Use Of Periodic Boundary Conditions Research Articles

The effect of segmentation depth in a helical fin tube bundle on the anisotropic turbulence state

The large eddy simulation approach was used to perform a numerical simulation of a flow around a helical segmented-fin tube bundle. This work focuses on the study of turbulence and the effect of segment depth on it. The simulation was conducted in an area away from the boundaries of the tube bundle, where the flow is fully-developed, and the use of periodic boundary conditions is possible. The computer-aided design of the helical segmented-fin tube geometry is incorporated into the computational grid from the immersed boundary technique. The Reynolds stress tensor was used to analyze the anisotropic state of turbulence. This flow is characterized by an anisotropic state generated by a flow with a preferential direction. A transfer of momentum in the inter-segment space and contiguous zones was observed. This intersegment flow generates a less anisotropic state of turbulence. This study aimed to understand a possible transformation of heat transfer with marginal geometrical changes and pressure drop increases.

Linear extrapolation method based on multiple equiproportional models for thermal performance prediction of ultra-large array.

Strong demand for developing the photothermal (PT) and electrothermal devices with ultra-large array is increasing. Thermal performance prediction is vital to optimize the key properties of the devices with ultra-large array. Finite element method (FEM) provides a powerful numerical approach for solving complex thermophysics issues. However, for calculating the performance of devices with ultra-large array, it is very memory-consuming and time-consuming to build an equal scale three-dimensional (3D) FEM model. For an ultra-large periodic array irradiated with a local heating source, the use of periodic boundary conditions could lead to considerable errors. To solve this problem, a linear extrapolation method based on multiple equiproportional models (LEM-MEM) is proposed in this paper. The proposed method builds several reduced-size FEM models to carry out simulation and extrapolation, which avoids dealing with the ultra-large arrays directly and greatly reduces the computation consumption. To verify the accuracy of LEM-MEM, a PT transducer with beyond 4000 × 4000 pixels is proposed, fabricated, tested and compared with the prediction results. Four different pixel patterns are designed and fabricated to test their steady thermal properties. The experimental results demonstrate that LEM-MEM has great predictability, and the maximum percentage error of average temperature is within 5.22% in four different pixel patterns. In addition, the measured response time of the proposed PT transducer is within 2 ms. The proposed LEM-MEM not only provides design guidance for optimizing PT transducers, but is also very useful for other thermal engineering problems in ultra-large array that requires facile and efficient prediction strategy.

Lipid Bicelles in the Study of Biomembrane Characteristics.

Simulations of lipid membranes typically make use of periodic boundary conditions to mimic macroscopically sized membranes and allow for comparison to experiments performed e.g. on planar lipid membranes or on unilamellar lipid vesicles. However, the lateral periodicity partly suppresses membrane fluctuations or membrane remodeling, processes that are of particular importance in the study of asymmetric membranes-i.e. membranes with integral or associated proteins and/or asymmetric lipid compositions. Here, we devised a simple albeit powerful lipid bicelle model system that (i) displays similar structural, dynamical, and mechanical properties compared to infinite periodic lipid membrane systems and allows (ii) for the study of asymmetric lipid bilayer systems and (iii) the unperturbed formation of local spontaneous curvature induced by lipids or proteins in molecular dynamics simulations. In addition, the system is characterized by largely unbiased thermal fluctuations as opposed to standard bilayer systems. Application of the bicelle system for an asymmetric lipid composition resembling the plasma membrane reveals that the cholesterol density for a tension-free plasma membrane with a vanishing spontaneous curvature is larger by 28% within the extracellular leaflet compared to the cytosolic leaflet.

Accurate molecular dynamics modeling of Pseudomonas aeruginosa outer membrane interaction with signaling molecules.

