Search results for: problem space

Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: Theresa Marie Miller, Ma. Nympha Joaquin

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The aim of this study was to check the predictive power of social-oriented and individual-oriented achievement motivation on student engagement and collaborative problem-solving skills in mathematics. A sample of 277 fourth year high school students from the Philippines were selected. Surveys and videos of collaborative problem solving activity were used to collect data from respondents. The mathematics teachers of the participants were interviewed to provide qualitative support on the data. Systemaitc correlation and regression analysis were employed. Results of the study showed that achievement motivations−SOAM and IOAM− linearly predicted student engagement but was not significantly associated to the collaborative problem-solving skills in mathematics. Student engagement correlated positively with collaborative problem-solving skills in mathematics. The results contribute to theorizing about the predictive power of achievement motivations, SOAM and IOAM on the realm of academic behaviors and outcomes as well as extend the understanding of collaborative problem-solving skills of 21st century learners.

Keywords: achievement motivation, collaborative problem-solving skills, individual-oriented achievement motivation, social-oriented achievement motivation, student engagement

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Authors: Claudio Calosi, Damiano Costa, Paolo Natali

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Determination is the relation that holds between certain kinds of properties, determinables – such as “being colored”, and others, determinates – such as “being red”. Subordination is the relation that holds between genus properties – such as “being an animal”, and others, species properties – such as “being human”'. It is widely held that Determination and Subordination share important similarities, yet also crucial differences. But what grounds such similarities and differences? This question is hardly ever addressed. The present paper provides the first step towards filling this gap in the literature. It argues that a locational theory of instantiation, roughly the view that to have a property is to occupy a location in quality space, holds the key for such an answer. More precisely, it argues that both principles of Determination and Subordination are just examples of more general principles of location. Consider Determination. The principle that everything that has a determinate has a determinable boils down to the claim that everything that has a precise location in quality space is in quality space – an eminently reasonable principle. The principle that nothing can have two determinates (at the same level of determination) boils down to the principle that nothing can be “multilocated” in quality space. In effect, the following provides a “translation table” between principles of location and determination: LOCATION DETERMINATION Functionality At Most One Determination Focus At Most One Determination & Requisite Determination* Exactness Requisite Determination* Super-Exactness Requisite Determination Exactitude Requisite Determination Converse-Exactness Determinable Inehritance This grounds the similarity between Determination and Subordination. What about the differences? The paper argues that the differences boil down to the mereological structure of the regions that are occupied in quality space, in particular whether they are simple or complex. The key technical detail is that Determination and Subordination induce a “set-theoretic rooted tree” structure over the domain of properties. Interestingly, the analysis also provides a possible justification for the Aristotelian claim that being is not a genus property – an argument that the paper develops in some detail.

Keywords: determinables/determinates, genus/species, location, Aristotle on being is not a genus

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Authors: Tarek Aboueldahab, Hanan Farag

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Parallel Job Shop Scheduling Problem (JSP) is a multi-objective and multi constrains NP- optimization problem. Traditional Artificial Intelligence techniques have been widely used; however, they could be trapped into the local minimum without reaching the optimum solution, so we propose a hybrid Artificial Intelligence model (AI) with Discrete Breeding Swarm (DBS) added to traditional Artificial Intelligence to avoid this trapping. This model is applied in the cost minimization of the Car Sequencing and Operator Allocation (CSOA) problem. The practical experiment shows that our model outperforms other techniques in cost minimization.

Keywords: parallel job shop scheduling problem, artificial intelligence, discrete breeding swarm, car sequencing and operator allocation, cost minimization

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Authors: Enkhjargal Bat-Ochir

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The global market of electrical and electronic equipment (EEE) has increasing rapidly while the lifespan of these products has become increasingly shorter. So, e-waste is becoming the world’s fastest growing waste stream. E-waste is a huge problem when it’s not properly disposed of, as these devices contain substances that are harmful to the environment and to human health as they contaminate the land, water, and air. This paper tends to highlight e-waste problem and harmful effects and can grasp the extent of the problem and take the necessary measures to solve it in Mongolia and to improve standards and human health.

