Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

ON FINDING COEFFICIENT OF GENERATING FUNCTION

This paper review the method of determining the coefficients of a generating function. Generating functions are a convenient tool for handling special constraints in selection and arrangement problems. It can be used in recurrence relations, inclusion exclusion events study, and polya’s enumeration formula. It may also help to solve some other combinatorial problems. Generating functions are a kind of abstract problem-solving technique once we understand it may easy to model a broad spectrum of combinatorial problems. In this paper, we will usesome vivid examples to demonstrate both the theoretical and applicable results of generating function

Inclusion and Exclusion probability

We use mathematical induction method to prove the Poincare Formula. To demonstrate the usefulness of this formula, we provide five examples. This formula is related to a broad class of counting problems in which several interacting properties either all must hold, or none must hold. When there are only two or three events that need to be counted, we usually use a Venn diagram. In section 4, we present a general mathematical formula to count any finite number of inclusion and exclusion events. This leads to an easy way to apply the Poincare Formula to define the probability

Water Out Shit In: a new paradigm for resource recovery

Phosphate is the most essential nutrient that must be recovered from waste streams in the future, because the easily minable phosphorus rock reserves will be depleted within 50 to 100 years. For an efficient recovery and reuse, a waste water flow with a high concentration and a low volume is needed. However, the present system of production, collection, transport and treatment of sanitary waste water is aimed at safe disposal of waste water and focussed on health and minimisation of environmental effect. This resulted in a diluted, large volume of sanitary waste water from which the resource recovery is less efficient. To accommodate the new requirement of recovery of nutrients, a novel approach combining the health and environment requirements with the recoverynecessity is needed.A new approach “Water Out Shit In” (WOSI) is proposed in this perspective paper.Application results in a single concentrated flow of waste water with a high concentration of organic load. Main feature of the WOSI approach is its system wide approach addressing all elements of the urban waste water chain from production to transportation to treatment and recovery. WOSI starts at the individual houses, ends at the resource recovery and reuse. In each stage, the main question is: how to remove water or prevent it from entering and how to increase the organic load.The chain starts in the houses. Reducing water consumption of the biggest sanitary waste water producers, i.e. the toilet, the shower and the washing machine, is a potentially effective step in this approach. Household and kerbside organic waste should be added into the sanitary sewer as much as possible. A small diameter gravitational in-house sewer is proposed to be used for collecting and transporting such highly-loaded flow.Within the transportation from household to the treatment, the storm water collection system could be disconnected from sanitary sewer system for preventing further dilution.The chain ends at the waste water treatment, which will be transformed into a resource recovery center via integrating several novel biotechnologies. Overall, a new paradigm for urban infrastructure and inner installation serving resource recovery is emerging

Semi-parametric Expected Shortfall Forecasting

Intra-day sources of data have proven effective for dynamic volatility and tail risk estimation. Expected shortfall is a tail risk measure, that is now recommended by the Basel Committee, involving a conditional expectation that can be semi-parametrically estimated via an asymmetric sum of squares function. The conditional autoregressive expectile class of model, used to indirectly model expected shortfall, is generalised to incorporate information on the intra-day range. An asymmetric Gaussian density model error formulation allows a likelihood to be developed that leads to semiparametric estimation and forecasts of expectiles, and subsequently of expected shortfall. Adaptive Markov chain Monte Carlo sampling schemes are employed for estimation, while their performance is assessed via a simulation study. The proposed models compare favourably with a large range of competitors in an empirical study forecasting seven financial return series over a ten year period

