In this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. This book introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings.

In this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. This book introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings./a

In a sequential packing problem, random objects are uniformly and independently selected from some space. A selected object is either packed or rejected, depending on the distance between it and the nearest object which has been previously packed. A saturated packing is said to exist when it is no longer possible to pack any additional selections. The random packing density is the average proportion of the space which is occupied by the packed objects at saturation. Results concerning the time of the first rejection in a packing sequence are given in Chapter 1. The accuracy of some common approximation formulas is investigated for several settings. The problems considered may be thought of as generalizations of the classical birthday problem. Exact results concerning random packing densities are generally known only for some packing sequences in one-dimensional spaces. In Chapter 2, the packing densities of various computer generated codes are examined. These stochastically constructed codes provide a convenient way to study packing in multidimensional spaces. Asymptotic approximation formulas are given for the packing densities which arise from several different coding schemes. In Chapter 3 the distribution of the number of random selections needed to achieve a saturated packing is considered. In each of the settings examined, the results are compared with analogous results from an associated random covering problem.

Simulations in Bulk Solids Handling Valuable resource for engineers and professionals dealing with bulk granular or powdered materials across industries using Discrete Element Methods (DEM) In many traditional university engineering programmes, no matter whether undergraduate or postgraduate, the behavior of granular materials is not covered in depth or at all. This omission leaves recent engineering graduates with little formal education in the major industrial area of bulk solids handling. This book teaches young professionals and engineers to find appropriate solutions for handling granular and powdered materials. It also provides valuable information for experienced engineers to gain an understanding and appreciation of the most significant simulation methods–DEM chief amongst them. For any student or professional involved with bulk solids handling, this book is a key resource to understand the most efficient and effective stimulation methods that are available today. Its comprehensive overview of the topic allows for upcoming professionals to ensure they have adequate knowledge in the field and for experienced professionals to improve their skills and processes.

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.