Equilibrium Moments Research Articles

Multiple-relaxation-time lattice Boltzmann model for double-diffusive convection with Dufour and Soret effects

This paper proposes a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for double-diffusive convection with Dufour and Soret (cross-diffusion) effects. The main strategy is to recover the Dufour and Soret terms by modifying the second-order equilibrium moments of the temperature and concentration distribution functions in the moment space, which is consistent with the philosophy of the LB method. As a result of this strategy, the present model is simpler and easier to implement when compared with the existing LB models. Numerical simulations show that double-diffusive convection with Dufour and Soret effects can be well simulated.

Lattice Boltzmann model with adjustable equation of state for coupled thermo-hydrodynamic flows

A novel lattice Boltzmann (LB) model with adjustable equation of state (EOS) is developed in this work for simulating coupled thermo-hydrodynamic flows. The velocity field is solved by the recently developed multiple-relaxation-time (MRT) LB equation for density distribution function (DF), by which an adjustable EOS can be recovered. As to the temperature field, a novel MRT LB equation for total energy DF is directly developed at the discrete level. By introducing a density-DF-related term into this LB equation and devising the equilibrium moment function for total energy DF, the viscous dissipation and compression work are consistently considered, and by modifying the collision matrix, the targeted energy conservation equation is recovered without deviation term. The full coupling of thermo-hydrodynamic effects is achieved via the adjustable EOS and the viscous dissipation and compression work. The present LB model is developed on the basis of the standard lattice, and various EOSs can be adopted in real applications. Moreover, both the Prandtl number and specific heat ratio can be arbitrarily adjusted. Furthermore, boundary condition treatment is also proposed on the basis of the judicious decomposition of DF into its equilibrium, force (source), and nonequilibrium parts. The local conservation of mass, momentum, and energy can be strictly satisfied at the boundary node. Numerical simulations of thermal Poiseuille and Couette flows are carried out with three different EOSs, and the numerical results are in good agreement with the analytical solutions. Then, natural convection in a square cavity with a large temperature difference is simulated for the Rayleigh number from 103 up to 108. Good agreement between the present and previous numerical results is observed, which further validates the present LB model for coupled thermo-hydrodynamic flows.

Computer simulation of the «engine - working machine» mechanical system

There was investigated the application for the purpose of diagnosing the technical condition of the unit, the internal combustion engine (ICE) - the working machine (WM) of advanced computer models of internal combustion engines with the additional function of determining the technical condition of machines (mechanisms) driven by the internal combustion engine. The mechanical system «ICE-working machine» is considered as a three- and two-mass system with lumped parameters. Equations of equilibrium moments are made that act on the selected concentrated masses, taking into account various nonlinearities (dry and viscous friction, dead zone, etc.), elasticity of the shafts and joints. The block diagrams of the ICE-PM system in the form of transfer functions are given. A computer simulation of this system was carried out with the presentation of the obtained computer structural diagrams and graphs of dynamic processes (angular velocities and shaft accelerations, etc.). Introducing into these schemes the values of the parameters characteristic of a specific unit ICE-PM by varying the values of different moments, it is possible in the static and dynamic modes to evaluate their influence on the technical state of ICE-PM. The use of a computer model allows to take into account the influence of these factors on informative diagnostic signals reflecting the technical condition of the internal combustion engine, since the level of signals characterizing the power indicators of the internal combustion engine is significantly higher than the level of signals reflecting elasticity and nonlinearity. The developed computer block diagram can be directly used in diagnostic complexes based on microprocessor systems, microcontrollers and microcomputers for diagnosing internal combustion engines and working machines under operational conditions.

Multiple-relaxation-time lattice Boltzmann model for simulating double-diffusive convection in fluid-saturated porous media

A multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating double-diffusive convection in porous media at the representative elementary volume scale. In the model, the equilibrium moments of the temperature and concentration distributions have been modified, which makes the effective thermal diffusivity and heat capacity ratio as well as the effective mass diffusivity and porosity decoupled. Numerical tests demonstrate that the present model can serve as an accurate numerical method for simulating double-diffusive convection in porous media.

