2D numerical simulation of submerged hydraulic jumps

Hydraulic jumps are usually used to dissipate energy in hydraulic engineering. In this paper, the turbulent submerged hydraulic jumps are simulated by solving the unsteady Reynolds averaged Navier–Stokes equations along with the continuity equation and the standard k–? equations for turbulence modeling. The Lagrangian moving grid method is employed for the simulation of the free surface. In the developed model, kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water elevation can be obtained along with velocity and pressure fields as part of the solution. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Comparisons with experimental measurements show that numerical model can simulate the velocity field, variation of free surface, maximum velocity, Reynolds shear and normal stresses at various stations with reasonable accuracy.     

Evaluating flood extent mapping of two hydraulic models, 1D HEC‐RAS and 2D LISFLOOD‐FP in comparison with aerial imagery observations in Gorgan flood plain,Iran

We compared flood mapping techniques using a one‐dimensional (1D) hydraulic model HEC‐RAS and two‐dimensional (2D) LISFLOOD‐FP for a 10‐km reach of Gorgan River in Iran. Both models were run using the same hydrologic input data. The input into the models was a steady discharge of 90 cm, corresponds to a flood peak occurred on March 25, 2012. Flood maps generated using these two models were compared with an observed flood inundation map, using F‐statistic. The roughness coefficients of the models were calibrated by maximizing the value of the F‐statistic. Based on the F‐statistic, LISFLOOD‐FP gives a slightly better result (F = 0.69) than HEC‐RAS (F = 0.67). Visual comparison of the flood extents generated by the two models showed reasonably good agreement. Validation was done using a flood event occurred on May 31, 2014. The LISFLOOD‐FP model gave a better result for validation as well. The 2D model showed more consistency in comparison with the 1D model.     

Decentralized controllers design for open-channel hydraulic systems via eigenstructure assignment

In this paper, we propose the design of both a proportional (P) and a proportional integral (PI) decentralized controller for open-channel hydraulic systems by assigning the closed-loop eigenstructure. The system dynamic is described by a linear, time-invariant model deduced from the Saint-Venant equations. A constant-volume control law is designed, satisfying the requirement of decentralization, typical of large-scale systems like the hydraulic one herein examined. The synthesis procedure followed in this paper allows us to derive a parametric expression for the set of feedback gains of decentralized controllers which achieve the desired eigenvalue assignment. The free parameters in this parametric expression can be used to assign eigenvectors as close to the desired ones as possible, while achieving the required eigenvalue assignment.     

Direct solution to problems of hydraulic jump in horizontal triangular channels

The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are available in technical literature for sequent depth ratios in horizontal triangular channels because it is presumed that the governing equation is a quintic equation. In the present study, considering physical concepts this quintic equation has been reduced to a quartic equation. In the next step, this quartic equation has been converted to a resolvent cubic equation and two quadratic equations. This research shows these steps clearly to reach an acceptable physical analytic solution for sequent depth ratios in horizontal triangular channels.     

Transboundary extraction of groundwater in the presence of hydraulic fracturing

We studied transboundary groundwater management problems in the presence of hydraulic fracturing. We found that the presence of risk suggests there should be caution when considering hydraulic fracturing. Our results from the cooperative solution show a decrease in hydraulic fracturing and increase in the steady state survival rate of groundwater. We also provide a Pigouvian type tax that could be imposed on natural gas developers.     

A Hybrid Model for Pricing and Hedging of Long-dated Bonds

Abstract

Long-dated fixed income securities play an important role in asset-liability management, in life insurance and in annuity businesses. This paper applies the benchmark approach, where the growth optimal portfolio (GOP) is employed as numéraire together with the real-world probability measure for pricing and hedging of long-dated bonds. It employs a time-dependent constant elasticity of variance model for the discounted GOP and takes stochastic interest rate risk into account. This results in a hybrid framework that models the stochastic dynamics of the GOP and the short rate simultaneously. We estimate and compare a variety of continuous-time models for short-term interest rates using non-parametric kernel-based estimation. The hybrid models remain highly tractable and fit reasonably well the observed dynamics of proxies of the GOP and interest rates. Our results involve closed-form expressions for bond prices and hedge ratios. Across all models under consideration we find that the hybrid model with the 3/2 dynamics for the interest rate provides the best fit to the data with respect to lowest prices and least expensive hedges.     

