Search results for: lattice%20equation

Authors: Imdat Taymaz, Erman Aslan, Kemal Cakir

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The Lattice Boltzmann Method (LBM) is performed to computationally investigate the laminar flow and heat transfer of an incompressible fluid with constant material properties in a 2D channel with a built-in triangular prism. Both momentum and energy transport is modelled by the LBM. A uniform lattice structure with a single time relaxation rule is used. Interpolation methods are applied for obtaining a higher flexibility on the computational grid, where the information is transferred from the lattice structure to the computational grid by Lagrange interpolation. The flow is researched on for different Reynolds number, while Prandtl number is keeping constant as a 0.7. The results show how the presence of a triangular prism effects the flow and heat transfer patterns for the steady-state and unsteady-periodic flow regimes. As an evaluation of the accuracy of the developed LBM code, the results are compared with those obtained by a commercial CFD code. It is observed that the present LBM code produces results that have similar accuracy with the well-established CFD code, as an additionally, LBM needs much smaller CPU time for the prediction of the unsteady phonema.

Keywords: laminar forced convection, lbm, triangular prism

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Authors: M. Zemouli, K. Amara, M. Elkeurti, Y. Benallou

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We present the molecular dynamic simulations results of the structural and dynamical properties of the zinc-blende GaBi over a wide range of temperature (300-1000) K. Our simulation where performed in the framework of the three-body Tersoff potential, which accurately reproduces the lattice constants and elastic constants of the GaBi. A good agreement was found between our calculated results and the available theoretical data of the lattice constant, the bulk modulus and the cohesive energy. Our study allows us to predict the thermodynamic properties such as the specific heat and the lattice thermal expansion. In addition, this method allows us to check its ability to predict the phase transition of this compound. In particular, the transition pressure to the rock-salt phase is calculated and the results are compared with other available works.

Keywords: Gallium compounds, molecular dynamics simulations, interatomic potential thermodynamic properties, structural phase transition

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Authors: Min Wang, Sergey Utev

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The lessons from the 2007-09 global financial crisis have driven scientific research, which considers the design of new methodologies and financial models in the global market. The quantum mechanics approach was introduced in the unpredictable stock market modeling. One famous quantum tool is Feynman path integral method, which was used to model insurance risk by Tamturk and Utev and adapted to formalize the path-dependent option pricing by Hao and Utev. The research is based on the path-dependent calculation method, which is motivated by the Feynman path integral method. The path calculation can be studied in two ways, one way is to label, and the other is computational. Labeling is a part of the representation of objects, and generating functions can provide many different ways of representing share price paths. In this paper, the recent works on graphical theoretical construction of individual share price path via matroid is presented. Firstly, a study is done on the knowledge of matroid, relationship between lattice path matroid and Tutte polynomials and ways to connect points in the lattice path matroid and Tutte polynomials is suggested. Secondly, It is found that a general binary tree can be validly constructed from a connected lattice path matroid rather than general lattice path matroid. Lastly, it is suggested that there is a way to represent share price paths via a general binary tree, and an algorithm is developed to construct share price paths from general binary trees. A relationship is also provided between lattice integer points and Tutte polynomials of a transversal matroid. Use this way of connection together with the algorithm, a share price path can be constructed from a given connected lattice path matroid.

Keywords: combinatorial construction, graphical representation, matroid, path calculation, share price, Tutte polynomial

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Authors: W. Hasan, H. Farhat, A. Alhilo, L. Tamimi

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Oil in water (O/W) emulsions are utilized extensively for cooling and lubricating cutting tools during parts machining. A robust Lattice Boltzmann (LBM) thermal-surfactants model, which provides a useful platform for exploring complex emulsions’ characteristics under variety of flow conditions, is used here for the study of the fluid behavior during conventional tools cooling. The transient thermal capabilities of the model are employed for simulating the effects of the flow conditions of O/W emulsions on the cooling of cutting tools. The model results show that the temperature outcome is slightly affected by reversing the direction of upper plate (workpiece). On the other hand, an important increase in effective viscosity is seen which supports better lubrication during the work.