Pseudomonas aeruginosa is an opportunistic pathogen responsible for lungs, urinary tract, and surgical wound infections. This gram-negative bacterium releases outer membrane vesicles (OMV) derived from the cell's outer membrane (OM), serving diverse functions in bacterial survival, including nutrient acquisition, signaling, antibiotic resistance, delivery vehicle, and host-immune response modulation. This work aims to develop an accurate in silico model of P. aeruginosa outer membrane using all-atom molecular dynamics (MD) to understand OMV biogenesis formation based on the prediction of the bilayer-couple model. This model predicts the intercalation of a signaling molecule name Pseudomonas Quinolone Signal (PQS) to the OM as the main driver for the vesicle formation. In this study, the asymmetric model OM is composed of PA14 Lipid A in the outer leaflet and a mixture of POPE and POPG phospholipids in the inner leaflet. Due to the use of periodic boundary conditions in MD simulations, the compositional asymmetry imposes a fixed ratio of lipid numbers between the two leaflets, which needs to be set with caution. It has been shown that many widely used methods of defining this ratio lack control over the stress state of the membrane. As a result, the generated membrane could have a non-zero per leaflet tension. We investigate the role of the initial stress state on the intercalation of PQS to the OM. Free energy calculation shows that the favorable position of PQS within the membrane would shift significantly by variation of per leaflet tension, which could have important implications on the bilayer-couple model of OMV biogenesis. In addition, we model various PQS analogs to probe the role of different functional groups of PQS on the spontaneous intercalation of this signaling molecule to the membrane.

Numerical Investigation of Particle Focusing Patterns in Laminar Pipe Flow With High Reynolds Numbers

The inertial focusing characteristics of particles in laminar flow pipes with high <i>Re</i> numbers were studied based on the “relative motion model”. In order to solve the problem of long pipes with high <i>Re</i> number flow, periodic boundary conditions were imposed on the inlet and outlet of the pipe. The research results show that the use of periodic boundary conditions can effectively reduce the computational, and the mechanical properties of particles in high <i>Re</i> flow can be calculated by using <i>L</i>=4<i>D</i> pipe. The difference from the low <i>Re</i> number is that as the <i>Re</i> number continues to increase,the lift force of the particles in the radial direction is no longer distributed as a parabola. The lift curve has a concave area between <i>r</i>⁺ =0.5 ~ 0.7, and there is a tendency for a new inertial focus point to appear in this section. By means of particles of <i>a</i>⁺ =1/17 for <i>Re</i> &gt; 1 000, this new focus point position is solvable. In addition, in the analysis of the flow field, a secondary flow occurs around the particle, and its intensity gradually increases with the <i>Re</i> number and the closeness of the particle to the wall. The generation of the secondary flow affects the spatial distribution of the particle lift.

A theory for the stabilization of polar crystal surfaces by a liquid environment.

Polar crystal surfaces play an important role in the functionality of many materials and have been studied extensively over many decades. In this article, a theoretical framework is presented that extends existing theories by placing the surrounding solution environment on an equal footing with the crystal itself; this is advantageous, e.g., when considering processes such as crystal growth from solution. By considering the polar crystal as a stack of parallel plate capacitors immersed in a solution environment, the equilibrium adsorbed surface charge density is derived by minimizing the free energy of the system. In analogy to the well-known diverging surface energy of a polar crystal surface at zero temperature, for a crystal in solution it is shown that the "polar catastrophe" manifests as a diverging free energy cost to perturb the system from equilibrium. Going further than existing theories, the present formulation predicts that fluctuations in the adsorbed surface charge density become increasingly suppressed with increasing crystal thickness. We also show how, in the slab geometry often employed in both theoretical and computational studies of interfaces, an electric displacement field emerges as an electrostatic boundary condition, the origins of which are rooted in the slab geometry itself, rather than the use of periodic boundary conditions. This aspect of the work provides a firmer theoretical basis for the recent observation that standard "slab corrections" fail to correctly describe, even qualitatively, polar crystal surfaces in solution.