ANALISIS PEMILIHAN KARTU GSM PRABAYAR DI KALANGAN MAHASISWA DENGAN PENDEKATAN RANTAI MARKOV (Studi Kasus pada Mahasiswa Universitas Bunda Mulia, Jurusan Manajemen, Semester 8)

<p>The many variety of GSM card and services enables the customers to change brands easily. This has caused a tighter competition between the brands. In order to face the competition, GSM operators need to understand the customers’ perception and judgment on the preference scale toward the atribute of the products and services. GSM card operators also need to understand the brand switching pattern and its competitior position in analysing the market today or in the future. By the analyses, the operator hopes to acquired some description of their position and product situation among the tight competition between4 operators. The description can then be used as input in determining the marketing strategies for the future. The objects in this research are analyzed using Markov’s chain method on brand switching. The analysis on customer’s judgments on the product attributes and services is aided by the use of descriptive statistics. The case study is performed on the 8th semester students of Bunda Mulia University, majoring in Management. The population is 105 students. The research method is by using survey and the type of research is descriptive research. The data collecting technique is through the use of questionnaire and literary review. The results shows that the source of reference of the customer’s choice which is 3.81% from the event, 12.38% from families, 29.52 from commercials, 45.71% from friends, and 8.57% from other unspecified sources. The prediction of the market from the five operators in consequential orders are (0.0695, 0.6401, 0.0295, 0.1207, 0.1402), and the prediction of equilibrium moment are (0.0218, 0.5805, 0.0264, 0.117, 0.2543).The biggest market share is owned by XL which is 64.01%, and the smallest is by mentari with the share of 2.95%. The biggest sorce of reference for the students in choosing operators is from promotion events with the percentage of 30.81% and from friends is only 19.88%. Looking at this result it can be suggested that operators should increase their services and increase their promotion events in gaining the market share of GSM users.</p><p> </p><p>Keyword : GSM cards, brand switching, Markov’s chain, market share</p>

Improving the low Mach number steady state convergence of the cascaded lattice Boltzmann method by preconditioning

Cascaded lattice Boltzmann method (LBM) involves the use of central moments in a multiple relaxation time formulation in prescribing the collision step. When the goal is to simulate low Mach number stationary flows, the greater the disparity between the magnitude of fluid speed and the sound speed, the higher is the numerical stiffness, which results in relatively large number of time steps for convergence of the LBM. One way to improve the steady state convergence of the scheme is to precondition the cascaded LBM, which reduces the disparities between the characteristic speeds or equivalently those between the eigenvalues of the system. In this paper we present a new preconditioned, two-dimensional cascaded LBM, where a preconditioning parameter is introduced into the equilibrium moments as well as the forcing terms. Particular focus is given to preconditioning differently the moments due to forcing at first and second orders so as to avoid any spurious effects in the emergent macroscopic equations. A Chapman–Enskog analysis performed on this approach shows consistency to the preconditioned Navier–Stokes equations. This modified central moment based scheme is then validated for accuracy by comparison against prior analytical or numerical results for certain benchmark problems, including those involving spatially variable body forces. Finally, significant steady state convergence acceleration of the preconditioned cascaded LBM is demonstrated for a set of characteristic parameters.

The Effects of Angular Velocity and Training Status on the Dynamic Control Equilibrium.

Thigh muscle imbalances may impair sports performance and cause injuries. Common diagnostic parameters of knee muscle balance lack practical applicability. This cross-sectional study aimed to evaluate the effects of angular velocity and training status on the dynamic control ratio at the equilibrium point representing the intersection of eccentric knee flexion and concentric knee extension moment-angle curves. 58 trained and 58 untrained male participants (22.1 years, 82.4 kg) performed concentric and eccentric knee flexions (prone position) and extensions (supine position) on an isokinetic dynamometer operating at 30 and 150°/s. Trained participants had significantly higher DCRe moments at all angular velocities compared with their untrained counterparts (trained 30,150 : 1.86, 1.90 Nm/kg; untrained 30,150 : 1.56, 1.60 Nm/kg; p<0.001, partial η²=0.345). Dynamic control equilibrium moments rose with increasing velocity (p=0.001, partial η²=0.095), whereas dynamic control equilibrium angles (trained 30,150 : 28.9, 30.8°; untrained 30,150 : 26.1, 27.0°) were influenced by training status (p=0.004, partial η²=0.072), but not by angular velocity (p=0.241, partial η²=0.012). Dynamic control equilibrium parameters detect thigh muscle balance and reflect the trained participants' capacity to resist high eccentric knee flexor moments, especially during fast movements. Direct links to muscular loading during sprinting are conceivable, but warrant further investigation. The assessment of dynamic control equilibrium moments and angles might help physiotherapists and coaches to improve functional muscle screening, injury prevention and purposeful return to sport.

