SHOCKS Impulse-Jerk(I-J) Plasticity/Fracture Burst Acoustic-Emission(BAE) NON:``1&#039;&#039;/$\omega $ -``Noise&#039;&#039;; Power-Law; Universality Power-Spectrum is I-J Time-Series Fourier-Transform: 1687 $<<<$ 1988: VERY-LONG PRE-&#034;Bak&#034;!!!

SHOCKS impulse-jerk(I-J) [apply strain/impulse to get stress/jerk ],{\{}VS. NON-shocks[apply stress to get strain]{\}}, plasticity/fracture BAE[E. S.: MSE 8.,310(71); PSS: (a) 5, 601/607(71); Xl..-Latt. Defects 5, 277(74); Scripta Met.: 6, 785(72); 8, 587/617(74); 3$^{rd}$ Tokyo A.-E. Symp. (76);Acta Met.25,383(77); JMMM 7, 312(78)] NON: ``1''/$\omega $ -``Noise''; Zipf(NON-Pareto); power-law ; universality power-spectrum is manifestly-demonstrated in ONLY ``PURE''-MATHS way to be nothing but d[F(t)=m(t)a(t)=Newton's (3$^{rd})$ Law of Motion=(I-J)]/dt I-Jderivative d(I-J)/dt=dF(t)/dt=[m(t)da(t)/dt+a(t)dm(t)/dt] REdiscovery!!! A/Siegel NON-shock PHYSICS derivation fails!!!; "PURE"-MATHS: dF(t)/dt=d$^{2}$p(t)/dt$^{2}$=[m(t)da(t)/dt+a(t)dm(t)/dt] TRIPLE-integral [VS. NON -shocks F = ma time-series DOUBLE-integral] Dichotomy: s(t) = [v$_{0}$+(1/2)a(t)t$^{2}$+EXTRA-TERM(S)], {\{}VS. s(t) = [v$_{0}$t+(1/2) at$^{2}$]{\}}, integral-transform formally defines power-spectrum Dichotomy: