Reliability of Harvested Rainfall as an Auxiliary Source of Non-potable Water

AbstractRainwater harvesting is an ancient practice that involves collecting, storing, and using precipitationto meeton-site water needs. This paper develops and demonstrates guidelines for sizing the capacity of storage tanks to provide areliable continuous supply of harvested rainwater for residential households. Operation of the rainwater harvesting system is simulated with a stochastic mass balance performed on an Excel spreadsheet. The daily volume of rainwater in an unbounded tank is tracked to determine the maximum accumulated deficit on a monthly basis. Results are summarized in dimensionless charts showing the minimum size of a rainwater storage tankneeded to meet water demands at specified levels of reliability

Importance of demand modelling in network water quality models: a review

Today, there is a growing interest in network water quality modelling. The water quality issues of interest relate to both dissolved and particulate substances. For dissolved substances the main interest is in residual chlorine and (microbiological) contaminant propagation; for particulate substances it is in sediment leading to discolouration. There is a strong influence of flows and velocities on transport, mixing, production and decay of these substances in the network. This imposes a different approach to demand modelling which is reviewed in this article. <br><br> For the large diameter lines that comprise the transport portion of a typical municipal pipe system, a skeletonised network model with a top-down approach of demand pattern allocation, a hydraulic time step of 1 h, and a pure advection-reaction water quality model will usually suffice. For the smaller diameter lines that comprise the distribution portion of a municipal pipe system, an all-pipes network model with a bottom-up approach of demand pattern allocation, a hydraulic time step of 1 min or less, and a water quality model that considers dispersion and transients may be needed. <br><br> Demand models that provide stochastic residential demands per individual home and on a one-second time scale are available. A stochastic demands based network water quality model needs to be developed and validated with field measurements. Such a model will be probabilistic in nature and will offer a new perspective for assessing water quality in the drinking water distribution system

Exploring the relationships between warm-season precipitation, potential evaporation, and “apparent” potential evaporation at site scale

Bouchet's complementary relationship and the Budyko hypothesis are two classic frameworks that are inter-connected. To systematically investigate the connections between the two frameworks, we analyze precipitation, pan evaporation, and potential evaporation data at 259 weather stations across the United States. The precipitation and pan evaporation data are from field measurement and the potential evaporation data are collected from a remote-sensing dataset. We use pan evaporation to represent apparent potential evaporation, which is different from potential evaporation. With these data, we study the correlations between precipitation and potential evaporation, and between precipitation and apparent potential evaporation. The results show that 93&thinsp;% of the study's weather stations exhibit a negative correlation between precipitation and apparent potential evaporation. Also, the aggregated data cloud of precipitation vs. apparent potential evaporation with 5312 warm-season data points from 259 weather stations shows a negative trend in which apparent potential evaporation decreases with increasing precipitation. On the other hand, no significant correlation is found in the data cloud of precipitation vs. potential evaporation, indicating that precipitation and potential evaporation are independent. We combine a Budyko-type expression, the Turc–Pike equation, with Bouchet's complementary relationship to derive upper and lower Bouchet–Budyko curves, which display a complementary relationship between apparent potential evaporation and actual evaporation. The observed warm-season data follow the trend of the Bouchet–Budyko curves. Our study shows the consistency between Budyko's framework and Bouchet's complementary relationship, with the distinction between potential evaporation and apparent potential evaporation. The formulated complementary relationship can be used in quantitative modeling practices.</p

Constructing Mutually Unbiased Bases in Dimension Six

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical approximations and corrected the number of triples existing for non-affine families (cf Table 3

A Factorization Algorithm for G-Algebras and Applications

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \in \mathcal{G}$, where $\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field. Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\"obner basis algorithm for $G$-algebras. This algorithm is useful for various applications, e.g. in analysis of solution spaces of systems of linear partial functional equations with polynomial coefficients, coming from $\mathcal{G}$. Additionally, it is possible to include inequality constraints for ideals in the input

Correlation or not correlation? This is the question in modeling residential water demand pulses

Published© 2013 The Authors. Published by Elsevier Ltd. This paper presents a comparison of two different modelling approaches for the generation of residential water demand pulses as Poisson processes. Both approaches are able to preserve the mean value of daily water demand. The main difference lies in the fact that the first considers the correlation between pulse durations and intensities whereas the second neglects it. Overall, the results of the applications aimed at reproducing the measured pulses in two households show that the increase in parameterization burden associated with taking correlation into account delivers a considerable improvement in the quality of model predictions

Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453