Stationary distributions of the multi-type ASEP

We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or systems of queues in tandem. Let $q$ be the asymmetry parameter of the system. The queueing construction generalises the one previously known for the totally asymmetric ($q=0$) case, by introducing queues in which each potential service is unused with probability $q^k$ when the queue-length is $k$. The analysis is based on the matrix product representation of Prolhac, Evans and Mallick. Consequences of the construction include: a simple method for sampling exactly from the stationary distribution for the system on a ring; results on common denominators of the stationary probabilities, expressed as rational functions of $q$ with non-negative integer coefficients; and probabilistic descriptions of "convoy formation" phenomena in large systems.Comment: 54 pages, 4 figure

Well design as a factor contributing to loss of water from the Floridan Aquifer, eastern Clay County, Florida

A number of wells penetrating the Floridan aquifer in eastern Clay County were found to be losing water to permeable zones above this aquifer. A differential in artesian pressure was observed in closely spaced wells of similar depth. Further investigation. revealed that the pressure differential in the wells was due to the design of the wells, of which there were four principal types. A comparison of the four types of wells in relation to the subsurface geology showed that three types of wells were open to the permeable zones above the Floridan aquifer. In such wells water of relatively high head from the Floridan aquifer moves up through the well bore and out into zones of relatively low head. The estimated water loss from poorly designed wells ranged from 32 to 180 gpm (gallons per minute). The artesian head loss in leaky wells ranged from 3 to 15 feet. A total loss of water of 39 mgd (million gallons per day) was estimated from all the leaky wells in the area. A significant decline of the piezometric surface of the Floridan aquifer was observed in eastern Clay County. Some of this decline can be attributed to the loss of water from the Floridan aquifer through these poorly designed wells. (Document has 16 pages.