Experimental Investigation of Elastodissipative Characteristics of Carbon-Fiber-Reinforced Plastics

A procedure is described for the experimental study of elastodissipative properties of carbon-fiber-reinforced plastic (CFRP) structures. Experimental values of dissipation factors are given for angle-ply structures with a reinforcing angle varying from 0 to 90°. Elastodissipative characteristics of two types of CFRP are identified. The values obtained can be used for predicting the properties of complex CFRP structures. It is shown that the energy absorption in sandwich structures with CFRP skins and a honeycomb core is mainly governed by properties of the skins.     

Mathematical modelling of hydraulic transients in simple systems

Efficiency and economy in the design and operation of a hydraulic system, as well as its safety, are objectives needing precise calculations of pressures and flowrates within the system. The calculations are typically very time-consuming and, depending on the characteristics of the system, very complicated and difficult to organize. A suitable mathematical modelling of the different ingredients in a hydraulic system is necessary to get useful results, which help fulfill those objectives. In this paper, the mathematical modelling used to develop a computer program to simulate hydraulic transients in a simple system is described. The program (DYAGATS), developed by the authors, is currently being used by organizations and consultancies to simulate and, consequently, analyze hydraulic transients in water systems. It makes use of the so-called elastic model, also known as waterhammer, to model the behavior of the fluid within the pipes. Also, lump models for the different elements that introduce, damp, modify, absorb, etc., perturbations in the systems are presented in a unified treatment. The main objective is to provide users with a powerful tool to devise the potential risks to which an installation may be exposed and to develop suitable protection strategies.     

A cognitively based simulation of academic science

The models used in social simulation to date have mostly been very simplistic cognitively, with little attention paid to the details of individual cognition. This work proposes a more cognitively realistic approach to social simulation. It begins with a model created by Gilbert (1997) for capturing the growth of academic science. Gilbert’s model, which was equation-based, is replaced here by an agent-based model, with the cognitive architecture CLARION providing greater cognitive realism. Using this cognitive agent model, results comparable to previous simulations and to human data are obtained. It is found that while different cognitive settings may affect the aggregate number of scientific articles produced, they do not generally lead to different distributions of number of articles per author. The paper concludes with a discussion of the correspondence between the model and the constructivist view of academic science. It is argued that using more cognitively realistic models in simulations may lead to novel insights. Isaac Naveh obtained a master’s degree in computer science at the University of Missouri. His research interests include hybrid cognitive models and multi-agent learning. Ron Sun is Professor of Cognitive Science at Rensselaer Polytechnic Institute, and formerly the James C. Dowell Professor of Engineering and Professor of Computer Science at University of Missouri-Columbia. He received his Ph.D in 1992 from Brandeis University. His research interest centers around studies of cognition, especially in the areas of cognitive architectures, human reasoning and learning, cognitive social simulation, and hybrid connectionist models. For his paper on integrating rule-based and connectionist models for accounting for human everyday reasoning, he received the 1991 David Marr Award from Cognitive Science Society. He is the founding co-editor-in-chief of the journal Cognitive Systems Research, and also serves on the editorial boards of many other journals. He is the general chair and program chair for CogSci 2006, and a member of the Governing Board of International Neural Networks Society. His URL is: http://www.cogsci.rpi.edu/~rsun     

Inter-comparison and validation of computational fluid dynamics codes in two-stage meandering channel flows