Polarization energies in the fragment molecular orbital method

Using isolated and polarized states of fragments, a method for computing the polarization energies in density functional theory (DFT) and density-functional tight-binding (DFTB) is developed in the framework of the fragment molecular orbital method. For DFTB, the method is extended into the use of periodic boundary conditions (PBC), for which a new component, a periodic self-polarization energy, is derived. The couplings of the polarization to other components in the pair interaction energy analysis (PIEDA) are derived for DFT and DFTB, and compared to Hartree-Fock and second-order Møller-Plesset perturbation theory (MP2). The effect of the self-consistent (DFT) and perturbative (MP2) treatment of the electron correlation on the polarization is discussed. The difference in the polarization in the bulk (PBC) and micro (cluster) solvation is elucidated.

The dimensional evolution of structure and dynamics in hard sphere liquids.

The formulation of the mean-field infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension d increases. A careful numerical assessment of the matter has long been hindered by the exponential increase in computational costs with d. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on Dd lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to d = 13. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite d by leveraging the standard liquid-state theory and, thus, help bridge the gap from the other direction. The relatively smooth evolution of both the structure and dynamics across the d gap allows us to relate the two approaches and to identify some of the missing features that a finite-d theory of glasses might hope to include to achieve near quantitative agreement.

FFT‐based homogenization with mixed uniform boundary conditions

AbstractThe fast Fourier transform (FFT) based homogenization method of Moulinec and Suquet has been established as a fast, accurate, and robust tool for periodic homogenization in solid mechanics. In a finite element context, Pahr and Zysset have introduced nonperiodic boundary conditions (PMUBC) for homogenization problems. We show how to implement PMUBC efficiently in an FFT‐based code using discrete sine and cosine transforms. Compared with the domain mirroring approach, we reduce the runtime by a factor of 2 to 3, and the memory requirements by a factor of 8. We show that the use of periodic boundary conditions for nonperiodic geometries yields vastly different results than with PMUBC. Furthermore, we examine the influence of the discretization method by comparing the staggered grid discretization with a finite element discretization.

Large eddy simulation of fully-developed flow in a helical segmented-fin tube bundle

The Large Eddy Simulation approach was used to perform a numerical simulation of a flow around a circular tube bundle. The model is based on numerical tools, such as the immersed boundary technique and the extrapolation of pressure in the solid region of the tube, to represent a helical segmented-fin tube geometry. The simulation was conducted in an area away from the boundaries of the tube bundle, where the flow is fully-developed, and the use of periodic boundary conditions was possible. The mean velocity and turbulence values of the results and experimental data were compared and showed good general agreement. From the instantaneous results, it was possible to observe and study different turbulent structures presented in the flow. Two counter-rotating horseshoe vortices were identified in the space between the fins, which can improve heat transfer. Furthermore, a relevant transfer of momentum in the inter-segment space and contiguous zones was observed.

The nuts and bolts of core-hole constrained ab initio simulation for K-shell x-ray photoemission and absorption spectra

X-ray photoemission (XPS) and near edge x-ray absorption fine structure (NEXAFS) spectroscopy play an important role in investigating the structure and electronic structure of materials and surfaces. Ab initio simulations provide crucial support for the interpretation of complex spectra containing overlapping signatures. Approximate core-hole simulation methods based on density functional theory (DFT) such as the delta-self-consistent-field (ΔSCF) method or the transition potential (TP) method are widely used to predict K-shell XPS and NEXAFS signatures of organic molecules, inorganic materials and metal–organic interfaces at reliable accuracy and affordable computational cost. We present the numerical and technical details of our variants of the ΔSCF and TP method (coined ΔIP-TP) to simulate XPS and NEXAFS transitions. Using exemplary molecules in gas-phase, in bulk crystals, and at metal–organic interfaces, we systematically assess how practical simulation choices affect the stability and accuracy of simulations. These include the choice of exchange–correlation functional, basis set, the method of core-hole localization, and the use of periodic boundary conditions (PBC). We particularly focus on the choice of aperiodic or periodic description of systems and how spurious charge effects in periodic calculations affect the simulation outcomes. For the benefit of practitioners in the field, we discuss sensible default choices, limitations of the methods, and future prospects.

