Search results for: discrete particle modelling

Authors: Hooman Dabirmanesh, Attila M. Zsaki

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The toppling failure mode in a rock mass is considerably different from the most common sliding failure type along an existing or an induced slip plane. Block toppling is observed in a rock mass which consists of both a widely-spaced basal cross-joint set and a closely-spaced discontinuity set dipping into the slope. For this case, failure occurs when the structure cannot bear the tensile portion of bending stress, and the columns or blocks overturn by their own weight. This paper presents a particle-based discrete element model of rock blocks subjected to a toppling failure where geometric conditions and interaction among blocks are investigated. A series of parametric studies have been conducted on particles’ size, arrangement and bond contact among of particles which are made the blocks. Firstly, a numerical investigation on a one-block system was verified. Afterward, a slope consisting of multi-blocks was developed to study toppling failure and interaction forces between blocks. The results show that the formation of blocks, especially between the block and basal plane surface, can change the process of failure. The results also demonstrate that the initial configuration of particles used to form the blocks has a significant role in achieving accurate simulation results. The size of particles and bond contacts have a considerable influence to change the progress of toppling failure.

Keywords: block toppling failure, contact interaction, discrete element, particle size, random generation

Procedia PDF Downloads 158

Authors: Yanbing Feng, Deqing Mei, Yancheng Wang, Zichen Chen

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With the advantage of low volume density, high specific surface area, light weight and good permeability, porous aluminum material has the potential to be used in automotive, railway, chemistry and construction industries, etc. A layered powder sintering and dissolution method were developed to fabricate the porous surface Al structure with high efficiency. However, the densification mechanism during the cold compaction of laminar composite powders is still unclear. In this study, multi particle finite element modelling (MPFEM) based on the cohesive zone method (CZM) is used to simulate the cold compaction behavior of laminar Al and NaCl composite powders. To obtain its densification mechanism, the macro and micro properties of final compacts are characterized and analyzed. The robustness and accuracy of the numerical model is firstly verified by experimental results and data fitting. The results indicate that the CZM-based multi particle FEM is an effective way to simulate the compaction of the laminar powders and the fracture process of the NaCl powders. In the compaction of the laminar powders, the void is mainly filled by the particle rearrangement, plastic deformation of Al powders and brittle fracture of NaCl powders. Large stress is mainly concentrated within the NaCl powers and the contact force network is formed. The Al powder near the NaCl powder or the mold has larger stress distribution on its contact surface. Therefore, the densification process of cold compaction of laminar Al and NaCl composite powders is successfully analyzed by the CZM-based multi particle FEM.

Keywords: cold compaction, cohesive zone, multi-particle FEM, numerical modeling, powder forming

Procedia PDF Downloads 121

Authors: Jie Yin, Jun Zhang

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Measuring the growth performance and critical supersaturation of particle group have a high reference value for constructing a supersaturated water vapor environment that can improve the removal efficiency of the high-concentration particle group. The critical supersaturation and the variation of the growth performance with supersaturation for high-concentration particles were measured by a flow cloud chamber. Findings suggest that the influence of particle concentration on the growth performance will reduce with the increase of supersaturation. Reducing residence time and increasing particle concentration have similar effects on the growth performance of the high-concentration particle group. Increasing particle concentration and shortening residence time will increase the critical supersaturation of the particle group. The critical supersaturation required to activate a high-concentration particle group is lower than that of the single-particle when the minimum particle size in the particle group is the same as that of a single particle.

