Down-to-earth temperatures: The mechanics of the thermal environment

This lecture describes some recent attempts at unravelling the mechanics of the temperature distribution near ground, especially during calm, clear nights. In particular, a resolution is offered of the so-called Ramdas paradox, connected with observations of a temperature minimum some decimetres above bare soil on calm clear nights, in apparent defiance of the Rayleigh criterion for instability due to thermal convection. The dynamics of the associated temperature distribution is governed by radiative and convective transport and by thermal conduction, and is characterised by two time constants, involving respectively quick radiative adjustments and slow diffusive relaxation. The theory underlying the work described here suggests that surface parameters like ground emissivity and soil thermal conductivity can exert appreciable influence on the development of nocturnal inversions.

Constraining form factors with the method of unitarity bounds

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also to isolate domains on the real axis and in the complex energy plane where zeros are excluded. In this lecture note, we review the mathematical techniques of this formalism in its standard form, known as the method of unitarity bounds, and recent developments which allow us to include information on the phase and modulus along a part of the unitarity cut. We also provide a brief summary of some results that we have obtained in the recent past, which demonstrate the usefulness of the method for precision predictions on the form factors.