Verdier specialization via weak factorization

Let X in V be a closed embedding, with V - X nonsingular. We define a constructible function on X, agreeing with Verdier's specialization of the constant function 1 when X is the zero-locus of a function on V. Our definition is given in terms of an embedded resolution of X; the independence on the choice of resolution is obtained as a consequence of the weak factorization theorem of Abramovich et al. The main property of the specialization function is a compatibility with the specialization of the Chern class of the complement V-X. With the definition adopted here, this is an easy consequence of standard intersection theory. It recovers Verdier's result when X is the zero-locus of a function on V. Our definition has a straightforward counterpart in a motivic group. The specialization function and the corresponding Chern class and motivic aspect all have natural `monodromy' decompositions, for for any X in V as above. The definition also yields an expression for Kai Behrend's constructible function when applied to (the singularity subscheme of) the zero-locus of a function on V.Comment: Minor revision. To appear in Arkiv f\"or Matemati

Sound and light from fractures in scintillators

Prompted by intriguing events observed in certain particle-physics searches for rare events, we study light and acoustic emission simultaneously in some inorganic scintillators subject to mechanical stress. We observe mechanoluminescence in ${Bi}_4{Ge}_{3}{O}_{12}$, ${CdWO}_{4}$ and ${ZnWO}_{4}$, in various mechanical configurations at room temperature and ambient pressure. We analyze how the light emission is correlated to acoustic emission during fracture. For ${Bi}_4{Ge}_{3}{O}_{12}$, we set a lower bound on the energy of the emitted light, and deduce that the fraction of elastic energy converted to light is at least $3 \times 10^{-5}$