Search results for: lattice model

Authors: Chetra Mang, Ahmadali Tahmasebimoradi, Xavier Lorang

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Lattice structures are widely used in various applications, especially in aeronautic, aerospace, and medical applications because of their high performance properties. Thanks to advancement of the additive manufacturing technology, the lattice structures can be manufactured by different methods such as laser beam melting technology. However, the presence of geometric defects in the lattice structures is inevitable due to the manufacturing process. The geometric defects may have high impact on the mechanical strength of the structures. This work analyzes the correlation between the manufacturing parameters and the mechanical strengths of the lattice structures. To do that, two types of the lattice structures; body-centered cubic with z-struts (BCCZ) structures made of Inconel718, and body-centered cubic (BCC) structures made of Scalmalloy, are manufactured by laser melting beam machine using Taguchi design of experiment. Each structure is placed on the substrate with a specific position and orientation regarding the roller direction of deposed metal powder. The position and orientation are considered as the manufacturing parameters. The geometric defects of each beam in the lattice are characterized and used to build the geometric model in order to perform simulations. Then, the mechanical strengths are defined by the homogeneous response as Young's modulus and yield strength. The distribution of mechanical strengths is observed as a function of manufacturing parameters. The mechanical response of the BCCZ structure is stretch-dominated, i.e., the mechanical strengths are directly dependent on the strengths of the vertical beams. As the geometric defects of vertical beams are slightly changed based on their position/orientation on the manufacturing substrate, the mechanical strengths are less dispersed. The manufacturing parameters are less influenced on the mechanical strengths of the structure BCCZ. The mechanical response of the BCC structure is bending-dominated. The geometric defects of inclined beam are highly dispersed within a structure and also based on their position/orientation on the manufacturing substrate. For different position/orientation on the substrate, the mechanical responses are highly dispersed as well. This shows that the mechanical strengths are directly impacted by manufacturing parameters. In addition, this work is carried out to study the uncertainty propagation of the geometric defects on the mechanical strength of the BCC lattice structure made of Scalmalloy. To do that, we observe the distribution of mechanical strengths of the lattice according to the distribution of the geometric defects. A probability density law is determined based on a statistical hypothesis corresponding to the geometric defects of the inclined beams. The samples of inclined beams are then randomly drawn from the density law to build the lattice structure samples. The lattice samples are then used for simulation to characterize the mechanical strengths. The results reveal that the distribution of mechanical strengths of the structures with the same manufacturing parameters is less dispersed than one of the structures with different manufacturing parameters. Nevertheless, the dispersion of mechanical strengths due to the structures with the same manufacturing parameters are unneglectable.

Keywords: geometric defects, lattice structure, mechanical strength, uncertainty propagation

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Rohin Sharma, Sumantu Chaulagain

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This paper presents calculations of total energy of InGaN alloy carried out in a disordered quasirandom structure for a triclinic super cell. This structure replicates the disorder and composition effect in the alloy. First principle calculations within the density functional theory with the local density approximation approach is employed to accurately determine total energy of the system. Lattice constants and band gaps associated with the ground states are then estimated for different concentration ratios of the alloy. We provide precise results of quasirandom structures of the alloy and their lattice constants with the total energy and band gap energy of the system for the range of seven different composition ratios and their respective lattice parameters.

Keywords: DFT, ground state, LDA, quasicrystal, triclinic super cell

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Authors: Mondher Yahyaoui

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A generalized vortex lattice method for complex lifting surfaces with flap and aileron deflection is formulated. The method is not restricted by the linearized theory assumption and accounts for all standard geometric lifting surface parameters: camber, taper, sweep, washout, dihedral, in addition to flap and aileron deflection. Thickness is not accounted for since the physical lifting body is replaced by a lattice of panels located on the mean camber surface. This panel lattice setup and the treatment of different wake geometries is what distinguish the present work form the overwhelming majority of previous solutions based on the vortex lattice method. A MATLAB code implementing the proposed formulation is developed and validated by comparing our results to existing experimental and numerical ones and good agreement is demonstrated. It is then used to study the accuracy of the widely used classical vortex-lattice method. It is shown that the classical approach gives good agreement in the clean configuration but is off by as much as 30% when a flap or aileron deflection of 30° is imposed. This discrepancy is mainly due the linearized theory assumption associated with the conventional method. A comparison of the effect of four different wake geometries on the values of aerodynamic coefficients was also carried out and it is found that the choice of the wake shape had very little effect on the results.

