Search results for: settlement equations

Authors: Jiang Zhenbo, Ishikura Ryohei, Yasufuku Noriyuki

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Improvement of soft clay deposits by the combination of surface stabilization and floating type cement-treated columns is one of the most popular techniques worldwide. On the basis of one dimensional consolidation model, a time-dependent skin friction model for the column-soil interaction is proposed. The nonlinear relationship between column shaft shear stresses and effective vertical pressure of the surrounding soil can be described in this model. The influence of column-soil surface roughness can be represented using a roughness coefficient R, which plays an important role in the design of column length. Based on the homogenization method, a part of floating type improved ground will be treated as an unimproved portion, which with a length of αH1 is defined as a time-dependent equivalent skin friction length. The compression settlement of this unimproved portion can be predicted only using the soft clay parameters. Apart from calculating the settlement of this composited ground, the load transfer mechanism is discussed utilizing model tests. The proposed model is validated by comparing with calculations and laboratory results of model and ring shear tests, which indicate the suitability and accuracy of the solutions in this paper.

Keywords: floating type improved foundation, time-dependent skin friction, roughness, consolidation

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Authors: Ni Zhenyu

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A human settlement is defined as the social activities, social relationships and lifestyles generated within a certain territory, which is also relatively independent territorial living space and domain composed of common people. Along with the advancement of technology and the development of society, the idea, presented in traditional research, that human settlements are deemed as substantial organic integrity with strong autonomy, are more often challenged nowadays. Spatial form of human settlements is one of the most outstanding external expressions with its subjectivity and autonomy, nevertheless, the projections of social, economic activities on certain territories are even more significant. What exactly is the relationship between human beings and the spatial form of the settlements where they live in? a question worth thinking over has been raised, that if a new view, a spatial anthropological one , can be constructed to review and respond to spatial form of human settlements based on research theories and methods of cultural anthropology within the profession of architecture. This article interprets how the typical spatial form of human settlements in the basin area of Bac Giang Province is formed under the collective impacts of local social order, land use condition, topographic features, and social contracts. A particular case of the settlement in Sizhai Village, City of Zhuji, Zhejiang Province is chosen to study for research purpose. Spatial form of human settlements are interpreted as a modeled integrity affected corporately by dominant economy, social patterns, key symbol marks and core values, etc.. Spatial form of human settlements, being a structured existence, is a materialized, behavioral, and social space; it can be considered as a place where human beings realize their behaviors and a path on which the continuity of their behaviors are kept, also for social practice a territory where currant social structure and social relationships are maintained, strengthened and rebuilt. This article aims to break the boundary of understanding that spatial form of human settlements is pure physical space, furthermore, endeavors to highlight the autonomy status of human beings, focusing on their relationships with certain territories, their interpersonal relationships, man-earth relationships and the state of existence of human beings, elaborating the deeper connotation behind spatial form of human settlements.

Keywords: spatial anthropology, human settlement, spatial pattern, spatial structure

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: S. Srednyak

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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Shahadat Hossain

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The United Nations (UN) declared Rohingya as the most oppressed nation in the world. The Rohingya's native place is Arakan, Myanmar, which is newly named Rakhine. The Rohingya have been forcibly migrated to Bangladesh, Malaysia, and other states for settlement for many years. Bangladesh has not been able to handle the pressure of Rohingya refugees, although it has been hosting Rohingya refugees for multiple decades. As a result, Rohingya refugees have been mixed with the local population. Some of the Rohingya people of Arakan already became citizens of Bangladesh after migrating to Bangladesh. The Rohingya have become Bangladeshis through intermarriage, kinship, labour, and business partnerships. Rohingya people preferred to settle in Bangladesh due to cultural, religious, and linguistic similarities. Some of the Rohingyas get an advantage also from the domestic political and voting equation of Bangladesh. This research tried to explore how the Rohingyas settled in Chattogram and Cox's Bazar and became one of the locals. The research sought to focus on their advantage, difficulties, and narrative.

