Sequential Packing Research Articles

3D-Multi Constrained Heterogeneous Packing Using Genetic Approach

This paper presents a combination of Genetic Algorithm (GA) and Tuning algorithm, for optimizing Three Dimensional (3D) arbitrary sized heterogeneous box packing into a container, by considering practical constraints facing in the logistics industries. Objective of this research is to pack four different shapes of boxes of varying sizes into a container of standard dimension, without violating various practical constraints. Inorder to obtain a real time feasible packing pattern, Genetic Algorithm is developed to maximize the container volume utilization and inturn profit [9]. It significantly improves the search efficiency with less computational time and loads most of the heterogeneous boxes into the container by considering its optimal position and orientation. Tuning algorithm is used to decode the genetic output into user understandable sequential packing pattern and to fill the left-out empty space inside the container. In general, GA in conjunction with the tuning algorithm is substantially better than those obtained by applying heuristics to the bin packing directly.

Mesostructural characterization of particulate composites via a contact detection algorithm of ellipsoidal particles

Particulate composites are composed of random packing of polydispersed particles, such as cementitious composites. The packing behavior of particles plays an important role in the mesostructural evolution of particulate composites. The preponderance of previous works has focused on the random packing of spherical, cylindrical or elliptical particles, and little is known about ellipsoidal particles. In the present work, a contact detection algorithm of ellipsoids is presented in detail, which can quantitatively describe relative positions of ellipsoids in a three-dimensional space. The accuracy and efficiency of the algorithm are tested and compared with algorithms developed in previous literature, and its reliability is verified by a random sequential packing model of polydispersed ellipsoids with semi-periodic boundary conditions. Moreover, the algorithm is applied to simulate a mesostructure model of cementitious composites. By means of stereological tools and section analysis technologies, the mesostructure of cementitious composites is quantitatively characterized. Finally, the reliability of the statistical results from the present methodology is verified by valid experimental and theoretical results.

An overlapping detection algorithm for random sequential packing of elliptical particles

Random sequential packing of particles is a subject of intense research in many branches of physics and engineering. The preponderance of preview work has focused on spherical particles and little is known about non-overlapping elliptical particles. In the present work, a new numerical algorithm is developed to detect overlapping of ellipses by a series of sequential coordinate transformations and a novel golden section search algorithm. The accuracy and efficiency of the numerical algorithm are tested and compared with algorithms developed in previous literature. Its stability is verified by visualizations of random sequential packing of monodispersed and polydispersed ellipses with different boundary conditions. Then, the algorithm is applied to investigate the influence of the shape of ellipses on the random packing fraction, as well as to study the influence of the shape and size of ellipses on the wall effect in the particle packing structure, and some numerical results are demonstrated. Finally, the reliability of the numerical algorithm extended to the three-dimensional space is also evaluated by checking overlapping of ellipsoidal particles.

Random packing of lines in a lattice cube

A study is made of the random sequential packing of complete lines in a cube of integer lattice points, with side N. For N<or=15 exact packing fractions are computed. It is found that if line occupation attempts arrive as a spatial Poisson process the packing has two distinct phases; initially where large numbers of potential adsorption sites are blocked, and subsequently where no further blocking occurs so that filling is exponential in time. It is shown that the ratio of the durations of the blocking to the nonblocking phases falls to zero as N-->infinity . In this limit, the packing fraction at time t is theta(t)=3/4(1-e-t). The rapid switch between phases in large systems creates a dramatic fall in the packing rate at the start of the process. This becomes a discontinuity as N-->infinity and is a consequence of the high aspect ratio of the packing objects. It provides a physical explanation for the diverging coefficients in expansions of theta(t) about t=0 for objects with diverging aspect ratio. After considering the three-dimensional case, the analysis is extended to d -dimensional cubes, for which it is conjectured that theta=d/2d-1 in the limit N-->infinity .

Application of genetic algorithm for modeling of dense packing of concrete aggregates

Sequential Packing Algorithm (SPA) was developed to model the dense packing of large assemblies of particulate materials (in the order of millions). These assemblies represent the real aggregate systems of portland cement or asphalt concrete. To improve the SPA performance, the program engine was updated with a genetic algorithm (GA) search module. Multi-cell packing procedures, fine adjustment of the algorithm’s parameters, as well as implementation of GA were effective tools to optimize the computational resources, to speed-up the SPA and to pack very large volumes of spherical entities. The developed algorithm generates and visualizes dense packings corresponding to concrete aggregates. The influence of model variables on the degree of packing and the corresponding distribution of particles was analyzed. Based on the simulation results, different particle size distributions of particulate materials are correlated to their packing degree. These packings agreed well with the standard requirements and available research data. The results of the research can be applied to the optimal proportioning of concrete mixtures.

