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As interconnects dominate circuit performance in modern FPGAs, placement becomes a crucial stage for timing closure. Traditional FPGA placers seldom consider the timing constraints, and thus may lead to illegal routing solutions. In this paper, we present an incremental timing-driven placement flow for advanced FPGAs. First, a timing-based global placement strategy is designed to guide heterogeneous blocks to desired locations with satisfied timing constraints. Then, a timing-aware packing algorithm is developed to mitigate the design complexity while improving the timing results. Finally, we propose a critical path-based optimization method to generate optimized layout without timing violations. We evaluate our algorithm based on industrial circuits using an advanced FPGA device. The experimental results show that our placer achieves an 5.1% improvement in worst slack, and produces placements that require 16.7% less time to route when compared with the leading commercial tool Xilinx Vivado.

The random packing of aggregate particles is an important factor affecting the mechanical properties of concrete at the mesoscopic scale. In the current study, a meso-mechanical pretreatment algorithm is developed to construct the random ellipsoidal aggregate model for the mesoscopic structure of fully graded concrete. The Fuller curve combined with equivalent diameter is adopted to ensure equality between the gradation and content of the random ellipsoidal aggregates and those of the actual geometric aggregates. A ‘removing occupied space’ method is proposed to improve the packing efficiency based on the background grids strategy. A modified search algorithm consisting of rough and fine detection for determining the overlaps is proposed to improve the optimised simulation of the meso-structure of cement-based composites. A random ellipsoidal aggregate model with different aspect ratios of ellipsoid is developed and compared with the existing algorithms to test the efficiency of the new pretreatment algorithm. The effect of the ellipsoidal shape on the random packing fraction is investigated based on the proposed pretreatment algorithm. The pretreatment algorithm proposed greatly improves the efficiency of packing and provides a powerful tool for the realisation of three-dimensional large-scale numerical meso-concrete.

The present study suggests a technique to estimate the burn rate of non-aluminized propellant compositions. A random packing algorithm is used to generate a three-dimensional propellant pack consisting of spherical Ammonium perchlorate (AP) particles and Hydroxyl-terminated poly butadiene (HTPB) binder. Intercept lengths of AP and HTPB were obtained by slicing the propellant pack and lines drawn on the sliced planes. The average intercept lengths were recorded and then used as thickness of AP and binder sandwich propellants. A discussion on the choice of parameters is made for both AP monopropellant flame and the diffusion flame. Comparison of burn rates of computational results is done with experimental studies reported in literature. A reasonable match has been obtained in these comparisons. Further, temperature sensitivity, which is an important factor, has been estimated and the values are closer to those reported from experimental studies than the values reported by earlier studies.

Human resources have played an important role in the production systems of manufacturing enterprises. At the same time, human resource allocation, as a scheduling problem, has attracted more and more attention from the industry and academia, with the increasing complexity of technology and the rising cost of workforce. However, the existing scheduling methods fail to fully consider the relationship between tasks and employees. In this paper we consider a single workgroup scheduling problem with the assumption of human resources variability. Jobs must be assigned to employees, where the number of processing personnel and the processing time are variable for one job. We model the problem as a combinatorial optimization problem and the objective considered is to minimize the maximum finish time which is called makespan. This problem is transformed into a two-dimension rectangle strip packing problem and we propose a hybrid optimization algorithm which combines scheduling algorithm with packing algorithm. Finally, different size cases are adopted to test the model. Results show the proposed strategy and algorithm are suitable for solving single workgroup scheduling very well.

Designers of machine-cut objects must often consider whether and how their design can be fabricated with their available materials. In contrast to tools that support preparing finished designs for fabrication, we investigate shortening the feedback loop between design creation and fabrication preparation. To this end, we present Fabricaide, a fabrication-aware tool that interleaves the processes of creating and preparing designs for fabrication. By providing live feedback on how parts should be placed onto material sheets, analyzing how much material is consumed, and alerting users when designs are infeasible, Fabricaide enables users to proactively tailor their design to their available material. Fabricaide achieves this with a custom packing algorithm that arranges parts onto material sheets at interactive speeds. Our qualitative user study shows how Fabricaide can support different workflows, encourage material-conscious design practices, and provide insights on how to further improve similar interfaces in the future.

