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We describe three distinct approaches to visualization for multiscale materials modelling research. These have been developed with the framework of the SimPhoNy FP7 EU-project, and complement each other in their requirements and possibilities. All have been integrated via wrappers to one or more of the simulation approaches within the SimPhoNy project. In this manuscript we describe and contrast their features. Together they cover visualization needs from electronic to macroscopic scales and are suited to simulations made on personal computers, workstations or advanced High Performance parallel computers. Examples as well as recommendations for future calculations are presented.

A Kozeny–Carman-based model of permeability for fibrous networks is proposed: the original model is extended by incorporating information about the local structure of the void space. Furthermore, it is demonstrated how in practice this added structural information can be retrieved from a three-dimensional digital image of a fibrous material. The proposed model is then validated for both foam- and water-deposited laboratory sheets of bleached kraft pulp (Scots pine) and chemi-thermo-mechanical pulp (CTMP, Norway spruce). The validation is carried out by comparing the model predictions against computationally determined permeability values. The related fluid-flow simulations are executed using the lattice-Boltzmann method together with high-resolution X-ray microtomography images. For both pulp materials, the sample sets had nearly equal porosities, but deviated substantially in their permeabilities. The proposed model was shown to improve prediction of permeability for the fibrous materials considered: the deviation between the predicted and computationally determined values was no more than 8%.

The MPI intercommunication framework was used for coupling of two lattice-Boltzmann solvers with suspended particles, which model advection and diffusion respectively of these particles in a carrier fluid. Simulation domain was divided into two parts, one with advection and diffusion, and the other with diffusion only (no macroscopic flow). Particles were exchanged between these domains at their common boundary by a direct process to process communication. By analysing weak and strong scaling, it was shown that the linear scaling characteristics of the lattice-Boltzmann solvers were not compromised by their coupling.

The lattice Boltzmann method is a well-established numerical approach for complex fluid flow simulations. Recently, general-purpose graphics processing units (GPUs) have become available as high-performance computing resources at large scale. We report on designing and implementing a lattice Boltzmann solver for multi-GPU systems that achieves 1.79 PFLOPS performance on 16,384 GPUs. To achieve this performance, we introduce a GPU compatible version of the so-called bundle data layout and eliminate the halo sites in order to improve data access alignment. Furthermore, we make use of the possibility to overlap data transfer between the host central processing unit and the device GPU with computing on the GPU. As a benchmark case, we simulate flow in porous media and measure both strong and weak scaling performance with the emphasis being on large-scale simulations using realistic input data.

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number $\mathrm{Re}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

Unlike conventional CFD methods, the lattice Boltzmann method (LBM) describes the dynamic behaviour of physical systems in a mesoscopic scale, based on discrete forms of kinetic equations. In addition to the classical collision-propagation scheme in which the physical and velocity spaces are coupled, finite-differences, finite volumes and finite-element schemes have been used for numerically solving the discrete kinetic equations. A major breakthrough in LB theory was the direct derivation of the LB equation from continuous kinetic equations, establishing a systematic link between the kinetic theory and the lattice Boltzmann method and determining the necessary conditions for the discretization of the velocity space. The lattices obtained by this method proved to be stable in flows over a wide range of parameters, by the use of high-order lattice Boltzmann schemes, leading to velocity sets which, when used in a discrete velocity kinetic scheme, ensures accurate recovery of the high-order hydrodynamic moments. This review presents the theoretical background of these kinetic methods. In particular, we focus on high-order discrete forms of the Boltzmann equation suitable for non-ideal fluids and on the lattice-Boltzmann collision-propagation method.

The lattice Boltzmann method is a well-established numerical approach for complex fluid flow simulations. Recently general-purpose graphics processing units have become accessible as high-performance computing resources at large-scale. We report on implementing a lattice Boltzmann solver for multi-GPU systems that achieves 0.69 PFLOPS performance on 16384 GPUs. In addition to optimizing the data layout on the GPUs and eliminating the halo sites, we make use of the possibility to overlap data transfer between the host CPU and the device GPU with computing on the GPU. We simulate flow in porous media and measure both strong and weak scaling performance with the emphasis being on a large scale simulation using realistic input data.

