3,185 research outputs found
Microfluidic multipoles: theory and applications
Microfluidic multipoles (MFMs) have been realized experimentally and hold
promise for "open-space" biological and chemical surface processing. Whereas
convective flow can readily be predicted using hydraulic-electrical analogies,
the design of advanced MFMs is constrained by the lack of simple, accurate
models to predict mass transport within them. In this work, we introduce the
first exact solutions to mass transport in multipolar microfluidics based on
the iterative conformal mapping of 2D advection-diffusion around a simple edge
into dipoles and multipolar geometries, revealing a rich landscape of transport
modes. The models were validated experimentally with a library of 3D printed
MFM devices and found in excellent agreement. Following a theory-guided design
approach, we further ideated and fabricated two new classes of spatiotemporally
reconfigurable MFM devices that are used for processing surfaces with
time-varying reagent streams, and to realize a multistep automated immunoassay.
Overall, the results set the foundations for exploring, developing, and
applying open-space MFMs.Comment: 16 pages, 5 figure
Improvements to the APBS biomolecular solvation software suite
The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve
the equations of continuum electrostatics for large biomolecular assemblages
that has provided impact in the study of a broad range of chemical, biological,
and biomedical applications. APBS addresses three key technology challenges for
understanding solvation and electrostatics in biomedical applications: accurate
and efficient models for biomolecular solvation and electrostatics, robust and
scalable software for applying those theories to biomolecular systems, and
mechanisms for sharing and analyzing biomolecular electrostatics data in the
scientific community. To address new research applications and advancing
computational capabilities, we have continually updated APBS and its suite of
accompanying software since its release in 2001. In this manuscript, we discuss
the models and capabilities that have recently been implemented within the APBS
software package including: a Poisson-Boltzmann analytical and a
semi-analytical solver, an optimized boundary element solver, a geometry-based
geometric flow solvation model, a graph theory based algorithm for determining
p values, and an improved web-based visualization tool for viewing
electrostatics
Fast integral equation methods for the Laplace-Beltrami equation on the sphere
Integral equation methods for solving the Laplace-Beltrami equation on the
unit sphere in the presence of multiple "islands" are presented. The surface of
the sphere is first mapped to a multiply-connected region in the complex plane
via a stereographic projection. After discretizing the integral equation, the
resulting dense linear system is solved iteratively using the fast multipole
method for the 2D Coulomb potential in order to calculate the matrix-vector
products. This numerical scheme requires only O(N) operations, where is the
number of nodes in the discretization of the boundary. The performance of the
method is demonstrated on several examples
Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method
Computational tools for characterizing electromagnetic scattering from
objects with uncertain shapes are needed in various applications ranging from
remote sensing at microwave frequencies to Raman spectroscopy at optical
frequencies. Often, such computational tools use the Monte Carlo (MC) method to
sample a parametric space describing geometric uncertainties. For each sample,
which corresponds to a realization of the geometry, a deterministic
electromagnetic solver computes the scattered fields. However, for an accurate
statistical characterization the number of MC samples has to be large. In this
work, to address this challenge, the continuation multilevel Monte Carlo
(CMLMC) method is used together with a surface integral equation solver. The
CMLMC method optimally balances statistical errors due to sampling of the
parametric space, and numerical errors due to the discretization of the
geometry using a hierarchy of discretizations, from coarse to fine. The number
of realizations of finer discretizations can be kept low, with most samples
computed on coarser discretizations to minimize computational cost.
Consequently, the total execution time is significantly reduced, in comparison
to the standard MC scheme.Comment: 25 pages, 10 Figure
Detecting chaos in particle accelerators through the frequency map analysis method
The motion of beams in particle accelerators is dominated by a plethora of
non-linear effects which can enhance chaotic motion and limit their
performance. The application of advanced non-linear dynamics methods for
detecting and correcting these effects and thereby increasing the region of
beam stability plays an essential role during the accelerator design phase but
also their operation. After describing the nature of non-linear effects and
their impact on performance parameters of different particle accelerator
categories, the theory of non-linear particle motion is outlined. The recent
developments on the methods employed for the analysis of chaotic beam motion
are detailed. In particular, the ability of the frequency map analysis method
to detect chaotic motion and guide the correction of non-linear effects is
demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection
Methods and Predictabilit
Development of an Advanced Force Field for Water using Variational Energy Decomposition Analysis
Given the piecewise approach to modeling intermolecular interactions for
force fields, they can be difficult to parameterize since they are fit to data
like total energies that only indirectly connect to their separable functional
forms. Furthermore, by neglecting certain types of molecular interactions such
as charge penetration and charge transfer, most classical force fields must
rely on, but do not always demonstrate, how cancellation of errors occurs among
the remaining molecular interactions accounted for such as exchange repulsion,
electrostatics, and polarization. In this work we present the first generation
of the (many-body) MB-UCB force field that explicitly accounts for the
decomposed molecular interactions commensurate with a variational energy
decomposition analysis, including charge transfer, with force field design
choices that reduce the computational expense of the MB-UCB potential while
remaining accurate. We optimize parameters using only single water molecule and
water cluster data up through pentamers, with no fitting to condensed phase
data, and we demonstrate that high accuracy is maintained when the force field
is subsequently validated against conformational energies of larger water
cluster data sets, radial distribution functions of the liquid phase, and the
temperature dependence of thermodynamic and transport water properties. We
conclude that MB-UCB is comparable in performance to MB-Pol, but is less
expensive and more transferable by eliminating the need to represent
short-ranged interactions through large parameter fits to high order
polynomials
Using global interpolation to evaluate the Biot-Savart integral for deformable elliptical Gaussian vortex elements
This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios. When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptical fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement between the three approaches
Analysis and Visualization of Higher-Order Tensors: Using the Multipole Representation
Materialien wie Kristalle, biologisches Gewebe oder
elektroaktive Polymere kommen häufig in verschiedenen
Anwendung, wie dem Prothesenbau oder der Simulation von
kĂĽnstlicher Muskulatur vor.