This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–ε turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y⁺, are satisfied. A rigorous inter-comparison of the codes is performed using large-scale experimental data from the UK Flood Channel Facility for a two-stage meandering channel. This example data set shows complex hydraulic behaviour without the additional complications found in natural rivers. Standardised methods are used to compare each model with the available experimental data. Results are shown for the streamwise and transverse velocities, secondary flow, turbulent kinetic energy, bed shear stress and free surface elevation. They demonstrate that the models produce similar results overall, although there are some differences in the predicted flow field and greater differences in turbulent kinetic energy and bed shear stress. This study is seen as an essential first step in the inter-comparison of some of the computational fluid dynamics codes used in the field of river engineering.     

A Definition of the Ground State Energy for Systems Composed of Infinitely Many Particles

Abstract

We introduce here one possible definition of the energy of an infinite non-periodic system of particles. We investigate the minimization of it, and the link with standard definitions of local ground state for such systems. The specific models under study are issued from Quantum Mechanics (namely from Density-Functional type theories) but our construction and analysis can be adapted to treat other cases.     

High order upwind scheme for modelling turbulent shallow water flow in hydraulic structures

An unstructured finite volume model for quasi-2D free surface flow with wet-dry fronts and turbulence modelling is presented. The convective flux is discretised with either a an hybrid second-order/first-order scheme, or a fully second order scheme, both of them upwind Godunov's schemes based on Roe's average. The hybrid scheme uses a second order discretisation for the two unit discharge components, whilst keeping a first order discretisation for the water depth [2]. In such a way the numerical diffusion is much reduced, without a significant reduction on the numerical stability of the scheme, obtaining in such a way accurate and stable results. It is important to keep the numerical diffusion to a minimum level without loss of numerical stability, specially when modelling turbulent flows, because the numerical diffusion may interfere with the real turbulent diffusion. In order to avoid spurious oscillations of the free surface when the bathymetry is irregular, an upwind discretisation of the bed slope source term [4] with second order corrections is used [2]. In this way a fully second order scheme which gives an exact balance between convective flux and bed slope in the hydrostatic case is obtained. The k – ε equations are solved with either an hybrid or a second order scheme. In all the numerical simulations the importance of using a second order upwind spatial discretisation has been checked [1]. A first order scheme may give rather good predictions for the water depth, but it introduces too much numerical diffusion and therefore, it excessively smooths the velocity profiles. This is specially important when comparing different turbulence models, since the numerical diffusion introduced by a first order upwind scheme may be of the same order of magnitude as the turbulent diffusion. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carbon-Fiber-Reinforced Plastics Based on an Imide Polymerizing Oligomer Binder with a Semi-Interpenetrating Structure

Semi-interpenetrating polymer networks (SIPNs) are synthesized based on a polyimide binder (imide polymerizing oligomer) with addition of polyamide acid. As acylating agents, they include derivatives of benzophenone-tetracarboxylic and diphenyloxide-tetracarboxylic acids and as aminocomponents - diaminodiphenylmethane, diaminodiphenyloxide, and metaphenylene diamine. It is shown that these systems form SIPNs of the snake-in-the-cage type. Uncured compositions forming melts at 300-330°C are used as binders for carbon-fiber-reinforced plastics (CFRP). The homophase structure of the SIPNs in CFRP is shown by dynamic mechanical tests. The interlaminar fracture toughness (G _1c) is measured by the method of a double cantilever beam. It is found that G _1c, as a function of the content (wt.%) of polyamid acid (PAA) in the initial composition used for obtaining CFRP, is of linear character, which is another confirmation of the homophase structure of the SIPNs. The interlaminar fracture toughness achieved for CFRP is 340 J/m² at a 30% PAA content in the initial composition, and the glass transition temperature, which determines the thermal stability of the composites, reaches 320°C. The prospects of employing these plastics in tribotechnics are discussed.     