Process level moderate deviations for stabilizing functionals

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization . In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs.

Optimization of a Computer Simulation Model for Packing of Concrete Aggregates

A simulation algorithm was developed for modeling the dense packing of large assemblies of particulate materials (in the order of millions). These assemblies represent the real aggregate systems of portland cement concrete. Two variations of the algorithm are proposed: sequential packing model and particle suspension model. A developed multicell packing procedure as well as fine adjustment of the algorithm's parameters were useful to optimize the computational resources (i.e., to realize the trade-off between the memory and packing time). Some options to speed up the algorithm and to pack very large volumes of spherical entities (up to 10 million) are discussed. The described procedure resulted in a quick method for packing of large assemblies of particulate materials. The influence of model variables on the degree of packing and the corresponding distribution of particles was analyzed. Based on the simulation results, different particle size distributions of particulate materials are correlated to their packing degree. The developed algorithm generates and visualizes dense packings corresponding to concrete aggregates. These packings show a good agreement with the standard requirements and available research data. The results of the research can be applied to the optimal proportioning of concrete mixtures.

Gaussian Limits for Multidimensional Random Sequential Packing at Saturation

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is asymptotically normal as $\lambda \to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.

Site-Directed Antibodies against the Stem Region Reveal Low pH-Induced Conformational Changes of the Semliki Forest Virus Fusion Protein

The E1 envelope protein of the alphavirus Semliki Forest virus (SFV) is a class II fusion protein that mediates low pH-triggered membrane fusion during virus infection. Like other class I and class II fusion proteins, during fusion E1 inserts into the target membrane and rearranges to form a trimeric hairpin structure. The postfusion structures of the alphavirus and flavivirus fusion proteins suggest that the "stem" region connecting the fusion protein domain III to the transmembrane domain interacts along the trimer core during the low pH-induced conformational change. However, the location of the E1 stem in the SFV particle and its rearrangement and functional importance during fusion are not known. We developed site-directed polyclonal antibodies to the N- or C-terminal regions of the SFV E1 stem and used them to study the stem during fusion. The E1 stem was hidden on neutral pH virus but became accessible after low pH-triggered dissociation of the E2/E1 heterodimer. The stem packed onto the trimer core in the postfusion conformation and became inaccessible to antibody binding. Generation of the E1 homotrimer on fusion-incompetent membranes identified an intermediate conformation in which domain III had folded back but stem packing was incomplete. Our data suggest that E1 hairpin formation occurs by the sequential packing of domain III and the stem onto the trimer core and indicate a tight correlation between stem packing and membrane merger.

Gaussian limits for random measures in geometric probability

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general results are used to deduce central limit theorems for measures induced by random graphs (nearest neighbor, Voronoi and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth–growth models) and statistics of germ–grain models.

The modelling of particle systems with real shapes.

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

Gaussian Fields and Random Packing

Consider sequential packing of unit volume balls in a large cube, in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a Gaussian field in the thermodynamic limit. The results cover related applied models, including ballistic deposition and spatial birth-growth models.

Limit Theory for Random Sequential Packing and Deposition

Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with finite input. We prove a law of large numbers and central limit theorem for the number of packed balls in the thermodynamic limit. We prove analogous results for numerous related applied models, including cooperative sequential adsorption, ballistic deposition, and spatial birth-growth models. The proofs are based on a general law of large numbers and central limit theorem for “stabilizing” functionals of marked point processes of independent uniform points in a large cube, which are of independent interest. “Stabilization” means, loosely, that local modifications have only local effects.

Observed phase changes and the random sequential packing model for elections in Japan

In Japan the nomination of candidates by some political parties in each constituency seems to have been often performed like car-parking in a street, which explains the territory making behaviour for each candidate. The car-parking model is a one-dimensional sequential packing model. We apply this model to the election data for the House of Councillors and the House of Representatives. We observe phase changes for the election data of the House of Councillors.

Numerical simulation of packed beds with monosized spheres in cylindrical containers

Abstract Several sequential packing models are applied to numerically construct packed beds of identical spheres in right circular cylindrical containers. The fixed packed beds are assembled on a base layer so that a newly added sphere is always placed at a vertical location that is stable under gravity. The newly added sphere may be positioned so that it is in contact with two spheres and the container wall (wall spheres) or three other spheres in the interior of the packing (inner spheres). The particular procedure by which wall spheres and inner spheres are added to the packing is determined by a given model. The sequential models calculate the center coordinates of each newly added sphere. The center coordinates are used to determine the overall void fraction and the radial void fraction in cylindrical containers with D / d ≥3 and are compared with experimental data.