A hydrodynamically-consistent MRT lattice Boltzmann model on a 2D rectangular grid

A multiple-relaxation time (MRT) lattice Boltzmann (LB) model on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LB model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the Navier–Stokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the two-dimensional decaying Taylor–Green vortex flow and lid-driven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model (Bouzidi et al. (2001) [28]) are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.

Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow

In this work, a third-order Chapman–Enskog analysis of the multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for multiphase flow is performed for the first time. The leading terms on the interaction force, consisting of an anisotropic and an isotropic term, are successfully identified in the third-order macroscopic equation recovered by the lattice Boltzmann equation (LBE), and then new mathematical insights into the pseudopotential LB model are provided. For the third-order anisotropic term, numerical tests show that it can cause the stationary droplet to become out-of-round, which suggests the isotropic property of the LBE needs to be seriously considered in the pseudopotential LB model. By adopting the classical equilibrium moment or setting the so-called “magic” parameter to 1/12, the anisotropic term can be eliminated, which is found from the present third-order analysis and also validated numerically. As for the third-order isotropic term, when and only when it is considered, accurate continuum form pressure tensor can be definitely obtained, by which the predicted coexistence densities always agree well with the numerical results. Compared with this continuum form pressure tensor, the classical discrete form pressure tensor is accurate only when the isotropic term is a specific one. At last, in the framework of the present third-order analysis, a consistent scheme for third-order additional term is proposed, which can be used to independently adjust the coexistence densities and surface tension. Numerical tests are subsequently carried out to validate the present scheme.

A lattice-Boltzmann scheme of the Navier–Stokes equation on a three-dimensional cuboid lattice

The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or a cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, either by adding a free parameter in the definition of moments or by extending the equilibrium moments. These models satisfy all isotropy conditions and are fully consistent to the Navier–Stokes equations. Here we developed a lattice Boltzmann model on a 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed the moment equations, derived from our MRT–LBM model through the Chapman–Enskog analysis, to be fully consistent with the Navier–Stokes equations. A second-order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities. The form of the second-order term and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the shear viscosity can be adjusted, independent of the stress-moment relaxation parameter, thus potentially improving the numerical stability of the model. The resulting cuboid MRT–LBM model is then validated through benchmark simulations using the laminar channel flow, the turbulent channel flow, and the 3D time-dependent, energy-cascading Taylor–Green vortex flow. The second-order accuracy of the proposed model is also demonstrated. The aspect ratios for numerical stability appear to be constrained at high flow Reynolds numbers, especially for turbulent flow simulations, an aspect requiring further investigation.

Experimental values of the rotational and vibrational constants of deuterated silyl fluoride

ABSTRACTAccurate experimental values of the αA and αB rotation–vibration interaction, and ωi, xij and gij vibrational constants have been extracted from the most recent high-resolution Fourier transform infrared and millimetre-wave measurements in the spectra of the prolate symmetric top SiD3F, between 400 and 2000 cm−1. From the experimental values of the ground state rotational and rovibrational interaction parameters, accurate equilibrium rotational constants have been derived: Ae = 1.432326 (12) cm−1 and Be = 0.4112012 (45) cm−1 for silyl fluoride. The effective ground state structure has also been determined from the observed moments of inertia of SiD3F: r0(Si-D) = 1.4755 (29) Å; r0(Si-F) = 1.5931 (26) Å; θ0(DSiD) = 110.47 (32)° and θ0(DSiF) = 108.45 (56)°. A merge of equilibrium moments of 28SiH3F and 28SiD3F yielded an experimental equilibrium structure of silyl fluoride. This geometry has been found in good agreement with semi-experimental median values, as well as with the recent semi-experimental ab initio equilibrium structure obtained using all data available of the various isotopic species of silyl fluoride.

