Impact-induced tensile waves in a kind of phase-transforming materials

This paper concerns the global propagation of impact-induced tensile waves in a kind of phase-transforming materials. It is well-known that the governing system of partial differential equations is hyperbolic-elliptic and the initial-boundary value problem is not well-posed at all levels of loading. By making use of fully nonlinear stress-strain curve to model this material, Dai and Kong succeeded in constructing a physical solution of the above initial-boundary value problem. For the impact of intermediate range, they assumed that $\beta<3\alpha$ in the stress-response function for simplicity. In this paper, we revisit the impact problem and consider the propagation of impact-induced tensile waves for all values of the parameters $\alpha$ and $\beta$. The physical solutions for all levels of loading are obtained completely.Comment: 14 pages; 5 figures; submitted to IMA Journal of Applied Mathematic

Numerical Study of Drop Motion on a Surface with Wettability Gradient and Contact Angle Hysteresis

In this work, the motion of a 2-D drop on a surface with given wettability gradient is studied numerically by a hybrid lattice-Boltzmann finite-difference method using the multiple-relaxation-time collision model. We incorporate the geometric wetting boundary condition that allows accurate implementation of a contact angle hysteresis model. The method is first validated through three benchmark tests, including the layered Poiseuille flow with a viscosity contrast, the motion of a liquid column in a channel with specified wettability gradient and the force balance for a static drop attached to a surface with hysteresis subject to a body force. Then, simulations of a drop on a wall with given wettability gradient are performed under different conditions. The effects of the Reynolds number, the viscosity ratio, the wettability gradient, as well as the contact angle hysteresis on the drop motion are investigated in detail. It is found that the capillary number of the drop in steady state is significantly affected by the viscosity ratio, the magnitudes of the wettability gradient and the contact angle hysteresis, whereas it only shows very weak dependence on the Reynolds number

Measuring the spectral running from cosmic microwave background and primordial black holes

We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, namely $|n_t|\lesssim 9.3\times 10^{-3}$ which will be very difficult to be measured by CMB data only in the future, and the absolute value of derived running of tensor spectral index is not larger than $2.1\times 10^{-4}$ at 95% confidence level.Comment: 5 pages, 3 figure