Search results for: fractional differential equation

Authors: Yuanhao Gao, Pin Lin, Kees Weijer

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In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model.

Keywords: optimal control model, Stokes equation, finite element method, conjugate gradient method

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Authors: Harley Stephens

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Although fiducial marker insertion is regarded as the ‘gold standard’ in terms of image guided radiotherapy (IGRT), its application must be considered carefully as the procedure can be invasive, time-consuming, and reliant on consultant expertise. Precision of the fiducials is dependent on these markers remaining in the same location and on the prostate not changing shape during the course treatment. To facilitate the acquirement of non-ionising IGRT and intra-fractional prostate tracking, Clarity TPUS was developed as an alternative imaging system. The main benefits of Clarity TPUS are that it is non-invasive, non-ionising and cost-effective. Other studies have compared fiducials to transabdominal ultrasound, which has since been proven to not be as accurate as trans-perineal imaging, as included in this study. CBCT fiducial translations and Clarity TPUS translations for 120 images as part of the PACE-C prostate SABR trial were retrospectively evaluated by three imaging specialists. Differences were analysed using correlation and Bland-Altman plots. Inter-observer matches agreed within 3mm 88.3 % of the time in left/right direction, 86.7 % of the time in in superior/inferior direction, and 91.7% of the time in ant/post direction. They agreed within 5mm more than 98.3 % of the time in all directions. The intra-class correlation co-efficient was calculated for each direction to show agreement between imaging specialist for inter-observer variability. Each was 0.95 or above, with 1 indicating perfect reliability. Agreement between observers was slightly higher for CBCT and fiducials at 98.7% agreement within 5 mm, compared to clarity TPUS where 96.7% agreement was seen within 5mm. Clarity TPUS has the benefit of no additional dose and intra-fractional monitoring, and results show a good correlation between the different modalities. Inter-observer variability is to be considered, and further research with a larger population would be of benefit.

Keywords: oncology, prostate radiotherapy, image guided radiotherapy, IGRT

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Authors: Zubier Arfan, Paul Johnson

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The electronification of financial markets and the rise of algorithmic trading has sparked a lot of interest from the mathematical community, for the market making-problem in particular. The research presented in this short paper solves the classic stochastic control problem in order to derive the strategy for a market-maker. It also shows how to calibrate and simulate the strategy with real limit order book data for back-testing. The ambiguity of limit-order priority in back-testing is dealt with by considering optimistic and pessimistic priority scenarios. The model, although it does outperform a naive strategy, assumes constant volatility, therefore, is not best suited to the LOB data. The Heston model is introduced to describe the price and variance process of the asset. The Trader's constant absolute risk aversion utility function is optimised by numerically solving a 3-dimensional Hamilton-Jacobi-Bellman partial differential equation to find the optimal limit order quotes. The results show that the stochastic volatility market-making model is more suitable for a risk-averse trader and is also less sensitive to calibration error than the constant volatility model.

Keywords: market-making, market-microsctrucure, stochastic volatility, quantitative trading

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Authors: Alpana Agarwal, Akhil Sharma

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This work presents a fully differential CMOS amplifier consisting of two self-biased gain boosted inverter stages, that provides an alternative to the power hungry operational amplifier. The self-biasing avoids the use of external biasing circuitry, thus reduces the die area, design efforts, and power consumption. In the present work, regulated cascode technique has been employed for gain boosting. The Miller compensation is also applied to enhance the phase margin. The circuit has been designed and simulated in 1.8 V 0.18 µm CMOS technology. The simulation results show a high DC gain of 100.7 dB, Unity-Gain Bandwidth of 107.8 MHz, and Phase Margin of 66.7^o with a power dissipation of 286 μW and makes it suitable candidate for the high resolution pipelined ADCs.

