Effective null Raychaudhuri equation

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde

Entropy bounds and field equations

For general metric theories of gravity, we compare the approach that describes-derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler) horizons, studied by making use of the notion of a limiting thermodynamic scale $l^*$ of matter, previously introduced in the context of entropy bounds. In doing this: i) a bound for the entropy of any lump of matter with a given energy-momentum tensor $T_{ab}$ is considered, in terms of a quantity which is independent of the theory of gravity we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; ii) by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald's entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity); iii) a notion of $l^*$ for horizons, and an expression for it, is given.Comment: 8 pages, 1 figure; v4: some typos corrected, one reference and some clarifications added, some editin

Impact of Thermal Aging on the Microstructure Evolution and Mechanical Properties of Lanthanum-Doped Tin-Silver-Copper Lead-Free Solders

The authors would like to thank Ste´phanie Blanc (Electrical Engineer at Schlumberger) for her useful contribution to the project, Claude Guyomard and Olivier Naegelen (Arts et Me´tiers ParisTech) for the die design and sample casting, respectively, and Jean-Marc Raulot for his enriching discussions.An extensive study is made to analyze the impact of pure lanthanum on the microstructure and mechanical properties of Sn-Ag-Cu (SAC) alloys at high temperatures. Different compositions are tested; the temperature applied for the isothermal aging is 150 C, and aging times of 10 h, 25 h, 50 h, 100 h, and 200 h are studied. Optical microscopy with cross-polarized light is used to follow the grain size, which is refined from 8 mm to 1 mm for as-cast samples and is maintained during thermal aging. Intermetallic compounds (IMCs) present inside the bulk Sn matrix affect the mechanical properties of the SAC alloys. Due to high-temperature exposure, these IMCs grow and hence their impact on mechanical properties becomes more significant. This growth is followed by scanning electron microscopy, and energy-dispersive spectroscopy is used for elemental mapping of each phase. A significant refinement in the average size of IMCs of up to 40% is identified for the as-cast samples, and the coarsening rate of these IMCs is slowed by up to 70% with no change in the interparticle spacing. Yield stress and tensile strength are determined through tensile testing at 20 C for as-cast samples and after thermal aging at 150 C for 100 h and 200h. Both yield stress and tensile strength are increased by up to 20% by minute lanthanum doping

Gravity from the entropy of light

The holographic principle, considered in a semiclassical setting, is shown to have direct consequences on physics at a fundamental level. In particular, a certain relation is pointed out to be the expression of holography in basic thermodynamics. It is argued moreover that through this relation holography can be recognized to induce gravity, and an expression for the gravitational lensing is obtained in terms of entropy over wavelength of black-body radiation, or, at a deeper level, in terms of maximum entropy over associated space to the elementary bit of information.Comment: 7 pages; v2: completion of the list of references; v3: the discussion is divided in Sections and the argument is described in more detail; v4: a statement is added (below eq.13) on what is the supposed difference between Jacobson's work in ref.21 and this attempt; addition of a paragraph in last Sectio