378 research outputs found
Time--Splitting Schemes and Measure Source Terms for a Quasilinear Relaxing System
Several singular limits are investigated in the context of a
system arising for instance in the modeling of chromatographic processes. In
particular, we focus on the case where the relaxation term and a
projection operator are concentrated on a discrete lattice by means of Dirac
measures. This formulation allows to study more easily some time-splitting
numerical schemes
An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field
This paper is concerned with the numerical approximation of the isothermal
Euler equations for charged particles subject to the Lorentz force. When the
magnetic field is large, the so-called drift-fluid approximation is obtained.
In this limit, the parallel motion relative to the magnetic field direction
splits from perpendicular motion and is given implicitly by the constraint of
zero total force along the magnetic field lines. In this paper, we provide a
well-posed elliptic equation for the parallel velocity which in turn allows us
to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system.
This scheme gives rise to both a consistent approximation of the Euler-Lorentz
model when epsilon is finite and a consistent approximation of the drift limit
when epsilon tends to 0. Above all, it does not require any constraint on the
space and time steps related to the small value of epsilon. Numerical results
are presented, which confirm the AP character of the scheme and its Asymptotic
Stability
Interaction between superconducting vortices and Bloch wall in ferrite garnet film
Interaction between a Bloch wall in a ferrite-garnet film and a vortex in a
superconductor is analyzed in the London approximation. Equilibrium
distribution of vortices formed around the Bloch wall is calculated. The
results agree quantitatively with magneto-optical experiment where an in-plane
magnetized ferrite-garnet film placed on top of NbSe2 superconductor allows
observation of individual vortices. In particular, our model can reproduce a
counter-intuitive attraction observed between vortices and a Bloch wall having
the opposite polarity. It is explained by magnetic charges appearing due to
discontinuity of the in-plane magnetization across the wall.Comment: 4 pages, 5 figure
An aqueous one-pot route to gold/quantum rod heterostructured nanoparticles functionalized with DNA
International audienc
A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support
The Flexure-based Microgap Rheometer (FMR)
Submitted to J. Rheol.We describe the design and construction of a new microrheometer designed to facilitate the viscometric study of complex fluids with very small sample volumes (1-10 μl)and gaps of micrometer dimensions. The Flexure-based Microgap Rheometer (FMR) is a
shear-rate-controlled device capable of measuring the shear stress in a plane Couette
configuration with directly-controlled gaps between 1 μm and 200 μm. White light
interferometry and a three-point nanopositioning stage using piezo-stepping motors are used to control the parallelism of the upper and lower shearing surfaces which are constructed from glass optical flats. A compound flexure system is used to hold the fluid sample testing unit between a drive spring connected to an ‘inchworm’ motor and an independent sensor spring. Displacements in the sensing flexure are detected using an inductive proximity sensor. Ready optical access to the transparent shearing surfaces enables monitoring of the structural evolution in the gap with a long working-distance video-microscope. This configuration then allows us to determine the microgap-dependent flow behavior of complex fluids over 5 decades of shear rate. We demonstrate the capability of the FMR by characterizing the complex stress and gap dependent flow behavior of a typical microstructured food product (mayonnaise) over the range of gaps from 8 to 100 μm and stresses from 10 to 1500 Pa. We correlate the gap-dependent rheological response to the microstructure of the emulsion and changes induced in the material by prolonged shearing.Dupont MIT Allianc
Simulation of Ablating Hypersonic Vehicles with Finite-Rate Surface Chemistry
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140434/1/6.2014-2124.pd
Single-molecule experiments in biological physics: methods and applications
I review single-molecule experiments (SME) in biological physics. Recent
technological developments have provided the tools to design and build
scientific instruments of high enough sensitivity and precision to manipulate
and visualize individual molecules and measure microscopic forces. Using SME it
is possible to: manipulate molecules one at a time and measure distributions
describing molecular properties; characterize the kinetics of biomolecular
reactions and; detect molecular intermediates. SME provide the additional
information about thermodynamics and kinetics of biomolecular processes. This
complements information obtained in traditional bulk assays. In SME it is also
possible to measure small energies and detect large Brownian deviations in
biomolecular reactions, thereby offering new methods and systems to scrutinize
the basic foundations of statistical mechanics. This review is written at a
very introductory level emphasizing the importance of SME to scientists
interested in knowing the common playground of ideas and the interdisciplinary
topics accessible by these techniques. The review discusses SME from an
experimental perspective, first exposing the most common experimental
methodologies and later presenting various molecular systems where such
techniques have been applied. I briefly discuss experimental techniques such as
atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers
(MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I
then present several applications of SME to the study of nucleic acids (DNA,
RNA and DNA condensation), proteins (protein-protein interactions, protein
folding and molecular motors). Finally, I discuss applications of SME to the
study of the nonequilibrium thermodynamics of small systems and the
experimental verification of fluctuation theorems. I conclude with a discussion
of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond.
Matt
Dynamics and Regulation of RecA Polymerization and De-Polymerization on Double-Stranded DNA
10.1371/journal.pone.0066712PLoS ONE86
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