Diagram Young

From what has already been diseussed in the sections above, it is sufficiently clear that all eharacteristie parameters derived from a stress-strain diagram (Young s modulus, (upper and lower) stress at yield and elongation at yield, stress at break and elongation at break) are functions of the deformation rate, test temperature and imposed state of stress. 

Young D A 1991 Phase Diagrams of the Elements (Los Angeies University of Caiifornia Press)... 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Young, D.A., Phase Diagrams of the Elements, University of California Press, Berkeley, CA, 1991. 

Figure 8.9. Diagram of the structure of a drawn polymer fibre. The Young s modulus of the crystallised portions is between 50 and 300 GPa, while that of the interspersed amorphous tangles will be only 0.1-5 GPa. Since the strains are additive, the overall modulus is a weighted average of...

For the present case, we have seven such partions of the five ligands which may be symbolized by Young diagrams. The number of rows in such a graph is the number of sorts of ligands, and the length of each... 

Figure 1.8 Diagram of Young s double-slit experiment.

Figure 3.1 (a) Schematic diagram (not to scale) of Young s double-slit experiment. The narrow slits acts as wave sources. Slits S and S2 behave as coherent sources that produce an interference pattern on screen C. (b) The fringe pattern formed on screen C could look like this. (Reproduced with permission from R. A. Serway Physics for Scientists and Engineers with Modern Physics, 3rd ed, 1990, Saunders, Figure 37.1.)... 

D. Definitions of Young diagrams, tableaux, and operators should be understood, as well as the property of the Young operator of projecting onto an irreducible representation (Theorems 1 and 2). 

From a given Young diagram we can, in n different ways, form a "Young tableau t by filling the boxes, in any order, with the site numbers 1,2,.., n. Fig. 2 shows examples of tableaux formed from the diagrams of Fig. 1. 

Theorem 1 The operator Y defined by (39) is, apart from a multiplicative constant, a primitive idempotent of <3n. Y operators belonging to the same Young diagram belong to the same irreducible representation, while those belonging to different diagrams belong to different representations. 

Thus, according to the criterion of Theorem 2, Subsection B, Y, Y belong to different IR s. This completes the proof of Theorem 1, stated above. By means of Theorem 1, we obtain a one-one correspondence (via the Young operators) between diagrams y and IR s 71 y T. We will sometimes refer to a representation and its diagram interchangeably. 

Since Qh is a direct product group, its irreducible representations are also direct products. We denote a representation of <3A by a Young diagram giving the representation of S , together with a letter g or u according as the representation is even or odd with respect to to-... 

It will prove to be important later on to be able to decide whether a certain relation is satisfied between two Young diagrams of the same order. We call this the transfer condition or T-condition . For one-part diagrams (Sn), this relation is defined as follows ... 

For both situations, therefore, we conclude that a partition p is r-active if and only if the transfer condition is satisfied for the partition diagram of p into the Young diagram of r. 

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