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The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
Packing of irregular objects is a problem not lending itself well to closed form solutions; however, the applicability to practical environmental science is quite important. For example, irregularly shaped soil particles pack differently as the sizes and shapes vary, leading to important outcomes for plant species to adapt root formations and ...
In the bin covering problem, the bin size is bounded from below: the goal is to maximize the number of bins used such that the total size in each bin is at least a given threshold. In the fair indivisible chore allocation problem (a variant of fair item allocation ), the items represent chores, and there are different people each of whom ...
which is an eigenvalue equation. Very often, only numerical solutions to the Schrödinger equation can be found for a given physical system and its associated potential energy. However, there exists a subset of physical systems for which the form of the eigenfunctions and their associated energies, or eigenvalues, can be found.
Many problems in the chemical and physical sciences can be related to packing problems where more than one size of sphere is available. Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing.
This produces the stacking ABCABCABC, which is in the [111] direction of a cubic crystal structure. In this context, a stacking fault is a local deviation from one of the close-packed stacking sequences to the other one. Usually, only one- two- or three-layer interruptions in the stacking sequence are referred to as stacking faults.
The equilibrium width is thus partially determined by the stacking-fault energy. When the SFE is high the dissociation of a full dislocation into two partials is energetically unfavorable, and the material can deform either by dislocation glide or cross-slip. Lower SFE materials display wider stacking faults and have more difficulties for cross ...
English: Illustration of the first eight blocks in the solution to the single-wide block-stacking problem by CMG Lee. The wood textures are from File: 16 wood samples.jpg . Date