Showing papers in "Physica A-statistical Mechanics and Its Applications in 2018"

Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties

Abstract: We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. For each evolution equation, we presented the exact solution for time variable and studied the semigroup principle. The Riemann–Liouville fractional operator verifies the semigroup principle but the associate evolution equation does not. The Caputo–Fabrizio fractional derivative does not satisfy the semigroup principle but surprisingly, the exact solution satisfies very well all the principle of semigroup. However, the Atangana–Baleanu for small time is the stretched exponential derivative, which does not satisfy the semigroup as operators. For a large time the Atangana–Baleanu derivative is the same with Riemann–Liouville fractional derivative, thus satisfies semigroup principle as an operator. The solution of the associated evolution equation does not satisfy the semigroup principle as Riemann–Liouville. With the connection between semigroup theory and the Markovian processes, we found out that the Atangana–Baleanu fractional derivative has at the same time Markovian and non-Markovian processes. We concluded that, the fractional differential operator does not need to satisfy the semigroup properties as they portray the memory effects, which are not always Markovian. We presented the exact solutions of some evolutions equation using the Laplace transform. In addition to this, we presented the numerical solution of a nonlinear equation and show that, the model with the Atangana–Baleanu fractional derivative has random walk for small time. We also observed that, the Mittag-Leffler function is a good filter than the exponential and power law functions, which makes the Atangana–Baleanu fractional derivatives powerful mathematical tools to model complex real world problems.

The statistical physics of active matter: from self-catalytic colloids to living cells

Abstract: These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of interacting agents able to extract energy stored in the environment to produce sustained directed motion. The local conversion of energy into mechanical work drives the system far from equilibrium, yielding new dynamics and phases. The emerging phenomena can be classified depending on the symmetry of the active particles and on the type of microscopic interactions. We focus here on steric and aligning interactions, as well as interactions driven by shape changes. The models that we present are all inspired by experimental realizations of either synthetic, biomimetic or living systems. Based on minimal ingredients, they are meant to bring a simple and synthetic understanding of the complex phenomenology of active matter.

Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel

Abstract: In this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana–Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form.

Modeling connected and autonomous vehicles in heterogeneous traffic flow

Abstract: The objective of this study was to develop a heterogeneous traffic-flow model to study the possible impact of connected and autonomous vehicles (CAVs) on the traffic flow. Based on a recently proposed two-state safe-speed model (TSM), a two-lane cellular automaton (CA) model was developed, wherein both the CAVs and conventional vehicles were incorporated in the heterogeneous traffic flow. In particular, operation rules for CAVs are established considering the new characteristics of this emerging technology, including autonomous driving through the adaptive cruise control and inter-vehicle connection via short-range communication. Simulations were conducted under various CAV-penetration rates in the heterogeneous flow. The impact of CAVs on the road capacity was numerically investigated. The simulation results indicate that the road capacity increases with an increase in the CAV-penetration rate within the heterogeneous flow. Up to a CAV-penetration rate of 30%, the road capacity increases gradually; the effect of the difference in the CAV capability on the growth rate is insignificant. When the CAV-penetration rate exceeds 30%, the growth rate is largely decided by the capability of the CAV. The greater the capability, the higher the road-capacity growth rate. The relationship between the CAV-penetration rate and the road capacity is numerically analyzed, providing some insights into the possible impact of the CAVs on traffic systems.

Topological data analysis of financial time series: Landscapes of crashes

Abstract: We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007–2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a ’persistence landscapes’. We quantify the temporal changes in persistence landscapes via their L p -norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the L p -norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of L p -norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which complements the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here.

The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method

Abstract: This paper aims to simulate the interaction between thermal surface radiation and nanofluid free convection in a two dimensional shallow cavity by lattice Boltzmann method. The supposed nanofluid is generated by a homogeneous mixture of water and nanoparticles of Al2O3. The upper and lower walls of cavity are maintained at cold and hot temperature, respectively; while the side walls are kept thermally insulated. The cavity aspect ratio is chosen as 5 which indicates a shallow one. The cavity all inner surfaces are considered as the gray diffuse emitters and reflectors of radiation. The computations are performed for the wide range of parameters as Ra = 104 and Ra = 105; e = 0 . 5 and e = 0 . 9 while nanoparticles volume fraction changes between 0.0 ≤ φ ≤ 0.04 at each case. As a result, the effects of emissivity and Rayleigh number are studied on the total heat transfer of radiation and free convection of nanofluid. The suitable validations are examined beside the useful grid study procedure. The results are presented as the profiles of velocity and temperature and also the streamlines and isotherms. Moreover the local and averaged Nusselt numbers are provided for the coupled and uncoupled states of radiation and free convection heat transfer mechanisms. It is seen that Nu m of total free convection and radiation would be more at higher Ra and e ; which indicates that radiation heat transfer coupled with free convection might affect the flow field and improve the Nusselt number.