Keywords: hybrid lattice Boltzmann method, Gunstensen model, thermal, surfactant-covered droplet, Marangoni stress

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Authors: M. Zemouli, K. Amara, M. Elkeurti, Y. Benallou

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We present a theoretical study of the structural, elastic and thermodynamic properties of the zinc-blende AlBi for a wide temperature range. The simulation calculation is performed in the framework of the molecular dynamics method using the three-body Tersoff potential which reproduces provide, with reasonable accuracy, the lattice constants and elastic constants. Our results for the lattice constant, the bulk modulus and cohesive energy are in good agreement with other theoretical available works. Other thermodynamic properties such as the specific heat and the lattice thermal expansion can also be predicted. In addition, this method allows us to check its ability to predict the phase transition of this compound. In particular, the transition pressure to the rock-salt phase is calculated and the results are compared with other available works.

Keywords: aluminium compounds, molecular dynamics simulations, interatomic potential, thermodynamic properties, structural phase transition

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Authors: Antonio Aguilar Aguilar, Eliezer Braun Guitler

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Using a previously developed procedure and with the aid of algebraic software, a two-dimensional generalized Ising model with a 4×2 unitary cell (UC), we obtain a Kagome Lattice with twelve different spin-spin values of interaction, in order to determine the partition function per spin L(T). From the partition function we can study the magnetic behavior of the system. Because of the competition phenomenon between spins, a very complex behavior among them in a variety of magnetic states can be observed.

Keywords: correlations, Ising, Kagome, exact functions

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Authors: Axel Thallemer, Aleksandar Kostadinov, Abel Fam, Alex Teo

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For centuries, the forming processes in nature served as a source of inspiration for both architects and designers. It seems as most human artifacts are based on ideas which stem from the observation of the biological world and its principles of growth. As a fact, in the cultural history of Homo faber, materials have been mostly used in their solid state: From hand axe to computer mouse, the principle of employing matter has not changed ever since the first creation. In the scope of history only recently and by the help of additive-generative fabrication processes through Computer Aided Design (CAD), designers were enabled to deconstruct solid artifacts into an outer skin and an internal lattice structure. The intention behind this approach is to create a new topology which reduces resources and integrates functions into an additively manufactured component. However, looking at the currently employed lattice structures, it is very clear that those lattice structure geometries have not been thoroughly designed, but rather taken out of basic-geometry libraries which are usually provided by the CAD. In the here presented study, a group of 20 industrial design students created new and unique lattice structures using natural paragons as their models. The selected natural models comprise both the animate and inanimate world, with examples ranging from the spiraling of narwhal tusks, off-shooting of mangrove roots, minimal surfaces of soap bubbles, up to the rhythmical arrangement of molecular geometry, like in the case of SiOC (Carbon-Rich Silicon Oxicarbide). This ideation process leads to a design of a geometric cell, which served as a basic module for the lattice structure, whereby the cell was created in visual analogy to its respective natural model. The spatial lattices were fabricated additively in mostly [X]3 by [Y]3 by [Z]3 units’ volumes using selective powder bed melting in polyamide with (z-axis) 50 mm and 100 µm resolution and subdued to mechanical testing of their elastic zone in a biomedical laboratory. The results demonstrate that additively manufactured lattice structures can acquire different properties when they are designed in analogy to natural models. Several of the lattices displayed the ability to store and return kinetic energy, while others revealed a structural failure which can be exploited for purposes where a controlled collapse of a structure is required. This discovery allows for various new applications of functional lattice structures within industrially created objects.

Keywords: bio-inspired, biomimetic, lattice structures, additive manufacturing

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Authors: Alpana Tiwari, N. K. Gaur

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We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: orientational glass, phonons, TR-coupling, lattice dynamics

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Authors: Nastaran Ahmadpour Samani, Shahram Talebi

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Added mass is an important quantity in analysis of the motion of a submerged object ,which can be calculated by solving the equation of potential flow around the object . Here, we consider systems in which a square object is submerged in a channel of fluid and moves parallel to the wall. The corresponding added mass at a given distance from the wall d and for the object size s (which is the side of square object) is calculated via lattice Blotzmann simulation . By changing d and s separately, their effect on the added mass is studied systematically. The simulation results reveal that for the systems in which d > 4s, the distance does not influence the added mass any more. The added mass increases when the object approaches the wall and reaches its maximum value as it moves on the wall (d -- > 0). In this case, the added mass is about 73% larger than which of the case d=4s. In addition, it is observed that the added mass increases by increasing of the object size s and vice versa.