This paper deals with strip packing metaheuristic algorithm selection using data mining techniques. Given a set of solved strip packing problem instances, the relationship between the instance characteristics and algorithm performance is learned and is used to predict the best algorithms to solve a new set of unseen problem instances. A framework capable of modelling this relationship for an automated packing algorithm selection is proposed. The ei¬€ectiveness of the proposed framework is evaluated in the context of a large set of strip packing problem instances and the state-of-the-art strip packing algorithms. The results suggest a 91% accuracy in correctly identifying the best algorithm for a given instance.

Field programmable gate array (FPGA) packing and placement without routability consideration could lead to unroutable results for high-utilization designs. Conventional FPGA packing and placement approaches are shown to have severe difficulties to yield good routability. In this paper, we propose an FPGA packing and placement engine called UTPlaceF that simultaneously optimizes wirelength and routability. A novel physical and congestion aware packing algorithm and a hierarchical detailed placement technique are proposed. UTPlaceF outperforms state-of-the-art FPGA placers simultaneously in runtime and solution quality on International Symposium on Physical Design (ISPD) 2016 benchmark suite. Compared with the top three winners of ISPD’16 FPGA placement contest, UTPlaceF can deliver 6.2%, 11.6%, and 29.1% better routed wirelength with shorter runtime.

This study provides a general framework for the creation of three-dimensional microstructures for anisotropic two-phase materials with complex morphologies. The ability to create synthetic microstructures that are statistically representative of real materials is dependent on the ability of the generation algorithm to meet the assigned statistics. Hence, the fidelity of the synthetic microstructure depends on the efficiency of the generation process. The generated microstructures were statistically evaluated with respect to the target distribution for grain size, shape, orientation and phase volume fraction. This serves a dual purpose of validation of the packing algorithm and quantification of the 3D microstructures.

The split delivery vehicle routing problem with two-dimensional loading constraints (2L-SDVRP) is a complex practical problem in the field of logistics. It aims at finding the optimal vehicle routes and two-dimensional packing layouts of items in each vehicle to minimize the transportation cost. In this work, we present a mathematical model of 2L-SDVRP with wide-ranging practical considerations. Then we propose an enhanced neighborhood search algorithm (ENS) incorporated with the maximum-space-utilization-based tabu search packing algorithm (MSUTS) to solve the 2L-SDVRP, where the MSUTS examines the feasibility of packing in each route. To accelerate the solving process, a sequence-optimization and random-splitting-based initialization strategy is further proposed. Meanwhile, three classical neighborhood operators are modified to adapt to the 2L-SDVRP with split delivery and two-dimensional packing. The proposed algorithms are tested on a large number of instances varying with scales and properties, which verifies the effectiveness of the proposed algorithm for solving the 2L-SDVRP. Observation of the results also infers the split delivery shows an economic advantage over the non-split case and the advantage becomes significant when the total area of items of each customer increases.

Irregular packing problems exist widely in industrial applications. To obtain better packing results, packing shapes are rotated freely during the packing process. However, equal angle-intervals are commonly used in the existing packing algorithms without considering the shape contour features, which may miss the best packing positions with the reduced packing quality. To solve this problem, an irregular packing algorithm is proposed based on a principal component analysis methodology in this paper. The principal components of convex features on the shapes are calculated. The rotation angles are then searched according to the first principal components. Finally, the shapes are rotated and packed based on the rotation angles. Experimental results show that the packing time is reduced and the material utilization is improved by the proposed algorithm.

