The hydraulic impact and alleviation phenomena numeric modeling in the industrial pumped pipelines

The issues of the hydropercussion phenomena mathematical modeling in the industrial pumped piping systems, with the pumps and dampeners included, to determine the impact absorbers effectiveness on the amplitude-frequency charac- teristics of these hydro-mechanical systems are considered. It’s still actual and many authors are still looking for the systems CFD issues research and resolution, see [6, 7]. Method of calculating the transient and frequency characteristics of the pipeline that contains a pump and a dampener, is based on nonlinear mathematical model. Simulation of overlapping stream with using industrial valves is provided by introducing the exponential law of diminishing cross-sectional area of the pipeline. The basis of calculation is the method of characteristics applied to the simplified Navier- Stokes equations

Modelling and simulation framework for reactive transport of organic contaminants in bed-sediments using a pure java object - oriented paradigm

Numerical modelling and simulation of organic contaminant reactive transport in the environment is being increasingly relied upon for a wide range of tasks associated with risk-based decision-making, such as prediction of contaminant profiles, optimisation of remediation methods, and monitoring of changes resulting from an implemented remediation scheme. The lack of integration of multiple mechanistic models to a single modelling framework, however, has prevented the field of reactive transport modelling in bed-sediments from developing a cohesive understanding of contaminant fate and behaviour in the aquatic sediment environment. This paper will investigate the problems involved in the model integration process, discuss modelling and software development approaches, and present preliminary results from use of CORETRANS, a predictive modelling framework that simulates 1-dimensional organic contaminant reaction and transport in bed-sediments

A Generic Path Algorithm for Regularized Statistical Estimation

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints lead to the popular lasso, fused-lasso, and other generalized $l_1$ penalized regression methods. Although there has been a lot of research in this area, developing efficient optimization methods for many nonseparable penalties remains a challenge. In this article we propose an exact path solver based on ordinary differential equations (EPSODE) that works for any convex loss function and can deal with generalized $l_1$ penalties as well as more complicated regularization such as inequality constraints encountered in shape-restricted regressions and nonparametric density estimation. In the path following process, the solution path hits, exits, and slides along the various constraints and vividly illustrates the tradeoffs between goodness of fit and model parsimony. In practice, the EPSODE can be coupled with AIC, BIC, $C_p$ or cross-validation to select an optimal tuning parameter. Our applications to generalized $l_1$ regularized generalized linear models, shape-restricted regressions, Gaussian graphical models, and nonparametric density estimation showcase the potential of the EPSODE algorithm.Comment: 28 pages, 5 figure

Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology

Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex task, such that we have little choice but to approach the problem with computational methods. Numerical continuation is a computational method for analysing the dynamics of nonlinear models by algorithmically detecting bifurcations. Here we aim to promote the use of numerical continuation tools by providing an introduction to nonlinear dynamics and numerical bifurcation analysis. Many numerical continuation packages are available, covering a wide range of system classes; a review of these packages is provided, to help both new and experienced practitioners in choosing the appropriate software tools for their needs.Comment: 14 pages, 2 figures, 2 table