Search results for: equivalent displacement method

Authors: Qinglin Shu

Abstract:

Based on the analysis of the structural vibration comfort of a domestic bridge, this paper studies the vibration reduction control principle of TMD, the derivation process of design parameter optimization and how to simulate TMD in the finite element software ANSYS. The research shows that, in view of the problem that the comfort level of a bridge exceeds the limit in individual working conditions, the vibration reduction control design of the bridge can effectively reduce the vibration of the structure by using TMD. Calculations show that when the mass ratio of TMD is 0.01, the vibration reduction rate under different working conditions is more than 90%, and the dynamic displacement of the TMD mass block is within 0.01m, indicating that the design of TMD is reasonable and safe.

Keywords: pedestrian bridges, human-induced vibration, comfort, tuned mass dampers

Procedia PDF Downloads 108

Authors: Kunya Bowornchockchai

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The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins method, Holt’s method, mean absolute percentage error (MAPE), exchange rate

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Authors: David Lindström

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We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

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Authors: Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The discontinuities is characterized using a hybrid spectral/numerical technique. This structure presents an arbitrary number of ports, each one with different orientation and dimensions. This article presents a hybrid method based on multimode contour integral and mode matching techniques. The process is based on segmentation and dividing the structure into key building blocks. We use the multimode contour integral method to analyze the blocks including irregular shape discontinuities. Finally, the multimode scattering matrix of the whole structure can be found by cascading the blocks. Therefore, the new method is suitable for analysis of a wide range of waveguide problems. Therefore, the present approach can be applied easily to the analysis of any multiport junctions and cascade blocks. The accuracy of the method is validated comparing with results for several complex problems found in the literature. CPU times are also included to show the efficiency of the new method proposed.

Keywords: segmentation, s parameters, simulation, optimization

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Authors: Ashish Ankus Yerunkar, Ravi Terkar

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Study aimed at evaluating the best process environment which could simultaneously satisfy requirements of both quality as well as productivity with special emphasis on reduction of cutting tool flank wear, because reduction in flank wear ensures increase in tool life. The predicted optimal setting ensured minimization of surface roughness. Purpose of this paper is focused on the analysis of optimum cutting conditions to get lowest surface roughness in turning SCM 440 alloy steel by Taguchi method. Design for the experiment was done using Taguchi method and 18 experiments were designed by this process and experiments conducted. The results are analyzed using ANOVA method. Taguchi method has depicted that the depth of cut has significant role to play in producing lower surface roughness followed by feed. The Cutting speed has lesser role on surface roughness from the tests. The vibrations of the machine tool, tool chattering are the other factors which may contribute poor surface roughness to the results and such factors ignored for analyses. The inferences by this method will be useful to other researches for similar type of study and may be vital for further research on tool vibrations, cutting forces etc.

Keywords: surface roughness (ra), machining, dry turning, taguchi method, turning process, anova method, mahr perthometer

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Authors: Andriati Nadhilah Widyarini, Ezra Margareth

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Introduction: Rhegmatogenous retinal detachment is a condition where there’s a break in the retina, which allows the vitreous to directly enter the subretinal space. Proliferative vitreoretinopathy (PVR) may develop due to this condition and can result in a new break, which could cause traction on the previously detached retina. Various methods of therapy can be done to treat this complication. Case: This case series involved 2 eyes of 2 patients who had total retinal detachment with advanced PVR. Pars plana vitrectomy was performed, and a 360-degree retinectomy procedure with perfluorocarbon liquid usage was done. This was followed by endo laser retinopexy to surround the border of retinectomy. 5000 cs silicone oil was used in 1 eye, whereas 12% of perfluoropropane gas was used in the other eye as a tamponade. These procedures were performed with meticulous attention to prevent any fluid from entering the subretinal space. Postoperative examination showed attachment of the retina and improvement of the patient’s visual acuity. Both eyes’ intraocular pressure was in the normal range. One eye developed retinal displacement, but no other complications occurred. Discussion: Rhegmatogenous retinal detachment with advanced PVR is a complex situation for vitreoretinal surgeons. PVR is characterized by the growth and migration of preretinal or subretinal membranes. PVR is the most common cause of retinal reattachment failure. A 360-degree retinectomy is an alternative surgical method to overcome this condition. Objectives of this procedure are releasing retinal traction caused by PVR, reducing the recurrence rate of PVR, and reattaching the retina to the pigment epithelial surface. Conclusion: 360-degree retinectomy provides satisfactory retinal reattachment and visual outcome improvement in rhegmatogenous retinal detachment with advanced PVR.

