We report on an ultrafast experimental and simulations study of the early relaxation events of photoexcited tryptophan in water. Experimentally, we used fluorescence up-conversion in both polychromatic and single wavelength detection modes in the 300-480 nm range with polarization dependence. We report on the time evolution of the Stokes shift, bandwidth, and anisotropy from tens of femtoseconds to picoseconds. These observables contain signatures of the simultaneous occurrence of intramolecular and solvent-molecule interactions, which we disentangle with the help of nonequilibrium molecular dynamics simulations. We also observe a breakdown of the linear response approximation to describe our results.

The Beverloo scaling for the gravity flow of granular materials through orifices has two distinct universal features. On the one hand, the flow rate is independent of the height of the granular column. On the other hand, less well-known yet more striking, the flow rate is fairly insensitive to the material properties of the grains (density, Young's modulus, friction coefficient, etc.). We show that both universal features are lost if work is done on the system at a high rate. In contrast to viscous fluids, the flow rate increases during discharge if a constant pressure is applied to the free surface of a granular column. Moreover, the flow rate becomes sensitive to the material properties. Nevertheless, a new universal feature emerges: the dissipated power scaled by the mean pressure and the flow rate follows a master curve for forced and unforced conditions and for all material properties studied. We show that this feature can be explained if the granular flow in the silo is assumed to be a quasistatic shear flow under the μ(I)-rheology.

17, 35 (1852)]and Beverloo et al. [W. Beverloo et al., Chem. Eng. Sci. 15, 260 (1961)], the flow rate of granular material discharging through a circular orifice from a silo has been described by means of dimensional analysis and experimental fits and explained through the free-fall arch model. Here, in contrast to the traditional approach, we derive a differential equation based on the energy balance of the system. This equation is consistent with the well-known Beverloo rule due to a compensation of energy terms. Moreover, this equation can be used to explore different conditions for silo discharges. In particular, we show how the effect of friction on the flow rate can be predicted. The theory is validated using discrete element method simulations.