New lifting relations for estimating LBM distribution functions from corresponding macroscopic quantities, based on equilibrium and non-equilibrium moments

Due to superior accuracy and stability of multiple relaxation time (MRT) collision operator over its single relaxation time (SRT) counterpart, new lifting relations are proposed here to construct single particle distribution functions for MRT-LBM from macroscopic variables. Using these lifting relations, a new hybrid FVM-LB method is presented (called Finite type-LB hybrid method), which is consistent with MRT-LBM. In this new hybrid method, single-particle distribution functions in MRT-LBM sub-domain boundaries are computed, using equilibrium and non-equilibrium moments. These moments are computed in Navier–Stokes/FVM sub-domain boundaries, using macroscopic variables and their derivatives. The new method is validated by solving three benchmark problems, i.e., two- and three-dimensional lid driven cavity flows and two-dimensional unsteady flow around a squared section cylinder. These problems are analyzed with pure FVM, pure LBM, and Finite type-LB hybrid method (FTLBHM) and the related results are compared with each other and with benchmark data. These comparisons clearly demonstrate the accuracy of the present novel methodology for simulating steady/unsteady flow fields in two and three dimensions.

Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media

In this paper, a two-dimensional eight-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman–Forchheimer-extended Darcy model. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous matrix are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman–Enskog analysis, the incompressible generalized Navier–Stokes equations can be recovered. Numerical simulations of several typical porous flows are carried out to validate the present MRT-LB model. It is found that the present numerical results agree well with the analytical solutions and/or other numerical results reported in the literature.

Electromagnetic Properties of Melt-Grown YBaCuO Superconductors Doped by Gd and Sm

Electromagnetic properties of YBa2Cu3Oy samples melt-grown in air and doped with small amounts of light rare earth (LRE) ions Gd and Sm were studied. The LRE doping creates a point-like disorder contributing to the second peak on the magnetization curve. In the eld range of the second peak the average magnetic moment, Mav, deduced from the magnetization curves exhibited strong uctuations. Mav is commonly regarded as an equilibrium moment close to the thermodynamic reversible one, obeying in intermediate elds a logarithmic eld dependence. However, in our experiments Mav(B) curves failed to follow such a dependence below irreversibility line. Mav(B) curves deduced from rather static measurements, done by SQUID magnetometer still showed the disturbance but signi cantly weaker. It indicates that this feature re ects the vortex dynamics in the second peak region. Its scaling with temperature was found to coincide with that of the pinning force.

The Gravity Field and Interior Structure of Enceladus

The small and active Saturnian moon Enceladus is one of the primary targets of the Cassini mission. We determined the quadrupole gravity field of Enceladus and its hemispherical asymmetry using Doppler data from three spacecraft flybys. Our results indicate the presence of a negative mass anomaly in the south-polar region, largely compensated by a positive subsurface anomaly compatible with the presence of a regional subsurface sea at depths of 30 to 40 kilometers and extending up to south latitudes of about 50°. The estimated values for the largest quadrupole harmonic coefficients (10(6)J2 = 5435.2 ± 34.9, 10(6)C22 = 1549.8 ± 15.6, 1σ) and their ratio (J2/C22 = 3.51 ± 0.05) indicate that the body deviates mildly from hydrostatic equilibrium. The moment of inertia is around 0.335MR(2), where M is the mass and R is the radius, suggesting a differentiated body with a low-density core.

A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media

In this paper, a two-dimensional (2D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating convection heat transfer in porous media at the representative elementary volume scale. In the model, a D2Q9 MRT-LB equation is adopted to simulate the flow field, while a D2Q5 MRT-LB equation is employed to simulate the temperature field. The generalized model is employed to model the momentum transfer, and the effect of the porous media is considered by introducing the porosity into the equilibrium moments, and adding a forcing term to the MRT-LB equation of the flow field in the moment space. The present MRT-LB model is validated by numerical simulations of several 2D convection problems in porous media. The present numerical results are in excellent agreement with the analytical solutions and/or the well-documented data reported in previous studies. It is also found that the present MRT-LB model shows better numerical stability than the LBGK model.

