Renewable Resource Management with Stock Externalities: Coastal Aquifers and Submarine Groundwater Discharge

This paper develops a hydrologic-ecologic-economic model of groundwater use. Particularly, we model coastal groundwater management and its effects on submarine groundwater discharge, nearshore marine water quality, and marine biota. We show that incorporating the external effects on nearshore resources increases the optimal sustainable steady-state head level. Numerical simulations are illustrated using data from the Kuki’o region on the island of Hawaii. Two different approaches for incorporating the nearshore resource are examined. Including algae’s market value in the objective function results in only slightly lower rates of extraction. When a minimum constraint is placed on the stock of the keystone species, however, greater conservation may be indicated. The constraint also results in non-monotonic paths of water extraction, head level, and water price in the optimal solution.groundwater management, marine ecology, dynamic optimization, safe minimum standard, sustainability science

Association of molecules using a resonantly modulated magnetic field

We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimising the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state, and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order $h \times 1$ MHz.Comment: 8 pages latex, figures revised, references updated and typos correcte

Optimal Management of a Hawaiian Coastal Aquifer with Near-Shore Marine Ecological Interactions

We optimize groundwater management in the presence of marine consequences of submarine groundwater discharge (SGD). Concern for marine biota increases the optimal steady-state head level of the aquifer. The model is discussed in general terms for any coastal groundwater resource where SGD has a positive impact on valuable near-shore resources. Our application focuses of the Kona Coast of Hawai’i, where SGD is being actively studied and where both near-shore ecology and groundwater resources are serious sociopolitical issues. To incorporate the consequences of water extraction on nearshore resources, we impose a safe minimum standard for the quantity of SGD. Efficient pumping rates fluctuate according to various growth requirements on the keystone marine algae and different assumptions regarding recharge rates. Desalination is required under average recharge conditions and a strict minimum standard, and under low recharge conditions regardless of minimum standards of growth.groundwater management, marine ecology, dynamic optimization, safe minimum standard, sustainability science.

Burnett-Weaver Debate Volume Two: Operation of the Holy Spirit, Design of Baptism, The Creed Criticised

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