Stability of lattice structure

Every junction in a stable latticework structure is made up of four quanta of matter each. Each quantum of matter tends to remain angularly equidistant from its neighbors. Each latticework square has four quanta of matter as its sides. Apparent repulsion between their bodies (as a result of adhesion between quanta of matter in contact at common junction point) tends to maintain shape of latticework square. Deformation of a latticework square changes its shape. One or more sides of the latticework square may tend to elongate. Since the quanta in the lattice structure are already under compression and their lengths are controlled by the compression, lengths of sides of a deformed latticework square will be automatically adjusted to suit the required shape. Similarly, if it is required to reduce lengths of latticework square’s sides, excess pressure from ends of quanta of matter will be able to reduce their lengths to suit the shape of latticework square. A reduction in length of a quantum of matter will be compensated by increase in its width. An increase in its length will be accompanied by a reduction in its width. At a stable junction point, with four quanta of matter, each quantum of matter is under stress to move in line with its neighbor and form quanta-chain. Such motion is prevented by presence of four quanta of matter at the junction. Stress between neighboring quanta of matter tends to keep angle between neighboring quanta of matter at equal value. If left free, a latticework square will automatically seek its most stable state in the shape of a perfect square. This is possible only if all sides of a latticework square are formed by quanta of matter of somewhat equal matter-content. If deformation of latticework square is too great, number of quanta of matter at its junctions may be increased to accommodate more quanta of matter or reduced to have lesser number of quanta of matter. In these cases, geometrical shape of latticework squares may be altered temporarily. In this state, the lattice structure remains under stress as long as the deformation remains in the lattice structure. Tendency of latticework squares and hence that of lattice structure to strive towards stable state, endows a lattice structure with its inherent property to strive towards isotropic, homogeneous and serene state. All deformations are opposed by equal and opposite stabilizing efforts.

Formation of lattice structure

If there are more than two quanta of matter in contact with each other (in the same spatial dimension, at a place), interactions due to adhesion between their matter-contents at points of direct contacts between them, may move all quanta of matter so that their ends meet at a point in space to form a junction. Inter-quanta adhesion will further move the quanta of matter angularly in common plane, so that all quanta of matter meeting at a junction settle at equal angular difference between adjacent quanta of matter. Each quantum of matter at every junction is capable to join another junction at its other end. Only stipulation is that all quanta of matter, joined by junctions are in the same spatial plane. Once, any two quanta of matter form a junction, all further additions to the junction will be in the same spatial plane. First two quanta of matter, which initiates build up of quanta-chain, determine spatial plane of all associated structures. Numerous junctions, formed at both ends of associated quanta of matter, form a latticework structure in its plane. Junctions in a regular latticework have to have equal numbers of quanta of matter and they should be of equal lengths. Geometrically, each junction may have three, four or six quanta of matter each. Sections of latticework structure formed by junctions with three quanta of matter each appear in the shape of series of hexagons. They are structurally very unstable and flaccid. This structure is easily destroyed during deformations of latticework structure. Sections of latticework structure formed by junctions with four quanta of matter each appear in the shape series of of squares. They are structurally stable and yielding. This structure can withstand reasonable deformation and return to its stable state easily. Sections of latticework structure formed by junctions with six quanta of matter each appear in the shape of series of triangles. They are structurally very stable and rigid. This structure prevents all reasonable deforming efforts. Nature chooses latticework structure that is stable and yielding. Latticework structure with four quanta of matter, to every stable junction, is superior construction. Each section of this latticework structure, which may be called a latticework square, has one quantum of matter as its side. In its stable and homogeneous state, sides of a latticework square are of equal length. During deformations, sides of latticework squares may change their lengths and the square may change its shape accordingly.

Quanta-chain

During lengthening process of a free quantum of matter, its ends may come in contact with other quanta of matter, which happens to be in its spatial dimension. Under such condition, the lengthening process of the quantum of matter is restricted, in the direction of the second quantum of matter. Matter-contents of the quanta of matter come in direct contact in the same spatial dimension. As magnitude of adhesion between their matter-contents (across their perimeters) is less than the magnitude of adhesion within each of their matter-contents, their matter-contents cannot merge. [Adhesion between contacting quanta of matter is due to their continuous movements and changes of directions]. If a lengthening-quantum of matter encounters other quanta of matter in other spatial dimensions, it will not be restricted in its growth. Adhesive effort between matter-contents of two quanta of matter (in direct contact) tends to keep the quanta of matter, pressing into each other. If the direction of this adhesive effort is perpendicular to the body of any one of the quanta of matter, they will remain in an equilibrium state. Should the direction of adhesive effort differ from being perpendicular to the body of any one of the quanta of matter, it may be considered as combination of two resolved components. One component, which is perpendicular to the body of any one of quanta of matter, keeps the quanta of matter pressed into each other. While, other component of adhesive effort tends to move one quantum of matter (whose body is at an angle to the body of the other) towards one end of the other quantum of matter. This is the most primary instance of induced motion in nature. Adhesive effort between two quanta of matter (in direct contact) tends to move either one or both of quanta of matter, towards each other’s ends, where together the quanta of matter form a junction and attempt to mutually turn their bodies to bring their (single-dimensional) bodies in a straight line. In this manner, free quanta of matter in space tend to form single-dimensional chains. Due to frequent ruptures of these quanta-chains and availability of free quanta of matter (in space) to migrate into ruptured 1D quanta-chain, there are far too many quanta of matter in any single dimensional quanta-chain. Excess number of quanta of matter in a quanta-chain compels all constituent quanta of matter in the quanta-chain to be held at reduced lengths in their single-dimensional status. Tendency of quanta of matter in the chain, to grow in length, keeps all constituent quanta of matter in quanta-chains under compression from their ends. Normally (in current state of universe), quanta of matter in a quanta-chain are maintained at the brink of their growth into second spatial dimension. Should a discontinuity develop in the quanta-chain, inherent property of constituent quanta of matter enable quanta-chain to grow in length. Thus, it becomes an inherent property of quanta-chains to grow (lengthen) into any discontinuity in its spatial dimension.