and then they were replaced in experimental (training program) group and control group randomly and answered to Wisconsin Card Sorting Test; covariance test results indicated that there were a significant in post-test scores of experimental group (p<0.005).

Keywords: cognitive flexibility, working memory exercises, problem solving, reaction time

Procedia PDF Downloads 423

Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli

Procedia PDF Downloads 139

Authors: Comfort Aina

Abstract:

Modern English, as we all know it to be a foreign language to many, will require training and re-training on the path of the teacher and learners alike. As a teacher, you cannot give that which you do not have. Teachers, many of whom are non-native speakers, are required to be competent in solving problems occurring in the teaching and learning processes. They should be conscious of up to date information about new approaches, methods, techniques as well as they should be capable in the use of information and communication technology (ICT) and, of course, should work on the improvement of their language components and competence. For teachers to be successful in these goals, they need to be encouraged and motivated. So, for EFL teachers to be successful, they are enrolled to in-service teacher training, ICT training, some of the training they undergo and the benefits accrued to it will be the focus of the paper.

Keywords: training, management, method, english language, EFL teachers

Procedia PDF Downloads 113

Authors: Malay K. Das, Bhanu P. Sahu

Abstract:

Furosemide is a weakly acidic diuretic indicated for treatment of edema and hypertension. It has very poor solubility but high permeability through stomach and upper gastrointestinal tract (GIT). Due to its limited solubility it has poor and variable oral bioavailability of 10-90%. The aim of this study was to enhance the oral bioavailability of furosemide by preparation of nanosuspensions. The nanosuspensions were prepared by nanoprecipitation with sonication using DMSO (dimethyl sulfoxide) as a solvent and water as an antisolvent (NA). The prepared nanosuspensions were sterically stabilized with polyvinyl acetate (PVA).These were characterized for particle size, ζ potential, polydispersity index, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), X-ray diffraction (XRD) pattern and release behavior. The effect of nanoprecipitation on oral bioavailability of furosemide nanosuspension was studied by in vitro dissolution and in vivo absorption study in rats and compared to pure drug. The stable nanosuspension was obtained with average size range of the precipitated nanoparticles between 150-300 nm and was found to be homogenous showing a narrow polydispersity index of 0.3±0.1. DSC and XRD studies indicated that the crystalline furosemide drug was converted to amorphous form upon precipitation into nanoparticles. The release profiles of nanosuspension formulation showed up to 81.2% release in 4 h. The in vivo studies on rats revealed a significant increase in the oral absorption of furosemide in the nanosuspension compared to pure drug. The AUC0→24 and Cmax values of nanosuspension were approximately 1.38 and 1.68-fold greater than that of pure drug, respectively. Furosemide nanosuspension showed 20.06±0.02 % decrease in systolic blood pressure compared to 13.37±0.02 % in plain furosemide suspension, respectively. The improved oral bioavailability and pharmacodynamics effect of furosemide may be due to the improved dissolution of furosemide in simulated gastric fluid which results in enhanced oral systemic absorption of furosemide from stomach region where it has better permeability.

Keywords: furosemide, nanosuspension, bioavailability enhancement, nanoprecipitation, oral drug delivery

Procedia PDF Downloads 572

Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

Procedia PDF Downloads 107

Authors: Abhilash Sahu, Amit Priyadarshi

Abstract:

In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

Procedia PDF Downloads 231

Authors: M. A. Rashed, A. S. Mansour, H. Faris, W. Afify

Abstract:

The calcarenites carbonate rocks of the Quaternary ridges, which extend along the northwestern Mediterranean coastal plain of Egypt, represent an excellent model for the transformation of loose sediments to real sedimentary rocks by the different stages of meteoric diagenesis. The depositional and diagenetic fabrics of the rocks, in addition to the strata orientation, highly affect their ultimate compressive strength and other geotechnical properties. There is a marked increase in the compressive strength (UCS) from the first to the fourth ridge rock samples. The lowest values are related to the loose packing, weakly cemented aragonitic ooid sediments with high porosity, besides the irregularly distributed of cement, which result in decreasing the ability of these rocks to withstand crushing under direct pressure. The high (UCS) values are attributed to the low porosity, the presence of micritic cement, the reduction in grain size and the occurrence of micritization and calcretization processes. The strata orientation has a notable effect on the measured (UCS). The lowest values have been recorded for the samples cored in the inclined direction; whereas the highest values have been noticed in most samples cored in the vertical and parallel directions to bedding plane. In case of the inclined direction, the bedding planes were oriented close to the plane of maximum shear stress. The lowest and highest anisotropy values have been recorded for the first and the third ridges rock samples, respectively, which may attributed to the relatively homogeneity and well sorted grain-stone of the first ridge rock samples, and relatively heterogeneity in grain and pore size distribution and degree of cementation of the third ridge rock samples, besides, the abundance of shell fragments with intra-particle pore spaces, which may produce lines of weakness within the rock.