Keywords: e -waste, recycle, electrical, Mongolia

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Authors: E. Marušić-Paloka, I. Pažanin, M. Prša

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Subject of this study is the stationary heat conduction problem through a pipe filled with incompressible viscous fluid. In previous work, we observed the existence and uniqueness theorems for the corresponding boundary-value problem and within we have taken into account the effects of the pipe's dilatation due to the temperature of the fluid inside of the pipe. The main difficulty comes from the fact that flow domain changes depending on the solution of the observed heat equation leading to a non-standard coupled governing problem. The goal of this work is to find solution estimate since the exact solution of the studied problem is not possible to determine. We use an asymptotic expansion in order of a small parameter which is presented as a heat expansion coefficient of the pipe's material. Furthermore, an error estimate is provided for the mentioned asymptotic approximation of the solution for inner area of the pipe. Close to the boundary, problem becomes more complex so different approaches are observed, mainly Theory of Perturbations and Separations of Variables. In view of that, error estimate for the whole approximation will be provided with additional software simulations of gotten situation.

Keywords: asymptotic analysis, dilated pipe, error estimate, heat conduction

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Khalil H. Al-Bayati, Khalid Omar Al-Baiti

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The energy expectation value for Li-like ions systems (Li, Be+ and Be2+) hasbeen calculated and examined within the ground state (1s2sα)^2 S and the excited state (1s3sα)^2 S in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wavefnctions.

Keywords: energy expectation value, atomic systems, ground and excited states, Hartree-Fock approximation

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Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Nusrat T. Chowdhury, M. F. Baki, A. Azab

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The production planning problem is concerned with specifying the optimal quantities to produce in order to meet the demand for a prespecified planning horizon with the least possible expenditure. Making the right decisions in production planning will affect directly the performance and productivity of a manufacturing firm, which is important for its ability to compete in the market. Therefore, developing and improving solution procedures for production planning problems is very significant. In this paper, we develop a Dantzig-Wolfe decomposition of a multi-item hierarchical production planning problem with capacity constraint and present a column generation approach to solve the problem. The original Mixed Integer Linear Programming model of the problem is decomposed item by item into a master problem and a number of subproblems. The capacity constraint is considered as the linking constraint between the master problem and the subproblems. The subproblems are solved using the dynamic programming approach. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any kind of infeasibility that arises while solving the problem. We compare the computational performance of the developed solution approach against the state-of-the-art heuristic procedure available in the literature. The results show that the proposed heuristic-based decomposition approach improves the solution quality by 20% as compared to the literature.

Keywords: inventory, multi-level capacitated lot-sizing, emission control, setup carryover

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Authors: Ghussoun Al-Jeiroudi

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Stochastic programming is one of the powerful technique which is used to solve real-life problems. Hence, the data of real-life problems is subject to significant uncertainty. Uncertainty is well studied and modeled by stochastic programming. Each day, problems become bigger and bigger and the need for a tool, which does deal with large scale problems, increase. Interior point method is a perfect tool to solve such problems. Interior point method is widely employed to solve the programs, which arise from stochastic programming. It is an iterative technique, so it is required a starting point. Well design starting point plays an important role in improving the convergence speed. In this paper, we propose a starting point for interior point method for multistage stochastic programming. Usually, the optimal solution of stage k+1 is used as starting point for the stage k. This point has the advantage of being close to the solution of the current program. However, it has a disadvantage; it is not in the feasible region of the current program. So, we suggest to take this point and modifying it. That is by adding to it a vector in the null space of the matrix of the unchanged constraints because the solution will change only in the null space of this matrix.