Cryosurgery is a surgical process of exploiting extreme cold heat circulating through one or more probes to demolish abundant benign and malignant lesions in biological tissues. However, the proper cryosurgical factors including probe number and multiple probe locations assigned to a specific target area are critical to freeze the tumor vicinity with maximum cryoinjury while diminishing the destruction of healthy tissue. In this study, we inaugurate a novel three-dimensional modeling analysis incorporated with optimal cryosurgical factors to improve the freezing efficacy of the multiprobe cryoablative process. A planning system based bubble-packing algorithm was exploited to acquire optimum cryoprobe layouts from multiple triangular cryoprobe arrays with the placement variants of 7, 14, and 20 mm in equidistance from each probe. Two-phase flow with coupled thermal transport model was used to explore thermal evolution in living tissues and optimize the ablation outputs during multiprobe cryosurgery. The results show that when the probes are in faraway (20 mm), the algorithm yields the minimum value of the objective function during multiprobe optimization of cryosurgery. In-vitro multiprobe experiments of bio-gel phantom and porcine live tissue were also implemented and acquired approximately 7 cm in diameter of iceball after t = 1400 s in both cases.

The paper proposes a way to examine whether cervical cells qualify as normal or abnormal on the basis of phase profiles, and to subsequently perform local fractal descriptions of their thre...

In this paper, a mathematical model is established for the three-dimensional packing problem. This model is a multi-objective optimization problem which considers two factors: volume utilization ratio and load utilization ratio. This paper uses heuristic algorithm to design on the basis of the actual experience of packing. At the same time, combining genetic algorithm and heuristic algorithm, a three-dimensional hybrid genetic heuristic algorithm (3D-HGH) is proposed. This algorithm improves the performance of heuristic algorithm and improves the utilization ratio. The results of three-dimensional visualization of loading are obtained by simulation experiments.

In this paper, we present a 1-space bounded cube packing algorithm with asymptotic competitive ratio 10.872.

In the existing methods for solving unequal circles packing problems, the initial configuration is given arbitrarily or randomly, but the impact of different initial configurations for existing packing algorithm to the speed of existing packing algorithm solving unequal circles packing problems is very large. The quasi-human seniority-order algorithm proposed in this paper can generate a better initial configuration for existing packing algorithm to accelerate the speed of existing packing algorithm solving unequal circles packing problems. In experiments, the quasi-human seniority-order algorithm is applied to generate better initial configurations for quasi-physical elasticity methods to solve the unequal circles packing problems, and the experimental results show that the proposed quasi-human seniority-order algorithm can greatly improve the speed of solving the problem.

Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing particles based on a constructiveadvancing front method, which usesMonte Carlo techniquesfor the generation of particle dimensions, is also shown. The method can be used toobtainvirtual dense packings of particles with severalgeometrical shapes. It employs continuous, discrete and empiricalstatistical distributionsin order to generate the dimensions of particles. The packingalgorithmis very flexible and allows alternatives for: 1- The direction of the advancing front (inwards or outwards), 2- The selection of the local advancing front, 3- The method for placing a mobile particle in contact with others and 4- The overlap checks. Thealgorithmalso allows obtaining highlyporous mediawhen it is slightly modified.Practical applicationsof the formulations are presented in the end of this paper.

The rectangular cutting and orthogonal packing problems which have many practical applications in industry and engineering are considered. Increasing the density of placement schemes leads to reducing the material usage in solving the rectangular cutting problems and reducing the unused resources at solving the orthogonal packing problems. This article contains the description of the developed packing compaction algorithm and its investigation. This algorithm uses six object selection rules, which select objects from a container for deleting and subsequent reallocation of them into freed spaces of the container. The packing compaction algorithm iteratively applies a one-pass heuristic algorithm which finds the best placement of the deleted objects in order to increase the density of the result packing. The effectiveness of the application of the proposed algorithm is investigated on the standard two-dimensional strip packing problems which are the rectangular cutting problems with only one container of a fixed width and an infinite length. Based on the test results, the effective sequence of application of the proposed rules used as the part of the packing algorithm was determined. The packing compaction algorithm is implemented in a general form which makes it possible for application in the rectangular cutting and orthogonal packing problems of arbitrary dimension.

