578 research outputs found
Influence of surface tension on the conical miniscus of a magnetic fluid in the field of a current-carrying wire
We study the influence of surface tension on the shape of the conical
miniscus built up by a magnetic fluid surrounding a current-carrying wire.
Minimization of the total energy of the system leads to a singular second order
boundary value problem for the function describing the axially
symmetric shape of the free surface. An appropriate transformation regularizes
the problem and allows a straightforward numerical solution. We also study the
effects a superimposed second liquid, a nonlinear magnetization law of the
magnetic fluid, and the influence of the diameter of the wire on the free
surface profile
Numerical analysis of the Navier-Stokes equations
summary:This paper discusses some conceptional questions of the numerical simulation of viscous incompressible flow which are related to the presence of boundaries
Suppressing the Rayleigh-Taylor instability with a rotating magnetic field
The Rayleigh-Taylor instability of a magnetic fluid superimposed on a
non-magnetic liquid of lower density may be suppressed with the help of a
spatially homogeneous magnetic field rotating in the plane of the undisturbed
interface. Starting from the complete set of Navier-Stokes equations for both
liquids a Floquet analysis is performed which consistently takes into account
the viscosities of the fluids. Using experimentally relevant values of the
parameters we suggest to use this stabilization mechanism to provide controlled
initial conditions for an experimental investigation of the Rayleigh-Taylor
instability
Interaction between Experiment, Modeling and Simulation of Spatial Aspects in the JAK2/STAT5 Signaling Pathway
Fundamental progress in systems biology can only be achieved if experimentalists and theoreticians closely collaborate. Mathematical models cannot be formulated precisely without deep knowledge of the experiments while complex biological systems can often not be understood fully without mathematical interpretation of the dynamic processes involved. In this article, we describe how these two approaches can be combined to gain new insights on one of the most extensively studied signal transduction pathways, the Janus kinase (JAK)/ signal transducer and activator of transcription (STAT) pathway. We focus on the parameters of a model describing how STAT proteins are transported from the membrane to the nucleus where STATs regulate gene expression. We discuss which parameters can be measured experimentally in different cell types and how the unknown parameters are estimated, what the limits of these techniques and how accurate the determinations are
Double Rosensweig instability in a ferrofluid sandwich structure
We consider a horizontal ferrofluid layer sandwiched between two layers of
immiscible non-magnetic fluids. In a sufficiently strong vertical magnetic
field the flat interfaces between magnetic and non-magnetic fluids become
unstable to the formation of peaks. We theoretically investigate the interplay
between these two instabilities for different combinations of the parameters of
the fluids and analyze the evolving interfacial patterns. We also estimate the
critical magnetic field strength at which thin layers disintegrate into an
ordered array of individual drops
High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiments a comparative standard second-order discretisation is significantly outperformed. We conduct a numerical stability study which indicates unconditional stability of the scheme
An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
Common efficient schemes for the incompressible Navier-Stokes equations, such
as projection or fractional step methods, have limited temporal accuracy as a
result of matrix splitting errors, or introduce errors near the domain
boundaries (which destroy uniform convergence to the solution). In this paper
we recast the incompressible (constant density) Navier-Stokes equations (with
the velocity prescribed at the boundary) as an equivalent system, for the
primary variables velocity and pressure. We do this in the usual way away from
the boundaries, by replacing the incompressibility condition on the velocity by
a Poisson equation for the pressure. The key difference from the usual
approaches occurs at the boundaries, where we use boundary conditions that
unequivocally allow the pressure to be recovered from knowledge of the velocity
at any fixed time. This avoids the common difficulty of an, apparently,
over-determined Poisson problem. Since in this alternative formulation the
pressure can be accurately and efficiently recovered from the velocity, the
recast equations are ideal for numerical marching methods. The new system can
be discretized using a variety of methods, in principle to any desired order of
accuracy. In this work we illustrate the approach with a 2-D second order
finite difference scheme on a Cartesian grid, and devise an algorithm to solve
the equations on domains with curved (non-conforming) boundaries, including a
case with a non-trivial topology (a circular obstruction inside the domain).
This algorithm achieves second order accuracy (in L-infinity), for both the
velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure
A new discrete velocity method for Navier-Stokes equations
The relation between Latttice Boltzmann Method, which has recently become
popular, and the Kinetic Schemes, which are routinely used in Computational
Fluid Dynamics, is explored. A new discrete velocity model for the numerical
solution of the Navier-Stokes equations for incompressible fluid flow is
presented by combining both the approaches. The new scheme can be interpreted
as a pseudo-compressibility method and, for a particular choice of parameters,
this interpretation carries over to the Lattice Boltzmann Method.Comment: 28 pages, 8 figure
Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods
This article is devoted to computing the lower and upper bounds of the
Laplace eigenvalue problem. By using the special nonconforming finite elements,
i.e., enriched Crouzeix-Raviart element and extension , we get
the lower bound of the eigenvalue. Additionally, we also use conforming finite
elements to do the postprocessing to get the upper bound of the eigenvalue. The
postprocessing method need only to solve the corresponding source problems and
a small eigenvalue problem if higher order postprocessing method is
implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues
simultaneously by solving eigenvalue problem only once. Some numerical results
are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure
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