Keywords: interior point methods, stochastic programming, null space, starting points

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Authors: Majid Abdolrazzagh-Nezhad, Salwani Abdullah

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The job-shop scheduling problem (JSSP) is an important decision facing those involved in the fields of industry, economics and management. This problem is a class of combinational optimization problem known as the NP-hard problem. JSSPs deal with a set of machines and a set of jobs with various predetermined routes through the machines, where the objective is to assemble a schedule of jobs that minimizes certain criteria such as makespan, maximum lateness, and total weighted tardiness. Over the past several decades, interest in meta-heuristic approaches to address JSSPs has increased due to the ability of these approaches to generate solutions which are better than those generated from heuristics alone. This article provides the classification, constraints and objective functions imposed on JSSPs that are available in the literature.

Keywords: job-shop scheduling, classification, constraints, objective functions

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Authors: Katherine Anson

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This paper takes a closer look at the use of day-to-day informal working practices in Latin American spatial, cultural activism against gentrification. Through a discursive analysis of the Ecuadorian communally made film documentary San Roque: A House for All (2015), and the study of the political conflict around the gentrification of the place, the essay illustrates how the purposeful showcase of indigenous uses of space claims ownership over the city’s downtown area. This argument concludes that by making visible everyday indigenous ways of production in relation to space, the video contests the neoliberalist aim to proletarianize the urban poor, and therefore, to transform them into a landless group. This approach demonstrates that through representations of their own cultural working practices grassroots organizations consciously deconstruct/contest the capitalist urbanization of space.

Keywords: cultural activism, gentrification, indigenous working traditions, neoliberalism, urban displacement, everyday forms of resistance

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Authors: Reut Lanyado, David Mendlovic

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Most biological methods for authentication require special equipment and, some of them are easy to fake. We proposed a method for authentication based on hand movement while typing a sentence with a regular camera. This technique uses the full video of the hand, which is harder to fake. In the first phase, we tracked the hand joints in each frame. Next, we represented a single frame for each individual using our Pose Agnostic Rotation and Movement (PARM) dimensional space. Then, we indicated a full video of hand movement in a fixed low dimensional space using this method: Fixed Dimension Video by Interpolation Statistics (FDVIS). Finally, we identified each individual in the FDVIS representation using unsupervised clustering and supervised methods. Accuracy exceeds 96% for 80 individuals by using supervised KNN.

Keywords: authentication, feature extraction, hand recognition, security, signal processing

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Authors: Siddhi Pedamkar, Reenu Singh

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This report is based on how a culture transforms from one era to another era in commercial space. This transformation is observed in commercial as well as residential spaces. The spaces have specific color concepts, surface detailing furniture, and function-specific layouts. But the cultural impact is very rarely seen in commercial spaces, mostly because the interior is divine by function to a large extent. Information was collected from books and research papers. A quantitative survey was conducted to understand people's perceptions about the impact of culture on design entities and how culture dictates the different types of space and their character. The survey also highlights the impact of types of interior lighting, colour schemes, and furniture types on the interior environment. The questionnaire survey helped in framing design parameters for contemporary interior design. The design parameters are used to propose design options for new-age furniture that can be used in co-working spaces. For the new and contemporary working spaces, new age design furniture, interior elements such as visual partition, semi-visual partition, lighting, and layout can be transformed by cultural changes in the working style of people and organization.

Keywords: commercial space, culture, environment, furniture, interior

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Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

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Gate Assignment Problem (GAP) is one of the most substantial issues in airport operation. In principle, GAP intends to maintain the maximum capacity of the airport through the best possible allocation of the resources (gates) in order to reach the optimum outcome. The problem involves a wide range of dependent and independent resources and their limitations, which add to the complexity of GAP from both theoretical and practical perspective. In this study, GAP was mathematically formulated as a three-objective problem. The preliminary goal of multi-objective formulation was to address a higher number of objectives that can be simultaneously optimized and therefore increase the practical efficiency of the final solution. The problem is solved by applying the second version of Non-dominated Sorting Genetic Algorithm (NSGA-II). Results showed that the proposed mathematical model could address most of major criteria in the decision-making process in airport management in terms of minimizing both airport/airline cost and passenger walking distance time. Moreover, the proposed approach could properly find acceptable possible answers.