Hypothesis While multiphase flows, particularly droplet dynamics, are ordinary in nature as well as in industrial processes, their mathematical and computational modelling continue to pose challenging research tasks - patent approaches for tackling them are yet to be found. The lack of analytical flow field solutions for non-trivial droplet dynamics hinders validation of computer simulations and, hence, their application in research problems. High-speed videos and computer vision algorithms can provide a viable approach to validate simulations directly against experiments. Experiments Droplets of water (or glycerol-water mixtures) impacting on both hydrophobic and superhydrophobic surfaces were imaged with a high-speed camera. The corresponding configurations were simulated using a lattice-Boltzmann multiphase scheme. Video frames from experiments and simulations were compared, by means of computer vision, over entire droplet impact events. Findings The proposed experimental validation procedure provides a detailed, dynamic one-on-one comparison of a droplet impact. The procedure relies on high-speed video recording of the experiments, computer vision, and on a software package for the analyzation routines. The procedure is able to quantitatively validate computer simulations against experiments and it is widely applicable to multiphase flow systems in general.

Various types of DNA viruses are known to elicit the formation of a large nuclear viral replication compartment and marginalization of the cell chromatin. We used three-dimensional soft x-ray tomography, confocal and electron microscopy, combined with numerical modelling of capsid diffusion to analyse the molecular organization of chromatin in herpes simplex virus 1 infection and its effect on the transport of progeny viral capsids to the nuclear envelope. Our data showed that the formation of the viral replication compartment at late infection resulted in the enrichment of heterochromatin in the nuclear periphery accompanied by the compaction of chromatin. Random walk modelling of herpes simplex virus 1–sized particles in a three-dimensional soft x-ray tomography reconstruction of an infected cell nucleus demonstrated that the peripheral, compacted chromatin restricts viral capsid diffusion, but due to interchromatin channels capsids are able to reach the nuclear envelope, the site of their nuclear egress., published version, peerReviewed

From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein. peerReviewed

The usual lattice-Boltzmann schemes for fluid flow simulations operate with square and cubic lattices. Instead of relying on square lattices it is possible to use rectangular and orthorombic lattices as well. Schemes using rectangular lattices can be constructed in several ways. Here we construct a rectangular scheme, with the BGK collision operator, by introducing 2 additional discrete velocities into the standard D2Q9 stencil and show how the same procedure can be applied in three dimensions by extending the D3Q19 stencil. The weights and scaling factors for the new stencils are found as the solutions of the well-known Hermite quadrature problem, assuring isotropy of the lattice tensors up to rank four (Philippi et al., Phys. Rev. E 73(5):056702, 2006) This isotropy is a necessary and sufficient condition for assuring the same second order accuracy of lattice-Boltzmann equation with respect to the Navier---Stokes hydrodynamic equations that is found with the standard D2Q9 and D3Q19 stencils. The numerical validation is done, in the two-dimensional case, by using the new rectangular scheme with D2R11 stencil for simulating the Taylor---Green vortex decay. The D3R23 stencil is numerically validated with three-dimensional simulations of cylindrical sound waves propagating from a point source.

Raindrops that impact on soil surface affect the pore structure and form compact soil surface seals. Damaged pore structure reduces water infiltration which can lead to increased soil erosion. We introduce here methods to characterize the properties of surface seals in a detailed manner. These methods include rainfall simulations, x-ray microtomography, image analysis and pore-scale flow simulations. Methods were tested using clay soil samples, and the results indicate that the sealing process changes several properties of the pore structure.

In fluid mechanics, multicomponent fluid systems are generally treated either as homogeneous solutions or as completely immiscible parts of a multiphasic system. In immiscible systems, the main task in numerical simulations is to find the location of the interface evolving over time, driven by normal and tangential surface forces. The lattice-Boltzmann method (LBM), on the other hand, is based on a mesoscopic description of the multicomponent fluid systems, and appears to be a promising framework that can lead to realistic predictions of segregation in non-ideal mixtures of partially miscible fluids. In fact, the driving forces in segregation are of a molecular nature: there is competition between the intermolecular forces and the random thermal motion of the molecules. Since these microscopic mechanisms are not accessible from a macroscopic standpoint, the LBM can provide a bridge linking the microscopic and macroscopic domains. To this end, the first purpose of this article is to present the kinetic equations in their continuum forms for the description of the mixing and segregation processes in mixtures. This paper is limited to isothermal segregation; non-isothermal segregation was discussed by Philippi et al. (Phil. Trans. R. Soc., vol. 369, 2011, pp. 2292–2300). Discretization of the kinetic equations leads to evolution equations, written in LBM variables, directly amenable for numerical simulations. Here the dynamics of the kinetic model equations is demonstrated with numerical simulations of a spinodal decomposition problem with dissolution. Finally, some simplified versions of the kinetic equations suitable for immiscible flows are discussed.