Keywords: sub-micron particles, heterogeneous condensation, critical supersaturation, nucleation

Procedia PDF Downloads 125

Authors: Lei Bi, Yunpeng Jiao, Chunjiang Liu, Jianhua Chen, Wei Ge

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Two energy paths are proposed from thermodynamic viewpoints. Energy consumption means total power input to the specific system, and it can be decomposed into energy retention and energy dissipation. Energy retention is the variation of accumulated mechanical energy in the system, and energy dissipation is the energy converted to heat by irreversible processes. Based on the Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) framework, different energy terms are quantified from the specific flow elements of fluid cells and particles as well as their interactions with the wall. Direct energy consumption statistics are carried out for both cold and hot flow in gas-solid fluidization systems. To clarify the statistic method, it is necessary to identify which system is studied: the particle-fluid system or the particle sub-system. For the cold flow, the total energy consumption of the particle sub-system can predict the onset of bubbling and turbulent fluidization, while the trends of local energy consumption can reflect the dynamic evolution of mesoscale structures. For the hot flow, different heat transfer mechanisms are analyzed, and the original solver is modified to reproduce the experimental results. The influence of the heat transfer mechanisms and heat source on energy consumption is also investigated. The proposed statistic method has proven to be energy-conservative and easy to conduct, and it is hopeful to be applied to other multiphase flow systems.

Keywords: energy consumption statistic, gas-solid fluidization, CFD-DEM, regime transition, heat transfer mechanism

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Authors: Mohsin Raza, Arne Bilberg, Thomas Ditlev Brunø, Ann-Louise Andersen, Filip SKärin

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Shifting from a dedicated or flexible manufacturing system to a reconfigurable manufacturing system (RMS) requires a significant amount of time, money, and effort. Therefore, it is vital to verify beforehand that the potential reconfigurable solution will be able to achieve the organizational objectives. Discrete event simulation offers the opportunity of assessing several reconfigurable alternatives against the set objectives. This study signifies the importance of using discrete-event simulation as a tool to verify several reconfiguration options. Two different industrial cases have been presented in the study to elaborate on the role of discrete event simulation in the implementation methodology of RMSs. The study concluded that discrete event simulation is one of the important tools to consider in the RMS implementation methodology.

Keywords: reconfigurable manufacturing system, discrete event simulation, Tecnomatix plant simulation, RMS

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Authors: Yu Zhao, Shinsuke Kato, Jianing Zhao

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Particles exhausted from cars have an adverse impacts on human health. The study developed a three-dimensional particle dispersion numerical model including particle coagulation to simulate the particle concentration distribution under idling conditions in a residential underground garage. The simulation results demonstrate that particle disperses much faster in the vertical direction than that in horizontal direction. The enhancement of particle dispersion in the vertical direction due to the increase of cars with engine running is much stronger than that in the car exhaust direction. Particle dispersion from each pair of adjacent cars has little influence on each other in the study. Average particle concentration after 120 seconds exhaust is 1.8-4.5 times higher than the initial total particles at ambient environment. Particle pollution in the residential underground garage is severe.

Keywords: dispersion, idling conditions, particle concentration, residential underground garage

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Authors: Zeinab Yazdanfar, Dilan Robert, Daniel Lester, S. Setunge

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Scour has been identified as the most common threat to bridge stability worldwide. Traditionally, scour around bridge piers is calculated using the empirical approaches that have considerable limitations and are difficult to generalize. The multi-physic nature of scouring which involves turbulent flow, soil mechanics and solid-fluid interactions cannot be captured by simple empirical equations developed based on limited laboratory data. These limitations can be overcome by direct numerical modeling of coupled hydro-mechanical scour process that provides a robust prediction of bridge scour and valuable insights into the scour process. Several numerical models have been proposed in the literature for bridge scour estimation including Eulerian flow models and coupled Euler-Lagrange models incorporating an empirical sediment transport description. However, the contact forces between particles and the flow-particle interaction haven’t been taken into consideration. Incorporating collisional and frictional forces between soil particles as well as the effect of flow-driven forces on particles will facilitate accurate modeling of the complex nature of scour. In this study, a coupled Computational Fluid Dynamics and Discrete Element Model (CFD-DEM) has been developed to simulate the scour process that directly models the hydro-mechanical interactions between the sediment particles and the flowing water. This approach obviates the need for an empirical description as the fundamental fluid-particle, and particle-particle interactions are fully resolved. The sediment bed is simulated as a dense pack of particles and the frictional and collisional forces between particles are calculated, whilst the turbulent fluid flow is modeled using a Reynolds Averaged Navier Stocks (RANS) approach. The CFD-DEM model is validated against experimental data in order to assess the reliability of the CFD-DEM model. The modeling results reveal the criticality of particle impact on the assessment of scour depth which, to the authors’ best knowledge, hasn’t been considered in previous studies. The results of this study open new perspectives to the scour depth and time assessment which is the key to manage the failure risk of bridge infrastructures.

