By Michael V. Sadovskll

This study monograph deals an advent to complex quantum box theoretical suggestions for many-particle structures past perturbation idea. numerous schemes for resummation of the Feynman diagrams are defined. The ensuing approximations are in particular like minded for strongly correlated fermion and boson platforms. additionally thought of is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion platforms with powerful appealing interplay. specifically, a box theoretic formula of "bosonization" is gifted; it's released right here for the 1st time. this system is utilized to the fractional quantum corridor influence, to the Coulomb plasma, and to numerous precisely solvable versions

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8, independently of the kind of pressure. An abrupt increase in the magnitude of the shear stress simultaneously with the contact and hydrostatic stress is needed for the phase transition to take place. In the middle of the impression, the values of these stresses become congruous. The accuracy of our estimations for the critical stresses depends mainly on the accuracy of the full-scale experiment. 4, the theoretically predicted isobars for the critical contact (black) and hydrostatic (grey) pressures almost coincide one with another.

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50) = Y 1 + α + ln sin ψ 3 2 3Y (1 − ν) √ because δV /V1 = 4−1 π cot ψ. 50) is a nonlinear equation for H V , since ξ = (H V − p∗ )/(H V − p1 ), H V / sin ψ = p1 + αY . Numerical methods can be used for solving this equation. 50) allow us to evaluate the effect of phase transformations on the size of the plastic zone and on the Vickers hardness H V . 46) at c = (2π)−1/2d (d is the impression diagonal) allow for the size of the transformation zone to be evaluated. 1 Introduction Brittle fracture and plastic deformation are the two processes that are known to take place during indentation in the majority of ceramic and semiconducting materials.