Keywords: RRD, retinectomy, pars plana, advanced PVR

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Authors: M. Barański

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The article presents a new vibration diagnostic method designed to (PM) machines with permanent magnets. Those devices are commonly used in small wind and water systems or vehicles drives. The author’s method is very innovative and unique. Specific structural properties of PM machines are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical PM machines and there was no method found to determine the technical condition of such machine basing on their own signals. In this article, the method genesis, the similarity of machines with permanent magnet to vibration sensor and simulation and laboratory tests results will be discussed. The method of determination the technical condition of electrical machine with permanent magnets basing on its own signals is the subject of patent application No P.405669, and it is the main thesis of author’s doctoral dissertation.

Keywords: vibrations, generator, permanent magnet, traction drive, electrical vehicle

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Jesus David Argueta Moreno, Justa Rufina Martel, Edith Gabriela Carrasco

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The Central American Coffee small, medium, and large corporations search for excellence, sustainability, and continuous improvement, triggers in a still unknown scale the Local expansion, crusading, and franchising strategies towards a more suitable commercial opportunity, where the dynamics of the Central American business displacement can be explained through the markets permeability traits. By considering the previously mentioned, the present study aims to evaluate the franchising potentialities offered by Central American Coffee business scenario, in order to explain dynamics of the business demography phenomena and its relevance on the Central American competitiveness landscape.

Keywords: competitiveness, franchising, business demography, Central American Coffee

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Bashara Want

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One of the key factors limiting the performance of magnetic memory is that the coercivity has a distribution with finite width, and the reversal starts at the weakest link in the distribution. So one must first know the distribution of coercivities in order to learn how to reduce the width of distribution and increase the coercivity field to obtain a system with narrow width. First Order Reversal Curve (FORC) method characterizes a system with hysteresis via the distribution of local coercivities and, in addition, the local interaction field. The method is more versatile than usual conventional major hysteresis loops that give only the statistical behaviour of the magnetic system. The FORC method will be presented and discussed at the conference.

Keywords: magnetic materials, hysteresis, first-order reversal curve method, nanostructures

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Authors: A.R. Eskandari, M.R. Eskandari

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A 2D complete identification algorithm for dielectric and multiple objects immersed in air is presented. The employed technique consists of initially retrieving the shape and position of the scattering object using a linear sampling method and then determining the electric permittivity and conductivity of the scatterer using adjoint sensitivity analysis. This inversion algorithm results in high computational speed and efficiency, and it can be generalized for any scatterer structure. Also, this method is robust with respect to noise. The numerical results clearly show that this hybrid approach provides accurate reconstructions of various objects.

Keywords: inverse scattering, microwave imaging, two-dimensional objects, Linear Sampling Method (LSM)

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Authors: Peng Li, Chuanri Li, Tao Li

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Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method and gives concrete processes on determining the factor set, the factor weight set, judgment set, and multi-grade fuzzy comprehensive evaluation. To determine the weight of factor set, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in the fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: reliability allocation, fuzzy arithmetic, allocation weight, linear programming

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: Janaki Rama Raju Patchamatla, Emani Pavan Kumar