Keywords: bridge scour, discrete element method, CFD-DEM model, multi-phase model

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Authors: Esmaeil Abbaszadeh Molaei, Zongyan Zhou, Aibing Yu

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The applications of liquid fluidizations have been increased in many parts of industries such as particle classification, backwashing of granular filters, crystal growth, leaching and washing, and bioreactors due to high-efficient liquid–solid contact, favorable mass and heat transfer, high operation flexibilities, and reduced back mixing of phases. In most of these multiphase operations the particles properties, i.e. size, density, and shape, may change during the process because of attrition, coalescence or chemical reactions. Previous studies, either experimentally or numerically, mainly have focused on studies of liquid-solid fluidized beds containing spherical particles; however, the role of particle shape on the hydrodynamics of liquid fluidized beds is still not well-known. A three-dimensional Discrete Element Model (DEM) and Computational Fluid Dynamics (CFD) are coupled to study the influence of particles shape on particles and liquid flow patterns in liquid-solid fluidized beds. In the simulations, ellipsoid particles are used to study the shape factor since they can represent a wide range of particles shape from oblate and sphere to prolate shape particles. Different particle shapes from oblate (disk shape) to elongated particles (rod shape) are selected to investigate the effect of aspect ratio on different flow characteristics such as general particles and liquid flow pattern, pressure drop, and particles orientation. First, the model is verified based on experimental observations, then further detail analyses are made. It was found that spherical particles showed a uniform particle distribution in the bed, which resulted in uniform pressure drop along the bed height. However for particles with aspect ratios less than one (disk-shape), some particles were carried into the freeboard region, and the interface between the bed and freeboard was not easy to be determined. A few particle also intended to leave the bed. On the other hand, prolate particles showed different behaviour in the bed. They caused unstable interface and some flow channeling was observed for low liquid velocities. Because of the non-uniform particles flow pattern for particles with aspect ratios lower (oblate) and more (prolate) than one, the pressure drop distribution in the bed was not observed as uniform as what was found for spherical particles.

Keywords: CFD, DEM, ellipsoid, fluidization, multiphase flow, non-spherical, simulation

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Authors: Tawfik Thelaidjia, Salah Chenikher

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Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, feature extraction from faulty bearing vibration signals is performed by a combination of the signal’s Kurtosis and features obtained through the preprocessing of the vibration signal samples using Db2 discrete wavelet transform at the fifth level of decomposition. In this way, a 7-dimensional vector of the vibration signal feature is obtained. After feature extraction from vibration signal, the support vector machine (SVM) was applied to automate the fault diagnosis procedure. To improve the classification accuracy for bearing fault prediction, particle swarm optimization (PSO) is employed to simultaneously optimize the SVM kernel function parameter and the penalty parameter. The results have shown feasibility and effectiveness of the proposed approach

Keywords: condition monitoring, discrete wavelet transform, fault diagnosis, kurtosis, machine learning, particle swarm optimization, roller bearing, rotating machines, support vector machine, vibration measurement

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Authors: Justin-Herve Noubissi, Jean Claude Kamgang, Eric Ramat, Januarius Asongu, Christophe Cambier

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The goal of our study is to analyse the impact of climatic factors in malaria transmission taking into account migration between Douala and Yaoundé, two cities of Cameroon country. We show how variations of climatic factors such as temperature and relative humidity affect the malaria spread. We propose a meta-population model of the dynamic transmission of malaria that evolves in space and time and that takes into account temperature and relative humidity and the migration between Douala and Yaoundé. We also integrate the variation of environmental factors as events also called mathematical impulsion that can disrupt the model evolution at any time. Our modelling has been done using the Discrete EVents System Specification (DEVS) formalism. Our implementation has been done on Virtual Laboratory Environment (VLE) that uses DEVS formalism and abstract simulators for coupling models by integrating the concept of DEVS.

Keywords: compartmental models, DEVS, discrete events, meta-population model, VLE

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Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

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Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: A. Hossein Madadi-Najafabadi, Masoud Nasiri

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The discrete element method is a powerful technique for numerical modeling the flow of granular materials such as direct reduced iron. It would enable us to study processes and equipment related to the production and handling of the material. However, the characteristics and properties of the granules have to be adjusted precisely to achieve reliable results in a DEM simulation. The main properties for DEM simulation are size distribution, density, Young's modulus, Poisson's ratio and the contact coefficients of restitution, rolling friction and sliding friction. In the present paper, the mentioned properties are determined for DEM simulation of DRI pellets. A reliable DEM simulation would contribute to optimizing the handling system of DRIs in an iron-making plant. Among the mentioned properties, Young's modulus is the most important parameter, which is usually hard to get for particulate solids. Here, an especial method is utilized to precisely determine this parameter for DRI.

Keywords: discrete element method, direct reduced iron, simulation parameters, granular material

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Authors: Sofia M. Karadimitriou, Kostas Triantafyllopoulos, Timothy Heaton

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Reduced dimension Dynamic Spatio-Temporal Models (DSTMs) jointly describe the spatial and temporal evolution of a function observed subject to noise. A basic state space model is adopted for the discrete temporal variation, while a continuous autoregressive structure describes the continuous spatial evolution. Application of such a DSTM relies upon the pre-selection of a suitable reduced set of basic functions and this can present a challenge in practice. In this talk, we propose an online estimation method for high dimensional spatio-temporal data based upon DSTM and we attempt to resolve this issue by allowing the basis to adapt to the observed data. Specifically, we present a wavelet decomposition in order to obtain a parsimonious approximation of the spatial continuous process. This parsimony can be achieved by placing a Laplace prior distribution on the wavelet coefficients. The aim of using the Laplace prior, is to filter wavelet coefficients with low contribution, and thus achieve the dimension reduction with significant computation savings. We then propose a Hierarchical Bayesian State Space model, for the estimation of which we offer an appropriate particle filter algorithm. The proposed methodology is illustrated using real environmental data.

Keywords: multidimensional Laplace prior, particle filtering, spatio-temporal modelling, wavelets

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: Bülent Kantar, Numan Ünaldı

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This paper presents a new method which includes robust and invisible digital watermarking on images that is colored. Colored images are used as watermark. Frequency region is used for digital watermarking. Discrete wavelet transform and discrete stationary wavelet transform are used for frequency region transformation. Low, medium and high frequency coefficients are obtained by applying the two-level discrete wavelet transform to the original image. Low frequency coefficients are obtained by applying one level discrete stationary wavelet transform separately to all frequency coefficient of the two-level discrete wavelet transformation of the original image. For every low frequency coefficient obtained from one level discrete stationary wavelet transformation, watermarks are added. Watermarks are added to all frequency coefficients of two-level discrete wavelet transform. Totally, four watermarks are added to original image. In order to get back the watermark, the original and watermarked images are applied with two-level discrete wavelet transform and one level discrete stationary wavelet transform. The watermark is obtained from difference of the discrete stationary wavelet transform of the low frequency coefficients. A total of four watermarks are obtained from all frequency of two-level discrete wavelet transform. Obtained watermark results are compared with real watermark results, and a similarity result is obtained. A watermark is obtained from the highest similarity values. Proposed methods of watermarking are tested against attacks of the geometric and image processing. The results show that proposed watermarking method is robust and invisible. All features of frequencies of two level discrete wavelet transform watermarking are combined to get back the watermark from the watermarked image. Watermarks have been added to the image by converting the binary image. These operations provide us with better results in getting back the watermark from watermarked image by attacking of the geometric and image processing.