Studying Architectural Structures Using BIM Tools

Structure is an essential component of architecture, and has always been. However, studying building structures appears to be deceptively complex. This stems from the roles and meanings that buildings possess in human history and civilizations. Buildings provide shelter, inspire productivity, embody cultural history, and certainly play an important part in many aspects of life. In fact, the role of architectural structures is constantly changing in building design as buildings today are life support systems, communication and data terminals, centers of education, justice, and community, and so much more. Thus, for AEC (Architecture, Engineering, and Construction) students, the subject is quite often marked by difficulty. Knowledge, technology and information sharing encompass areas that have significantly affected the learning process for 21 st century students. In this environment, computational and simulation tools play a vital supporting and inspiring role. This research proposes a method to develop and enhance the understanding of fundamental principles of architectural and structural analysis using Building Information Modeling (BIM) tools. Without the traditional teaching emphasis on first understanding single elements such as beams, columns, bearing walls, etc., two dimensionally, using the laws of statics and strength of materials, this research will utilize BIM tools to help students create whole three dimensional structural systems and then investigate structural solutions. BIM tools enhance the understanding of structural analysis fundamentals such as the force equilibrium, support reactions, shear force, and bending moment diagrams in an integrated and much inspiring fashion. This approach will allow AEC students to advance a deep learning and long-term retention in studying architectural structures. Understanding the whole structural systems concepts at an earlier stage will enable students to think and later practice in an integrated fashion to meet the demands of today's as well as tomorrow's high-efficient building structures.

A statistically accurate modified quasilinear Gaussian closure for uncertainty quantification in turbulent dynamical systems

We develop a novel second-order closure methodology for uncertainty quantification in damped forced nonlinear systems with high dimensional phase-space that possess a high-dimensional chaotic attractor. We focus on turbulent systems with quadratic nonlinearities where the finite size of the attractor is caused exclusively by the synergistic activity of persistent, linearly unstable directions and a nonlinear energy transfer mechanism. We first illustrate how existing UQ schemes that rely on the Gaussian assumption will fail to perform reliable UQ in the presence of unstable dynamics. To overcome these difficulties, a modified quasilinear Gaussian (MQG) closure is developed in two stages. First we exploit exact statistical relations between second order correlations and third order moments in statistical equilibrium in order to decompose the energy flux at equilibrium into precise additional damping and enhanced noise on suitable modes, while preserving statistical symmetries; in the second stage, we develop a nonlinear MQG dynamical closure which has this statistical equilibrium behavior as a stable fixed point of the dynamics. Our analysis, UQ schemes, and conclusions are illustrated through a specific toy-model, the forty-modes Lorenz 96 system, which despite its simple formulation, presents strongly turbulent behavior with a large number of unstable dynamical components in a variety of chaotic regimes. A suitable version of MQG successfully captures the mean and variance, in transient dynamics with initial data far from equilibrium and with large random fluctuations in forcing, very cheaply at the cost of roughly two ensemble members in a Monte-Carlo simulation.

Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems

Limit equilibrium methods, satisfying both force and moment equilibrium can be formulated using assumptions on the internal variables or the external variables. Even though most stability methods are based on force and moment equilibrium, as well as the Mohr–Coulomb yield criterion, there are great differences between the results of the different formulations due to variations in the assumptions. The authors believe that the use of the interslice force function f(x), the thrust line or the base normal forces should provide an equivalent concept at the ultimate/failure state. In the present study, the authors have used the well-known bearing capacity solutions to determine f(x), the thrust line and the base normal forces for a “horizontal slope”. The equivalence between the different formulations under the ultimate condition is demonstrated. It is shown that it is not important which forces are used in the stability formulation, external boundary forces or internal forces, if only that the ultimate state is considered. It is also demonstrated in the present paper that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution using a classical bearing capacity problem.

Parâmetros físicos do solo relacionados com o avanço da frente de molhamento

Este estudo visou contribuir, no âmbito metodológico, nas áreas da ciência do solo e da irrigação, notadamente na microirrigação na obtenção "in situ" de parâmetros físicos e hídricos do Argissolo Vermelho Distrófico arênico (PVd). Foi projetado um sistema "multigotejador" cuja aplicação está vinculada aos princípios do "Método do Gotejador" na obtenção da condutividade hidráulica K(h) e da curva de retenção de água no solo q(h). Vazões aplicadas de 2, 4 e 8 L h-1 e suas respectivas áreas de molhamento e de saturação, foram medidas no momento do equilíbrio dinâmico. O valor médio de sorptividade calculado foi de 2,68 cm h-0,5, sendo obtidos os valores de h = 2,22, b = 0,44 e hw = -2,29 cm de H2O. Usando-se os valores dos parâmetros do solo, a curva característica de retenção de água no solo (CCRAS) e a função da condutividade hidráulica em função do conteúdo de água do solo, foram estimadas e representadas graficamente. A curva característica obtida com dados experimentais de campo não foi igual àquela obtida em laboratório, conforme metodologia padrão, mas foi possível obter uma função exponencial que permite corrigir os valores da umidade volumétrica do solo.