Keywords: airport management, gate assignment problem, mathematical modeling, genetic algorithm, NSGA-II

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Authors: Luojie Tang

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Riverside space is an important public space and ecological corridor in urban areas, but mountainous urban rivers are often overlooked due to their deep valleys and poor accessibility. This article takes the Qing Shui Xi River in Chongqing as an example, and through long-term field inspections, measurements, interviews, and online surveys, summarizes the problems of poor accessibility, limited space for renovation, lack of waterfront facilities, excessive artificial intervention, low average runoff, severe river water pollution, and difficulty in integrated watershed management in riverside space. Based on the current situation and drawing on relevant experiences, this article summarizes the design methods for riverside space in deep valley rivers in mountainous urban areas. Regarding spatial design techniques, the article emphasizes the importance of integrating waterfront spaces into the urban public space system and vertical linkages. Furthermore, the article suggests different design methods and improvement strategies for the already developed areas and new development areas. Specifically, the article proposes a planning and design strategy of "protection" and "empowerment" for new development areas and an updating and transformation strategy of "improvement" and "revitalization" for already developed areas. In terms of ecological restoration methods, the article suggests three focus points: increasing the runoff of urban rivers, raising the landscape water level during dry seasons, and restoring vegetation and wetlands in the riverbank buffer zone while protecting the overall pattern of the watershed. Additionally, the article presents specific design details of the Qingshuixi River to illustrate the proposed design and restoration techniques.

Keywords: deep-cut river, design method, mountainous city, Qingshuixi river in Chongqing, waterfront space design

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Authors: Loris Franchi, Daniele Calvi, Sabrina Corpino

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This paper presents a design methodology in which stakeholders are assisted with the exploration of a so-called negotiation space, aiming to the maximization of both group social welfare and single stakeholder’s perceived utility. The outcome results in less design iterations needed for design convergence while obtaining a higher solution effectiveness. During the early stage of a space project, not only the knowledge about the system but also the decision outcomes often are unknown. The scenario is exacerbated by the fact that decisions taken in this stage imply delayed costs associated with them. Hence, it is necessary to have a clear definition of the problem under analysis, especially in the initial definition. This can be obtained thanks to a robust generation and exploration of design alternatives. This process must consider that design usually involves various individuals, who take decisions affecting one another. An effective coordination among these decision-makers is critical. Finding mutual agreement solution will reduce the iterations involved in the design process. To handle this scenario, the paper proposes a design methodology which, aims to speed-up the process of pushing the mission’s concept maturity level. This push up is obtained thanks to a guided negotiation space exploration, which involves autonomously exploration and optimization of trade opportunities among stakeholders via Artificial Intelligence algorithms. The negotiation space is generated via a multidisciplinary collaborative optimization method, infused by game theory and multi-attribute utility theory. In particular, game theory is able to model the negotiation process to reach the equilibria among stakeholder needs. Because of the huge dimension of the negotiation space, a collaborative optimization framework with evolutionary algorithm has been integrated in order to guide the game process to efficiently and rapidly searching for the Pareto equilibria among stakeholders. At last, the concept of utility constituted the mechanism to bridge the language barrier between experts of different backgrounds and differing needs, using the elicited and modeled needs to evaluate a multitude of alternatives. To highlight the benefits of the proposed methodology, the paper presents the design of a CubeSat mission for the observation of lunar radiation environment. The derived solution results able to balance all stakeholders needs and guaranteeing the effectiveness of the selection mission concept thanks to its robustness in valuable changeability. The benefits provided by the proposed design methodology are highlighted, and further development proposed.