Applications of Hybrid Monte Carlo to Bayesian Generalized Linear Models: Quasicomplete Separation and Neural Networks

Abstract

The “leapfrog” hybrid Monte Carlo algorithm is a simple and effective MCMC method for fitting Bayesian generalized linear models with canonical link. The algorithm leads to large trajectories over the posterior and a rapidly mixing Markov chain, having superior performance over conventional methods in difficult problems like logistic regression with quasicomplete separation. This method offers a very attractive solution to this common problem, providing a method for identifying datasets that are quasicomplete separated, and for identifying the covariates that are at the root of the problem. The method is also quite successful in fitting generalized linear models in which the link function is extended to include a feedforward neural network. With a large number of hidden units, however, or when the dataset becomes large, the computations required in calculating the gradient in each trajectory can become very demanding. In this case, it is best to mix the algorithm with multivariate random walk Metropolis—Hastings. However, this entails very little additional programming work.     

Introduction to Fibonacci and Lucas hybrinomials

ABSTRACT

The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the Fibonacci and Lucas hybrinomials, i.e. polynomials, which are a generalization of the Fibonacci hybrid numbers and the Lucas hybrid numbers, respectively.     

Structured Markov Chain Monte Carlo

Abstract

This article introduces a general method for Bayesian computing in richly parameterized models, structured Markov chain Monte Carlo (SMCMC), that is based on a blocked hybrid of the Gibbs sampling and Metropolis—Hastings algorithms. SMCMC speeds algorithm convergence by using the structure that is present in the problem to suggest an appropriate Metropolis—Hastings candidate distribution. Although the approach is easiest to describe for hierarchical normal linear models, we show that its extension to both nonnormal and nonlinear cases is straightforward. After describing the method in detail we compare its performance (in terms of run time and autocorrelation in the samples) to other existing methods, including the single-site updating Gibbs sampler available in the popular BUGS software package. Our results suggest significant improvements in convergence for many problems using SMCMC, as well as broad applicability of the method, including previously intractable hierarchical nonlinear model settings.     

Some autoregressive moving average processes with generalized Poisson marginal distributions

Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987,J. Time Ser. Anal.,8, 261–275; 1988,Statist. Hefte,29, 281–300) and McKenzie (1988,Adv. in Appl. Probab.,20, 822–835). The models have the same autocorrelation structure as their counterparts of standard ARMA models. Various properties, such as joint distribution, time reversibility and regression behavior, for each model are investigated.     

Piecewise Rigid Body Mechanics

Summary. We propose a new three-dimensional dynamic theory of transforming materials intended to make realistic simulations of the dynamic behavior of these materials accessible. The theory is appropriate for materials whose free energy function rises steeply from its energy wells. Essentially, the theory is the multiwell analog of ordinary rigid body mechanics with three additional features: the full stress is not treated as arbitrary (the average limiting tractions on each interface enter the theory as unknowns), a certain component of the local balance of linear momentum is used, and kinetic laws for interfacial motion are introduced based on ideas of Eshelby and Abeyaratne and Knowles. In an interesting special case of the resulting equations of motion, all material constants together with all information about the shape of the body collapse to a single dimensionless constant. We prove well-posedness up to the time of a collision between interfaces, and do a preliminary study of the problem of annihilation and nucleation of interfaces. Conservation laws and a dissipation inequality are identified. We also give generalizations of the theory to magnetic and thermodynamic piecewise rigid media. A probable application area for the theory is the assessment of the use of transforming materials at small scale as ``motors' for propulsion or actuation.     

Numerical Solution to Hybrid Stochastic Differential Systems

Abstract

In this article numerical methods for solving hybrid stochastic differential systems of Itô-type are developed by piecewise application of numerical methods for SDEs. We prove a convergence result if the corresponding method for SDEs is numerically stable with uniform convergence in the mean square sense. The Euler and Runge–Kutta methods for hybrid stochastic differential equations are specifically described and the order of the error is given for the Euler method. A numerical example is given to illustrate the theory.