CALANIE: Anisotropic elastic correction to the total energy, to mitigate the effect of periodic boundary conditions

CALANIE (CALculation of ANIsotropic Elastic energy) computer program evaluates the elastic interaction correction to the total energy of a localized object, for example a defect in a material simulated using an ab initio or molecular statics approach, resulting from the use of periodic boundary conditions. The correction, computed using a fully elastically anisotropic Green’s function formalism, arises from the elastic interaction between a defect and its own periodically translated images. The long-range field of elastic displacements produced by the defect is described in the elastic dipole approximation. Applications of the method are illustrated by two case studies, one involving an ab initio investigation of point defects and vacancy migration in FCC gold, and another a molecular statics simulation of a dislocation loop. We explore the convergence of the method as a function of the simulation cell size, and note the significance of taking into account the elastic correction in the limit where the size of the defect is comparable with the size of the simulation cell. Program summaryProgram Title: CALANIE, version 2.0Program Files doi:http://dx.doi.org/10.17632/3h6xffk9h6.1Licensing provisions: Apache License, Version 2.0Programming language: C/C++Nature of problem: Periodic boundary conditions (PBCs) are often used in the context of ab initio and molecular statics atomic scale simulations. A localized defect in a crystalline material, simulated using PBCs, interacts elastically with its own periodically translated images, and this gives rise to a systematic error in the computed defect formation and migration energies. Evaluating the correction to the total energy resulting from effects of elastic interaction between a defect and its periodic images, to alleviate the contribution to the total energy arising from PBCs, is an essential aspect of any accurate total energy calculation performed using PBCs.Solution method: The energy of interaction between a localized defect and its periodically translated images is computed in the linear elasticity approximation. The energy of elastic interaction is expressed analytically in terms of the elastic dipole tensor of the defect and elastic Green’s function. Elements of the dipole tensor are computed as a part of the simulation evaluating the formation energy of the defect. Elastic Green’s function and its first and second derivatives are computed numerically from the elastic constants of the material. The method and the corresponding numerical procedures are implemented in the CALANIE computer program. The program evaluates matrix elements of the elastic dipole tensor of a localized defect and the elastic correction to the total energy arising from the use of periodic boundary conditions.Restrictions: The approach assumes the validity of the linear elasticity approximation. This limits the accuracy of evaluation of the elastic correction, which becomes less precise if the size of the defect is comparable with the size of the simulation cell.Unusual features: An open source code, containing full detail of the relevant theoretical concepts, algorithms and numerical implementation.

Reduced Model to Compute AC Losses of Twisted Multifilamentary Superconductors

Classical numerical techniques remain very computationally expensive to model the magnetization of twisted multifilamentary superconductors in three dimensions because they require solving a large system of equations. In this paper, a reduced model is proposed to approximate the ac losses of these types of wires. It is established through the projection of the physical problem in a helical Frenet basis and the use of periodic boundary conditions on a slice of the wire. The reduced model on the slice leads to systems of more reasonable size leading to smaller and faster simulations than when the whole wire is modeled. Simulation results show that the proposed method leads to computed losses similar to those obtained on a whole wire. Several simulation cases are proposed to prove the validity of the proposed model, and a comparison to some ac loss measurements is proposed to show the effectiveness of the proposed approach. The implementation relies on the H-formulation and is solved with the open-source solver, Getdp.

Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations

In this work, we focus on the development of the use of Periodic Boundary Conditions (PBC) with sources at oblique incidence in a Discontinuous Galerkin Time Domain (DGTD) framework. Whereas in the context of the Finite Difference Time Domain (FDTD) methods, an abundant literature can be found, for DGTD, the amount of contributions reporting on such methods is remarkably low. In this paper, we supplement the existing references using the field transform technique with an analysis of the continuous system using the method of characteristics and provide an energy estimate. Furthermore, we also study the discrete stability of the resulting DGTD scheme. Additional details about sources, observables (reflectance, transmittance and diffraction efficiency), and the use of Complex Frequency-Shifted Perfectly-Matched Layers (CFS-PMLs) in this framework are also given. After numerical validations, two realistic test-cases are considered in the context of nanophotonics with the Diogenes DGTD solver (http://diogenes.inria.fr).

Plane and plane-radial discrete breathers in fcc metals

Discrete breather (DB) is a time-periodic, spatially localized vibrational mode in a perfect nonlinear lattice. In this study, two new types of DBs are reported in fcc metals (Al, Cu and Ni), based on the molecular dynamics simulations using standard embedded atom method interatomic potentials. All calculations are performed at a zero temperature in a three-dimensional computational cell with the use of periodic boundary conditions. A plane DB is excited in a single (111) atomic plane by displacing the atoms from their equilibrium lattice sites according to a specific pattern corresponding to a delocalized vibrational mode in a two-dimensional triangular lattice. This plane DB is delocalized in two dimensions and localized in one dimension, normal to the excited (111) plane. It is shown that in all studied metals the plane DBs have maximal lifetimes of 17–22 ps in the range of initial amplitudes of 0.15–0.30 Å. Herewith the studied mode demonstrates a hard type of nonlinearity, i.e. its frequency increases with amplitude. The second new type of DB is the plane-radial DB obtained by imposing a radial localizing function on the plane DB. This disk-type DB is localized in all three dimensions. The time evolution of the atomic displacement amplitudes and the kinetic energy are studied. The DBs of this type can exist for 9 and 4 ps in Cu and Ni, respectively, and then they decay by dissipating their vibrational energy onto neighboring atoms. The long-lived plane-radial DB in Al is not found.

Improved approximation of transverse and shear stiffness for high volume fraction uniaxial composites

With uniaxial composites, the matrix material properties dominate the overall transverse and shear composite stiffness. Knowledge of these quantities are of practical importance in composite structures such as large wind turbine blades, which despite having a predominantly uniaxial layup, have both their torsional response and buckling behavior as critical design considerations. Accurate estimations of transverse and torsional rigidity for high volume fraction composites are currently dependent on extensive experimental work due to the low reliability and precision of transverse/shear micromechanical models. The Continuous Periodic Fiber Model is proposed to improve these predictions by considering fiber-fiber interactions through the use of periodic boundary conditions. Experimental data and standard models are used to validate the results and quantify the predictive improvements relative to traditional methods. The Continuous Periodic Fiber Model offers greatly improved accuracy for transverse stiffness estimations, reducing the average difference from the experiments by a factor of 1.7 (an average difference with experiment of 14% compared to the next best approach value of 24%) as well as modest improvements for the shear moduli.

A method for computing the three-dimensional radial distribution function of cloud particles from holographic images

Abstract. Reliable measurements of the three-dimensional radial distribution function for cloud droplets are desired to help characterize microphysical processes that depend on local drop environment. Existing numerical techniques to estimate this three-dimensional radial distribution function are not well suited to in situ or laboratory data gathered from a finite experimental domain. This paper introduces and tests a new method designed to reliably estimate the three-dimensional radial distribution function in contexts in which (i) physical considerations prohibit the use of periodic boundary conditions and (ii) particle positions are measured inside a convex volume that may have a large aspect ratio. The method is then utilized to measure the three-dimensional radial distribution function from laboratory data taken in a cloud chamber from the Holographic Detector for Clouds (HOLODEC).