Keywords: concurrent engineering, artificial intelligence, negotiation in engineering design, multidisciplinary optimization

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Authors: Mareye Zeleke Mekonen

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The Kafficho language has distinct issues in information retrieval because of its restricted resources and dearth of standardized methods. In this endeavor, with the cooperation and support of linguists and native speakers, we investigate the creation of information retrieval systems specifically designed for the Kafficho language. The Kafficho information retrieval system allows Kafficho speakers to access information easily in an efficient and effective way. Our objective is to conduct an information retrieval experiment using 220 Kafficho text files, including fifteen sample questions. Tokenization, normalization, stop word removal, stemming, and other data pre-processing chores, together with additional tasks like term weighting, were prerequisites for the vector space model to represent each page and a particular query. The three well-known measurement metrics we used for our word were Precision, Recall, and and F-measure, with values of 87%, 28%, and 35%, respectively. This demonstrates how well the Kaffiho information retrieval system performed well while utilizing the vector space paradigm.

Keywords: Kafficho, information retrieval, stemming, vector space

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Authors: Balamurali Gunji, B. B. V. L. Deepak, B. B. Biswal, Amrutha Rout, Golak Bihari Mohanta

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Robots play an important role in the operations like pick and place, assembly, spot welding and much more in manufacturing industries. Out of those, assembly is a very important process in manufacturing, where 20% of manufacturing cost is wholly occupied by the assembly process. To do the assembly task effectively, Assembly Sequences Planning (ASP) is required. ASP is one of the multi-objective non-deterministic optimization problems, achieving the optimal assembly sequence involves huge search space and highly complex in nature. Many researchers have followed different algorithms to solve ASP problem, which they have several limitations like the local optimal solution, huge search space, and execution time is more, complexity in applying the algorithm, etc. By keeping the above limitations in mind, in this paper, a new automated optimal robotic assembly sequence planning using Artificial Bee Colony (ABC) Algorithm is proposed. In this algorithm, automatic extraction of assembly predicates is done using Computer Aided Design (CAD) interface instead of extracting the assembly predicates manually. Due to this, the time of extraction of assembly predicates to obtain the feasible assembly sequence is reduced. The fitness evaluation of the obtained feasible sequence is carried out using ABC algorithm to generate the optimal assembly sequence. The proposed methodology is applied to different industrial products and compared the results with past literature.

Keywords: assembly sequence planning, CAD, artificial Bee colony algorithm, assembly predicates

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Authors: Xiaobao Han, Huacong Li, Jia Li

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For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model.

Keywords: linear parameter varying (LPV), parameterized Lyapunov function (PLF), linear matrix inequalities (LMI), diagonal dominance pre-compensator

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: flow-shop scheduling problem, makespan, Petri nets, state equation

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Authors: Yang-Kuei Lin, Yun-Xi Zhang

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This research focuses on the bicriteria correlated parallel machine scheduling problem. The two objective functions considered in this problem are to minimize maximum lateness and total weighted completion time. We first present a mixed integer programming (MIP) model that can find the entire efficient frontier for the studied problem. Next, we have proposed a bicriteria heuristic that can find non-dominated solutions for the studied problem. The performance of the proposed bicriteria heuristic is compared with the efficient frontier generated by solving the MIP model. Computational results indicate that the proposed bicriteria heuristic can solve the problem efficiently and find a set of diverse solutions that are uniformly distributed along the efficient frontier.

Keywords: bicriteria, correlated parallel machines, heuristic, scheduling

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Authors: Bankole Wright

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The late 20th to the early 21st century has been predominantly characterized by the movement of individuals from one country to another country or countries. The chief reasons for migration have always been premised on socio-cultural, socio-political and socio-economic factors, with influences of migration finding expression through various ways. Indeed, migration experiences have formed points of subjectivity which functions as agencies that propel migrants to strongly quest for migrating from their home space to other socio-cultural space that performs the role of escape for them. This paper interrogates the discourse of migration, agency and subjectivity in Helon Habila’s Travellers. The essay explores the interconnectedness between migration which is the physical [as deployed in this paper] movement from one location to another, agency as seen in the ability to act based on various ideological frameworks within which the action is taken, and subjectivity which identifies with the predominant factors that influence human actions; and how these connections are responsible for defining the diaspora individual. The discourse of what makes migrants desire to move from their various spaces is as critical as the experiences they face in their various host land. Hence, this paper demonstrates, through the analysis of an African diasporic novel, that the quest for migration is mostly determined by certain agencies in the diaspora home space, which characters have been subjects of and desire to escape. Traveller is a novel which chronicles the various experiences of migrants who journey from their various home space to another land as a result of different agencies that precipitated their migration. This paper engages these agencies as impediments to human survival.