Keywords: Lattice Boltzmann simulation , added mass, square, variable size

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Authors: Mitsuhiro Okayasu

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To better understand the lattice characteristics of lead zirconate titanate (PZT) ceramics, the lattice orientations and domain-switching characteristics have been directly examined during loading and unloading using various experimental techniques. Upon loading, the PZT ceramics are fractured linear and nonlinearly during the compressive loading process. The strain characteristics of the PZT ceramic were directly affected by both the lattice and domain switching strain. Due to the piezoelectric ceramic, electrical activity of lightning-like behavior occurs in the PZT ceramics, which attributed to the severe domain-switching leading to weak piezoelectric property. The characteristics of domain-switching and reverse switching are detected during the loading and unloading processes. The amount of domain-switching depends on the grain, due to different stress levels. In addition, two patterns of 90˚ domain-switching systems are characterized, namely (i) 90˚ turn about the tetragonal c-axis and (ii) 90˚ rotation of the tetragonal a-axis. In this case, PZT ceramic was loaded by the thermal stress at 80°C. Extent of domain switching is related to the direction of c-axis of the tetragonal structure, e.g., that axis, orientated close to the loading direction, makes severe domain switching. It is considered that there is 90˚ domain switching, but in actual, the angle of domain switching is less than 90˚, e.g., 85.4° ~ 90.0°. In situ TEM observation of the domain switching characteristics of PZT ceramic has been conducted with increasing the sample temperature from 25°C to 300°C, and the domain switching like behavior is directly observed from the lattice image, where the severe domain switching occurs less than 100°C.

Keywords: PZT, lead zirconate titanate, piezoelectric ceramic, domain switching, material property

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: Bayram Sahin, Baris Gezdirici, Murat Ceylan, Ibrahim Ates

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In this experimental study, the effects of heat transfer and flow characteristics on lattice geometric heat sinks, where high rates of heat removal are required, were investigated. The design parameters were Reynolds number, the height of heat sink (H), horizontal (Sy) and vertical (Sx) distances between heat sinks. In the experiments, the Reynolds number ranged from 4000 to 20000; heat sink heights were (H) 20 mm and 40 mm; the distances (Sy) between the heat sinks in the flow direction were45 mm, 32 mm, 23.3 mm; the distances (Sx) between the heat sinks perpendicular to the flow direction were selected to be 23.3 mm, 12.5 mm and 6 mm. A total of 90 experiments were conducted and the maximum Nusselt number and minimum friction coefficient were targeted. Experimental results have shown that heat sinks in lattice geometry have a significant effect on heat transfer enhancement. Under the different experimental conditions, the highest increase in Nusselt number was 283% while the lowest increase was calculated as 66% as compared with the straight channel results. The lowest increase in the friction factor was also obtained as 173% according to the straight channel results. It is seen that the increase in heat sink height and flow velocity increased the level of turbulence in the channel, leading to higher Nusselt number and friction factor values.

Keywords: forced convection, heat transfer enhancement, lattice geometric heat sinks, pressure drop

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Authors: Fama Jallow, Melody Neaves, Professor Mcgregor

