Richard Philip Llewellyn Sear

Statistical physicists have long studied systems where the variable of interest spans many orders of magnitude, the classic example is the relaxation times of glassy materials, which are often found to follow power laws. A power-law dependence has been found for the probability of transmission of COVID-19, as a function of length of time a susceptible person is in contact with an infected person. This is in data from the United Kingdom's COVID-19 app. The amount of virus in infected people spans many orders of magnitude. Inspired by this I assume that the power-law behaviour found in COVID-19 transmission, is due to the effective transmission rate varying over orders of magnitude from one contact to another. I then use a model from statistical physics to estimate that if a population all wear FFP2/N95 masks, this reduces the effective reproduction number for COVID-19 transmission by a factor of approximately nine.

In an externally imposed electrolyte (salt) concentration gradient, charged
colloids drift at speeds of order one micrometre per second. This phenomenon is
known as diffusiophoresis. In systems with multiple salts and 'crossed' salt
gradients, a nonlocal component of the electric field associated with a
circulating (solenoidal) ion current can arise. This is in addition to the
conventional local component that depends only on the local salt gradients.
Here we report experimental observations verifying the existence of this
nonlocal contribution. To our knowledge this is the first observation of
nonlocal diffusiophoresis. The current develops quasi-instantaneously on the
time scale of salt diffusion. Therefore, in systems with multiple salts and
crossed salt gradients, one can expect a nonlocal contribution to
diffusiophoresis which is dependent on the geometry of the system as a whole
and appears as a kind of instantaneous 'action-at-a-distance' effect. The
interpretation is aided by a magnetostatic analogy. Our experiments are
facilitated by a judicious particle-dependent choice of salt (potassium
acetate) for which the two local contributions to diffusiophoresis almost
cancel, effectively eliminating conventional diffusiophoresis. This enables us
to clearly identify the novel, nonlocal effect and may be useful in other
contexts, for example in sorting particle mixtures.

We elucidate the origin of the critical Stokes number
$\mathrm{St}_\mathrm{c}$ for inertial particle capture by obstacles in flow
fields, and explain the empirical observation made by Araujo et al. [Phys. Rev.
Lett. 97, 138001 (2006)] that the capture efficiency grows as
$(\mathrm{St}-\mathrm{St}_\mathrm{c})^\beta$ with $\beta=1/2$ for some critical
Stokes number. This behaviour, which is inaccessible to classic perturbation
theory, derives from the global structure of the phase space of particle
trajectories from which viewpoint it is both generic and inevitable except in
the limit of highly singular stagnation point flows which we example. In the
context of airborne disease transmission, the phenomenon underlies the sharp
decline in filtration efficiency of face coverings for micron-sized aerosol
droplets.