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The idea of increasing the existing train speeds and introduction of the high-speed trains in India as a part of Vision-2020 is really challenging from both economic viability and technical feasibility. More than economic viability, technical feasibility has to be thoroughly checked for safe operation and execution. Trains moving at high speeds need a well-established firm and safe track thoroughly tested against vibration effects. With increased speeds of trains, the track structure and layered soil-structure interaction have to be critically assessed for vibration and displacements. Physical establishment of track, testing and experimentation is a costly and time taking process. Software-based modelling and simulation give relatively reliable, cost-effective means of testing effects of critical parameters like sleeper design and density, properties of track and sub-grade, etc. The present paper reports the applicability of infinite elements in reducing the unrealistic stress-wave reflections from so-called soil-structure interface. The influence of the infinite elements is quantified in terms of the displacement time histories of adjoining soil and the deformation pattern in general. In addition, the railhead response histories at various locations show that the numerical model is realistic without any aberrations at the boundaries. The numerical model is quite promising in its ability to simulate the critical parameters of track design.

Keywords: high speed railway track, finite element method, Infinite elements, vibration analysis, soil-structure interface

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Authors: Matthias Banholzer, Hagen Müller, Michael Pfitzner

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Gas internal combustion engines are widely used as propulsion systems or in power plants to generate heat and electricity. While there are different types of injection methods including the manifold port fuel injection and the direct injection, the latter has more potential to increase the specific power by avoiding air displacement in the intake and to reduce combustion anomalies such as backfire or pre-ignition. During the opening process of the injector, multiple flow regimes occur: subsonic, transonic and supersonic. To cover the wide range of Mach numbers a compressible pressure-based solver is used. While the standard Pressure Implicit with Splitting of Operators (PISO) method is used for the coupling between velocity and pressure, a high-resolution non-oscillatory central scheme established by Kurganov and Tadmor calculates the convective fluxes. A blending function based on the local Mach- and CFL-number switches between the compressible and incompressible regimes of the developed model. As the considered operating points are well above the critical state of the used fluids, the ideal gas assumption is not valid anymore. For the real gas thermodynamics, the models based on the Soave-Redlich-Kwong equation of state were implemented. The caloric properties are corrected using a departure formalism, for the viscosity and the thermal conductivity the empirical correlation of Chung is used. For the injector geometry, the dimensions of a diesel injector were adapted. Simulations were performed using different nozzle and needle geometries and opening curves. It can be clearly seen that there is a significant influence of all three parameters.

Keywords: high pressure gas injection, hybrid solver, hydrogen injection, needle opening process, real-gas thermodynamics

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Authors: Aymen Laadhari, Gábor Székely

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This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: finite element method, implicit, level set, membrane, Newton method

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Authors: Junwu Tian

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Chinese poetics originated in the pre-Qin period, while Western poetics came into being in the Hellenistic period. Although there was no mutual communication and influence between the two kinds of poetics due to both geographical distance and chronological displacement, the Sino-Western thinkers shared much in common, particularly in the social function of literature and art, the pursuit of unified and harmonious aesthetics, the advocacy of poets’ subjective initiative in the creative process of literature and art. In the sphere of rhetoric, the poetics of the pre-Qin scholars and their Greek counterparts also had heterogeneous similarities. By comparing the aesthetic ideas of Confucius, Mencius, Xun Zi, and Deng Xi with those of Plato, Aristotle, and Protagoras, this paper intends to reveal the common concerns of Chinese and Western poetics in the context of heterogeneous cultures and in their respective origin periods.

Keywords: Pre-Qin poetics, ancient Greek poetics, heterogeneous similarity, origin period

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

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Authors: Ayub Khan, Net Ram Garg, Geeta Jain

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In this paper, backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

Keywords: backstepping method, fractional order, synchronization, chaotic system

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Authors: R. Ziaie Moayed, B. Mohammadi-Haji

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Stone columns have been widely employing to improve the load-settlement characteristics of soft soils. The results of two small scale displacement control loading tests on stone columns were used in order to validate numerical finite element simulations. Additionally, a series of numerical calculations of static loading have been performed on strengthened raft footing to investigate the effects of using stone columns on bearing capacity of footings. The bearing capacity of single and group of stone columns under static loading compares with unimproved ground.