Keywords: migration, agency, subjectivity, Helon Habila, diaspora, home, space

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Authors: Rajeev, N. K. Raigar

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In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: operational matrix of differentiation, similarity transformation, shifted second kind chebyshev wavelets, stefan problem

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Authors: Nicola Menga, Giuseppe Carbone

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Although contact mechanics has been widely focused on the study of contacts between half-space, it has been recently pointed out that in presence of finite thickness elastic layers the results of the contact problem show significant difference in terms of the main contact quantities (e.g. contact area, penetration, mean pressure, etc.). Actually, there exist a wide range of industrial application demanding for this kind of studies, such as seals leakage prediction or pressure-sensitive coatings for electrical applications. In this work, we focus on the contact between a rigid profile and an elastic layer of thickness h confined under two different configurations: rigid constrain and applied uniform pressure. The elastic problem at hand has been formalized following Green’s function method and then numerically solved by means of a matrix inversion. We study different contact conditions, both considering and neglecting adhesive interactions at the interface. This leads to different solution techniques: Adhesive contacts equilibrium solution is found, in term of contact area for given penetration, making stationary the total free energy of the system; whereas, adhesiveless contacts are addressed defining an equilibrium criterion, again on the contact area, relying on the fracture mechanics stress intensity factor KI. In particular, we make the KI vanish at the edges of the contact area, as peculiar for adhesiveless elastic contacts. The results are obtained in terms of contact area, penetration, and mean pressure for both adhesive and adhesiveless contact conditions. As expected, in the case of a uniform applied pressure the slab turns out much more compliant than the rigidly constrained one. Indeed, we have observed that the peak value of the contact pressure, for both the adhesive and adhesiveless condition, is much higher for the rigidly constrained configuration than in the case of applied uniform pressure. Furthermore, we observed that, for little contact area, both systems behave the same and the pull-off occurs at approximately the same contact area and mean contact pressure. This is an expected result since in this condition the ratio between the layers thickness and the contact area is very high and both layer configurations recover the half-space behavior where the pull-off occurrence is mainly controlled by the adhesive interactions, which are kept constant among the cases.

Keywords: contact mechanics, adhesion, friction, thick layer

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Authors: Mohsen Farshad

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Information and force definition has been intertwined with the concept of entropy for many years. The displacement information of degrees of freedom with Brownian motions at a given temperature in space emerges as an entropic force between species. Here, we use this concept of entropy to understand the underlying physics behind the formation of attractive and repulsive forces by imagining that space is filled with free Brownian degrees of freedom. We incorporate the radius of bodies and the distance between them into entropic force relation systematically. Using this modified gravitational entropic force, we derive the attractive entropic force between bodies without considering their spin. We further hypothesize a possible mechanism for the formation of the repulsive force between two bodies. We visually elaborate that the repulsive entropic force will be manifested through the rotation of degrees of freedom around the spinning particles.

Keywords: entropy, information, force, Brownian Motions

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Authors: Jorge Gonzalez-Camus

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

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

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Authors: Brian E. Usibe

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This paper addresses the problem of a linear crack located in the middle of a homogeneous elastic media under normal tension-compression harmonic loading. The problem of deformation of the fractured media is solved using the direct finite element numerical procedure, including the analysis of the dynamic field variables of the problem. A finite element algorithm that satisfies the unilateral Signorini contact constraint is also presented for the solution of the contact interaction of the crack faces and how this accounts for the qualitative and quantitative changes in the solution when determining the dynamic fracture parameter.

Keywords: harmonic loading, linear crack, fracture parameter, wave number, FEA, contact interaction

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