New facilitated transport membranes for CO2 capture and separation

We have synthesized new facilitated transport membranes comprising high-molecular-weight polyvinylamine (PVAm) as the fixed site carrier and aminoacid salt (e.g., piperazine glycinate (PG) or lithium glycinate (LG)) as the mobile carrier for facilitated transport of CO2. PVAm samples with different molecular weights were synthesized through free radical polymerization by adjusting the monomer concentration and initiator amount. The synthesized PVAm showed both a higher molecular weight and a higher solution viscosity than the commercially available PVAm (Lupamin® 9095 from BASF Corporation). The high viscosity of the PVAm solution at a low concentration allowed for the preparation of much thinner membranes. It could also help reducing penetration of the polymer solution into the pores of the substrate, further minimizing the mass transfer resistance. Consequently, a high CO2 permeance could be obtained from thin membranes with the thicknesses of 100 – 200 nm. The PVAm/PG blend solution was coated onto different substrates including polyethersulfone (PES) and polysulfone (PSf) substrates. Sodium dodecyl sulfate (SDS) surfactant was incorporated in the coating solution to improve the adhesion between the membrane layer and the substrate in some cases. The resultant PVAm/PG membranes exhibited a high CO2 permeance of about 1100 GPU and a high CO2/N2 mixed gas selectivity of more than 140 at the typical flue gas temperature of 57°C along with 17% water vapor, which is the desirable performance for post-combustion CO2 capture from coal-fired power plants

Multiple Facets of Damage Caused by Exposure to Low-Dose Radiation and the Legal Remedy

In addition to the toll in human life, there are at least three facets of damage caused by the protracted exposure to low-dose radiation: bodily injury, mental anguish, and property injury. After examining cases and compensation schemes in the United States and Taiwan, this article concludes that both the Taiwanese administrative compensation scheme and U.S. federal courts\u27 interpretation of the Price-Anderson Act favor finding injury to the claimants\u27 property, but not adverse effects to their health. To redress the injustice caused by the systemic bias, this article argues that the tort system should be adapted to tolerate gray area, such as the adoption of the probability of causation. This article further argues that the probability of causation should be applied in calculating damages in the radiation-exposure context

Bayesian Semi-parametric Expected Shortfall Forecasting in Financial Markets

Bayesian semi-parametric estimation has proven effective for quantile estimation in general and specifically in financial Value at Risk forecasting. Expected short-fall is a competing tail risk measure, involving a conditional expectation beyond a quantile, that has recently been semi-parametrically estimated via asymmetric least squares and so-called expectiles. An asymmetric Gaussian density is proposed allowing a likelihood to be developed that leads to Bayesian semi-parametric estimation and forecasts of expectiles and expected shortfall. Further, the conditional autoregressive expectile class of model is generalised to two fully nonlinear families. Adaptive Markov chain Monte Carlo sampling schemes are employed for estimation in these families. The proposed models are clearly favoured in an empirical study forecasting eleven financial return series: clear evidence of more accurate expected shortfall forecasting, compared to a range of competing methods is found. Further, the most favoured models are those estimated by Bayesian methods

Bayesian Assessment of Dynamic Quantile Forecasts

Methods for Bayesian testing and assessment of dynamic quantile forecasts are proposed. Specifically, Bayes factor analogues of popular frequentist tests for independence of violations from, and for correct coverage of a time series of, quantile forecasts are developed. To evaluate the relevant marginal likelihoods involved, analytic integration methods are utilised when possible, otherwise multivariate adaptive quadrature methods are employed to estimate the required quantities. The usual Bayesian interval estimate for a proportion is also examined in this context. The size and power properties of the proposed methods are examined via a simulation study, illustrating favourable comparisons both overall and with their frequentist counterparts. An empirical study employs the proposed methods, in comparison with standard tests, to assess the adequacy of a range of forecasting models for Value at Risk (VaR) in several financial market data series

Bayesian time-varying quantile forecasting for Value-at-Risk in financial markets

Recently, Bayesian solutions to the quantile regression problem, via the likelihood of a Skewed-Laplace distribution, have been proposed. These approaches are extended and applied to a family of dynamic conditional autoregressive quantile models. Popular Value at Risk models, used for risk management in finance, are extended to this fully nonlinear family. An adaptive Markov chain Monte Carlo sampling scheme is adapted for estimation and inference. Simulation studies illustrate favourable performance, compared to the standard numerical optimization of the usual nonparametric quantile criterion function, in finite samples. An empirical study generating Value at Risk forecasts for ten major financial stock indices finds significant nonlinearity in dynamic quantiles and evidence favoring the proposed model family, for lower level quantiles, compared to a range of standard parametric volatility models, a semi-parametric smoothly mixing regression and some nonparametric risk measures, in the literature