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The quest for sustainable energy sources has driven significant interest in hydrogen production as a clean and efficient fuel. Alkaline water electrolysis (AWE) has emerged as a prominent method for generating hydrogen, necessitating the development of advanced electrode designs with improved performance characteristics. Additive manufacturing (AM) by laser powder bed fusion (LPBF) method presents an opportunity to tailor electrode microstructures and properties, enhancing their performance. This research proposes investigating the AM of electrodes with different lattice structures to optimize hydrogen production. The primary objective is to employ advanced modeling techniques to identify and select two optimal lattice structures for electrode fabrication. LPBF will be used to fabricate electrodes with precise control over lattice geometry, pore size, and distribution. The performance evaluation will encompass energy consumption and porosity analysis. AWE will assess energy efficiency, aiming to identify lattice structures with enhanced hydrogen production rates and reduced power requirements. Computed tomography (CT) scanning will analyze porosity to determine material integrity and mass transport characteristics. The research aims to bridge the gap between AM and hydrogen production by investigating lattice structures potential in electrode design. By systematically exploring lattice structures and their impact on performance, this study aims to provide valuable insights into the design and fabrication of highly efficient and cost-effective electrodes for AWE. The outcomes hold promise for advancing hydrogen production through AM. The research will have a significant impact on the development of sustainable energy sources. The findings from this study will help to improve the efficiency of AWE, making it a more viable option for hydrogen production. This could lead to a reduction in our reliance on fossil fuels, which would have a positive impact on the environment. The research is also likely to have a commercial impact. The findings could be used to develop new electrode designs that are more efficient and cost-effective. This could lead to the development of new hydrogen production technologies, which could have a significant impact on the energy market.

Keywords: hydrogen production, electrode, lattice structure, Africa

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Authors: W. Hasan, H. Farhat

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A hybrid quasi-steady thermal lattice Boltzmann model was used to study the combined effects of temperature and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain’s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably.

Keywords: lattice Boltzmann method, Gunstensen model, thermal, contact angle, high viscosity ratio

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Authors: Luma Al-Tamimi, Hassan Farhat, Wessam Hasan

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A three-dimensional (3D) hybrid quasi-steady thermal lattice Boltzmann model is developed to couple the effects of surfactant, temperature, interfacial tension, and contact angle. This 3D model is an extended scheme of a previously introduced two-dimensional (2D) hybrid lattice Boltzmann model. The 3D model is used to study the combined multi-physics effects on emulsion systems flowing in rectangular microchannels with and without confinements, where the suspended phase is made of droplets, plugs, or a mixture of both. The simulation results show that emulsion systems with plugs as the suspended phase are more efficient than with droplets, whereas mixed systems that form large plugs through coalescence have even greater efficiency. The 3D contact angle model generates matching results to those of the 2D model, which were validated with experiments. Furthermore, the effects of various confinements on adhering single drop systems are investigated for delineating their influence on the power required for transporting the suspended phase through the channel. It is shown that the deeper the constriction is, the lower the system efficiency. Increasing the surfactant concentration or fluid temperature in a channel with confinement carries a substantial positive effect on oil droplet transportation.

Keywords: lattice Boltzmann method, thermal, contact angle, surfactants, high viscosity ratio, porous media

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Authors: Osman Adiguzel

Abstract:

Shape memory effect is a peculiar property exhibited by certain alloy systems and based on martensitic transformation, and shape memory properties are closely related to the microstructures of the material. Shape memory effect is linked with martensitic transformation, which is a solid state phase transformation and occurs with the cooperative movement of atoms by means of lattice invariant shears on cooling from high-temperature parent phase. Lattice twinning and detwinning can be considered as elementary processes activated during the transformation. Thermally induced martensite occurs as martensite variants, in self-accommodating manner and consists of lattice twins. Also, this martensite is called the twinned martensite or multivariant martensite. Deformation of shape memory alloys in martensitic state proceeds through a martensite variant reorientation. The martensite variants turn into the reoriented single variants with deformation, and the reorientation process has great importance for the shape memory behavior. Copper based alloys exhibit this property in metastable β- phase region, which has DO3 –type ordered lattice in ternary case at high temperature, and these structures martensiticaly turn into the layered complex structures with lattice twinning mechanism, on cooling from high temperature parent phase region. The twinning occurs as martensite variants with lattice invariant shears in two opposite directions, <110 > -type directions on the {110}- type plane of austenite matrix. Lattice invariant shear is not uniform in copper based ternary alloys and gives rise to the formation of unusual layered structures, like 3R, 9R, or 18R depending on the stacking sequences on the close-packed planes of the ordered lattice. The unit cell and periodicity are completed through 18 atomic layers in case of 18R-structure. On the other hand, the deformed material recovers the original shape on heating above the austenite finish temperature. Meanwhile, the material returns to the twinned martensite structures (thermally induced martensite structure) in one way (irreversible) shape memory effect on cooling below the martensite finish temperature, whereas the material returns to the detwinned martensite structure (deformed martensite) in two-way (reversible) shape memory effect. Shortly one can say that the microstructural mechanisms, responsible for the shape memory effect are the twinning and detwinning processes as well as martensitic transformation. In the present contribution, x-ray diffraction, transmission electron microscopy (TEM) and differential scanning calorimetry (DSC) studies were carried out on two copper-based ternary alloys, CuZnAl, and CuAlMn.

