Numerical Solution of Linear Fredholm Integro-Differential Equations by Non-standard Finite Difference Method

In this article we consider a non-standard finite difference method for numerical solution of linear Fredholm integro-differential equations. The non-standard finite difference method and the repeated / composite trapezoidal quadrature method are used to transform the Fredholm integro-differential equation into a system of non-linear algebraic equations. The numerical experiments on some linear model problems show the simplicity and efficiency of the proposed method. It is observed from the numerical experiments that our method is convergent and second order accurate

Escherichia coli inactivation kinetics in anaerobic digestion of dairy manure under moderate, mesophilic and thermophilic temperatures

Batch anaerobic digestion experiments using dairy manure as feedstocks were performed at moderate (25°C), mesophilic (37°C), and thermophilic (52.5°C) temperatures to understand E. coli, an indicator organism for pathogens, inactivation in dairy manure. Incubation periods at 25, 37, and 52.5°C, were 61, 41, and 28 days respectively. Results were used to develop models for predicting E. coli inactivation and survival in anaerobic digestion. For modeling we used the decay of E. coli at each temperature to calculate the first-order inactivation rate coefficients, and these rates were used to formulate the time - temperature - E. coli survival relationships. We found the inactivation rate coefficient at 52.5°C was 17 and 15 times larger than the inactivation rate coefficients at 25 and 37°C, respectively. Decimal reduction times (D10 ; time to achieve one log removal) at 25, 37, and 52.5°C, were 9 -10, 7 - 8 days, and \u3c 1 day, respectively. The Arrhenius correlation between inactivation rate coefficients and temperatures over the range 25 -52.5°C was developed to understand the impacts of temperature on E. coli inactivation rate. Using this correlation, the time - temperature - E. coli survival relationships were derived. Besides E. coli inactivation, impacts of temperature on biogas production, methane content, pH change, ORP, and solid reduction were also studied. At higher temperatures, biogas production and methane content was greater than that at low temperatures. While at thermophilic temperature pH was increased, at mesophilic and moderate temperatures pH were reduced over the incubation period. These results can be used to understand pathogen inactivation during anaerobic digestion of dairy manure, and impacts of temperatures on performance of anaerobic digesters treating dairy manure

Assessing Linkages between E. coli Levels in Streambed Sediment and Overlying Water in an Agricultural Watershed in Iowa during the First Heavy Rain Event of the Season

This study involved field observations in Squaw Creek watershed, located in central Iowa, to investigate the impact of a heavy rain event (rainfall of 71 mm in 24 h) on E. coli levels in the streambed sediment and overlying water. We assessed relationships between streamflow and E. coli and nutrient levels in the water column and streambed sediment. The results showed that during a heavy rain event, E. coli levels in the water column varied considerably, ranging from 360 to 37,553 CFU per 100 mL with a mean of 7,598 CFU per 100 mL. Elevated streamflow resulted in greater levels of E. coli in the water column. Streambed sediment E. coli levels ranged from 896 to 6,577 CFU per 100 g with a mean of 3,355 CFU per 100 g. Regression analysis found exponential relationships between streamflow and E. coli levels in the water column (R2 = 0.56) and between streamflow and E. coli levels in the streambed sediment (R2 = 0.45). R2 values of the exponential relationship between streamflow and water column E. coli levels increased considerably when regressions for the rising and falling limbs of the hydrograph were performed separately (R2 = 0.64 and 0.94, respectively). The exponential relationship between total suspended solids (TSS) and water column E. coli levels yielded an R2 of 0.38, while TSS and streamflow yielded an exponential relationship with an R2 of 0.64. The results presented here provide information on in-stream bacteria dynamics of an agricultural watershed during the first heavy rain of the season. We anticipate that the results will improve the understanding of in-stream E. coli transport during rain events and provide insight for policy makers to allocate E. coli loads in impaired water bodies

Solving Nonlinear Two Point Boundary Value Problems Using Exponential Finite Difference Method

In this article, we present exponential finite difference scheme for solving nonlinear two point boundary value problems with Dirichlet's boundary conditions . The local truncation error and under appropriate condition we have discussed the convergence of the proposed method. Numerical experiments demonstrate the use and computational efficiency of the method. Numerical results show that this method is at least fourth order accurate, which is good agreement with the theoretically established order of the method

Cooperative Emission of a Coherent Superflash of Light

We investigate the transient coherent transmission of light through an optically thick cold stron-tium gas. We observe a coherent superflash just after an abrupt probe extinction, with peak intensity more than three times the incident one. We show that this coherent superflash is a direct signature of the cooperative forward emission of the atoms. By engineering fast transient phenomena on the incident field, we give a clear and simple picture of the physical mechanisms at play.Comment: 4 Fig., 5 page

A high flux source of cold strontium atoms

We describe an experimental apparatus capable of achieving a high loading rate of strontium atoms in a magneto-optical trap operating in a high vacuum environment. A key innovation of this setup is a two dimensional magneto-optical trap deflector located after a Zeeman slower. We find a loading rate of 6x10^9/s whereas the lifetime of the magnetically trapped atoms in the 3P2 state is 54s.Comment: 12 pages, 16 figure