On Bitcoin markets (in)efficiency and its evolution

Abstract: We study efficiency of two Bitcoin markets (with respect to the US dollar and Chinese yuan) and its evolution in time. As inefficiency can manifest through various channels, we utilize the Efficiency Index of Kristoufek & Vosvrda (2013) which can cover different types of (in)efficiency measures. We find strong evidence of both Bitcoin markets remaining mostly inefficient between 2010 and 2017 with exceptions of several periods directly connected to cooling down after the bubble-like price surges.

Long-range correlations and asymmetry in the Bitcoin market

Abstract: This work studies long-range correlations and informational efficiency of the Bitcoin market for the period from June 30, 2013 to June 3rd, 2017. To this end, the detrended fluctuation analysis (DFA) was implemented over sliding windows to estimate long-range correlations for price returns. It was found that the Bitcoin market exhibits periods of efficiency alternating with periods where the price dynamics are driven by anti-persistence. The pattern is replicated by prices samples at day, hour and second frequencies. The Bitcoin market also presents asymmetric correlations with respect to increasing and decreasing price trending, with the former trend linked to anti-persistence of returns dynamics.

An extended two-lane car-following model accounting for inter-vehicle communication

Abstract: In this paper, we develop a novel car-following model with inter-vehicle communication to explore each vehicle’s movement in a two-lane traffic system when an incident occurs on a lane. The numerical results show that the proposed model can perfectly describe each vehicle’s motion when an incident occurs, i.e., no collision occurs while the classical full velocity difference (FVD) model produces collision on each lane, which shows the proposed model is more reasonable. The above results can help drivers to reasonably adjust their driving behaviors when an incident occurs in a two-lane traffic system.

A new car-following model for autonomous vehicles flow with mean expected velocity field

Abstract: Due to the development of the modern scientific technology, autonomous vehicles may realize to connect with each other and share the information collected from each vehicle. An improved forward considering car-following model was proposed with mean expected velocity field to describe the autonomous vehicles flow behavior. The new model has three key parameters: adjustable sensitivity, strength factor and mean expected velocity field size. Two lemmas and one theorem were proven as criteria for judging the stability of homogeneousautonomous vehicles flow. Theoretical results show that the greater parameters means larger stability regions. A series of numerical simulations were carried out to check the stability and fundamental diagram of autonomous flow. From the numerical simulation results, the profiles, hysteresis loop and density waves of the autonomous vehicles flow were exhibited. The results show that with increased sensitivity, strength factor or field size the traffic jam was suppressed effectively which are well in accordance with the theoretical results. Moreover, the fundamental diagrams corresponding to three parameters respectively were obtained. It demonstrates that these parameters play almost the same role on traffic flux: i.e. before the critical density the bigger parameter is, the greater flux is and after the critical density, the opposite tendency is. In general, the three parameters have a great influence on the stability and jam state of the autonomous vehicles flow.

Crime prediction through urban metrics and statistical learning

Abstract: Understanding the causes of crime is a longstanding issue in researcher’s agenda. While it is a hard task to extract causality from data, several linear models have been proposed to predict crime through the existing correlations between crime and urban metrics. However, because of non-Gaussian distributions and multicollinearity in urban indicators, it is common to find controversial conclusions about the influence of some urban indicators on crime. Machine learning ensemble-based algorithms can handle well such problems. Here, we use a random forest regressor to predict crime and quantify the influence of urban indicators on homicides. Our approach can have up to 97% of accuracy on crime prediction, and the importance of urban indicators is ranked and clustered in groups of equal influence, which are robust under slightly changes in the data sample analyzed. Our results determine the rank of importance of urban indicators to predict crime, unveiling that unemployment and illiteracy are the most important variables for describing homicides in Brazilian cities. We further believe that our approach helps in producing more robust conclusions regarding the effects of urban indicators on crime, having potential applications for guiding public policies for crime control.