Thermal interface materials (TIMs), which transmit heat from semiconductor chips, are indispensable in today’s microelectronic devices. Designing superior TIMs for increasingly demanding integration requirements, especially for server-level hardware with high power density chips, remains a particularly coveted yet challenging objective. This is because achieving desired degrees of thermal-mechanical attributes (e.g. high thermal conductivity, low elastic modulus, low viscosity) poses contradictory challenges. For instance, embedding thermally conductive fillers (e.g. metallic particles) into a compliant yet considerably less conductive matrix (e.g. polymer) enhances heat transmission, however at the expense of overall compliance. This leads to extensive trial-and-error based empirical approaches for optimal material design. Specifically, high volume fraction filler loading, role of filler size distribution, mixing of various filler types are some outstanding issues that need further clarification. To that end, we first forward a generic packing algorithm with ability to simulate a variety of filler types and distributions. Secondly, by modeling the physics of heat/force flux, we predict effective thermal conductivity, elastic modulus and viscosity for various packing cases.

A 3.883-competitive online square packing algorithm with one active bin is described. We study the problem of online packing of squares into bins with only one active bin.We describe a new one-space bounded packing algorithm.We improve upper bounds of the previous online one-space bounded algorithms: a 4.5-competitive algorithm from 2010 (Chen et al.) and a 4.3-competitive algorithm from 2013 (Chin et al.).

A new Particle Vortex Method, called Diffused Vortex Hydrodynamics (DVH), is presented in this paper. The DVH is a meshless method characterized by the use of a regular distribution of points close to a solid surface to perform the vorticity diffusion process in the boundary layer regions. This redistribution avoids excessive clustering or rarefaction of the vortex particles providing robustness and high accuracy to the method. The generation of the regular distribution of points is performed through a packing algorithm which is embedded in the solver. The packing algorithm collocates points regularly around body of arbitrary shape allowing an exact enforcement on the solid surfaces of the no-slip boundary condition. The present method is tested and validated on different problems of increasing complexities up to flows with Reynolds number equal to 100,000 (without using any subgrid-scale turbulence model).

Experiments and heterogeneous simulations are combined to investigate cracking behavior of sheared asphalt mixture. A series of direct shear tests are performed at different temperatures with a self-manufactured direct shear test setup, and then a heterogeneous fracture modeling approach based on the random aggregate generation and packing algorithm and the bilinear cohesive crack model is utilized to simulate shear fracture processes. Two kinds of fracture, the single crack type for −20 and −10 °C, and the double crack type for 0 and 5 °C, are observed. Some internal mechanisms are analyzed based on numerical simulations.

Advancing front packing algorithms have proven to be very efficient in 2D for obtaining high density sets of particles, especially disks. However, the extension of these algorithms to 3D is not a trivial task. In the present paper, an advancing front algorithm for obtaining highly dense sphere packings is presented. It is simpler than other advancing front packing methods in 3D and can also be used with other types of particles. Comparison with respect to other packing methods have been carried out and a significant improvement in the volume fraction (VF) has been observed. Moreover, the quality of packings was evaluated with indicators other than VF. As additional advantage, the number of generated particles with the algorithm is linear with respect to time.

The packing algorithm does not need to calculate NFP.The discretized packing points are used as a priority order.The packing contours are collided along four directions.The packing time is reduced and the material utilization rate is improved. Freeform surfaces, also called sculptured surfaces, have wide applications in clinical prosthesis and manufacturing. The free-form contour of product needs to be packed before it is machined from raw materials. The No-Fit Polygon methods are not suitable to the complex contours packing because calculating No-Fit Polygons for non-convex polygons is time-consuming. A contour packing algorithm for free-form contour machining is proposed in this paper. The parking area of materials is discretized based on a bottom-left and the lowest gravity center strategy. The packing contour is collided in four directions to increase the material utilization. Experimental results show that the packing time is reduced and the material utilization is improved using the proposed algorithm.

A three-dimensional (3D) heterogeneous fracture modeling technology is presented to simulate complex crack evolution in quasi-brittle asphalt mixture. In this technology, the random aggregate generation and packing algorithm is employed to create 3D heterogeneous numerical model of asphalt mixture, and the cohesive elements with the tension/shear softening laws are inserted into both the mastic matrix and the aggregate–mastic interfaces as potential cracks. The nucleation and coalescence of microcracks, and inception and propagation of main macrocracks are carefully studied under uniaxial tension and temperature of −10 °C. The effects of the averaged coarse aggregate size and the cohesive fracture parameters on performance of asphalt mixture are also evaluated.

