Implementation of sustainable sanitation in existing urban areas: long-term strategies for an optimised solution.

If technologies for decentralised sanitation and reuse (DESAR) and for natural stormwater management should at least partially replace existing systems, then intensive reconstruction work becomes essential. A conversion can only be realised successively over a long period due to high construction and financial expenses and requires new strategies. This paper presents the development and practical implementation of a mathematical tool to find an optimised strategy for the realisation of alternative and more decentralised drainage and sanitation concepts in existing urban areas. The succession of construction measures (e.g. the implementation of decentralised greywater recycling) for the whole period of consideration is determined based upon a mathematical optimisation model on the condition that the favoured future state is known. The model describes the complex interdependencies of the urban water and nutrient cycle and enables the minimisation of both financial efforts and ecological impacts on the way toward the future state. The results of the implementation for a rural area in Germany show that the mathematical optimisation is an adequate instrument to support decision-making processes in finding strategies for the realisation of sustainable urban water management.     

Fast method to compute the scalar product of gradient and given vector

The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) ^tv. In the standard method for computingg(u) ^tv the amount of work grows withn·#(f). In this note a new method for computingg(u) ^tv is presented. The new method is considerably faster, its amount of work only grows with #(f).     

The possibility of evolving a theory for predicting the service life of reinforced concrete structures

The development in recent years with increasing air pollution, increasing need of energy saving and last not least the growing number of damage in old structures leads to a raising demand to calculate the durability of structures, too. The paper has been prepared by request of the RILEM Technical Committee 45-LTO to show that, in principle, it is possible to evolve a theory for predicting the service life of r.c. structures and to sketch a way how that could be achieved. A lot of necessary basic data can be found scattered in the literature. To collect these data will be the first step to take.     

Consistent structure determination of a noisy measurement system model

This paper describes a fast and accurate method for defining the structure of a noisy measurement system model without a previous parameters evaluation. The procedure is based on the following steps: (i) choosing a stable system structure; (ii) determing the real model order; (iii) estimating the model parameters. In (i) a value of the model order greater than the supposed one is assumed; in (ii), in order to determine the real structure, samples of the input/output signals of the actual model and the over-parametrised one are used; in (iii), by means of unbiased identification techniques, the model parameters are evaluated. The proposed method can be used both in batch and real-time processing. Experimental results concerning a single input-single output linear process with different model order and noise statistical properties are given.     

How to avoid logarithms in comparisons with uniform random variables

In many algorithms for sampling from non-uniform distributions the logarithm of a uniform deviate must be compared with some test quantity. It is shown that all these comparisons can be done efficiently without calling a logarithm subprogram: two procedures for this task are presented and compared.     

On plastic potentials for anisotropic metals and their derivation from the texture function

Summary Plastic yielding of anisotropic metals can be either described by a macroscopic constitutive relation or assessed by means of a model which correlates single and polycrystal behaviors. The mathematical identification of the plastic work rate derived from the two approaches, for all strain rate tensors, leads to a fit of the polycrystal yield surface by an analytical function. When a quadratic from is assumed, the macroscopic anisotropy parameters become explicit functions of the texture coefficients. This identification method is applied to calculate yield surfaces andR-values of rolled and annealed steel sheets: theR-values and in general the flow rule, are more significantly modified by the fitting than the yield surface. Thus, it is worth extending the method to more general constitutive relations which may be given by the form of their work function: alternative forms of the work function for plastic materials are explored, especially in the bearing of convexity and homogeneity where quadratic forms have a distinct advantage. Finally, it is shown that the identification of the work function allows to express the phenomenological coefficients as analytical functions of the texture parameters for many forms of the work function; in the other cases, these coefficients may be obtained by linear or non-linear regression.