Keywords: watermarking, DWT, DSWT, copy right protection, RGB

Procedia PDF Downloads 507

Authors: Payel Das, Gnaneshwar Nelakanti

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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

Procedia PDF Downloads 446

Authors: Shervin Khazaeli, Shahab Haj-zamani

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Recently, advanced geotechnical engineering problems related to soil movement, particle loss, and modeling of local failure (i.e. discontinua) as well as modeling the in-contact structures (i.e. continua) are of the great interest among researchers. The aim of this research is to meet the requirements with respect to the modeling of the above-mentioned two different domains simultaneously. To this end, a coupled numerical method is introduced based on Discrete Element Method (DEM) and eXtended-Finite Element Method (X-FEM). In the coupled procedure, DEM is employed to capture the interactions and relative movements of soil particles as discontinua, while X-FEM is utilized to model in-contact structures as continua, which may consist of different types of discontinuities. For verification purposes, the new coupled approach is utilized to examine benchmark problems including different contacts between/within continua and discontinua. Results are validated by comparison with those of existing analytical and numerical solutions. This study proves that extended-finite-discrete element method can be used to robustly analyze not only contact problems, but also other types of discontinuities in continua such as (i) crack formations and propagations, (ii) voids and bimaterial interfaces, and (iii) combination of previous cases. In essence, the proposed method can be used vastly in advanced soil-structure interaction problems to investigate the micro and macro behaviour of the surrounding soil and the response of the embedded structure that contains discontinuities.

Keywords: contact problems, discrete element method, extended-finite element method, soil-structure interaction

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Authors: Prudhvinath Reddy Ankireddy, Narasimha Mangadoddy

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Spiral concentrators are commonly used in various industries, including mineral and coal processing, to efficiently separate materials based on their density and size. In these concentrators, a mixture of solid particles and fluid (usually water) is introduced as feed at the top of a spiral channel. As the mixture flows down the spiral, centrifugal and gravitational forces act on the particles, causing them to stratify based on their density and size. Spiral flows exhibit complex fluid dynamics, and interactions involve multiple phases and components in the process. Understanding the behavior of these phases within the spiral concentrator is crucial for achieving efficient separation. An experimental bi-component particle interaction study is conducted in this work utilizing magnetite (heavier density) and silica (lighter density) with different proportions processed in the spiral concentrator. The observation separation reveals that denser particles accumulate towards the inner region of the spiral trough, while a significant concentration of lighter particles are found close to the outer edge. The 5th turn of the spiral trough is partitioned into five zones to achieve a comprehensive distribution analysis of bicomponent particle segregation. Samples are then gathered from these individual streams using an in-house sample collector, and subsequent analysis is conducted to assess component segregation. Along the trough, there was a decline in the concentration of coarser particles, accompanied by an increase in the concentration of lighter particles. The segregation pattern indicates that the heavier coarse component accumulates in the inner zone, whereas the lighter fine component collects in the outer zone. The middle zone primarily consists of heavier fine particles and lighter coarse particles. The zone-wise results reveal that there is a significant fraction of segregation occurs in inner and middle zones. Finer magnetite and silica particles predominantly accumulate in outer zones with the smallest fraction of segregation. Additionally, numerical simulations are also carried out using the computational fluid dynamics (CFD) model based on the volume of fluid (VOF) approach incorporating the RSM turbulence model. The discrete phase model (DPM) is employed for particle tracking, thereby understanding the particle segregation of magnetite and silica along the spiral trough.