Keywords: shape memory effect, martensitic transformation, twinning and detwinning, layered structures

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Authors: Norjan Jumaa, David Graham

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We present a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. The motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure less Naiver-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test case. Here, we present results for some complex flow problems including two dimensional single and multiple mode Rayleigh-Taylor instability and we obtain good results when comparing with those in the literature. The main focus of our work is related to interactions between aerated or non-aerated waves and structures so we also present results for both high viscosity and low viscosity waves.

Keywords: lattice Boltzmann method, multiphase flows, Rayleigh-Taylor instability, waves

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Authors: Mahmood Heshmati, Farhang Daneshmand

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Material scientists and engineers have introduced novel materials with complex geometries due to the recent technological advances and promotion of manufacturing methods. Among them, lattice structures with graded architectures denoted by functionally graded porous materials (FGPMs) have been developed to optimize the structural response. FGPMs are achieved by tailoring the size and density of the internal pores in one or more directions that lead to the desired mechanical properties and structural responses. Also, FGPMs provide more flexible transition and the possibility of designing and fabricating structural elements with complex and variable properties. In this paper, wave propagation in lattice structures with functionally graded (FG) porosity is investigated in order to examine the ability of shock absorbing effect. The behavior of FG porous beams with different porosity distributions under impact load and the effects of porosity distribution and porosity content on the wave speed are studied. Important conclusions are made, along with a discussion of the future scope of studies on FGPMs structures.

Keywords: functionally graded, porous materials, wave propagation, impact load, finite element

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Authors: Cavidan Yakupoglu, Kurt Rohloff

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In this study, we aim to provide a novel parameter selection model for the BFVrns scheme, which is one of the prominent FHE schemes. Parameter selection in lattice-based FHE schemes is a practical challenges for experts or non-experts. Towards a solution to this problem, we introduce a hybrid principles-based approach that combines theoretical with experimental analyses. To begin, we use regression analysis to examine the parameters on the performance and security. The fact that the FHE parameters induce different behaviors on performance, security and Ciphertext Expansion Factor (CEF) that makes the process of parameter selection more challenging. To address this issue, We use a multi-objective optimization algorithm to select the optimum parameter set for performance, CEF and security at the same time. As a result of this optimization, we get an improved parameter set for better performance at a given security level by ensuring correctness and security against lattice attacks by providing at least 128-bit security. Our result enables average ~ 5x smaller CEF and mostly better performance in comparison to the parameter sets given in [1]. This approach can be considered a semiautomated parameter selection. These studies are conducted using the PALISADE homomorphic encryption library, which is a well-known HE library. The abstract goes here.

Keywords: lattice cryptography, fully homomorphic encryption, parameter selection, LWE, RLWE

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Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud

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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.

Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch

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Authors: Muhammad Yousaf, Shoaib Usman

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Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm basedon a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 103 to 106 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was16.66 percent at Ra number 105.

Keywords: Lattice Boltzmann method, natural convection, nusselt number, rayleigh number, roughness

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Authors: Karina C. Azzolin, Luis E. Kosteski, Alisson S. Milani, Raquel C. Zydeck

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This work aims to represent Numerically tests experimentally developed in reduced scale walls with horizontal and inclined cuts by using the Lattice Discrete Element Method (LDEM) implemented On de Abaqus/explicit environment. The cuts were performed with depths of 20%, 30%, and 50% On the walls subjected to centered and eccentric loading. The parameters used to evaluate the numerical model are its strength, the failure mode, and the in-plane and out-of-plane displacements.