Keywords: aileron deflection, camber-surface-bound vortices, classical VLM, generalized VLM, flap deflection

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Authors: Paul Okonkwo, Howard Smith

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This paper describes a methodology to integrate the Athena Vortex Lattice Aerodynamic Software for automated operation in a multivariate optimisation of the Blended Wing Body Aircraft. The Athena Vortex Lattice code developed at the Massachusetts Institute of Technology by Mark Drela allows for the aerodynamic analysis of aircraft using the vortex lattice method. Ordinarily, the Athena Vortex Lattice operation requires a text file containing the aircraft geometry to be loaded into the AVL solver in order to determine the aerodynamic forces and moments. However, automated operation will be required to enable integration into a multidisciplinary optimisation framework. Automated AVL operation within the JAVA design environment will nonetheless require a modification and recompilation of AVL source code into an executable file capable of running on windows and other platforms without the –X11 libraries. This paper describes the procedure for the integrating the FORTRAN written AVL software for automated operation within the multivariate design synthesis optimisation framework for the conceptual design of the BWB aircraft.

Keywords: aerodynamics, automation, optimisation, AVL

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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: P. Karlsson, M. Åsberg, R. Eriksson, P. Krakhmalev, N. Strömberg

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Additive manufacturing of lattice structures is promising for lightweight design, but the mechanical response of the lattices structures is not fully understood. This investigation presents the results of simulation and experimental investigations of the grid and shell-based gyroid lattices. Specimens containing selected lattices were designed with an in-house software and manufactured from 316L steel with Renishaw AM400 equipment. Results of simulation and experimental investigations correlated well.

Keywords: additive manufacturing, computed tomography, material characterization, lattice structures, robust lightweight design

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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: Anthony Overmars, Sitalakshmi Venkatraman

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This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography

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

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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

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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: Ali Abdul Kadhim, Fue Lien

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Solid particle distribution on an impingement surface has been simulated utilizing a graphical processing unit (GPU). In-house computational fluid dynamics (CFD) code has been developed to investigate a 3D turbulent impinging jet using the lattice Boltzmann method (LBM) in conjunction with large eddy simulation (LES) and the multiple relaxation time (MRT) models. This paper proposed an improvement in the LBM-cellular automata (LBM-CA) probabilistic method. In the current model, the fluid flow utilizes the D3Q19 lattice, while the particle model employs the D3Q27 lattice. The particle numbers are defined at the same regular LBM nodes, and transport of particles from one node to its neighboring nodes are determined in accordance with the particle bulk density and velocity by considering all the external forces. The previous models distribute particles at each time step without considering the local velocity and the number of particles at each node. The present model overcomes the deficiencies of the previous LBM-CA models and, therefore, can better capture the dynamic interaction between particles and the surrounding turbulent flow field. Despite the increasing popularity of LBM-MRT-CA model in simulating complex multiphase fluid flows, this approach is still expensive in term of memory size and computational time required to perform 3D simulations. To improve the throughput of each simulation, a single GeForce GTX TITAN X GPU is used in the present work. The CUDA parallel programming platform and the CuRAND library are utilized to form an efficient LBM-CA algorithm. The methodology was first validated against a benchmark test case involving particle deposition on a square cylinder confined in a duct. The flow was unsteady and laminar at Re=200 (Re is the Reynolds number), and simulations were conducted for different Stokes numbers. The present LBM solutions agree well with other results available in the open literature. The GPU code was then used to simulate the particle transport and deposition in a turbulent impinging jet at Re=10,000. The simulations were conducted for L/D=2,4 and 6, where L is the nozzle-to-surface distance and D is the jet diameter. The effect of changing the Stokes number on the particle deposition profile was studied at different L/D ratios. For comparative studies, another in-house serial CPU code was also developed, coupling LBM with the classical Lagrangian particle dispersion model. Agreement between results obtained with LBM-CA and LBM-Lagrangian models and the experimental data is generally good. The present GPU approach achieves a speedup ratio of about 350 against the serial code running on a single CPU.