A packing algorithm for spatial multiplexing of orbital angular momentum states in a single diffractive structure is presented. Simulation results show the possibility to multiplex more than 200 states.

In Cloud Manufacturing environment, massive 3D Printing services in various types provide users with the ability of mass customization. The large number of 3D printing tasks bring more challenges on printing task scheduling to improve 3D printers’ utilization and thus saving time and materials. This paper establishes the model of 3D printing process in different types and figures out the existence of auxiliary processes. Aiming at decreasing the ratio of auxiliary process time consumption, this paper develops an algorithm derived from the rectangle packing problem to pack printing tasks whose model size are relatively small into one task and print them all in one 3D printing process. Experiments show that the ratio of auxiliary process time consumption significantly reduced by this algorithm.

Selection of optimal aggregate proportions is the main part of the concrete mix design optimization. Assuming circular aggregates, a new Sequential Packing Algorithm (SPA) is proposed to densify arrangement of arbitrary circles. To achieve the densest packing of circles, the porosity packed circle assemblies is optimized by a Genetic Algorithm (GA) search module. Proper adjustment of the algorithm’s parameters and selection of the initial population are effective tools for speeding up the computational progress. The model exactly solves known problems. Finally, Ideal-grading curve is presented after the implementation of GA on the data set.

A modified collective rearrangement algorithm, based on the sphere-assembly representation of the particle shape, is presented for simulating random packings of nonspherical particles and arbitrary shapes. Compared to other collective rearrangement methods, the modification introduced by this algorithm consists in i) avoiding the particle-to-container shrinking procedure by allowing particles to sequentially settle down and ii) in a stability constraint applied to all the particles in the packing. The coupling of these criteria ensures that all the particles are stable and contacting each other, allowing for an unambiguous detection of contacts, which is important in the evaluation of the effective properties desired in many engineering applications, such as percolation thresholds and effective conductivity. The effect of the internal parameters of the algorithm is investigated, showing that random close packings can be obtained. The algorithm is applied to simulate packings of rigid ellipsoids and cylinders with different aspect ratios, which are compared with simulation results provided by other packing algorithms, showing the consistency of our method. Simulations of inter-penetrating particles, mixtures of particles with different shapes and packings of agglomerates are shown, which confirm the applicability of the method to a broad range of packing problems of practical interest and, in particular, for fuel cell applications.

Aiming at billet stacking problem of the rolling mill, an IBF algorithm is used to assign the billet to the warehouse positions. The utilization of non-empty warehouse positions and shuffles are considered in the algorithm. Computational experiments demonstrate that the proposed algorithm is feasible and effective, competitive and able to find more high-quality solutions for problem instances than artificial method.

We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.

Random packing of particles has served as a topic of intense research in the chemical, physical, engineering, and material fields. The majority of previous works focused on the random packing models of spherical, cylindrical, and ellipsoidal particles, whereas little is known about polyhedral particles. In this article, a modeling study of the random packing of convex polyhedral particles is presented in detail, using an interparticle contact detection algorithm, a particle-to-container wall intersection detection algorithm, and a random sequential packing algorithm for hard particles, and the accuracy and efficiency of the contact detection algorithm are compared with those of methods from the literature. With the random packing model and a specified particle size distribution, mesostructure models of particulate composites with mono-/polydisperse particles were generated and validated by a sectioning analysis algorithm. Based on quantitative stereological theories and the sectioning analysis algorithm, the effects of particle shape on the mesostructures composed of the monodisperse and polydisperse particles were evaluated. Further, the statistical results were verified by validation against experimental results from the literature and theoretical results.