Feasibility of a method for finding flow permeability of porous materials, based on combining computerised X-ray micro-tomography and numerical simulations, is assessed. The permeability is found by solving fluid flow through the complex 3D pore structures obtained by tomography for actual material samples. We estimate overall accuracy of the method and compare numerical and experimental results. Factors contributing to uncertainty of the method include numerical error arising from the finite resolution of tomographic images and the rather small sample size available with the present tomographic techniques. The total uncertainty of computed values of permeability is, however, not essentially larger than that of experimental results. We conclude that the method provides a feasible alternative for finding fluid flow properties of the kind of materials studied. It can be used to estimate all components of permeability tensor and is useful in cases where direct measurements are not achievable. Analogous metho...

During the last decade, the lattice-Boltzmann method (LBM) as a valuable tool in computational fluid dynamics has been increasingly acknowledged. The widespread application of LBM is partly due to the simplicity of its coding. The most well-known algorithms for the implementation of the standard lattice-Boltzmann equation (LBE) are the two-lattice and two-step algorithms. However, implementations of the two-lattice or the two-step algorithm suffer from high memory consumption or poor computational performance, respectively. Ultimately, the computing resources available decide which of the two disadvantages is more critical. Here we introduce a new algorithm, called the swap algorithm, for the implementation of LBE. Simulation results demonstrate that implementations based on the swap algorithm can achieve high computational performance and have very low memory consumption. Furthermore, we show how the performance of its implementations can be further improved by code optimization.

The lattice-Boltzmann (LB) method is commonly used for the simulation of fluid flows at the hydrodynamic level of description. Due to its kinetic theory origins, the standard LB schemes carry more degrees of freedom than strictly needed, e.g., for the approximation of solutions to the Navier-stokes equation. In particular, there is freedom in the details of the so-called collision operator. This aspect was recently utilized when an entropic stabilizer, based on the principle of maximizing local entropy, was proposed for the LB method [I. V. Karlin, F. Bosch, and S. S. Chikatamarla, ¨ Phys. Rev. E 90, 031302(R) (2014)]. The proposed stabilizer can be considered as an add-on or extension to basic LB schemes. Here the entropic stabilizer is investigated numerically using the perturbed double periodic shear layer flow as a benchmark case. The investigation is carried out by comparing numerical results obtained with six distinct LB schemes. The main observation is that the unbounded, and not explicitly controllable, relaxation time for the higher-order moments will directly influence the leading-order error terms. As a consequence, the order of accuracy and, in general, the numerical behavior of LB schemes are substantially altered. Hence, in addition to systematic numerical validation, more detailed theoretical analysis of the entropic stabilizer is still required in order to properly understand its properties. peerReviewed

The lattice-Boltzmann equation is a low-order approximation of the Boltzmann equation (BE) and its solution involve errors affected by high-order moments that cannot be controlled or retrieved with this approximation. These 'ghost' moments contribute to instability issues. The regularization method is discussed in this paper in connection with kinetic projections and we show that solutions of the LB equations, with improved stability ranges, may be found, in a systematic way, based on increasingly order projections of the continuous Boltzmann equation (BE) onto subspaces generated by finite set of Hermite polynomials. publishedVersion

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases. Published by AIP Publishing. acceptedVersion

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of the tracer pulse. The lattice-Boltzmann method is a popular tool for simulating flow through porous materials, and for similar reasons it is an attractive tool for modeling the matrix diffusion phenomenon. In this work sorption of the tracer particles is also included in such simulations with this method. The proposed approach is compared with conventional methods for modeling matrix diffusion phenomena.

Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of a tracer pulse. Analytical and numerical methods exist for modeling matrix diffusion, but there are still some features of this phenomenon, which are difficult to address using traditional approaches. To this end we propose to use the lattice-Boltzmann method with point-like tracer particles. These particles move in a continuous space, are advected by the flow, and there is a stochastic force causing them to diffuse. This approach can be extended to include particle-particle and particle-wall interactions of the tracer. Numerical results that can also be considered as validation of the LBM approach, are reported. As the reference we use recently-derived analytical solutions for the breakthrough curve of the tracer.