Keywords: structural masonry, wall chases, small scale, numerical model, lattice discrete element method

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Authors: M. Abir Hossain, M. Shahjada Tarafder

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This paper deals with the analysis of potential flow past two-dimensional body by discretizing the body into panels where the Laplace equation was applied to each panel. The Laplace equation was solved at each panel by applying the boundary conditions. The boundary condition was applied at each panel to mathematically formulate the problem and then convert the problem into a computer-solvable problem. Kutta condition was applied at both the leading and trailing edges to see whether the condition is satisfied or not. Another approach that is applied for the analysis is Vortex Lattice Method (VLM). A vortex ring is considered at each control point. Using the Biot-Savart Law the strength at each control point is calculated and hence the pressure differentials are measured. For the comparison of the analytic result with the experimental result, different NACA section hydrofoil is used. The analytic result of NACA 0012 and NACA 0015 are compared with the experimental result of Abbott and Doenhoff and found significant conformity with the achieved result.

Keywords: Kutta condition, Law of Biot-Savart, pressure differentials, potential flow, vortex lattice method

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Authors: Jean Yves Trepanier, Sami Ammar, Sagnik Banik

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Lattice Boltzmann Method has been advantageous in simulating complex boundary conditions and solving for fluid flow parameters by streaming and collision processes. This paper includes the study of three different test cases in a confined domain using the method of the Lattice Boltzmann model. 1. An SRT (Single Relaxation Time) approach in the Lattice Boltzmann model is used to simulate Lid Driven Cavity flow for different Reynolds Number (100, 400 and 1000) with a domain aspect ratio of 1, i.e., square cavity. A moment-based boundary condition is used for more accurate results. 2. A Thermal Lattice BGK (Bhatnagar-Gross-Krook) Model is developed for the Rayleigh Benard convection for both test cases - Horizontal and Vertical Temperature difference, considered separately for a Boussinesq incompressible fluid. The Rayleigh number is varied for both the test cases (10^3 ≤ Ra ≤ 10^6) keeping the Prandtl number at 0.71. A stability criteria with a precise forcing scheme is used for a greater level of accuracy. 3. The phase change problem governed by the heat-conduction equation is studied using the enthalpy based Lattice Boltzmann Model with a single iteration for each time step, thus reducing the computational time. A double distribution function approach with D2Q9 (density) model and D2Q5 (temperature) model are used for two different test cases-the conduction dominated melting and the convection dominated melting. The solidification process is also simulated using the enthalpy based method with a single distribution function using the D2Q5 model to provide a better understanding of the heat transport phenomenon. The domain for the test cases has an aspect ratio of 2 with some exceptions for a square cavity. An approximate velocity scale is chosen to ensure that the simulations are within the incompressible regime. Different parameters like velocities, temperature, Nusselt number, etc. are calculated for a comparative study with the existing works of literature. The simulated results demonstrate excellent agreement with the existing benchmark solution within an error limit of ± 0.05 implicates the viability of this method for complex fluid flow problems.

Keywords: BGK, Nusselt, Prandtl, Rayleigh, SRT

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Authors: David A. Harness

Abstract:

Natural evolution of ATP cognitive systems is to meet AI peer review standards. ATP process of axiom selection from Mizar to prove a conjecture would be further refined, as in all human and machine learning, by solving the real world problem of the proposed AI peer review challenge: Determine which conjecture forms the higher confidence level constructive proof between Standard Model of Physics SU(n) lattice gauge group operation vs. present non-standard 4D GEM EOS SU(n) lattice gauge group spatially extended operation in which the photon and electron are the first two trace angular momentum invariants of a gravitoelectromagnetic (GEM) energy momentum density tensor wavetrain integration spin-stress pressure-volume equation of state (EOS), initiated via 32 lines of Mathematica code. Resulting gravitoelectromagnetic spectrum ranges from compressive through rarefactive of the central cosmological constant vacuum energy density in units of pascals. Said self-adjoint group operation exclusively operates on the stress energy momentum tensor of the Einstein field equations, introducing quantization directly on the 4D spacetime level, essentially reformulating the Yang-Mills virtual superpositioned particle compounded lattice gauge groups quantization of the vacuum—into a single hyper-complex multi-valued GEM U(1) × SU(1,3) lattice gauge group Planck spacetime mesh quantization of the vacuum. Thus the Mizar corpus already contains all of the axioms required for relevant DeepMath premise selection and unambiguous formal natural language parsing in context deep learning.