Keywords: CUDA, GPU parallel programming, LES, lattice Boltzmann method, MRT, multi-phase flow, probabilistic model

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Authors: Nir Schreiber, Reuven Cohen, Simi Haber

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

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

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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: David A. Harness

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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: Tobias Horstmann, Thomas Le Garrec, Daniel-Ciprian Mincu, Emmanuel Lévêque

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Despite the efficiency and low dissipation of the stream-collide formulation of the Lattice Boltzmann (LB) algorithm, which is nowadays implemented in many commercial LBM solvers, there are certain situations, e.g. mesh transition, in which a classical finite-volume or finite-difference formulation of the LB algorithm still bear advantages. In this paper, we present an algorithm that combines the node-based streaming of the distribution functions with a second-order finite volume discretization of the advection term of the BGK-LB equation on a uniform D2Q9 lattice. It is shown that such a coupling is possible for a multi-domain approach as long as the overlap, or buffer zone, between two domains, is achieved on at least 2Δx. This also implies that a direct coupling (without buffer zone) of a stream-collide and finite-volume LB algorithm on a single grid is not stable. The critical parameter in the coupling is the CFL number equal to 1 that is imposed by the stream-collide algorithm. Nevertheless, an explicit filtering step on the finite-volume domain can stabilize the solution. In a further investigation, we demonstrate how such a coupling can be used for mesh transition, resulting in an intrinsic conservation of mass over the interface.

Keywords: algorithm coupling, finite volume formulation, grid refinement, Lattice Boltzmann method

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Authors: Ju-Hong Lee, Chong-Jia Ciou

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This paper deals with the problem of two-dimensional (2-D) recursive two-channel quincunx quadrature mirror filter (QQMF) banks design. The analysis and synthesis filters of the 2-D recursive QQMF bank are composed of 2-D recursive digital allpass lattice filters (DALFs) with symmetric half-plane (SHP) support regions. Using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters, we facilitate the design of the proposed QQMF bank. For finding the coefficients of the 2-D recursive SHP DALFs, we present a structure of 2-D recursive digital allpass filters by using 2-D SHP recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive QQMF bank is that the resulting 2-D recursive QQMF bank provides better performance than the existing 2-D recursive QQMF banks. Simulation results are also presented for illustration and comparison.

Keywords: all-pass digital filter, lattice structure, quincunx QMF bank, symmetric half-plane digital filter

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Authors: Abir Yahya, Hacen Dhahri, Khalifa Slimi

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The present paper deals with a numerical simulation of temperature field inside a solid oxide fuel cell (SOFC) components. The temperature distribution is investigated using a co-flow planar SOFC comprising the air and fuel channel and two-ceramic electrodes, anode and cathode, separated by a dense ceramic electrolyte. The Lattice Boltzmann method (LBM) is used for the numerical simulation of the physical problem. The effects of inlet temperature, anode thermal conductivity and current density on temperature distribution are discussed. It was found that temperature distribution is very sensitive to the inlet temperature and the current density.

Keywords: heat sources, Lattice Boltzmann method, solid oxide fuel cell, temperature

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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: F. Karim

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In this paper, triangular lattice index-guiding photonic crystal fibers (PCFs) are synthesized to compensate the chromatic dispersion of a single mode fiber (SMF-28) for an 80 km optical link operating at 1.55 µm, by using the directed tabu search algorithm. Hole-to-hole distance, circular air-hole diameter, solid-core diameter, ring number and PCF length parameters are optimized for this purpose. Three Synthesized PCFs with different physical parameters are compared in terms of their objective functions values, residual dispersions and compensation ratios.

Keywords: triangular lattice index-guiding photonic crystal fiber, dispersion compensation, directed tabu search, synthesis

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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: K. R. Phaneesh, Anirudh Bhat, G. Mukherjee, K. T. Kashyap

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Extensive Monte Carlo Potts model simulations were performed on 2D square lattice to investigate the effects of simulated higher temperatures effects on grain growth kinetics. A range of simulation temperatures (KTs) were applied on a matrix of size 10002 with Q-state 64, dispersed with a wide range of second phase particles, ranging from 0.001 to 0.1, and then run to 100,000 Monte Carlo steps. The average grain size, the largest grain size and the grain growth exponent were evaluated for all particle fractions and simulated temperatures. After evaluating several growth parameters, the critical temperature for a square lattice, with eight nearest neighbors, was found to be KTs = 0.4.

Keywords: average grain size, critical temperature, grain growth exponent, Monte Carlo steps

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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: 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: 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: Seung-Yeon Kim

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The Ising model, consisting magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising model has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising model explains the gas-liquid phase transitions accurately. However, the Ising model in a nonzero magnetic field has been one of the most intriguing and outstanding unsolved problems. We study analytically the partition function zeros in the complex magnetic-field plane and the Yang-Lee edge singularity of the infinite-range Ising model in an external magnetic field. In addition, we compare the Yang-Lee edge singularity of the infinite-range Ising model with that of the square-lattice Ising model in an external magnetic field.

Keywords: Ising ferromagnet, magnetic field, partition function zeros, Yang-Lee edge singularity

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Authors: A. Zerarka, W. Djoudi

Abstract:

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

Abstract:

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

Abstract:

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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