Keywords: CMOS amplifier, gain boosting, inverter-based amplifier, self-biased inverter

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

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This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control

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Authors: Olga V. Kharchenko

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Applicability of a KTA crystal-based laser system with optical parametric oscillators (OPO) generation to lidar sounding of the atmosphere in the spectral range 3–4 µm is studied in this work. A technique based on differential absorption lidar (DIAL) method and differential optical absorption spectroscopy (DOAS) is developed for lidar sounding of trace atmospheric gases (TAG). The DIAL-DOAS technique is tested to estimate its efficiency for lidar sounding of atmospheric trace gases.

Keywords: atmosphere, lidar sounding, DIAL, DOAS, trace gases, nonlinear crystal

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Authors: Libo Jiang, Huan Li, Rongling Wu

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Ordinary differentiation equations (ODE) have proven to be powerful for reconstructing precise and informative gene regulatory networks (GRNs) from dynamic gene expression data. However, joint modeling and analysis of all genes, essential for the systematical characterization of genetic interactions, are challenging due to high dimensionality and a complex pattern of genetic regulation including activation, repression, and antitermination. Here, we address these challenges by unifying variable selection and game theory through ODE. Each gene within a GRN is co-expressed with its partner genes in a way like a game of multiple players, each of which tends to choose an optimal strategy to maximize its “fitness” across the whole network. Based on this unifying theory, we designed and conducted a real experiment to infer salt tolerance-related GRNs for Euphrates poplar, a hero tree that can grow in the saline desert. The pattern and magnitude of interactions between several hub genes within these GRNs were found to determine the capacity of Euphrates poplar to resist to saline stress.

Keywords: gene regulatory network, ordinary differential equation, game theory, LASSO, saline resistance

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Authors: Giselle Maggie Fer Castañeda, Diego Iván González

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The objective of this work was to study the autoshaped choice behavior in the Donahoe, Burgos and Palmer (DBP) neural network model and analyze it under the matching law. Autoshaped choice can be viewed as a form of economic behavior defined as the preference between alternatives according to their relative outcomes. The Donahoe, Burgos and Palmer (DBP) model is a connectionist proposal that unifies operant and Pavlovian conditioning. This model has been used for more than three decades as a neurobehavioral explanation of conditioning phenomena, as well as a generator of predictions suitable for experimental testing with non-human animals and humans. The study consisted of different simulations in which, in each one, a ratio of reinforcement was established for two alternatives, and the responses (i.e., activations) in each of them were measured. Choice studies with animals have demonstrated that the data generally conform closely to the generalized matching law equation, which states that the response ratio equals proportionally to the reinforcement ratio; therefore, it was expected to find similar results with the neural networks of the Donahoe, Burgos and Palmer (DBP) model since these networks have simulated and predicted various conditioning phenomena. The results were analyzed by the generalized matching law equation, and it was observed that under some contingencies, the data from the networks adjusted approximately to what was established by the equation. Implications and limitations are discussed.

Keywords: matching law, neural networks, computational models, behavioral sciences

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation

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Authors: Yuhanis Ibrahim, Sung-Pil Lee

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This study attempts to address factors that contribute to outline public art factors assessment, memorial monument specifically. Memorial monuments hold significant and rich message whether the intention of the art is to mark and commemorate important event or to inform younger generation about the past. Public monument should relate to the public and raise awareness about the significant issue. Therefore, by investigating the impact of the existing public memorial art will hopefully shed some lights to the upcoming public art projects’ stakeholders to ensure the lucid memorial message is delivered to the public directly. Public is the main actor as public is the fundamental purpose that the art was created. Perception is framed as one of the reliable evaluation tools to assess the public art impact factors. The Malaysia National Monument was selected to be the case study for the investigation. The public’s perceptions were gathered using a questionnaire that involved (n-115) participants to attain keywords, and next Semantical Differential Methodology (SDM) was adopted to evaluate the perceptions about the memorial monument. These perceptions were then measured with Reliability Factor and then were factorised using Factor Analysis of Principal Component Analysis (PCA) method to acquire concise factors for the monument assessment. The result revealed that there are four factors that influence public’s perception on the monument which are aesthetic, audience, topology, and public reception. The study concludes by proposing the factors for public memorial art assessment for the next future public memorial projects especially in Malaysia.