This paper develops a mesoscale finite element method for realistic modeling of complex cohesive fracture in asphalt mixture with a given gradation. A random aggregate generation and packing algorithm is employed to create 2D and 3D heterogeneous asphalt mixture specimens, and cohesive elements with tension/shear softening laws are inserted into both mastic and aggregate-mastic interfaces to simulate crack initiation and propagation. The nucleation and coalescence of microcracks and propagation of macrocracks in 2D and 3D specimens is realistically modeled in detail with a few important conclusions drawn. The effects of coarse aggregate distributions on performance of asphalt mixture are also evaluated.

The many endless rivers of text now available present a serious challenge in the task of gleaning, analyzing and discovering useful information. In this paper, we describe a methodology for visualizing a text stream in real-time, modeled as a dynamic graph and its derived map. The approach automatically groups similar messages into clusters displayed as “countries”, with keyword summaries, using semantic analysis, graph clustering and map generation techniques. It handles the need for visual stability across time by dynamic graph layout and Procrustes projection, enhanced with a novel stable component packing algorithm. The result provides a continuous, succinct view of ever-changing topics of interest. To make these ideas concrete, we describe their application to an experimental web service called TwitterScope.

Information entropy dimension (ED) has been used earlier in the characterization of the particle size distribution (PSD) in complex multi-particle granular media. In this work the ED is first proposed as an indicator of the packing density on the basis of the theoretical based interpretation of the ED in the granular media PSD context. A one-parametric exact self-similar PSD model, where the information ED is known, together with a 2-D computational random packing algorithm, are used to test the ability of the ED as an indicator of packing density. It is found that the packing density increases when the ED does. Moreover, results show a strong linear dependence between packing density and the ED. Empirical results from a large soil data base also reinforce the computational results. As ED may be estimated from field or laboratory data, the above mentioned results suggest its use as an indicator of packing density in complex granular media and material science in order to predict their properties.

An optimization procedure for the layout assessment of electrically large but finite planar arrays is presented. The synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints. Moreover, the size of the radiators is taken into account, which results in a hard nonoverlapping, between the elements, constraint. The latter should not be violated if we want the attained solution not only to obey the far-field mask, but also to be physically realizable. As stated, the optimization problem is twofold. An antenna design is associated with a packing problem. In order to take the constraints on the layout into account and solve the whole problem, we propose the constraint relaxation approach, which is equipped with a packing algorithm. Our study is applied to various initial geometries, and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint. Several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented, which show the applicability and merit of the method.

This paper proposes a new packing algorithm for strips cutting method in steel plate cutting technology. It remarks the shapes by many horizontal lines. It firstly searches the best sequence and each shape’s angle for packing all shapes by genetic simulated annealing algorithm, and then a new heuristic algorithm which satisfies the practical need of strips cutting technology based on the bottom-left algorithm is used to complete the automatic layout of two dimensional irregular shapes. In the end, satisfactory results of optimal layout are obtained.

Local microscopic particle density variation stemming from packing density far below unity is one of the important aspects of digital tape recording. In this paper, we present a modeling methodology for simulating realistic particle packing in particulate tape media. The packing algorithm is able to generate randomly dispersed tape particles with packing density as high as 34%-40% and user-defined parameters such as easy axes orientation, aspect ratio variation, size distribution, etc. Micromagnetic modeling of recording characteristics have also been conducted to study the impact of various aspects of packing.

A digital computational approach has been developed to simulate realistic structures of packed beds. The underlying principle of the method is digitisation of the particles and packing space, enabling the generation of realistic structures. Previous publications [Caulkin, R., Fairweather, M., Jia, X., Gopinathan, N., & Williams, R.A. (2006). An investigation of packed columns using a digital packing algorithm. Computers & Chemical Engineering, 30, 1178–1188; Caulkin, R., Ahmad, A., Fairweather, M., Jia, X., & Williams, R. A. (2007). An investigation of sphere packed shell-side columns using a digital packing algorithm. Computers & Chemical Engineering, 31, 1715–1724] have demonstrated the ability of the code in predicting the packing of spheres. For cylindrical particles, however, the original, random walk-based code proved less effective at predicting bed structure. In response to this, the algorithm has been modified to make use of collisions to guide particle movement in a way which does not sacrifice the advantage of simulation speed. Results of both the original and modified code are presented, with bulk and local voidage values compared with data derived by experimental methods. The results demonstrate that collisions and their impact on packing structure cannot be disregarded if realistic packing structures are to be obtained.

This work presents a review of the findings into the ability of a digitally based particle packing algorithm, called DigiPac, to predict bed structure in a variety of packed columns, for a range of generic pellet shapes frequently used in the chemical and process engineering industries. Resulting macroscopic properties are compared with experimental data derived from both invasive and non-destructive measurement techniques. Additionally, fluid velocity distributions, through samples of the resulting bed structures, are analysed using lattice Boltzmann method (LBM) simulations and are compared against experimental data from the literature.

The void structure of particulate solids has been studied with the aid of a numerical packing algorithm based on the minimisation of an energy potential. This algorithm has been used to form densely packed assemblies of spherical and fibrous particles. The void space within these materials has been characterised using an algorithm that finds chains of voids that pass through the assemblies. The tortuosity (as defined by Carman [P.C. Carman, Fluid flow through granular beds, Trans. Instn. Chem. Engrs., v15 pp 150–166, 1937.]) and mean diameter of these chains have been determined and examined as important parameters that are relevant to the permeability of these materials. Tortuosity was approximately constant in the spherical particle assemblies, while the void size varied with the particle size. In general, the spherical particle assemblies showed much smaller void sizes (relative to the particle diameter) and lower tortuosity than the fibrous materials. The tortuosity of the fibrous materials was found to be a function of both the aspect ratio of the fibres, and the packing efficiency of the assembly.

This paper on the fundamental structural properties of shell-side packed columns presents an investigative study using a novel packing algorithm with the aim of validation against experimental results. The novel contribution in the predictive approach employed is the digitalisation of particles, container and packing space to generate complex life-like stochastic packing structures of particulate systems at relatively high speed (when compared to traditional vector-based approaches) which are comparable with experimentally packed beds without need for further conversion of numerical data. A variety of packed column simulations, comprising more complex beds than often seen in the literature, namely shell-side beds with increasing complexity of internal structure and packed with spherical particles, have been undertaken and the resulting averaged numerical data compared like-for-like with experimental results with key trends reproduced. The overall aim of this work is to demonstrate the usefulness of the technique and associated computer code as an engineering aide for research, design and optimisation of the performance of packed bed systems of any geometric complexity in terms of packing structure, as well as to highlight possible areas for further development of the code.

A new multi-threaded memetic algorithm (genetic algorithm with local optimizations) for the ISO 3832 luggage packing standard is presented. Apart from producing high-quality results, the algorithm also exploits the highly parallel computer architectures that are becoming more common as well as packing more boxes than other state-of-the-art algorithms. We also provide the first comparison of state-of-the-art packing algorithms for a real world trunk geometry.

A novel approach has been developed to numerically pack spheres in cylinders. The packing algorithm uses a simple sequential technique that is based on a dimensionless packing parameter. The dimensionless packing parameter includes both axial and radial variables in order to determine a sphere's sequential placement within a cylindrical packing structure. The numerical simulation has been applied to the loose packing of identical spheres in cylindrical containers with D/d ≥ 2.0. The predicted results for the mean porosity and the radial porosity distributions are validated against the available experimental data for spheres in cylindrical containers. The simulated results are highly accurate and the simple packing algorithm requires minimal computational prerequisites.

A simulation model is proposed for the dense packing of particulate, spherical material. The model assumes that the centers of the spheres are randomly generated at the grid of the cubic lattice. The biggest possible spheres are packed first; they are limited by the sequence of minimum diameters, which are determined by a reduction coefficient and the number of packing trials. Based on these assumptions, a very fast packing algorithm was developed. Using this algorithm, the influence of geometrical parameters and model variables on the degree of packing and the corresponding distribution of particles was analyzed. According to the simulation results, three different modules are suggested to estimate the packing degree for a given particle distribution, and also to distinguish between ‘initially loose’ and ‘initially pre-packed’ conditions.