Keywords: Rohingya, refugee, Bangladesh, Rohingya settlement

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: S. Chandrakaran, Aarthy D.

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Abstract: Under reamed piles are piles which are of different types like bored cast in-situ pile or bored compaction concrete piles where one or more bulbs are provided. In this paper, the design procedure of under reamed pile by both experimental study and numerical study using PLAXIS 3D Foundation software was studied. The soil chosen for study was M Sand. The Single and double under reamed pile modelling was made using mild steel. The pile load test experiment was conducted in the laboratory and the ultimate compression load for 25 mm settlement on single and double under reamed pile was observed and finally the result was compared with conventional pile (pile without bulb). The parametric influence on under reamed pile was studied by varying the geometrical parameters like diameter of bulbs, spacing between bulbs, position of bulbs and number of bulbs. The results of the numerical model showed that when the diameter of bulb D u =2.5D, the ultimate compression load for an under-reamed pile with a single bulb increased by 55 % compared to a pile without a bulb. It was observed that when the spacing between the bulbs was S=6D u with three different positions of bulb from bottom of pile as D u , 2D u and 3D u , the ultimate compression load increased by 88%, 94% and 73 % respectively, compared to the ultimate compression load for 25 mm settlement on conventional pile and if spacing was more than 6D u , ultimate compression load for 25 mm settlement started to decrease. It was observed that when the bucket length was more than 2D u , the ultimate compression

Keywords: load capcity, under remed bulb . sand, model study, sand

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.

Keywords: nonlinear, stability, buckling, modified newmark method

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Authors: Hlabishi Peter Ntloana

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This paper aims to present the effectiveness of the Spatial Planning and Land Use Management Act, 2013, in addressing key spatial challenges in Fetakgomo Tubatse Local Municipality, mainly focusing on Apel nodal point. Spatial Planning and Land Use Management Act, 2013, popularly known as SPLUMA, aimed at addressing emerging and existing spatial planning and land use management challenges in South Africa. There are critical key spatial challenges that are continuously encountered in Apel Nodal Point, which include dispersed rural settlement mainly in a communal settlement. The spatial patterns and rural settlements development patterns are a challenge, and such results in uncoordinated human settlements. The objective of this research paper is to analyze the spatial planning of Apel nodal points and determine the effectiveness of the SPLUMA policy. Key Informant interviews were conducted with 20 participants, and also the municipal Spatial Development Framework was considered to explore more challenges and proposed recommendations. The results divulged that there is a huge gap in addressing spatial planning, mainly in rural areas, and correlation with the findings of the Municipal Spatial Development framework. In conclusion, spatial planning remains a critical dilemma in most rural settlements, and there must be programmes and strategies to balance the effectiveness of spatial planning in urban and rural settlements.

Keywords: land use management, rural settlement, spatial development framework, spatial planning

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Jan Ceselsky

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Construction and reconstruction of settlements and individual municipalities, environmental management and the creation, deployment of the forces of production and building transport and technical equipment requires a large expenditure of material and human resources. That is why the economic aspects of the majority decision in these planes built in the foreground and are often decisive. Thereby but more serious is that the economic aspects of the settlement, the creation and function remain in their whole, unprocessed, and can not speak of a set of individual techniques and methods traditional indicators and experiments with new approaches. This is true both at the level of the national economy, and in their own urban designs. Still a few remain identified specific economic shaping patterns of settlement and the less it is possible to speak of their control. Also practical assessing economics of specific solutions are often used non-apt indicators in addition to economics usually identifies with the lowest acquisition cost or high-intensity land use with little regard for functional efficiency and little studied much higher operating and maintenance costs.

Keywords: investment, municipal engineering, value for money, construction

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Authors: Hawre Hasan Hama, Choman Mahmood H. Rashid

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The four-year armed conflict between the Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK) ended in September 1998 under the terms of the Washington Agreement. Since then, there has been a quarter-century of durable peace between the two combatant parties, though they have often been at odds politically. Based on interviews with Kurdish political leaders from both parties, this paper argues that sharing or dividing power across all four dimensions of state power — political, military, territorial, and economic — has played a vital role ensuring the durability of the peace settlement. The paper traces the KDP-PUK power sharing system through three stages: the transition stage (1998-2006), the “golden” period (2006-2013), the “weakening” period (2013 to present).

