Pamphlet for Hapgoods Incorporated.

Pamphlet detailing the services provided by Hapgoods Incorporated

Manufactured caverns in carbonate rock

Disclosed is a process for manufacturing underground caverns suitable in one embodiment for storage of large volumes of gaseous or liquid materials. The method is an acid dissolution process that can be utilized to form caverns in carbonate rock formations. The caverns can be used to store large quantities of materials near transportation facilities or destination markets. The caverns can be used for storage of materials including fossil fuels, such as natural gas, refined products formed from fossil fuels, or waste materials, such as hazardous waste materials. The caverns can also be utilized for applications involving human access such as recreation or research. The method can also be utilized to form calcium chloride as a by-product of the cavern formation process

Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics

The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that the combined effects of migration and noise cannot account for the stabilization. The missing ingredient is the dependence of the oscillations' frequency upon their amplitude; with that, noise-induced differences between patches are amplified due to the frequency gradient. Migration among desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the functional dependence of the desynchronization upon diffusion strength and frequency differences. The oscillations' amplitude is shown to be (almost) noise independent. The results are compared with a numerical integration of the marginally stable Lotka-Volterra equations. An unstable system is extinction-prone for small noise, but stabilizes at larger noise intensity