Keywords: factor analysis, public art, public perception, semantical differential methodology

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Authors: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

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Authors: Edina Koch, Péter Hudacsek

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In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: culvert, dynamic load, HS small model, railway transition zone

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Authors: Falek Kamel

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Various approaches are usually used in the dynamic analysis of beams vibrating transversally. For this, numerical methods allowing the solving of the general eigenvalue problem are utilized. The equilibrium equations describe the movement resulting from the solution of a fourth-order differential equation. Our investigation is based on the finite element method. The findings of these investigations are the vibration frequencies obtained by the Jacobi method. Two types of the elementary mass matrix are considered, representing a uniform distribution of the mass along with the element and concentrated ones located at fixed points whose number is increased progressively separated by equal distances at each evaluation stage. The studied beams have different boundary constraints representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculus stage is to obtain the lowest number of beam parts that gives a frequency comparable to that issued from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are used for the second type of mass representation in the same manner.

Keywords: structural elements, beams vibrating, dynamic analysis, finite element method, Jacobi method

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge-Kutta solution using 38 time steps.

Keywords: impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision

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Authors: D. J. Dahigaonkar, D. G. Wakde

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The performance analysis of low voltage low power CMOS OTA is presented in this paper. The differential input single output OTA is simulated in 180nm CMOS process technology. The simulation results indicate high bandwidth of the order of 7.04GHz with 0.766mW power consumption and transconductance of -71.20dB. The total harmonic distortion for 100mV input at a frequency of 1MHz is found to be 2.3603%. In addition to this, to establish comparative analysis of designed OTA and analyze effect of technology scaling, the differential input single output OTA is further simulated using 350nm CMOS process technology and the comparative analysis is presented in this paper.

Keywords: Operational Transconductance Amplifier, Total Harmonic Distortions, low voltage/low power, power dissipation

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Authors: Soumiya Bhattacharjee, P. K. Champati Ray, Shovan L. Chattoraj, Mrinmoy Dhara

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The entire Himalayan range is globally renowned for rainfall-induced landslides. The prime focus of the study is to determine rainfall based threshold for initiation of landslides that can be used as an important component of an early warning system for alerting stake holders. This research deals with temporal dimension of slope failures due to extreme rainfall events along the National Highway-58 from Karanprayag to Badrinath in the Garhwal Himalaya, India. Post processed 3-hourly rainfall intensity data and its corresponding duration from daily rainfall data available from Tropical Rainfall Measuring Mission (TRMM) were used as the prime source of rainfall data. Landslide event records from Border Road Organization (BRO) and some ancillary landslide inventory data for 2013 and 2014 have been used to determine Intensity Duration (ID) based rainfall threshold. The derived governing threshold equation, I= 4.738D^-0.025, has been considered for prediction of landslides of the study region. This equation was validated with an accuracy of 70% landslides during August and September 2014. The derived equation was considered for further prediction of landslides of the study region. From the obtained results and validation, it can be inferred that this equation can be used for initiation of landslides in the study area to work as a part of an early warning system. Results can significantly improve with ground based rainfall estimates and better database on landslide records. Thus, the study has demonstrated a very low cost method to get first-hand information on possibility of impending landslide in any region, thereby providing alert and better preparedness for landslide disaster mitigation.

Keywords: landslide, intensity-duration, rainfall threshold, TRMM, slope, inventory, early warning system

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Authors: Mohammad Mahmoud Mandurah

Abstract:

The existence of InfoMiracles in scripture is evidence that the scripture has a divine origin. It is also evidence to the existence of God. An InfoMiracle is an information-based miracle. The basic component of an InfoMiracle is a piece of information that could not be obtained by a human except through a divine channel. The existence of a sufficient number of convincing InfoMiracles in a scripture necessitates the existence of the divine source to these InfoMiracles. A mathematical equation is developed to prove that the Qur’an has a divine origin, and hence, prove the existence of God. The equation depends on a single variable only, which is the number of InfoMiracles in the Qur’an. The Qur’an is rich with InfoMiracles. It is shown that the existence of less than 30 InfoMiracles in the Qur’an is sufficient proof to the existence of God and that the Qur’an is a revelation from God.

Keywords: InfoMiracle, God, mathematical proof, miracle, probability

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Authors: Pezhman Taghipour Birgani, Mehdi Shekarzadeh

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In this paper, the propagation of lamb waves in three-layer joints is investigated using global matrix method. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with the lowest attenuation. The characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using global matrix method. Attenuation and phase velocity dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of the characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. The purpose of present paper is to find a combination of frequencies and modes with minimum attenuation in high and low frequencies. These frequencies and modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.

Keywords: three-layer adhesive joints, viscoelastic, lamb waves, global matrix method

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Authors: Muhanad Al-Jubouri

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A local scour is the most important of the several scours impacting bridge performance and security. Even though scour is widespread in bridges, especially during flood seasons, the experimental tests could not be applied to many standard highway bridges. A computational fluid dynamics numerical model was used to solve the problem of calculating local scouring and deposition for non-cohesive silt and clear water conditions near single and double cylindrical piers with the effect of floating debris. When FLOW-3D software is employed with the Rang turbulence model, the Nilsson bed-load transfer equation and fine mesh size are considered. The numerical findings of single cylindrical piers correspond pretty well with the physical model's results. Furthermore, after parameter effectiveness investigates the range of outcomes based on predicted user inputs such as the bed-load equation, mesh cell size, and turbulence model, the final numerical predictions are compared to experimental data. When the findings are compared, the error rate for the deepest point of the scour is equivalent to 3.8% for the single pier example.

Keywords: local scouring, non-cohesive, clear water, computational fluid dynamics, turbulence model, bed-load equation, debris

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Authors: Susana Marques

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Research on how store environment cues influence consumers’ store choice decision criteria, such as store operations, product quality, monetary price, store image and sales promotion, is sparse. Especially absent research on the simultaneous impact of multiple store environment cues. The authors propose a comprehensive store choice model that includes: three types of store environment cues as exogenous constructs; various store choice criteria as possible mediating constructs, and store patronage intentions as an endogenous construct. On the basis of testing with a sample of 561 customers of hypermarkets, the model is partially supported. This study used structural equation modelling to test the proposed model.

Keywords: store choice, store patronage, structural equation modelling, retailing

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Authors: Jon Cobb, Nasir

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Due to higher switching frequencies, the conducted Electromagnetic interference (EMI) noise is generated in a converter. It degrades the performance of a switching converter. Therefore, it is an essential requirement to mitigate EMI noise of high performance converter. Moreover, it includes two types of emission such as common mode (CM) and differential mode (DM) noise. CM noise is due to parasitic capacitance present in a converter and DM noise is caused by switching current. However, there is dire need to understand the main cause of EMI noise. Hence, we propose a novel method to predict conducted EMI noise of different converter topologies during early stage. This paper also presents the comparison of conducted electromagnetic interference (EMI) noise due to different SMPS topologies. We also make an attempt to develop an EMI noise model for a converter which allows detailed performance analysis. The proposed method is applied to different converter, as an example, and experimental results are verified the novel prediction technique.

Keywords: EMI, electromagnetic interference, SMPS, switch-mode power supply, common mode, CM, differential mode, DM, noise

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: two-lobe bearing, thermal effect, static, dynamic characteristics

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Authors: Florian Vincent Haase, Adrian Dierl, Anna Henke, Ralf Woll, Ennes Sarradj

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Structured sheet metals and structured sandwich sheet metals are three-dimensional, lightweight structures with increased stiffness which are used in the automotive industry. The impedance, a figure of resistance of a structure to vibrations, will be determined regarding plain sheets, structured sheets, and structured sandwich sheets. The aim of this paper is generating an experimental design in order to minimize costs and duration of experiments. The design of experiments will be used to reduce the large number of single tests required for the determination of correlation between the impedance and its influencing factors. Full and fractional factorials are applied in order to systematize and plan the experiments. Their major advantages are high quality results given the relatively small number of trials and their ability to determine the most important influencing factors including their specific interactions. The developed full factorial experimental design for the study of plain sheets includes three factor levels. In contrast to the study of plain sheets, the respective impedance analysis used on structured sheets and structured sandwich sheets should be split into three phases. The first phase consists of preliminary tests which identify relevant factor levels. These factor levels are subsequently employed in main tests, which have the objective of identifying complex relationships between the parameters and the reference variable. Possible post-tests can follow up in case additional study of factor levels or other factors are necessary. By using full and fractional factorial experimental designs, the required number of tests is reduced by half. In the context of this paper, the benefits from the application of design for experiments are presented. Furthermore, a multistage approach is shown to take into account unrealizable factor combinations and minimize experiments.

Keywords: structured sheet metals, structured sandwich sheet metals, impedance measurement, design of experiment

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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: Veniamin Boiarkin, Bruno Bogaz Zarpelão, Muttukrishnan Rajarajan

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The manufacturing sector is a vital component of most economies, which leads to a large number of cyberattacks on organisations, whereas disruption in operation may lead to significant economic consequences. Adversaries aim to disrupt the production processes of manufacturing companies, gain financial advantages, and steal intellectual property by getting unauthorised access to sensitive data. Access to sensitive data helps organisations to enhance the production and management processes. However, the majority of the existing data-sharing mechanisms are either susceptible to different cyber attacks or heavy in terms of computation overhead. In this paper, a privacy-preserving data-sharing scheme for smart utilities is proposed. First, a customer’s privacy adjustment mechanism is proposed to make sure that end-users have control over their privacy, which is required by the latest government regulations, such as the General Data Protection Regulation. Secondly, a local differential privacy-based mechanism is proposed to ensure the privacy of the end-users by hiding real data based on the end-user preferences. The proposed scheme may be applied to different industrial control systems, whereas in this study, it is validated for energy utility use cases consisting of smart, intelligent devices. The results show that the proposed scheme may guarantee the required level of privacy with an expected relative error in utility.

Keywords: data-sharing, local differential privacy, manufacturing, privacy-preserving mechanism, smart utility

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: exponentially shrinking sheet, magnetic field, mixed convection, suction

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Authors: R. Srinivas, K. V. Ramana

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This paper presents a novel method called VESTAL to label vertebrae and inter vertebral discs. Each vertebra has certain statistical features properties. To label vertebrae and discs, a new equation to model the path of spinal cord is derived using statistical properties of the spinal canal. VESTAL uses this equation for labeling vertebrae and discs. For each vertebrae and inter vertebral discs both posterior, interior width, height are measured. The calculated values are compared with real values which are measured using venires calipers and the comparison produced 95% efficiency and accurate results. The VESTAL is applied on 50 patients 350 MR images and obtained 100% accuracy in labeling.

Keywords: spine, vertebrae, inter vertebral disc, labeling, statistics, texture, disc

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Authors: Nilanjana Chanda, Rangeet Bhattacharyya

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Grover’s search algorithm is the fastest possible quantum mechanical algorithm to search a certain element from an unstructured set of data of N items. The algorithm can determine the desired result in only O(√N) steps. It has been demonstrated theoretically and experimentally on two-qubit systems long ago. In this work, we investigate the fidelity of Grover’s search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence on its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). We consider that the environment experiences thermal fluctuations, which leave its signature in the second-order term of the master equation through its appearance as a regulator. The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms, and we find that there exists a competition between them, leading to an optimum drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

Keywords: dissipation, fidelity, quantum master equation, relaxation, system-environment coupling

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Authors: Babak Safaei, Ahmad Ghanbari, Arash Rahmani

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In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios.

Keywords: double-walled carbon nanotubes, nonlocal continuum elasticity, free vibrations, molecular dynamics simulation, generalized differential quadrature method

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