Space, the new frontier

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Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.Comment: 18 pages, 4 figures .eps, JPA styl

Coherent optical control of spin-spin interaction in doped semiconductors

We provide a theory of laser-induced interaction between spins localized by impurity centers in a semiconductor host. By solving exactly the problem of two localized spins interacting with one itinerant exciton, an analytical expression for the induced spin-spin interaction is given as a function of the spin separation, laser energy, and intensity. We apply the theory to shallow neutral donors (Si) and deep rare-earth magnetic impurities (Yb) in III-V semiconductors. When the photon energy approaches a resonance related to excitons bound to the impurities, the coupling between the localized spins increases, and may change from ferromagnetic to anti-ferromagnetic. This light-controlled spin interaction provides a mechanism for the quantum control of spins in semiconductors for quantum information processing; it suggests the realization of spin systems whose magnetic properties can be controlled by changing the strength and the sign of the spin-spin interaction.Comment: 10 pages, 5 figure

Space... the New Frontier

Space exploration - united states space progra

Catalytic Oxidation of Sulfur Dioxide in Wastewater

Sulfur dioxide has been shown to be an effective wastewater disinfectant. The aqueous sulfur dioxide creates and oxygen demand in the effulent which must be removed prior to discharge. Oxidation to sulfate is one means of accomplishing this task. Experiments were carried out to determine the effectiveness of transition metals and activated carbon as catalysts for the oxidation of S+IV species in wastewater. Both the metals and carbon are known catalysis, but what inhibitory effect the wastewater might have was unknown. Effectiveness was defined as a combination of catalyst life, effluent quality, and cost. Tradition metals were eliminated as potential catalysts due to the high metal concentrations found in the effluent. The acidic nature of 500 mg/l SO2 dissolved in wastewater (pH 2.5) would dissolve the metals or cause them to desorb from a carbon base. Using downflow contractors, activated carbon was shown to catalyze the reaction as long as sufficient oxygen was available. At a loading rate of 5.5 h carbon/1 and a hydraulic loading of 38 M^3/M^2 * day, 24 hour runs were accomplished without SO2 breakthrough (less than 4 mg/1). Longer runs resulted in gradual breakthrough (40 mg SO2/1 after 96 hours). The cause of the failure was assumed to be the self-poisoning of the catalyst by sulfuric acid (the product of SO2 oxidation) and/or the reduced solubility of oxygen in the sulfuric acid solution. Carbon regeneration, as a catalyst, was accomplished by backwashing the column with tap water. The cost of sulfur dioxide disinfection ranged from $0.23 -$0.73/1000 gallons treated. In general, this process was much more costly than other disinfection systems

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

A Study of Trihalomethane Precursors in Deer Creek Reservoir

Deer Creek Reservoir and tributaries were monitored from May to December 1983 in a study of the occurrence of trihalomethane (THM) precursors in the reservoir and nutrient dynamics of the reservoir system. Microcosms were used to study the effect of the following parameters on THM precursor production in the reservoir system: phosphorus loading, sediment, algal growth, and application of algicide. Additionally, THM precursor concentrations of interstitial water were analyzed in reservoir and microcosm sediment samples. Microcosms treated with ahigh phosphorus loading (70 ug/1) had THM precursor concentrations significantly higher than those measured in microcosms treated with a low phosphorus loading (10 ug/1). The presence of sediment in microcosms did not significantly affect THM precursor concentrations. Algae growth did result in THM production significantly aboce that measured in microcosms without algae growth. No correlation between total organic carbon and terminal total trihalomethane concentrations was found to exist in microcosms. Potassium permanganate and copper sulface were used as algicides. Applications of 0.3 mg/1 potassium permanganate and 50 ug/1 copper sulfate as Cu^+2 did not appear to affect THM precursor, total phosphorus, total suspended solids, or volatile suspended solids concentrations in the microcosms. Anoxic phosphorus release occurred in dark microcosms after the dissolved oxygen concentration dropped below approximately 3.0 mg/1. Considering all data collected, no significant difference in THM precursor concentraion could be detected between tributary and reservoir samples. THM precursor concentrations in tributaries were found to vary significantly be season. Samples collected from three depths within the reservoir were not found to have significantly different mean terminal total trihalomethane concentrations over the sampling period. No correlation between total organic carbon and terminal total trihalomethane concentrations was found to exist. Total phosphorus concentrations in tributaries were quite high, particularly in Main and Daniels Creeks

Comparison of the Effects of Ice and 3.5% Menthol Gel on Blood Flow and Muscle Strength of the Lower Arm

Context: Soft-tissue injuries are commonly treated with ice or menthol gels. Few studies have compared the effects of these treatments on blood flow and muscle strength. Objective: To compare blood flow and muscle strength in the forearm after an application of ice or menthol gel or no treatment. Design: Repeated measures design in which blood-flow and muscle-strength data were collected from subjects under 3 treatment conditions. Setting: Exercise physiology laboratory. Participants: 17 healthy adults with no impediment to the blood flow or strength in their right arm, recruited through word of mouth. Intervention: Three separate treatment conditions were randomly applied topically to the right forearm: no treatment, 0.5 kg of ice, or 3.5 mL of 3.5% menthol gel. To avoid injury ice was only applied for 20 min. Main Outcome Measures: At each data-collection session blood flow (mL/min) of the right radial artery was determined at baseline before any treatment and then at 5, 10, 15, and 20 min after treatment using Doppler ultrasound. Muscle strength was assessed as maximum isokinetic flexion and extension of the wrist at 30°/s 20, 25, and 30 min after treatment. Results: The menthol gel reduced (–42%, P \u3c .05) blood flow in the radial artery 5 min after application but not at 10, 15, or 20 min after application. Ice reduced (–48%, P \u3c .05) blood flow in the radial artery only after 20 min of application. After 15 min of the control condition blood flow increased (83%, P \u3c .05) from baseline measures. After the removal of ice, wrist-extension strength did not increase per repeated strength assessment as it did during the control condition (9–11%, P \u3c .05) and menthol-gel intervention (8%, P \u3c .05). Conclusions: Menthol has a fast-acting, short-lived effect of reducing blood flow. Ice reduces blood flow after a prolonged duration. Muscle strength appears to be inhibited after ice application