To assess whether it is possible to make accurate vertical measurements of the jaws from panoramic radiographs.Five dry skulls were shifted 5 mm forwards and backwards and tilted 5 degrees up and down in the sagittal plane. Panoramic radiographs of each skull were obtained in nine different positions. In the maxilla, three reference lines were used and vertical measurements were made at the distal surfaces of the first premolar and first molar and in the midline. In the mandible, measurements were made at the distal surfaces of the first premolar and first molar, and at the mental foramen on both sides, and in the midline. The points and lines were marked manually and the radiographs were digitized, magnified and measured.Sagittal shifting and tilting had only a slight effect on measurements in the mandible. Sagittal tilting of the head had the greatest effect on all the measurements made from the line between the articular eminences to the alveolar crest, as well as measurements in the maxillary midline.The line between the articular eminences is unsuitable as a reference line for measurements of the tooth-bearing areas. A slight misalignment of the head does not significantly affect the vertical measurements in the mandible or of the posterior maxilla if the reference lines are in the same vertical plane as the teeth.

We introduce a mass-flux-based inlet boundary condition for the lattice-Boltzmann method. The proposed boundary condition requires minimal amount of boundary data, it produces a steady-state velocity field which is accurate close to the inlet even for arbitrary inlet geometries, and yet it is simple to implement. We demonstrate its capability for both simple and complex inlet geometries by numerical experiments. For simple inlet geometries, we show that the boundary condition provides very accurate inlet velocities when Re less than or similar to 1. Even with moderate Reynolds number, the inlet velocities are accurate for practical purposes. Furthermore, the potential of our boundary condition to produce inlet velocities which convincingly adapt to complex inlet geometries is highlighted with two specific examples. Copyright (C) 2009 John Wiley & Sons, Ltd.

In a series of 69 human cadavers (age range 18-95 years), the tortuosity of the lingual artery and its association to age, sex, death of cardiovascular disease and general atherosclerotic state as assessed at necropsy were studied. The tortuosity increased significantly with age, but there were no sex differences. Within the three age groups there were no significant associations between arterial tortuosity and death from cardiovascular disease or general atherosclerotic state.

The lattice Boltzmann (LB) method, based on mesoscopic modeling of transport phenomena, appears to be an attractive alternative for the simulation of complex fluid flows. Examples of such complex dynamics are multiphase and multicomponent flows for which several LB models have already been proposed. However, due to theoretical or numerical reasons, some of these models may require application of high-order lattice-Boltzmann equations (LBEs) and stencils. Here, we will present a derivation of LBEs from the discrete-velocity Boltzmann equation (DVBE). By using the method of characteristics, high-order accurate equations are conveniently formulated with standard numerical methods for ordinary differential equations (ODEs). In particular, we will derive implicit LB schemes due to their stability properties. A simple algorithm is presented which enables implementation of the implicit schemes without resorting to, e.g. change of variables. Finally, some numerical experiments with high-order equations and stencils together with two specific multiphase models are presented.

Several authors have determined clinically the width of attached gingiva (AG) over the deciduous and early permanent dentitions in children. They have noticed that when comparing the width of AG over deciduous teeth to the width of AG over the succeeding newly erupted permanent teeth, a clear diminishing in AG can be seen. The aim of the present cross-sectional study was to assess the width of radiologically-defined AG (RAG) over the permanent teeth of 6-, 10- and 12-year-old children. Altogether 123 subjects were recruited. The mucogingival junction (MGJ) was revealed with Schiller's iodine solution and marked over each tooth with a piece of metal wire before taking a panoramic radiograph. The width of RAG over permanent teeth was measured from the radiographs as the midfacial distance from the cementoenamel junction to the mucogingival junction. When comparing the width of RAG over 1st molars and the 1st and 2nd incisors, statistically significant differences were found between 6- and 10-year-olds, between 6- and 12-year-olds and between 10- and 12-year-olds. For the 1st maxillary incisor, the difference in width was not statistically significant between ages 10 and 12 years. The findings seem to justify the conclusion that an inadequate width of AG will correct itself from 6 to 12 years of age without interference by means of periodontal surgery.

We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is further demonstrated with numerical experiments.