Keywords: compressive strength, anisotropy, calcarenites, Egypt

Procedia PDF Downloads 371

Authors: Zengda Li

Abstract:

The tectonic evolution of the Beishan orogen, which forms part of the Central Asian Orogenic Belt, remains debated. This study reports the identification of three Triassic granitic plutons representing two distinct stages of magmatism in southern Beishan orogen. Zircon U–Pb dating constrains the early stage as 238–237 Ma and the late stage as 229–227 Ma. The granitoids belong to high-K calc-alkaline and shoshonitic series and exhibit alkalic-calcic and calc-alkalic features, and are weakly peraluminous rocks. Most of these granitoids are highly fractionated I-type and A-type granites. They have relatively high Isr values (0.7049–0.7086) and weak negative εNd(t) values of −1.5 to −2.1, with young Nd model ages of 1.04–0.91 Ga, indicating a crustal contribution. They also show markedly positive zircon εHf(t) values (+3.4 to +11.8) and two-stage Hf model ages of 1.06–0.69 Ga, indicating a mixture of mantle and crustal components. The lithospheric mantle beneath this region incorporating older subducted materials was metasomatized by fluids or melts. Partial melting of the metasomatized lithospheric mantle resulted in underplated magmas, which provided the heat and material input to generate the granitoids. The Middle Triassic granitic plutons show moderate negative Eu anomalies, enrichment of LILEs and depletion in Nb, Ta, and Ti suggesting partial melting of crustal components in response to the underplated mantle-derived magmas, probably linked to lithospheric delamination and asthenospheric upwelling. The Late Triassic granitic plutons show characteristics of post-orogenic granite with strong negative anomalies of Eu, Ba, Nb, Sr, P, and Ti, indicating fractional crystallization and crustal contamination during the emplacement process.

Keywords: Triassic, magmatism, geochronology, petrogenesis, Beishan orogen

Procedia PDF Downloads 153

Authors: S. H. Lee, M. J. Park, O. M. Kwon

Abstract:

In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of this systems are obtained by solving a set of Linear Matrix Inequalities(LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: multi-agent, linear matrix inequalities (LMIs), kronecker product, sampled-data, Lyapunov method

Procedia PDF Downloads 526

Authors: Sait Ali Uymaz, Gülay Tezel

Abstract:

This paper presents the comparison results on the performance of the Cuckoo Search (CS) algorithm for constrained optimization problems. For constraint handling, CS algorithm uses penalty method. CS algorithm is tested on thirteen well-known test problems and the results obtained are compared to Particle Swarm Optimization (PSO) algorithm. Mean, best, median and worst values were employed for the analyses of performance.

Keywords: cuckoo search, particle swarm optimization, constrained optimization problems, penalty method

Procedia PDF Downloads 555

Authors: Areej Isam Barham

Abstract:

The implementation of Japanese lesson study approach in the mathematics classroom has been grown worldwide as a model of professional development for teachers. In Qatar, the implementation of IMPULS-QU lesson study program aimed to establish a robust organizational improvement model of professional development for mathematics teachers in Qatar schools. This study describes the implementation of a lesson study model at Al-Markhyia Independent Primary School through different stages; and discusses how the planning process, the research lesson, and the post discussion participates in providing teachers and researchers with a successful research lesson for teacher professional development. The research followed a case study approach in one mathematics classroom. Two teachers and one professional development specialist participated the planning process. One teacher conducted the research lesson study by introducing a problem solving related to the concept of the ‘Mean’ in a mathematics class, 21 students in grade 6 participated in solving the mathematic problem, 11 teachers, 4 professional development specialists, and 4 mathematics professors observed the research lesson. All previous participants except the students participated in a pre and post-lesson discussion within this research. This study followed a qualitative research approach by analyzing the collected data through different stages in the research lesson study. Observation, field notes, and semi-structured interviews conducted to collect data to achieve the research aims. One feature of this lesson study research is that this research describes the implementation for a lesson study as a new experience for one mathematics teacher and 21 students after 3 years of conducting IMPULS-QU project in Al-Markhyia school. The research describes various stages through the implementation of this lesson study model starting from the planning process and ending by the post discussion process. Findings of the study also address the impact of lesson study approach in teaching mathematics for the development of teachers from their point views. Results of the study show the benefits of using lesson study from the point views of participated teachers, theory perceptions about the essential features of lesson study, and their needs for future development. The discussion of the study addresses different features and issues related to the implementation of IMPULS-QU lesson study model in the mathematics classroom. In the light of the study, the research presents recommendations and suggestions for future professional development.

Keywords: lesson study, mathematics education, mathematics teaching experience, teacher professional development

Procedia PDF Downloads 184

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: approximation, evolutionary PDE, Finite Element Method, temporomandibular disorders, variational spline

Procedia PDF Downloads 377

Authors: Habtamu Garoma Debela, Gemechis File Duressa

Abstract:

In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

Procedia PDF Downloads 141