AB INITIO МОДЕЛИРОВАНИЕ ВЛИЯНИЯ КРЕМНИЯ НА ОБРАЗОВАНИЕ КАРБИДА Fe3C В ОЦК-ЖЕЛЕЗЕ

Results of first-principles simulation of silicon influence of the energy of cementite formation and on partial enthalpy are presented in the article. Simulation was carried out in the frameworks of the Density Functional Theory (DFT) using the full-potential- linearized-augumented-plane-wave method (FP LAPW) taking into account the generalized gradient approximation (GGA’96) in WIEN2k software package. Various concentrations of silicon admixtures in cementite were studied, namely 1,6, 3,2 and 6 at. % for both the position of displacement of iron atom (positions S and G) and of carbon atom (position C). Volumetric optimization of all structures was carried out. Equilibrium parameters of the grid were determined both for cementite without admixtures (a = 4,510; b = 5,063; c = 6,747 Å), and for cementite with silicon, which excellently comply with experimental and theoretical data. Formation energy for concentration of 3,2 at. % in position C turned out to be –0,03 electron-volt, which can signify cementite’s stabilization. Though at that, partial enthalpy for all positions of silicon is positive which means that silicon remains in solid solution BCC-Fe, which is in a good compliance with results of other theoretical and experimental works. It was determined that the more is concentration of silicon, the lower is average magnetic moment on iron atoms. Moreover, it became possible to show that energy characteristics of the system significantly depend on the size of a super cell. This effect is connected with the use of periodic boundary conditions during calculations, and shows the presence of interactions between silicon atoms in neighboring super cells

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions.

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t^{-3/2} hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

Investigations on performance and emission characteristics of an industrial low swirl burner while burning natural gas, methane, hydrogen-enriched natural gas and hydrogen as fuels

Although many detailed chemical reaction mechanisms, skeletal mechanisms and reduced mechanisms are available in the literature to modeling the natural gas, they are computational expensive, required high power computing especially for three dimensional complex geometries with intense meshes. For example, though the DRM19 reduced mechanism does not include NO and NO2 species, it includes 19 species and 84 reactions. On the other hand, Eddy Dissipation combustion model in which the overall rate of reaction is mainly controlled by turbulent mixing can be utilized as a practical approach for fast burning and fast reaction fuels such as natural gas. Unlike fossil fuels, hydrogen is a renewable energy and quite clean in terms of carbon monoxide and carbon dioxide emissions. However, numerical and experimental studies on hydrogen combustion in burners are very restricted. In this study, the combustion of natural gas in an industrial low swirl burner–boiler system has been experimentally investigated. The results obtained from the experimental setup have been utilized as boundary conditions for CFD simulations. With the use of Eddy Dissipation method, methane-air-2-step reaction mechanism is used for modeling of natural gas as methane gas and the reaction mechanism has been modified for natural gas considering the natural gas properties to reveal the similarities and differences of both fuels in modeling. In addition, the combustion performances of natural gas with the use of full and periodic models, which are geometric models of the burner–boiler pair, are compared. Moreover, in order to reveal the effect of the hydrogen-enriched natural gas and pure hydrogen on the performance of low swirl burner–boiler considering the combustion emissions, four various gas contents (thermal load ratio: 75%NG + 25%H2, 50%NG + 50%H2, 25%NG + 75%H2, 100%H2) at the same thermal load have been investigated. The turbulent flames of the industrial low swirl burner have been studied numerically using ANSYS Fluent 16.0 for the solution of governing equations. The results obtained in this study show that with the utilizing Eddy Dissipation method, natural gas can be modeled as methane gas with well-known methane-air-2step reaction mechanism or as natural gas with modified methane-air-2step reaction mechanism with approximate results. Additionally, the use of periodic boundary condition, which enables studying with 1/4 of geometric model, gives satisfactory results with less number of meshes when compared to the full model. Furthermore, in the case of using hydrogen-enriched natural gas or pure hydrogen instead of natural gas as the fuel, the combustion emissions of the burner–boiler such as CO and CO2 are remarkably decreasing compared to the natural gas. However, the NOx emissions are significantly increasing especially due to thermal NO.