The anatomy of the facial, transverse facial and infraorbital arteries and their tortuosity was studied in 69 human cadavers (age range 18-95 years). The types of facial vascularisation were divided into four categories according to the gradually diminishing relative dominance of the facial artery. Type A, in which the facial artery was dominant, comprised 22% of the cases; type B 49%; type C 20%; and the variant of the hypoplastic facial artery, type D, 9% of the cases. The type of vascularisation was not dependent on age or sex. The tortuosity of all three arteries showed a statistically significant increase with age. A weak correlation was found between the relative dominance and the tortuosity of the facial artery.

Summary The use of cylindrical image layers in pantomographic roentgen diagnosis of fractures of the middle third of the face and base of the skull, is presented. Three-dimensional pictures are presented from the horizontal, backward tilt (retroversion) and forward tilt (anteversion) projections as well as the projection of the base of the skull, which yield most information. Of these, the horizontal projection may be considered to be the projection which provides the best basic picture of the middle third of the face. The backward tilt projection reveals the bone structures of the central area and fractures in them best. Fractures in the lateral region are best seen in the forward tilt projection. The radiography of the base of the skull and the lateral walls on one film also presents a new application of the pantomographic technique. The positions of the patient used in taking these roentgenograms with a new pantomographic device developed for patients in a horizontal position are explained, and photographs of them presented. The future aims of this investigation series are referred to in the discussion.

Central neurilemmomas involving the jaws are rare benign tumours probably originating from the neural sheath. We report 2 cases involving the posterior part of the mandible. The 1st case (male, age 20 years) had no symptoms of a tumour, which was discovered by accident in an orthopantomogram. The 2nd case (female, age 66 years) had experienced pain because of a tumour. The radiographic appearance of these tumours seemed to be non-specific. These 2 neurilemmomas have recurred, probably due to incomplete primary removal of the tumour.

In a series of 79 autopsies performed on subjects aged from 18 to 95 years occlusions in the external carotid, maxillary and inferior alveolar arteries were rare: only two cases were found in the maxillary and one in the inferior alveolar arteries. Tortuosity of the arteries increased with age, being most extensive in the external carotid and least in the inferior alveolar artery. Variations in the diameter of the maxillary artery occurred in 11 persons (14%), the incidence increasing with age. The youngest person showing such changes was aged 55 years. The average diameter of the arterial lumen of the inferior alveolar artery decreased with advancing age. This narrowing of the lumen also correlated with the loss of teeth. Calcified atherosclerotic plaques in the carotid bifurcation were present in 59% of the cases studied. In persons aged over 60 years a correlation was found between the carotid calcifications and coronary artery disease.

Simplicity of coding is usually an appealing feature of the lattice-Boltzmann method (LBM). Conventional implementations of LBM are often based on the two-lattice or the two-step algorithm, which however suffer from high memory consumption and poor computational performance, respectively. The aim of this work was to identify implementations of LBM that would achieve high computational performance with low memory consumption. Effects of memory addressing schemes were investigated in particular. Data layouts for velocity distribution values were also considered, and they were found to be related to computational performance. A novel bundle data layout was therefore introduced. Addressing schemes and data layouts were implemented for the Lagrangian, compressed-grid (shift), swap, two-lattice, and two-step algorithms. Implementations were compared for a wide range of fluid volume fractions. Simulation results indicated that indirect addressing implementations yield high computational performance. However, they achieved low memory consumption only for very low fluid volume fractions. Semi-direct addressing implementations could also provide high computational performance. The bundle data layout was found to be competitive, sometimes by a wide margin, in all the cases considered.

The present study reports a case in which a clinically asymptomatic radiolucent change surrounded by a sclerotic wall developed below the second molar in the mandible of a middle-aged man. The change was diagnosed as a typical case of Stafne bone cavity. In the earlier literature, development of a mandibular bone cavity has been described in only three patients. The appearance of bone cavities in a mandible that has previously been found normal indicates that these defects are not congenital but developmental processes.

Because of their degree of mobility, the first and second cervical vertebrae differ both anatomically and functionally from the other vertebrae. It follows therefore, that trauma of these two vertebrae create fractures of a singular nature (HOHL 1964, BYRNE et al 1972 and TERMANSEN 1974). In road accidents especially, great pressure may be directed exclusively to the cervical vertebrae. The initial state of these injuries cannot always be determined due, for instance, to the unconscious state of the victim.