Keywords: peace settlement, enduring peace, power-sharing and power dividing, Iraqi Kurdistan.

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Authors: Erdal Akyol, Mutlu Alkan

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Multi criteria decision analysis (MDCA) covers both data and experience. It is very common to solve the problems with many parameters and uncertainties. GIS supported solutions improve and speed up the decision process. Weighted grading as a MDCA method is employed for solving the geotechnical problems. In this study, geotechnical parameters namely soil type; SPT (N) blow number, shear wave velocity (Vs) and depth of underground water level (DUWL) have been engaged in MDCA and GIS. In terms of geotechnical aspects, the settlement suitability of the municipal area was analyzed by the method. MDCA results were compatible with the geotechnical observations and experience. The method can be employed in geotechnical oriented microzoning studies if the criteria are well evaluated.

Keywords: GIS, spatial analysis, multi criteria decision analysis, geotechnics

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Authors: Nagmani Lnu

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Often, Quality Engineering refers to testing the applications that either have a User Interface (UI) or an Application Programming Interface (API). We often find mature test practices, standards, and automation regarding UI or API testing. However, another kind is present in almost all types of industries that deal with data in bulk and often get handled through something called a Batch Application. This is primarily an offline application companies develop to process large data sets that often deal with multiple business rules. The challenge gets more prominent when we try to automate batch testing. This paper describes the approaches taken to test a Batch application from a Financial Industry to test the payment settlement process (a critical use case in all kinds of FinTech companies), resulting in 100% test automation in Test Creation and Test execution. One can follow this approach for any other batch use cases to achieve a higher efficiency in their testing process.

Keywords: batch testing, batch test automation, batch test strategy, payments testing, payments settlement testing

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

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

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Authors: Mohammad Vahedi Torshizi

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In this investigation, at first, bending stress, contact stress, Safety factor of bending and Safety factor of contact between sun gear and planet gear tooth was determined using mathematical equations. Also, The amount of Sun Revolution in, Speed carrier, power Transmitted of the sun, sun torque, sun peripheral speed, Enter the tangential force gears, was calculated using mathematical equations. According to the obtained results, maximum of bending stress and contact stress occurred in three plantary and low status of four plantary. Also, maximum of Speed carrier, sun peripheral speed, Safety factor of bending and Safety factor of contact obtained in four plantary and maximum of power Transmitted of the sun, Enter the tangential force gears, bending stress and contact stress was in three pantry and factors And other factors were equal in the two planets.

Keywords: bending stress, contact stress, plantary, mathematical equations

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Jatupon Em-Udom, Nirand Pisutha-Arnond

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The phase-field-crystal, PFC, approach is a density-functional-type material model with an atomic resolution on a diffusive timescale. Spatially, the model incorporates periodic nature of crystal lattices and can naturally exhibit elasticity, plasticity and crystal defects such as grain boundaries and dislocations. Temporally, the model operates on a diffusive timescale which bypasses the need to resolve prohibitively small atomic-vibration time steps. The PFC model has been used to study many material phenomena such as grain growth, elastic and plastic deformations and solid-solid phase transformations. In this study, the pressure-controlled dynamic equation for the PFC model was developed to simulate a single-component system under externally applied pressure; these coupled equations are important for studies of deformable systems such as those under constant pressure. The formulation is based on the non-equilibrium thermodynamics and the thermodynamics of crystalline solids. To obtain the equations, the entropy variation around the equilibrium point was derived. Then the resulting driving forces and flux around the equilibrium were obtained and rewritten as conventional thermodynamic quantities. These dynamics equations are different from the recently-proposed equations; the equations in this study should provide more rigorous descriptions of the system dynamics under externally applied pressure.