Diese und viele weitere Materialien haben gemeinsam, dass sie
unter gewissen Umständen ihre Form und andere
Materialeigenschaften ändern.
Um diese Veränderung beschreiben zu können, werden, abhängig
von der Anwendung, verschiedene Tensoren unterschiedlicher
Ordnung benutzt.
Durch die Komplexität und die starke Abhängigkeit der
Tensorbedeutung von der Anwendung, gibt es bisher kein
Verfahren Tensoren höherer Ordnung darzustellen, welches
standardmäßig benutzt wird.
Auch bezogen auf einzelne Anwendungen gibt es nur sehr wenig
Arbeiten, die sich mit der visuellen Darstellung dieser
Tensoren auseinandersetzt.
Diese Arbeit beschäftigt sich mit diesem Problem.
Es werden drei verschiedene Methoden präsentiert, Tensoren
höherer Ordnung zu analysieren und zu visualisieren.
Alle drei Methoden basieren auf der sogenannte deviatorischen
Zerlegung und der Multipoldarstellung.
Mit Hilfe der Multipole können die Symmetrien des Tensors
und damit des beschriebenen Materials bestimmt werden.
Diese Eigenschaft wird in fĂĽr die Visualisierung
des Steifigkeitstensors benutzt.
Die zweite Methode basiert direkt auf den Multipolen und kann
damit beliebige Tensoren in drei Dimensionen darstellen.
Dieses Verfahren wird anhand des Kopplungs Tensors, ein Tensor
dritter Ordnung, vorgestellt.
Die ersten zwei Verfahren sind lokale Glyph-basierte Verfahren.
Das dritte Verfahren ist ein erstes globales
Tensorvisualisierungsverfahren, welches Tensoren beliebiger
Ordnung und Symmetry in drei Dimensionen mit Hilfe eines
linienbasierten Verfahrens darstellt.Materials like crystals, biological tissue or electroactive
polymers are frequently used in applications like prosthesis
construction or the simulation of artificial musculature.
These and many other materials have in common that they
change their shape and other material properties under
certain circumstances.
To describe these changes, different tensors of different
order, dependent of the application, are used.
Due to the complexity and the strong dependency of the
tensor meaning of the application, there is, by now, no
visualization method that is used by default.
Also for specific applications there are only a few methods
that address the visual analysis of higher-order tensors.
This work adresses this problem.
Three different methods to analyse and visualize tensors of
higher order will be provided.
All three methods are based on the so called deviatoric
decomposition and the multipole representation.
Using the multipoles the symmetries of a tensor and, therefore,
of the described material, can be calculated.
This property is used to visualize the stiffness tensor.
The second method uses the multipoles directly and can be
used for each tensor of any order in three dimensions.
This method is presented by analysing the third-order
coupling tensor.
These two techniques are glyph-based visualization methods.
The third one, a line-based method, is, according to our
knowledge, a first global visualization method that can be
used for an arbitrary tensor in three dimensions
Self-induced decoherence in dense neutrino gases
Dense neutrino gases exhibit collective oscillations where "self-maintained
coherence" is a characteristic feature, i.e., neutrinos of different energies
oscillate with the same frequency. In a non-isotropic gas, however, the flux
term of the neutrino-neutrino interaction has the opposite effect of causing
kinematical decoherence of neutrinos propagating in different directions, an
effect that is at the origin of the "multi-angle behavior" of neutrinos
streaming off a supernova core. We cast the equations of motion in a form where
the role of the flux term is manifest. We study in detail the symmetric case of
equal neutrino and antineutrino densities where the evolution consists of
collective pair conversions ("bipolar oscillations"). A gas of this sort is
unstable in that an infinitesimal anisotropy is enough to trigger a run-away
towards flavor equipartition. The "self-maintained coherence" of a perfectly
isotropic gas gives way to "self-induced decoherence."Comment: Revtex, 16 pages, 12 figure
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