Search results for "Euler"
showing 10 items of 159 documents
Properties of condensed spin-aligned atomic hydrogen from variational calculations
1979
The optimal Jastrow-type ground-state wave function of spin-aligned atomic hydrogen is calculated using the pair potential of Kolos and Wolniewicz. The optimization is performed by solving the Euler equation in the hypernetted chain approximation. Accurate energies as well as pair-distribution functions are obtained. The Bose-Einstein condensate fraction is evaluated from the one-particle momentum distribution. The pair distribution function is also used to obtain stability criteria for the system and minimal values for the aligning magnetic field are calculated at low densities. The resulting values of the minimal aligning fields are considerably higher than those obtained previously.
Fractional visco-elastic Euler–Bernoulli beam
2013
Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…
On numerical simulation of the continuous casting process
1988
In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.
Conical Two-Phase Swirl Flow Atomizers—Numerical and Experimental Study
2021
This paper presents the results of numerical simulations for the developed and discussed conical two-phase atomizers with swirl flow, differing in the ratio of the height of the swirl chamber to its diameter. Experiments were carried out for SAN-1 with HS/DS = 1 and SAN-2 with HS/DS = 4 atomizers. The study was conducted over a range of Reynolds number for liquid ReL = (1400
Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function
2021
We give an overview on the work developed in recent years about certain classes of incomplete Riemann solvers for hyperbolic systems. These solvers are based on polynomial or rational approximations to |x|, and they do not require the knowledge of the complete eigenstructure of the system, but only a bound on the maximum wave speed. Our solvers can be readily applied to nonconservative hyperbolic systems, by following the theory of path-conservative schemes. In particular, this allows for an automatic treatment of source or coupling terms in systems of balance laws. The properties of our schemes have been tested with some challenging numerical experiments involving systems such as the Euler…
Eulerian-Eulerian modelling and computational fluid dynamics simulation of wire mesh demisters in MSF plants
2014
Purpose – The purpose of this study is to focus on simulation of wire mesh demisters in multistage flash desalination (MSF) plants. The simulation is made by the use of computational fluid dynamics (CFD) software. Design/methodology/approach – A steady state and two-dimensional (2D) model was developed to simulate the demister. The model employs an Eulerian-Eulerian approach to simulate the flow of water vapor and brine droplets in the demister. The computational domain included three zones, which are the vapor space above and below the demister and the demister. The demister zone was modeled as a tube bank arrange or as a porous media. Findings – Sensitivity analysis of the model showed t…
Eulerian–Lagrangian modeling and computational fluid dynamics simulation of wire mesh demisters in MSF plants
2016
Abstract This study focuses on computational fluid dynamics model (CFD) for simulation of demisters in multistage flash desalination (MSF). The Eulerian–Lagrangian model (steady-state and two-dimensional) was developed to simulate the demister. The model was used to simulate the flow of water vapor and brine droplets in the demister. The computational domain includes the following three zones: the vapor space above the demister, the vapor space below the demister, and the demister. The demister zone was modeled as tube banks. A sensitivity analysis of the model revealed that vapor velocity is the main parameter that affects demister performance. Additionally, the analysis indicated that vap…
Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method
2015
ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…
Topological invariants of stable immersions of oriented 3-manifolds in R4
2012
Abstract We show that the Z -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R 4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants l + and l − introduced by V. Goryunov (1997) [7] . We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.
Classical sequences revisited with permutations avoiding dotted pattern
2011
International audience; Inspired by the definition of the barred pattern-avoiding permutation, we introduce the new concept of dotted pattern for permutations. We investigate permutations classes avoiding dotted patterns of length at most 3, possibly along with other classical patterns. We deduce some enumerating results which allow us to exhibit new families of permutations counted by the classical sequences: 2^n, Catalan, Motzkin, Pell, Fibonacci, Fine, Riordan, Padovan, Eulerian.