The L-L estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

We first obtain the L^p-L^q estimates of solutions to the Cauchy problem for one-dimensional damped wave equation

     

Numerical modeling of 3-D flow on porous broad crested weirs

Gabion weirs with optional design as a broad crested weirs are suitable structures to reduce flash flood with a minimal negative impact on the water environment. In the present study, the 3-D flow was simulated around gabion weirs with respect to free-surface water. The Reynolds-averaged Navier–Stokes equations are solved to predict water surface over the gabion weir. The VOF method with the geometric reconstruction scheme was applied to treat the complex free-surface flow. Simulations were performed using three variants of the k–ε and the RSM models to find the water level and velocity distribution profile and results are compared with several experimental data available in the literature. The structured mesh was used for all domains with high dense mesh near the solid region. A comparison between experimental data and simulations indicates that the k–ε model can be used to predict the complex flow and water level with high accuracy.     

Global stability of a delayed SIR epidemic model with density dependent birth and death rates

An SIR   epidemic model with density dependent birth and death rates is formulated. In our model it is assumed that the total number of the population is governed by logistic equation. The transmission of infection is assumed to be of the standard form, namely proportional to I(t-h)/N(t-h)$I(t-h)/N(t-h)$ where N(t)$N(t)$ is the total (variable) population size, I(t)$I(t)$ is the size of the infective population and a time delay h   is a fixed time during which the infectious agents develop in the vector. We consider transmission dynamics for the model. Stability of an endemic equilibrium is investigated. The stability result is stated in terms of a threshold parameter, that is, a basic reproduction number _R0$R_0$.     

Computing tolerance limits for the lifetime of a k-out-of-n:F system based on prior information and censored data

Exact guaranteed-coverage and expected-coverage Bayesian tolerance limits for the lifetime distribution of a k-out-of-n:F system are computed by solving nonlinear equations. The bounds are based on exponential component test data and available prior information concerning the expected component lifetime which is described by an inverted gamma distribution. The Bayesian tolerance limits are valid for single (right or left), double and progressive (standard or general) censoring, and even have frequentist validity in the noninformative case. The derived results allow the reliability engineer to judge the quality of a system prior to assembly, which offers obvious practical and economic benefits. Minimum and expected percentages of conforming systems are assessed by constructing suitable tolerance limits. Even though the viewpoints are different, the Bayesian tolerance limits that adopt the natural diffuse prior coincide numerically with recently published conditional tolerance limits in the double censoring case. The proposed Bayesian approach may be deemed as an extension of the existing frequentist methodology under double censoring that also takes into account the presence of prior information and general progressive censoring. The perspective developed simplifies and unifies the computation of tolerance limits with both frequentist and Bayesian interpretations, and also provides a probabilistic way of updating the tolerance limits in the light of new, relevant data, which is especially important in the dynamic analysis of a sequence of data. Moreover, the Bayesian approach is shown to outperform the frequentist viewpoint in terms of accuracy. In most situations, the use of substantial prior information significantly increases the accuracy level and considerably reduces the required number of failures to attain a specified degree of accuracy. Two illustrative numerical examples are studied, including the analysis of a system of water pumps for cooling a reactor. The results developed are extended to the Weibull case with unknown scale parameter and other probability models.     

A note on iterative process for G-multi degree reduction of Bézier curves

In the paper [A. Rababah, S. Mann, Iterative process for G²-multi degree reduction of Bézier curves, Applied Mathematics and Computation 217 (2011) 8126-8133], Rababah and Mann proposed an iterative method for multi-degree reduction of Bézier curves with C¹ and G²-continuity at the endpoints. In this paper, we provide a theoretical proof for the existence of the unique solution in the first step of the iterative process, while the proof in their paper applies only in some special cases. Also, we give a complete convergence proof for the iterative method. We solve the problem by using convex quadratic optimization.     

On Gibbs measures of P-adic Potts model on the cayley tree

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ? _p) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ? p and p ≥ 3 (resp. q ? 2², p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ? p if p ≥ 3 and q ? 2² if p = 2.     

Verification of model for adsorption and reduction of chromium(VI) by Escherichia coli 33456 using chitosan bead as a supporting medium

A non-steady-state mathematical model system for the kinetics of adsorption and reduction of Cr(VI) by Escherichia coli (E. coli) biofilm on chitosan bead (EBCB) process was derived. The mechanisms in the model system included Cr(VI) adsorption by chitosan beads, Cr(VI) bioreduction by E. coli cells and Cr(VI) mass transport diffusion. Batch kinetic tests were performed to determine surface diffusivity of Cr(VI), adsorption parameters for Cr(VI) and biokinetic parameters of E. coli 33456. Experiments were conducted using an EBCB reactor system with high recycled rate to approximate a completely-mixed flow reactor for model verification. The experimental results indicated that E. coli biofilm bioregenerated the chitosan beads after E. coli biofilm has grown significantly. Cr(VI) reducing efficiency by E. coli was about 84% when Cr(VI) concentration in the influent was 5 mg/L at a steady-state condition. The concentration of suspended E. coli cells reached up to 10 mg/L while the thickness of attached E. coli cells was estimated to be 150 μm at a steady-state condition by model prediction. The comparisons of experimental data and model simulation show that EBCB model system for Cr(VI) adsorption and reduction can predict the experimental results well.     

Steady state numerical simulation of the particle collection efficiency of a new urban sustainable gravity settler using design of experiments by FVM

The aim of this work is to analyze the efficiency of a new sustainable urban gravity settler to avoid the solid particle transport, to improve the water waste quality and to prevent pollution problems due to rain water harvesting in areas with no drainage pavement. In order to get this objective, it is necessary to solve particle transport equations along with the turbulent fluid flow equations since there are two phases: solid phase (sand particles) and fluid phase (water). In the first place, the turbulent flow is modelled by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible viscous flows through the finite volume method (FVM) and then, once the flow velocity field has been determined, representative particles are tracked using the Lagrangian approach. Within the particle transport models, a particle transport model termed as Lagrangian particle tracking model is used, where particulates are tracked through the flow in a Lagrangian way. The full particulate phase is modelled by just a sample of about 2,000 individual particles. The tracking is carried out by forming a set of ordinary differential equations in time for each particle, consisting of equations for position and velocity. These equations are then integrated using a simple integration method to calculate the behaviour of the particles as they traverse the flow domain. The entire FVM model is built and the design of experiments (DOE) method was used to limit the number of simulations required, saving on the computational time significantly needed to arrive at the optimum configuration of the settler. Finally, conclusions of this work are exposed.     

Multicyclicity of unbounded normal operators and polynomial approximation in C

A remarkable and much cited result of Bram [J. Bram, Subnormal operators, Duke Math. J. 22 (1955) 75-94] shows that a star-cyclic bounded normal operator in a separable Hilbert space has a cyclic vector. If, in addition, the operator is multiplication by the variable in a space L²(m) (not only unitarily equivalent to it), then it has a cyclic vector in L^∞(m). We extend Bram's result to the case of a general unbounded normal operator, implying by this that the (classical) multiplicity and the multicyclicity of the operator (cf. [N.K. Nikolski, Operators, Functions and Systems: An Easy Reading, vol. 2, Math. Surveys Monogr., vol. 93, Amer. Math. Soc., Providence, 2002]) coincide. It follows that if m is a sigma-finite Borel measure on C (possibly with noncompact support), then there is a nonnegative finite Borel measure τ equivalent to m and such that L²(C,τ) is the norm-closure of the polynomials in z.