Existence and non-existence for time-dependent mean field games with strong aggregation

We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form $$-\sigma m^\alpha $$ - σ m α ,$$\alpha \ge 2/N$$ α ≥ 2 / N , where m is the population density and N is the dimension of the state space. We prove the existence of solutions under the assumption that $$\sigma $$ σ is small enough. For large $$\sigma $$ σ , we show that existence may fail whenever the time horizon T is large.

A Quadratic Mean Field Games Model for the Langevin Equation

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker–Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

Assessment of natural regeneration of longleaf pine (Pinus palustris) 15 years post-regeneration control

We assessed natural regeneration of longleaf pine (Pinus palustris Mill.) using the data col-lected from the Escambia Experimental Forest in southern Alabama. Fifteen years following the regeneration control, natural regeneration of longleaf remained patchy across a wide range of site/stand conditions, with slightly more than half of all plots containing regeneration, but the den-sity of seedlings and saplings varied significantly. The abundance of seedlings ≤ 1-year-old was positively related to stand age and time since last fire, but negatively related to overstory basal area. The abundance of seedlings and saplings was positively related to stand age, but negatively related to time since last fire and overstory basal area. The probability of achieving ≥ 15,000 seedlings > 1-year-old but ≤ 1-m-tall ha-1 and ≥ 1,250 saplings > 1-m-tall ha-1 was, respectively, positively related to the ratio of time since last fire to overstory basal area and the ratio of quadratic mean diameter to site index. A longer fire interval (> two to three years) should be adopted to naturally regenerate longleaf. We did not find clear zones of exclusion present in natural regeneration even though over-story trees, seedlings and saplings tended to be repulsive spatially and > 80% grass stage seedlings and saplings occurred outside tree crowns.

Comparison of Transmission Measurement Methods of Elastic Waves in Phononic Band Gap Materials

Periodic cellular structures can exhibit metamaterial properties, such as phononic band gaps. In order to detect these frequency bands of strong wave attenuation experimentally, several devices for wave excitation and measurement can be applied. In this work, piezoelectric transducers are utilized to excite two additively manufactured three-dimensional cellular structures. For the measurement of the transmission factor, we compare two methods. First, the transmitted waves are measured with the same kind of piezoelectric transducer. Second, a laser Doppler vibrometer is employed to scan the mechanical vibrations of the sample on both the emitting and receiving surfaces. The additional comparison of two different methods of spatial averaging of the vibrometer data, that is, the quadratic mean and arithmetic mean, provides insight into the way the piezoelectric transducers convert the transmitted signal. Experimental results are supported by numerical simulations of the dispersion relation and a simplified transmission simulation.