Keywords: spiral concentrator, bi-component particle segregation, computational fluid dynamics, discrete phase model

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Authors: Sung-Sik Park, Han Chang, Kyung-Hun Chae, Sae-Byeok Lee

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In this study, a three-dimensional (3D) Particle method without using grid was developed for analyzing large deformation of soils instead of using ordinary finite element method (FEM) or finite difference method (FDM). In the 3D Particle method, the governing equations were discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. The Mohr-Coulomb failure criterion was incorporated into the 3D Particle method to determine soil failure. The yielding and hardening behavior of soil before failure was also considered by varying viscosity of soil. First of all, an unconfined compression test was carried out and the large deformation following soil yielding or failure was simulated by the developed 3D Particle method. The results were also compared with those of a commercial FEM software PLAXIS 3D. The developed 3D Particle method was able to simulate the 3D large deformation of soils due to soil yielding and calculate the variation of normal and shear stresses following clay deformation.

Keywords: particle method, large deformation, soil column, confined compressive stress

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Authors: Rupinder Kaur, Harjot Kaur

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The objective of this paper is to present the study of the effect of varying thickness on rotating composite disks made from Al-SiC_P having different particle sizes. Mathematical modeling is used to calculate the effect of varying thickness with different particle sizes on rotating composite disks in radial as well as tangential directions with thermal gradients. In comparison to various particle sizes with varied thicknesses, long-term deformation occurs. The results are displayed visually, demonstrating how creep deformation decreases with changing particle size and thickness.

Keywords: creep, varying thickness, particle size, stresses and strain rates

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Authors: Gürkan Şakar, Akgün Alsaran, Emrah E. Özbaldan

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In this study, lateral buckling analysis of composite beams with particle additive was carried out experimentally and numerically. The effects of particle type, particle addition ratio on buckling loads of composite beams were determined. The numerical studies were performed with ANSYS package. In the analyses, clamped-free boundary condition was assumed. The load carrying capabilities of composite beams were influenced by different particle types and particle addition ratios.

Keywords: lateral buckling, nanoparticle, composite beam, numeric analysis

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: Sathwik Sarvadevabhatla Kasyap, Kostas Senetakis

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The mechanical behavior of geological materials is very complex, and this complexity is related to the discrete nature of soils and rocks. Characteristics of a material at the grain scale such as particle size and shape, surface roughness and morphology, and particle contact interface are critical to evaluate and better understand the behavior of discrete materials. This study investigates experimentally the micro-mechanical behavior of quartz sand grains with emphasis on the influence of the presence of microparticles in their contact region. The outputs of the study provide some fundamental insights on the contact mechanics behavior of artificially coated grains and can provide useful input parameters in the discrete element modeling (DEM) of soils. In nature, the contact interfaces between real soil grains are commonly observed with microparticles. This is usually the case of sand-silt and sand-clay mixtures, where the finer particles may create a coating on the surface of the coarser grains, altering in this way the micro-, and thus the macro-scale response of geological materials. In this study, the micro-mechanical behavior of Leighton Buzzard Sand (LBS) quartz grains, with interference of different microparticles at their contact interfaces is studied in the laboratory using an advanced custom-built inter-particle loading apparatus. Special techniques were adopted to develop the coating on the surfaces of the quartz sand grains so that to establish repeatability of the coating technique. The characterization of the microstructure of coated particles on their surfaces was based on element composition analyses, microscopic images, surface roughness measurements, and single particle crushing strength tests. The mechanical responses such as normal and tangential load – displacement behavior, tangential stiffness behavior, and normal contact behavior under cyclic loading were studied. The behavior of coated LBS particles is compared among different classes of them and with pure LBS (i.e. surface cleaned to remove any microparticles). The damage on the surface of the particles was analyzed using microscopic images. Extended displacements in both normal and tangential directions were observed for coated LBS particles due to the plastic nature of the coating material and this varied with the variation of the amount of coating. The tangential displacement required to reach steady state was delayed due to the presence of microparticles in the contact region of grains under shearing. Increased tangential loads and coefficient of friction were observed for the coated grains in comparison to the uncoated quartz grains.