Measure the structure similarity of nodes in complex networks based on relative entropy

Abstract: Similarity of nodes is a basic structure quantification in complex networks. Lots of methods in research on complex networks are based on nodes’ similarity such as node’s classification, network’s community structure detection, network’s link prediction and so on. Therefore, how to measure nodes’ similarity is an important problem in complex networks. In this paper, a new method is proposed to measure nodes’ structure similarity based on relative entropy and each node’s local structure. In the new method, each node’s structure feature can be quantified as a special kind of information. The quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information. Then relative entropy is used to measure the difference between each pair of nodes’ structural information. At last the value of relative entropy between each pair of nodes is used to measure nodes’ structure similarity in complex networks. Comparing with existing methods the new method is more accuracy to measure nodes’ structure similarity.

The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average

Abstract: As a form of cryptocurrency, the issue of informational efficiency of Bitcoin has received much attention recently. We add to the literature by investigating nine forms of cryptocurrencies, i.e., Bitcoin, Ripple, Ethereum, NEM, Stellar, Litecoin, Dash, Monero and Verge, with a battery of efficiency tests and the empirical results indicate that all these cryptocurrencies are inefficient markets. What is more, we further construct a value-weighted Cryptocurrency Composite Index (CCI) and show that CCI and Dow Jones Industrial Average are persistently cross-correlated.

Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics

Abstract: In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics The first half of these notes considers classical systems, and the second half, quantum systems In Lecture 1, I briefly review the glass transition problem as a paradigm of slow relaxation and dynamical arrest in classical many-body systems I discuss theoretical perspectives on how to think about glasses, and in particular how to model them in terms of kinetically constrained dynamics In Lecture 2, I describe how via large deviation methods it is possible to define a statistical mechanics of trajectories which reveals the dynamical phase structure of systems with complex relaxation such as glasses Lecture 3 is about closed (ie isolated) many-body quantum systems I review thermalisation and many-body localisation, and consider the possibility of slow thermalisation and quantum non-ergodicity in the absence of disorder, thus connecting with some of the ideas of the first lecture Lecture 4 is about open quantum systems, that is, quantum systems interacting with an environment I review the description of open quantum dynamics within the Markovian approximation in terms of quantum master equations and stochastic quantum trajectories, and explain how to extend the dynamical large deviation method to study the statistical properties of ensembles of quantum jump trajectories My overall aim is to draw analogies between classical and quantum non-equilibrium and find connections in the way we think about problems in these areas

Modeling and prediction of rheological behavior of Al2O3-MWCNT/5W50 hybrid nano-lubricant by artificial neural network using experimental data

Abstract: In this paper, the artificial neural network model and new correlation based on experimental data are proposed to predict Rheological behavior of Al2O3-MWCNT/5W50. The ANN model has three inputs including temperature, volume fraction and share rate. Predictions of suggested models were evaluated by using statistical and graphical validations approaches. The results revealed that the maximum values of margin of deviation are 0.07% and 7.3% for ANN and correlation outputs, respectively. The findings showed that an artificial neural network can predict the relative viscosity of the nanofluid more accurately than empirical correlation.

Impact of dedicated lanes for connected and autonomous vehicle on traffic flow throughput

Abstract: This paper presents an application of a recently proposed methodology for modeling connected and autonomous vehicles (CAVs) in heterogeneous traffic flow, to investigate the impact of setting dedicated lanes for CAVs on traffic flow throughput. A fundamental diagram approach was introduced which reveals the pros and cons of setting dedicated lanes for CAVs under various CAV penetration rates and demand levels. The performance of traffic flow under different number of CAV dedicated lanes is compared with mixed flow situation. Simulation results indicate that at a low CAV penetration rate, setting CAV dedicated lanes deteriorates the performance of the overall traffic flow throughput, particularly under a low density level. When CAVs reach a dominant role in the mixed flow, the merits of setting dedicated lanes also decrease. The benefit of setting CAV dedicated lane can only be obtained within a medium density range. CAV penetration rate and individual CAV performance are significant factors that decide the performance of CAV dedicated lane. The higher level of performance the CAV could achieve, the greater benefit it will attain through the deployment of CAV dedicated lane. Besides, the performance of CAV dedicated lane can be improved through setting a higher speed limit for CAVs on the dedicated lane than vehicles on other normal lanes. This work provides some insights into the impact of the CAV dedicated lane on traffic systems, and helpful in deciding the optimal number of dedicated lanes for CAVs.

Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural convection & mixed convection

Abstract: Nano scale method of lattice Boltzmann is developed to predict the fluid flow and heat transfer of air through the inclined lid driven 2-D cavity while a large heat source is considered inside it. Two case studies are supposed: first one is a pure natural convection at Grashof number from 400 to 4000 000 and second one is a mixed convection at Richardson number from 0.1 to 10 at various cavity inclination angles. Using LBM to simulate the constant heat flux boundary condition along the obstacle, is presented for the first time while the buoyancy forces affect the velocity components at each inclination angle; hence the collision operator of LBM and also a way to estimate the macroscopic velocities should be modified. Results are shown in the terms of streamlines and isotherms, beside the profiles of velocity, temperature and Nusselt number. It is observed that the present model of LBM is appropriately able to simulate the supposed domain. Moreover, the effects of inclination angle are more important at higher values of Richardson number.

An appetizer to modern developments on the Kardar–Parisi–Zhang universality class

Abstract: The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.

Melting process in porous media around two hot cylinders: Numerical study using the lattice Boltzmann method

Abstract: Instantaneous melting of ice is accelerated inside a horizontal rectangular cavity with two vertically arranged cylinders using metallic porous matrix made of Ni-Steel alloys. The enthalpy-based lattice Boltzmann method (LBM) with a double distribution function (DDF) is employed at the representative elementary volume (REV) scale. Single-phase model is used and there is a local thermal equilibrium between porous structure and ice. Inserting metallic porous material into the base PCM results in the enhancement of the heat conduction and weakening of the natural convection flow. Concentric pattern of the solid–liquid interface persists in porous samples comparing to the pure PCM melting. Reducing porosity causes decrease of the full melting time and thermal storage capacity of the system. Thermal conductivity ratio has to be enlarged in porous samples with higher porosity from energy saving viewpoint.

Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel

Abstract: In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic chemical system with Caputo–Fabrizio and Atangana–Baleanu fractional time derivatives in Liouville–Caputo sense. We utilize the q-homotopy analysis transform method to compute the approximate solutions. We find the optimal values of h so we assure the convergence of the approximate solutions. Finally, we compare our results numerically with the finite difference method and excellent agreement is found.

Scaling properties of extreme price fluctuations in Bitcoin markets

Abstract: Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation distributions. Motivated by the rise of novel digital assets based on blockchain technology, we study the distributions of cryptocurrency price fluctuations. We consider Bitcoin returns over various time intervals and from multiple digital exchanges, in order to investigate the existence of universal scaling behavior in the tails, and ascertain whether the scaling exponent supports the presence of a finite second moment. We provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges, corresponding to a power-law. We estimate the scaling exponent and find an asymptotic power-law behavior with 2 α 2 . 5 suggesting that Bitcoin returns, in addition to being more volatile, also exhibit heavier tails than stocks, which are known to be around 3. Our results also imply the existence of a finite second moment, thus providing a fundamental basis for the usage of standard financial theories and covariance-based techniques in risk management and portfolio optimization scenarios.

A link prediction method for heterogeneous networks based on BP neural network

Abstract: Most real-world systems, composed of different types of objects connected via many interconnections, can be abstracted as various complex heterogeneous networks. Link prediction for heterogeneous networks is of great significance for mining missing links and reconfiguring networks according to observed information, with considerable applications in, for example, friend and location recommendations and disease–gene candidate detection. In this paper, we put forward a novel integrated framework, called MPBP (Meta-Path feature-based BP neural network model), to predict multiple types of links for heterogeneous networks. More specifically, the concept of meta-path is introduced, followed by the extraction of meta-path features for heterogeneous networks. Next, based on the extracted meta-path features, a supervised link prediction model is built with a three-layer BP neural network. Then, the solution algorithm of the proposed link prediction model is put forward to obtain predicted results by iteratively training the network. Last, numerical experiments on the dataset of examples of a gene–disease network and a combat network are conducted to verify the effectiveness and feasibility of the proposed MPBP. It shows that the MPBP with very good performance is superior to the baseline methods.