Keywords: driving forces and flux, evolution equation, non equilibrium thermodynamics, Onsager’s reciprocal relation, phase field crystal model, thermodynamics of single-component solid

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Authors: Ashwini V. Chavan, Sukhanand S. Bhosale

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Challenges of weak soil subgrade are often resolved either by stabilization or reinforcing it. However, it is also practiced to reinforce the granular fill to improve the load-settlement behavior of over weak soil strata. The inclusion of reinforcement in the engineered granular fill provided a new impetus for the development of enhanced Soil-Structure Interaction (SSI) models, also known as mechanical foundation models or lumped parameter models. Several researchers have been working in this direction to understand the mechanism of granular fill-reinforcement interaction and the response of weak soil under the application of load. These models have been developed by extending available SSI models such as the Winkler Model, Pasternak Model, Hetenyi Model, Kerr Model etc., and are helpful to visualize the load-settlement behavior of a physical system through 1-D and 2-D analysis considering beam and plate resting on the foundation respectively. Based on the literature survey, these models are categorized as ‘Reinforced Pasternak Model,’ ‘Double Beam Model,’ ‘Reinforced Timoshenko Beam Model,’ and ‘Reinforced Kerr Model.’ The present work reviews the past 30+ years of research in the field of SSI models for reinforced foundation systems, presenting the conceptual development of these models systematically and discussing their limitations. Special efforts are taken to tabulate the parameters and their significance in the load-settlement analysis, which may be helpful in future studies for the comparison and enhancement of results and findings of physical models.

Keywords: geosynthetics, mathematical modeling, reinforced foundation, soil-structure interaction, ground improvement, soft soil

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Akhila Palat, B. Umashankar

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Back-to-back Mechanically Stabilized Earth (MSE) walls are cost-effective soil-retaining structures that can tolerate large settlements compared to conventional gravity retaining walls. They are also an economical way to meet everyday earth retention needs for highway and bridge grade separations, railroads, commercial and residential developments. But, existing design guidelines (FHWA/BS/ IS codes) do not provide a mechanistic approach for the design of back-to-back reinforced retaining walls. The settlement analysis of such structures is limited in the literature. A better understanding of the deformations of this wall system requires an analytical tool that incorporates the properties of backfill material, foundation soil, and geosynthetic reinforcement, and account for the soil–structure interactions in a realistic manner. This study was conducted to investigate the effect of reinforced back-to-back MSE walls on wall settlements and facing deformations. Back-to-back reinforced retaining walls were modeled and compared using commercially available finite difference package FLAC 2D. Parametric studies were carried out for various angles of shearing resistance of backfill material and foundation soil, and the axial stiffness of the reinforcement. A 6m-high wall was modeled, and the facing panels were taken as full-length panels with nominal thickness. Reinforcement was modeled as cable elements (two-dimensional structural elements). Interfaces were considered between soil and wall, and soil and reinforcement.

Keywords: back-to-back walls, numerical modeling, reinforced wall, settlement

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Shokoufeh Sadeghifard

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This study is a review of the nature of soil arching that develops in the upper layer of soil during drilling processes before pulling product pipe inside the hole. This study is based on the results of some parametric studies which are investigating the behavior of drained sandy soil above HDD borehole using Plaxis finite element solution. The influence of drilling mud injection in these series of analyses has been ignored. However, a suitable drilling mud pressure helps to achieve stable arch when the height of soil cover over the drilling borehole is not enough. In this study, the soil response to the formation of a HDD borehole is compared to arching theory developed by Terzaghi (1943). It is found that Terzaghi’s approach is capable of describing all of the behaviour seen when a stable arch forms. According to the numerical results, a suitable safe depth of 4D, D is borehole diameter, is suggested for typical range of HDD borehole in sandy soil.

Keywords: HDD, Plaxis, finite element, arching, settlement, drilling

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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

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

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Authors: Ebru Dural, M. Zulfu Asık

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

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

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