Keywords: circular raft footing, numerical analysis, validation, vertically encased stone column

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Authors: A. Tavangari, N. Salehzadeh

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In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny-Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: penny-shaped crack, stress intensity factor, fracture mechanics, Ritz method

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Authors: Reza Samsami

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The aim of the study was to degradation of polycyclic aromatic hydrocarbons (PAHs) by proxy-acid method. The amounts of PAHs were determined in a silty-clay soil sample of an aged oil refinery field in Abadan, Iran. Proxy-acid treatment method was investigated. The results have shown that the proxy-acid system is an effective method for degradation of PAHs. The results also demonstrated that the number of fused aromatic rings have not significant effects on PAH removal by proxy-acid method. The results also demonstrated that the number of fused aromatic rings have not significant effects on PAH removal by proxy-acid method.

Keywords: proxy-acid treatment, silty-clay soil, PAHs, degradation

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Authors: Emy Nayana Pinto, Denise Bomtempo Birche De Carvalho

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In the present study, the harmful use of illicit drugs is seen as a public health problem and as one of the expressions of the social question, since its consequences fall mainly on the poorer classes of the population. This perspective is a counterpoint to the dominant paradigm on illicit drug policy at the global level, whose centrality lies within the criminal justice arena. The 'drug problem' is internationally combated through fragmented approaches that focus its actions on banning and criminalizing users. In this sense, the research seeks to answer the following key questions: What are the influences of the prohibitionism in the recommendations of the United Nations (UN), the World Health Organization (WHO), and the formulation of drug policies in member countries? What are the actors that have been provoking the prospect of breaking with the prohibitionist paradigm? What is the WHO contribution to the rupture with the prohibitionist paradigm and the displacement of the drug problem in the field of public health? The general objective of this work is to seek evidence from the perspective of rupture with the prohibitionist paradigm in the field of drugs policies at the global and regional level, through analysis of documents of the World Health Organization (WHO), between the years of 2001 to 2016. The research was carried out in bibliographical and documentary sources. The bibliographic sources contributed to the approach with the object and the theoretical basis of the research. The documentary sources served to answer the research questions and evidence the existence of the perspective of change in drug policy. Twenty-two documents of the UN system were consulted, of which fifteen had the contribution of the World Health Organization (WHO). In addition to the documents that directly relate to the subject of the research, documents from various agencies, programs, and offices, such as the Joint United Nations Program on HIV/AIDS (UNAIDS) and the United Nations Office on Drugs and Crime (UNODC), which also has drugs as the central or transversal theme of its performance. The results showed that from the 2000s it was possible to find in the literature review and in the documentary analysis evidence of the critique of the prohibitionist paradigm parallel to the construction of a new perspective for drug policy at the global level and the displacement of criminal justice approaches for the scope of public health, with the adoption of alternative and pragmatic interventions based on human rights, scientific evidence and the reduction of social damages and health by the misuse of illicit drugs.

Keywords: illicit drugs, international organizations, prohibitionism, public health, World Health Organization

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Authors: Mehdi Moghimi

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Doctrines associated with situational prevention considers 'place of committing crime' as one of the fundamental elements of a crime. Meanwhile, with regard to causing or having effect on a crime situation, 'place' can be one of the pivotal indices in situational prevention analyses. This study aims at examining the role of place in construction of a crime situation and explaining the relationship between 'place' and situational preventive measures and procedures. Also, how to identify high-crime places, types of high-crime places and the factors influencing their creation are among the most important secondary objectives of this article. Concerning the purpose, it is a practical study whose material has been written through a documentary method using original sources (English), books and written and translated articles etc. This article is written in two main parts. In the first section, cognitive-conceptual issues about 'place' as one of the main causes of crime situation, and its effective interaction with situational preventive measures will be reviewed. The second part of this paper will focus on criminological examination of places and critical locations of crime and provide situational preventive measures to deal with the situation. 'Crime displacement' and 'geographical distribution of benefits'are also considered as the possible consequences of implementing preventive strategies. The results of the study suggest that the inventory of offenses is distributed according to the spatial characteristics. Moreover, according to the criminological characteristics governing region or location, offenders choose the place of crime based on a logical calculation. Therefore, some locations, regions or neighborhoods are permanent places of occurring lots of crimes. As a result, considering "place", preventive measures and procedures can be systematically directed, and using the most effective ways, limited preventive resources are utilized in the most critical places. Finally, some suggestions for further research and application are provided in line with more favorable promotion of situational preventive measures.