Conformable derivative approach to anomalous diffusion

Abstract: By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg–Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

Statistical properties and multifractality of Bitcoin

Abstract: Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of “Brexit” on June 23, 2016 to GBP–USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP–USD exchange rate, Bitcoin was robust to Brexit.

Identifying influential nodes in complex networks based on the inverse-square law

Abstract: How to identify influential nodes in complex networks continues to be an open issue. A number of centrality measures have been presented to address this problem. However, these studies focus only on a centrality measure and each centrality measure has its own shortcomings and limitations. To solve problems above, in this paper, a novel method is proposed to identify influential nodes based on the inverse-square law. The mutual attraction between different nodes has been defined in complex network, which is inversely proportional to the square of the distance between two nodes. Then, the definition of intensity of node in a complex network is proposed and described as the sum of attraction between a pair of nodes in the network. The ranking method is presented based on the intensity of node, which can be considered as the influence of the node. In order to illustrate the effectiveness of the proposed method, several experiments are conducted to identify vital nodes simulations on four real networks, and the superiority of the proposed method can be demonstrated by the results of comparison experiments.

Modeling electric bicycle’s lane-changing and retrograde behaviors

Abstract: Recently, electric bicycle (EB) has been one important traffic tool due to its own merits. However, EB’s motion behaviors (especially at a signalized/non-signalized intersection) are more complex than those of vehicle since it always has lane-changing and retrograde behaviors. In this paper, we propose a model to explore EB’s lane-changing and retrograde behaviors on a road with a signalized intersection. The numerical results indicate that the proposed model can qualitatively describe each EB’s lane-changing and retrograde behaviors near a signalized intersection, and that lane-changing and retrograde behaviors have prominent impacts on the signalized intersection (i.e., prominent jams and congestions occur). The above results show that EB should be controlled as a vehicle, i.e., lane-changing and retrograde behaviors at a signalized intersection should strictly be prohibited to improve the operational efficiency and traffic safety at the signalized intersection.

Bitcoin technical trading with artificial neural network

Abstract: This paper explores Bitcoin intraday technical trading based on artificial neural networks for the return prediction. In particular, our deep learning method successfully discovers trading signals through a seven layered neural network structure for given input data of technical indicators, which are calculated by the past time-series data over every 15 min. Under feasible settings of execution costs, the numerical experiments demonstrate that our approach significantly improves the performance of a buy-and-hold strategy. Especially, our model performs well for a challenging period from December 2017 to January 2018, during which Bitcoin suffers from substantial minus returns. Furthermore, various sensitivity analysis is implemented for the change of the number of layers, activation functions, input data and output classification to confirm the robustness of our approach.

A speed guidance strategy for multiple signalized intersections based on car-following model

Abstract: Signalized intersection has great roles in urban traffic system. The signal infrastructure and the driving behavior near the intersection are paramount factors that have significant impacts on traffic flow and energy consumption. In this paper, a speed guidance strategy is introduced into a car-following model to study the driving behavior and the fuel consumption in a single-lane road with multiple signalized intersections. The numerical results indicate that the proposed model can reduce the fuel consumption and the average stop times. The findings provide insightful guidance for the eco-driving strategies near the signalized intersections.

Develop the lattice Boltzmann method to simulate the slip velocity and temperature domain of buoyancy forces of FMWCNT nanoparticles in water through a micro flow imposed to the specified heat flux

Abstract: Lattice Boltzmann method ability is improved to simulate the mixed convection of Water / FMWCNT nanofluid inside a two dimensional microchannel. The influences of gravity on hydrodynamic and thermal domains are studied while the microchannel walls are imposed by a constant thermal heat flux at three different case studies as no-gravity, R i = 1 and R i = 10 . The flow Reynolds number is chosen as one and the liquid micro flow conditions are involved by B = 0.005, B = 0.01 and B = 0.02. The mass fraction of carbon nanotubes in water are selected as ϕ = 0 , ϕ = 0 .1% and ϕ = 0 .2%. Double population distribution functions of “f” and “g” are used in lattice Boltzmann method. To the best of author’s knowledge, there is no article concerned the way of heat flux boundary condition simulation by LBM considering the buoyancy forces effects on nanofluid slip velocity. Generate a rotational cell due to gravity in entrance region which leads to observe the negative slip velocity phenomenon can be presented as the several interesting achievements of this work.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

Abstract: In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton’s iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.