Keywords: contact interface, microparticles, micro-mechanical behavior, quartz sand

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Authors: Alexander S. Andreev, Olga A. Peregudova

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In this paper, we propose a discrete tracking control of nonholonomic mobile robots with two degrees of freedom. The electro-mechanical model of a mobile robot moving on a horizontal surface without slipping, with two rear wheels controlled by two independent DC electric, and one front roal wheel is considered. We present back-stepping design based on the Euler approximate discrete-time model of a continuous-time plant. Theoretical considerations are verified by numerical simulation. The work was supported by RFFI (15-01-08482).

Keywords: actuator dynamics, back stepping, discrete-time controller, Lyapunov function, wheeled mobile robot

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Authors: Shukran M. Dadayev

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To author's best knowledge, in this paper, the Basic Properties and Research methods of a Fundamental Particle is studied for the first time. That's to say, Fundamental Particle has not been discovered in the Nature yet. Because Fundamental Particle consists of specific Physical, Geometrical and Internal bases. Geometrical and Internal characteristics that are considered significant for the elementary and fundamental particles aren’t basic properties, characteristics or criteria of a Fundamental Particle. Of course, completely new Physical and Visual experimental methods of Quantum mechanics and Behavioral-Physical investigations of Particles are needed to study and discover the Fundamental Particle. These are new Physical, Visual and Behavioral-Physical experimental methods for describing and discovering the Fundamental Particle in the Nature and Microworld. Fundamental Particle consists of the same Energy-Mass-Motion system and a symmetry of Energy-Mass-Motion. Fundamental Particle supplies each of the elementary particles with the same Energy-Mass-Motion system at the same time and regulates each of the particles. Fundamental Particle gives Energy, Mass and Motion to each particles at the same time, each of the Particles consists of acquired Energy-Mass-Motion system and symmetry. Energy, Mass, Motion given by the Fundamental Particle to the particles are Symmetrical Equivalent and they remain in their primary shapes in all cases. Fundamental Particle gives Energy-Mass-Motion system and symmetry consisting of different measures and functions to each of the particles. The Motion given by the Fundamental Particle to the particles is Gravitation, Gravitational Interaction not only gives Motion, but also cause Motion by attracting. All Substances, Fields and Cosmic objects consist of Energy-Mass-Motion. The Field also includes specific Mass. They are always Energetic, Massive and Active. Fundamental Particle establishes the bases of the Nature. Supplement and Regulating of all the particles existing in the Nature belongs to Fundamental Particle.

Keywords: basic properties of a fundamental particle, behavioral-physical and visual methods, energy-mass-motion system and symmetrical equivalence, fundamental particle

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: David C. Ni

Abstract:

Contemporary models for N-body systems are based on temporal, two-body, and mass point representation of Newtonian mechanics. Other mainstream models include 2D and 3D Ising models based on local neighborhood the lattice structures. In Quantum mechanics, the theories of collective modes are for superconductivity and for the long-range quantum entanglement. However, these models are still mainly for the specific phenomena with a set of designated parameters. We are therefore motivated to develop a new construction directly from the complex-variable N-body systems based on the extended Blaschke functions (EBF), which represent a non-temporal and nonlinear extension of Lorentz transformation on the complex plane – the normalized momentum spaces. A point on the complex plane represents a normalized state of particle momentums observed from a reference frame in the theory of special relativity. There are only two key parameters, normalized momentum and nonlinearity for modelling. An algorithm similar to Jenkins-Traub method is adopted for solving EBF iteratively. Through iteration, the solution sets show a form of σ + i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various distributions, such as 1-peak, 2-peak, and 3-peak etc. distributions and some of them are analog to the canonical distributions. The results of the numerical analysis demonstrate continuum-to-discreteness transitions, evolutional invariance of distributions, phase transitions with conjugate symmetry, etc., which manifest the construction as a potential candidate for the unification of statistics. We hereby classify the observed distributions on the finite convergent domains. Continuous and discrete distributions both exist and are predictable for given partitions in different regions of parameter-pair. We further compare these distributions with canonical distributions and address the impacts on the existing applications.

Keywords: blaschke, lorentz transformation, complex variables, continuous, discrete, canonical, classification

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Authors: Mishu Gupta, Rama Gupta

Abstract:

It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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