Keywords: automated theorem proving, constructive quantum field theory, information theory, neural networks

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Authors: Yanmin Zhao, Siu Ming Yiu

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To claim the ownership for an executable program is a non-trivial task. An emerging direction is to add a watermark to the program such that the watermarked program preserves the original program’s functionality and removing the watermark would heavily destroy the functionality of the watermarked program. In this paper, the first watermarking signature scheme with the watermark and the constraint function hidden in the symmetric key setting is constructed. The scheme uses well-known techniques of lattice trapdoors and a lattice evaluation. The watermarking signature scheme is unforgeable under the Short Integer Solution (SIS) assumption and satisfies other security requirements such as the unremovability security property.

Keywords: short integer solution (SIS) problem, symmetric-key setting, watermarking schemes, watermarked signatures

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Authors: Zainab A. Bu Sinnah, David I. Graham

Abstract:

The Lattice Boltzmann Method has been developed and used to simulate both steady and unsteady fluid flow problems such as turbulent flows, multiphase flow and flows in the vascular system. As an example, the study of blood flow and its properties can give a greater understanding of atherosclerosis and the flow parameters which influence this phenomenon. The blood flow in the vascular system is driven by a pulsating pressure gradient which is produced by the heart. As a very simple model of this, we simulate plane channel flow under periodic forcing. This pulsatile flow is essentially the standard Poiseuille flow except that the flow is driven by the periodic forcing term. Moment boundary conditions, where various moments of the particle distribution function are specified, are applied at solid walls. We used a second-order single relaxation time model and investigated grid convergence using two distinct approaches. In the first approach, we fixed both Reynolds and Womersley numbers and varied relaxation time with grid size. In the second approach, we fixed the Womersley number and relaxation time. The expected second-order convergence was obtained for the second approach. For the first approach, however, the numerical method converged, but not necessarily to the appropriate analytical result. An explanation is given for these observations.

Keywords: Lattice Boltzmann method, single relaxation time, pulsatile flow, moment based boundary condition

Procedia PDF Downloads 208

Authors: W. H. Zheng, J. Li, F. J. Hong

Abstract:

Thin liquid film evaporation in ultrathin nanoporous membranes, which reduce the viscous resistance while still maintaining high capillary pressure and efficient liquid delivery, is a promising thermal management approach for high-power electronic devices cooling. Given the challenges and technical limitations of experimental studies for accurate interface temperature sensing, complex manufacturing process, and short duration of membranes, a dimensionless lattice Boltzmann method capable of restoring thermophysical properties of working fluid is particularly derived. The evaporation of R134a to its pure vapour ambient in nanoporous membranes with the pore diameter of 80nm, thickness of 472nm, and three porosities of 0.25, 0.33 and 0.5 are numerically simulated. The numerical results indicate that the highest heat transfer coefficient is about 1740kW/m²·K; the highest heat flux is about 1.49kW/cm² with only about the wall superheat of 8.59K in the case of porosity equals to 0.5. The dissipated heat flux scaled with porosity because of the increasing effective evaporative area. Additionally, the self-regulation of the shape and curvature of the meniscus under different operating conditions is also observed. This work shows a promising approach to forecast the membrane performance for different geometry and working fluids.

Keywords: high heat flux, ultrathin nanoporous membrane, thin film evaporation, lattice Boltzmann method

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Authors: Zhuofan Cheng, Qiongda Hu, Mohammed El-Hajjar, Basel Halak

Abstract:

Multiple-input multiple-output (MIMO) systems can allow significantly higher data rates compared to single-antenna-aided systems. They are expected to be a prominent part of the 5G communication standard. However, these decoders suffer from high power consumption. This work presents a design technique in order to improve the energy efficiency of MIMO systems; this facilitates their use in the next generation of battery-operated communication devices such as mobile phones and tablets. The proposed optimization approach consists of the use of low complexity lattice reduction algorithm in combination with an adaptive VLSI implementation. The proposed design has been realized and verified in 65nm technology. The results show that the proposed design is significantly more energy-efficient than conventional K-best MIMO systems.

Keywords: energy, lattice reduction, MIMO, VLSI

Procedia PDF Downloads 299