random sequential packing of cubes

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Random Sequential Packing Of Cubes

Author : Mathieu Dutour Sikiri?
ISBN : 9789814307833
Genre : Mathematics
File Size : 67. 52 MB
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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.

Random Packing And Random Covering Sequences

Author : Clifton Dickerson Sutton
ISBN : STANFORD:36105025699922
Genre :
File Size : 60. 20 MB
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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.

Mathematical Constants

Author : Steven R. Finch
ISBN : 0521818052
Genre : Mathematics
File Size : 83. 14 MB
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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.

Advances In The Mechanics And The Flow Of Granular Materials

Author : Mohsen Shahinpoor
ISBN : 0872010139
Genre : Technology & Engineering
File Size : 90. 3 MB
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Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Foams And Emulsions

Author : J.F. Sadoc
ISBN : 0792356160
Genre : Technology & Engineering
File Size : 55. 14 MB
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A general and introductory survey of foams, emulsions and cellular materials. Foams and emulsions are illustrations of some fundamental concepts in statistical thermodynamics, rheology, elasticity and the physics and chemistry of divided media and interfaces. They also give rise to some of the most beautiful geometrical shapes and tilings, ordered or disordered. The chapters are grouped into sections having fairly loose boundaries. Each chapter is intelligible alone, but cross referencing means that the few concepts that may not be familiar to the reader can be found in other chapters in the book. Audience: Research students, researchers and teachers in physics, physical chemistry, materials science, mechanical engineering and geometry.

Zentralblatt F R Mineralogie

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ISBN : UCSD:31822009795196
Genre : Crystallography
File Size : 27. 78 MB
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Cellular Patterns

Author : Antonio Siber
ISBN : 9781351048651
Genre : Medical
File Size : 81. 39 MB
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The mechanics underlying the form and structure of biological tissues is being increasingly investigated and appreciated, with new results appearing at a fast pace. Cellular Patterns covers the salient elements of this thriving field of research in a textbook style, including both historic landmark results and recent achievements. By building on concepts such as packing, confinement, surface tension, and elastic instabilities, the book explains the structure and the shape of sheet-like and bulk tissues by adapting the mechanics of continuous media to living matter. It reviews experimental results and empirical laws, and wherever possible, it discusses more than a single theoretical interpretation of a given phenomenon. The in-depth treatment of technical details, the many boxes summarizing essential physical and biological ideas, and an extensive set of problems make this book suitable as a complementary textbook for a graduate course in biophysics and as a standalone reference for students and researchers in biophysics, bioengineering, and mathematical biology interested in the mechanics of tissue.

Applied Probability

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ISBN : UOM:39015027168452
Genre : Journal of applied probability
File Size : 40. 14 MB
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ISBN : UCAL:B4022902
Genre :
File Size : 62. 66 MB
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Mathematical Reviews

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ISBN : UOM:39015065183561
Genre : Mathematics
File Size : 34. 26 MB
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