A New Approach to Mixed/Boundary Friction Prediction Using the Logistics Curve

There is a strong focus on improving the energy efficiency of machines. Over the last 20-30 years, one way to improve energy efficiency has been to reduce lubricant viscosity. This also has the effect of leading to thinner oil films between the machine’s moving surfaces and is likely to lead to increased mixed/boundary friction. Accurately predicting friction in the mixed/boundary friction regime is therefore becoming of great importance. The work reported here suggests that commonly used asperity friction models significantly underestimate friction in the mixed/boundary friction, and a new model, based on a logistic curve fit, gives a better estimate of mixed/boundary friction, provides good agreement with experimental friction data (from Mini Traction Machine experiments), and is much more straightforward for engineers and tribologists to apply for the estimation of mixed/boundary friction losses.

Finite-time boundary stabilization of fractional reaction-diffusion systems

This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are presented to ensure the FTS of FRDSs via the designed boundary controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system’s coefficients. Under the designed boundary controller, sufficient conditions are presented to guarantee the robust FTS of uncertain FRDSs. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.

Indications of a Decrease in the Depth of Deep Convective Cores with Increasing Aerosol Concentration During the CACTI Campaign

An aerosol indirect effect on deep convective cores (DCCs), by which increasing aerosol concentration increases cloud-top height via enhanced latent heating and updraft velocity, has been proposed in many studies. However, the magnitude of this effect remains uncertain due to aerosol measurement limitations, modulation of the effect by meteorological conditions, and difficulties untangling meteorological and aerosol effects on DCCs. The Cloud, Aerosol, and Complex Terrain Interactions (CACTI) campaign in 2018-19 produced concentrated aerosol and cloud observations in a location with frequent DCCs, providing an opportunity to examine the proposed aerosol indirect effect on DCC depth in a rigorous and robust manner. For periods throughout the campaign with well mixed boundary layers, we analyze relationships that exist between aerosol variables (condensation nuclei concentration >10 nm, 0.4% cloud condensation nuclei concentration, 55-1000 nm aerosol concentration, and aerosol optical depth) and meteorological variables [level of neutral buoyancy (LNB), convective available potential energy, mid-level relative humidity, and deep layer vertical wind shear] with the maximum radar echo top height and cloud-top temperature (CTT) of DCCs. Meteorological variables such as LNB and deep-layer shear are strongly correlated with DCC depth. LNB is also highly correlated with three of the aerosol variables. After accounting for meteorological correlations, increasing values of the aerosol variables (with the exception of one formulation of AOD) are generally correlated at a statistically significant level with a warmer CTT of DCCs. Therefore, for the study region and period considered, increasing aerosol concentration is mostly associated with a decrease in DCC depth.

Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

We prove that among all doubly connected domains of R n of the form B 1 \ B 2 , where B 1 and B 2 are open balls of fixed radii such that B 2 ⊂ B 1 , the first non-trivial Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature.