By rearranging the weakly singular boundary, integral equations developed by Han and Atluri, an SGBEM-CG, which is abbreviated as CG, is developed in this chapter. The CG, representing a single grain of a material, can include arbitrarily shaped voids, inclusions (of a different material), and microcracks. The CG has a stiffness matrix and a load vector, which have similar physical meanings to the traditional displacement FEM. The stiffness matrix is symmetric, positive-definite, and has the same number of rigid-body modes. Different CGs, each with different isotropic material properties, can be directly coupled by the assembly procedure, and are used to directly and efficiently model the microstructure of heterogeneous composite materials. Some examples are also presented, with microcracks interacting with inclusions and holes. This provides some insight of a possible future study of the micro-cracking and damage of heterogeneous material. By introducing stochastic variations of the shapes of CG, and stochastic variations of the properties of the constituent materials, the realistic statistical bounds on the overall properties of composite materials will be determined in future studies.

In the sixth and final chapter, we continue to trace how Lucretius rehabilitates Roman men and their performed gender. Although I resume exploring the sexual language and figures by which Lucretius depreciates male presumptions of anatomical and sociological advantage, in “Vir Recreandus” I also tease out from the poem a positive argument about masculinity. Following the poet’s cues, I construct what an Epicurean man is, what he can do, what he is for, and how he can flourish in Lucretius’ reordering of the world. This Epicurean homo turns out to be manly in behaviors that, in part, map onto traditional scripts for a vir even while acting and self-regarding in ways that Romans would deem strange indeed. Much to Cicero’s vexation, Epicurean men become Rome’s true patriots.

Creativity and its trance states can extend to lifesaving acts of heroism that far exceed ordinary human limitations. By entering a creative trance in the middle of a raging forest fire, the firefighter Wag Dodge invented a new way to reroute the path of flames. Altered states can also occur when individuals lift a multi-thousand-pound vehicle to rescue a person trapped beneath it. They display what is colloquially called hysterical strength, which this book calls extraordinary human strength (EHS). With its enormous power and focused open mind, EHS has congruence with extreme yoga capacities in the philosophy of Patanjali. There is a possible dominance of the dorsal system of the brain in EHS and potential effects of adrenaline, norepinephrine, and cortisol. An inquiry into the origin of its power examines quantum sources, such as vacuum energy and possible chameleon scalar fields with suggested correspondences in neural quantum processes and Eastern philosophies.

The momentum exchange between lattice atoms and conduction electrons together with the stress gradient along the metal wire embedded into the rigid confinement are two major driving forces for electromigration-induced evolution of stress and vacancy concentration. The growth of mechanical stress causes an evolution of a variety of defects that are inevitably present in the metal, leading to void formation. It affects the electrical properties of the interconnect. In order to estimate the time to failure caused by voiding, the kinetics of stress evolution should be resolved until the first void is nucleated. Then the analysis of the void size evolution should be performed in order to trace changes in resistances of individual voided lines and vias. In this chapter, we review the major results that have been achieved with the 1D phenomenological EM model. We demonstrate its capability to predict the transient and steady-state distributions of the vacancy concentration and the hydrostatic stress, a void nucleation, and its growth, and also a drift of small voids along a metal wire. Despite its simplified nature, the 1D model is capable of addressing the confinement effect of ILD/IMD dielectric on EM-induced degradation, and also the effect of metal grain structure.

An accurate analysis of the stress evolution in a metal line loaded with an electric current requires solution of a number of coupled partial differential equations (PDEs). The continuity equations, describing the evolution of concentrations of vacancies and plated atoms along the line, are linked with the force balance equation yielding the elastic stress evolution due to interaction of the metal line volumetric deformation with the rigid confinement. The electric current density distribution is found by solving the corresponding Laplace equation. Accounting for the polycrystalline structure of the metals used as conductors in on-chip interconnects, and proper consideration of a variety of venues for diffusion of vacancies, such as grain boundaries and interfaces with liners and capping layers, requires a comprehensive 2D or 3D analysis. Following void nucleation, which happens when the tensile stress reaches a critical value, the void shape and size are described by a combination of the Cahn–Hilliard and Allen–Kahn equations with the phase-field formalism. Detailed description of these coupled PDEs and results of their solution for a number of cases using finite element analysis (FEA) are demonstrated in this chapter. A good fit between simulation results and measurements is demonstrated throughout the chapter.

The three sections of Chapter 7 explore (1) the collapse of the birth and death contraries; (2) the rebirth topos; and (3) the Buddhist doctrine of the unborn. The first section concentrates on A Piece of Monologue of the late 1970s, noting its allusions to cycles of rebirth and scenes of wall gazing and repeated evocations of a ‘beyond’ resonating with Schopenhauerian will-lessness and Buddhist scriptures. In the second section, probing the drama of rebirth throughout Beckett’s writings, allusions to a Schopenhauerian hellish existence are linked to parallels between Dantean and Buddhist conceptions of hell and purgatory. In contrast, Ill Seen Ill Said’s last pages are seen to allude to an end to rebirth in a coming home to the void via detachment from illusion. This chapter’s third and longest section concerns the convergence of the Beckettian theme of unbornness with the Buddhist doctrine of an original and immanent state of mind beyond birth and death.

This chapter discusses the atomistic account of motion, as an example of the first reactions to the Eleatic challenge by succeeding natural philosophers. The atomists are shown to change the logical basis by implicitly employing a different conception of negation that allows them to understand Being and non-Being as on a par. It also enables them to build a different ontological basis in which non-Being qua void plays a central role in natural philosophy. This new ontological basis allows the atomists to integrate the phenomenal world into their philosophy and to deal with the mereological problems bequeathed by Zeno’s paradoxes. The starting point for this development is the idea that what truly is must in some way also be responsible for the appearances of the phenomenal world. Generation on the phenomenal level is now understood as the combination and separation of aggregates of atoms, while change consists in the rearrangement of some parts of the aggregate. Although the atomists’ notion of the void can be seen as a predecessor to a notion of space, they do not in fact react to the spatio-temporal paradoxes of Zeno.

In Shakespeare, Borges found a precursor of his own philosophical preoccupations with the negation of personal identity and with the transmission of a cultural legacy. ’Everything and Nothing’ (1960) and the later ’A Page on Shakespeare’ (1964) explore the first of these concerns. Compensating somewhat for his sense of nothingness, Shakespeare exploited the roles of actor and playwright to create and impersonate multiple selves. Regarding him as the epitome of reworking and recycling pre-existent stories and plots, Borges exemplifies a flawed approach to Shakespeare’s legacy in the character of Sogel in a late story entitled ’Shakespeare’s Memory’.