Acute pancreatitis.

The etiology of acute pancreatitis in children is widely varied and includes idiopathic, drug-related, congenital, and posttraumatic causes. Most children have abdominal pain and tenderness without evidence of peritonitis, and most patients will have elevated serum amylase levels initially or after a delay of about 12 hours. If the diagnosis remains equivocal or in the setting of trauma, an abdominal CT scan should be obtained. Initial treatment for all forms of acute pancreatitis includes bowel rest and support with intravenous fluids. A nasogastric tube should only be placed for symptomatic relief and prophylactic broad-spectrum antibiotics should be given only in the setting of necrotizing pancreatitis, especially if patients are receiving pharmacologic immunosuppression. Fever or decline in clinical status should prompt CT scan with intravenous contrast and possible fine needle aspiration to detect the presence of sterile or infected necrotizing pancreatitis. Positive cultures or severely worsening clinical status are indications for necrosectomy and debridement with sequential packing and explorations. All patients who have had an episode of gallstone pancreatitis should have a cholecystectomy after resolution of pancreatic inflammation but before discharge from the hospital.

Sequential packing algorithm for channel assignment under cochannel and adjacent-channel interference constraint

Generally, the channel-assignment problem (CAP) for mobile cellular systems is solved by graph-coloring algorithms. These algorithms, though sometimes can yield an optimal solution, do not supply any information on whether an optimal solution has been found or bow far away it is from the optimum. In view of these undesirable features, two relevant results are presented. First, a lower bound for the minimum number of channels required to satisfy a given call-traffic demand is derived. This lower bound is tighter than the existing ones under certain conditions and can be used as a supplement for other approximate algorithms. Second, we propose an efficient heuristic algorithm to solve this problem. Although the CAP is nondeterministic polynomial (NP) complete in general, our algorithm provides an optimal solution for a special class of network topologies. For the general case, promising results are obtained, and numerical examples show that our algorithm has a better performance than many existing algorithms.

Multiple Container Packing: A Case Study of Pipe Packing

While the problem of packing single containers and pallets has been thoroughly investigated very little attention has been given to the efficient packing of multiple container loads. Normally in practice a multiple container load is packed by a single container algorithm used in a greedy fashion. This paper introduces the issues involved in multiple container loading. It lays out three different strategies for solving the problem: sequential packing using a single container heuristic, pre-allocating items to the containers and choosing container loads using simultaneous packing models. The principal simultaneous models are pattern selection IP models. We present an application of packing pipes in shipping containers using two pattern selection IP models, a pattern selection heuristic, a sequential greedy algorithm and a pre-allocation method. The experimental results use randomly generated data sets. We discuss several useful insights into the methods and show that for this application the pattern selection methods perform best.

Methods of simulating random patterns of non-spherical objects and their application

We consider two mechanisms for simulating spatial patterns of hard-core non-spherical particles, namely the random sequential packing (RSP) and the Markov chain Monte Carlo (MCMC) procedures. The former is described as follows: we put a particle one-by-one into a finite region by sampling its location x and direction θ uniformly at random; if it does not overlap with other particles put before, it is put successfully, otherwise, we discard it and try another uniform sampling of (x, θ); by repeating the above, we can obtain a set of non-overlapping particles. The MCMC procedure is the following: we first give a certain non-overlapping pattern of non-spherical particles prepared in a random or a regular manner; then we select a particle and sample its new trial location x and direction θ at random; if the new sample (x, θ) is accepted, i.e. it does not overlap with other particles, the selected particle is moved to the new ‘position’, otherwise the particle is retained at the old position; by repeating the above, a series of a set of non-overlapping particles is generated.

Methods of simulating random patterns of non-spherical objects and their application

We consider two mechanisms for simulating spatial patterns of hard-core non-spherical particles, namely the random sequential packing (RSP) and the Markov chain Monte Carlo (MCMC) procedures. The former is described as follows: we put a particle one-by-one into a finite region by sampling its location x and direction θ uniformly at random; if it does not overlap with other particles put before, it is put successfully, otherwise, we discard it and try another uniform sampling of (x, θ); by repeating the above, we can obtain a set of non-overlapping particles. The MCMC procedure is the following: we first give a certain non-overlapping pattern of non-spherical particles prepared in a random or a regular manner; then we select a particle and sample its new trial location x and direction θ at random; if the new sample (x, θ) is accepted, i.e. it does not overlap with other particles, the selected particle is moved to the new ‘position’, otherwise the particle is retained at the old position; by repeating the above, a series of a set of non-overlapping particles is generated.