207 research outputs found
A frictionless microswimmer
We investigate the self-locomotion of an elongated microswimmer by virtue of
the unidirectional tangential surface treadmilling. We show that the propulsion
could be almost frictionless, as the microswimmer is propelled forward with the
speed of the backward surface motion, i.e. it moves throughout an almost
quiescent fluid. We investigate this swimming technique using the special
spheroidal coordinates and also find an explicit closed-form optimal solution
for a two-dimensional treadmiler via complex-variable techniques.Comment: 6 pages, 4 figure
Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies
A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter
as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small
impedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is an
arbitrary continuous function that can be chosen by the experimenter and N(∆)
is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965
Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory
We present two open-source (BSD) implementations of ellipsoidal harmonic
expansions for solving problems of potential theory using separation of
variables. Ellipsoidal harmonics are used surprisingly infrequently,
considering their substantial value for problems ranging in scale from
molecules to the entire solar system. In this article, we suggest two possible
reasons for the paucity relative to spherical harmonics. The first is
essentially historical---ellipsoidal harmonics developed during the late 19th
century and early 20th, when it was found that only the lowest-order harmonics
are expressible in closed form. Each higher-order term requires the solution of
an eigenvalue problem, and tedious manual computation seems to have discouraged
applications and theoretical studies. The second explanation is practical: even
with modern computers and accurate eigenvalue algorithms, expansions in
ellipsoidal harmonics are significantly more challenging to compute than those
in Cartesian or spherical coordinates. The present implementations reduce the
"barrier to entry" by providing an easy and free way for the community to begin
using ellipsoidal harmonics in actual research. We demonstrate our
implementation using the specific and physiologically crucial problem of how
charged proteins interact with their environment, and ask: what other
analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure
Damage Accumulation in Cyclically-Loaded Glass-Ceramic Matrix Composites Monitored by Acoustic Emission
Barium osumilite (BMAS) ceramic matrix composites reinforced with SiC-Tyranno fibers are tested in a cyclic loading protocol. Broadband acoustic emission (AE) sensors are used for monitoring the occurrence of different possible damage mechanisms. Improved use of AE indices is proposed by excluding low-severity signals based on waveform parameters, rather than only threshold criteria. The application of such improvements enhances the accuracy of the indices as accumulated damage descriptors. RA-value, duration, and signal energy follow the extension cycles indicating moments of maximum or minimum strain, while the frequency content of the AE signals proves very sensitive to the pull-out mechanism
The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography
The problem of determining the neuronal current inside the brain from
measurements of the induced magnetic field outside the head is discussed under
the assumption that the space occupied by the brain is approximately spherical.
By inverting the Geselowitz equation, the part of the current which can be
reconstructed from the measurements is precisely determined. This actually
consists of only certain moments of one of the two functions specifying the
tangential part of the current. The other function specifying the tangential
part of the current as well as the radial part of the current are completely
arbitrary. However, it is also shown that with the assumption of energy
minimization, the current can be reconstructed uniquely. A numerical
implementation of this unique reconstruction is also presented
A scattering and absorption identity for metamaterials: Experimental results and comparison with theory
Inverse Modeling for MEG/EEG data
We provide an overview of the state-of-the-art for mathematical methods that
are used to reconstruct brain activity from neurophysiological data. After a
brief introduction on the mathematics of the forward problem, we discuss
standard and recently proposed regularization methods, as well as Monte Carlo
techniques for Bayesian inference. We classify the inverse methods based on the
underlying source model, and discuss advantages and disadvantages. Finally we
describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur
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