Search results for "Equations"
showing 10 items of 955 documents
Propagation of plane and cylindrical waves in turbulent superfluid helium
2014
In this paper, the equations that govern the propagation of plane and cylindrical waves in turbulent superfluid solutions in some simplified cases are determined.
Efficient analysis of waveguide filters by the integral equation technique and the BI-RME method
2003
This paper presents the study of rectangular waveguide filters with rounded corners in the cross-section of the waveguides. These components are suitable for low-cost mass production and can be rigorously analyzed by efficient CAD tools. The analysis approach described in this paper is based on the integral equation technique in conjunction with the boundary integral-resonant mode expansion method. Two representative examples are also reported.
Well-posedness of Prandtl equations with non-compatible data
2013
In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.
Rotationally symmetric 1-harmonic flows from D2 TO S 2: Local well-posedness and finite time blowup
2010
The 1-harmonic flow from the disk to the sphere with constant Dirichlet boundary conditions is analyzed in the case of rotational symmetry. Sufficient conditions on the initial datum are given, such that a unique classical solution exists for short times. Also, a sharp criterion on the boundary condition is identified, such that any classical solution will blow up in finite time. Finally, nongeneric examples of finite time blowup are exhibited for any boundary condition.
WING FLUTTER SUPPRESSION ENHANCEMENT USING A WELL-SUITED ACTIVE CONTROL MODEL
2007
State-space theory is employed here to model a new active wing flutter suppression control. In this paper, the design of a flutter suppression control law, for the NASA Benchmark Active Control Technology wing, is proposed through a single input-single output controller and unsteady aerodynamics is modelled using the Theodorsen's theory. Wing dynamic model is obtained by combining the aeroelastic equations of motion with the actuator model presented. Open-loop dynamic behaviour is examined for a single feedback variable that combines pitch and plunge accelerations. Here, a new formulation of control law, based on classical control techniques and featuring two feedback closed-loops, is succ…
Mathematical modelling of alternating electromagnetic and hydrodynamic fields, induced by bar type conductors in a cylinder
2009
The heating of buildings by ecologically clean and compact local devices is an interesting and actual problem. One of the modern areas of applications developed during last ten years is an effective usage of electrical energy by alternating current to produce heat energy. This work presents the mathematical model of one of such devices. It is a finite cylinder with viscous incompressible liquid and with metal electrodes of the form of bars placed parallel to the cylinder axis in the liquid. These conductors are connected to the alternating current. First published online: 14 Oct 2010
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
Resonant activation in polymer translocation: new insights into the escape dynamics of molecules driven by an oscillating field
2010
The translocation of molecules across cellular membranes or through synthetic nanopores is strongly affected by thermal fluctuations. In this work we study how the dynamics of a polymer in a noisy environment changes when the translocation process is driven by an oscillating electric field. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics, by taking into account the harmonic interactions between adjacent monomers and the excluded-volume effect by introducing a Lennard–Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by num…
Modelling and simulation of gas-liquid hydrodynamics in mechnically stirred tanks
2007
Abstract Computational fuid dynamics (CFD) is an increasingly important tool for carrying out realistic simulations of process equipment. In the case of multiphase systems the development of CFD models is less advanced than for single-phase systems. In the present work CFD simulations of gas–liquid stirred tanks are reported. An Eulerian–Eulerian multi-fluid approach is used in conjunction with the simplest two-phase extension of the k–ɛ turbulence model. All bubbles are assumed to share the same size. The effect of inter-phase forces on simulation results is separately considered. As concerns drag, it is shown that the sole parameter needed to characterize the dispersed phase behaviour is …
Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates
2018
We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial discretization, we decrease the error and increase the reliability of the numerical method. An extensive survey of vortex splitting symmetries is presented for different aspect ratios of the harmonic trapping potential. The symmetries of the splitting patterns observed in the simulated dynamics are found to be in good agreement with predictions obtained by solving the dominant dynamical instabilities from the corresponding Bogoliubov equations. Furthermore, we observe…