Keywords: crime prevention, place, police crime, situational crime prevention

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Authors: Salman Ali Nisar, Koshi Suzuki

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Precedence Diagram Method (PDM) with its additional relationships i.e., start-to-start, finish-to-finish, and start-to-finish, between activities provides more flexible schedule than traditional Critical Path Method (CPM). But, changing the duration of critical activities in PDM network will have anomalous effect on critical path. Researchers have proposed some classification of critical activity effects. In this paper, we do further study on classifications of critical activity effect and provide more information in detailed. Furthermore, we determine the maximum amount of time for each class of critical activity effect by which the project managers can control the dynamic feature (shortening/lengthening) of critical activities and project duration more efficiently.

Keywords: construction project management, critical path method, project scheduling, precedence diagram method

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Authors: Xiangming Ge, Bing Pan, Wei He, Hao Chen, Yong Zhou, Jiayao Wu, Weijiang Chu

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How the extraction and penetration of spudcan affect the performance of the adjacent pile foundation supporting the jacket platform was studied in the program FLAC3D depending on a wind farm project in Bohai sea. The simulations were conducted at the end of the spudcan penetration, which induced a pockmark in the seabed. The effects of the distance between the pile foundation and the pockmark were studied. The displacement at the mudline arose when the pockmark was closer. The bearing capacity of this jacket platform with deep pile foundations has been less influenced by the process of spudcan penetration, which can induce severe stresses on the pile foundation. The induced rotation was also satisfied with the rotation-controlling criteria.

Keywords: offshore foundation, pile-soil interaction, spudcan penetration, FLAC3D

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Authors: Nir Schreiber, Reuven Cohen, Simi Haber

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The Potts model has been widely explored in the literature for the last few decades. While many analytical and numerical results concern with the traditional two site interaction model in various geometries and dimensions, little is yet known about models where more than two spins simultaneously interact. We consider a ferromagnetic four site interaction Potts model on the square lattice (FFPS), where the four spins reside in the corners of an elementary square. Each spin can take an integer value 1,2,...,q. We write the partition function as a sum over clusters consisting of monochromatic faces. When the number of faces becomes large, tracing out spin configurations is equivalent to enumerating large lattice animals. It is known that the asymptotic number of animals with k faces is governed by λᵏ, with λ ≈ 4.0626. Based on this observation, systems with q < 4 and q > 4 exhibit a second and first order phase transitions, respectively. The transition nature of the q = 4 case is borderline. For any q, a critical giant component (GC) is formed. In the finite order case, GC is simple, while it is fractal when the transition is continuous. Using simple equilibrium arguments, we obtain a (zero order) bound on the transition point. It is claimed that this bound should apply for other lattices as well. Next, taking into account higher order sites contributions, the critical bound becomes tighter. Moreover, for q > 4, if corrections due to contributions from small clusters are negligible in the thermodynamic limit, the improved bound should be exact. The improved bound is used to relate the critical point to the finite correlation length. Our analytical predictions are confirmed by an extensive numerical study of FFPS, using the Wang-Landau method. In particular, the q=4 marginal case is supported by a very ambiguous pseudo-critical finite size behavior.

Keywords: entropic sampling, lattice animals, phase transitions, Potts model

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