153,927 research outputs found
3D CFD study of hydrodynamics and mass transfer phenomena for spiral wound membrane submerged-type feed spacer with different node geometries and sizes
Modification of the spacer geometry is a promising approach to increase the efficiency of reverse osmosis (RO) spiral wound membrane modules. Column nodes and spherical nodes are considered in this three-dimensional computational fluid dynamic (CFD) study to evaluate the hydrodynamic and mass transfer performance of submerged spacers with different node geometries and sizes. Small-scale CFD analysis results reveal that the column node has better mass transfer performance than the spherical node geometry because column nodes divert more flow to the filaments, leading to higher local velocity at the region between the filament and wall. Furthermore, when the dimensionless node diameter ratio of the column nodes increases from 0.3 to 1.2, Sherwood number and wall shear increase by 25% and 8% respectively at the expense of higher global friction factor (44%). A sea water RO full-scale analysis revealed that column node spacers yield higher average flux than spherical nodes and conventional spacers at high feed inlet velocity (> 0.1 m/s), because the mixing effects by the spacer that improve mass transfer are more prominent
Emergent Properties of Tumor Microenvironment in a Real-life Model of Multicell Tumor Spheroids
Multicellular tumor spheroids are an important {\it in vitro} model of the
pre-vascular phase of solid tumors, for sizes well below the diagnostic limit:
therefore a biophysical model of spheroids has the ability to shed light on the
internal workings and organization of tumors at a critical phase of their
development. To this end, we have developed a computer program that integrates
the behavior of individual cells and their interactions with other cells and
the surrounding environment. It is based on a quantitative description of
metabolism, growth, proliferation and death of single tumor cells, and on
equations that model biochemical and mechanical cell-cell and cell-environment
interactions. The program reproduces existing experimental data on spheroids,
and yields unique views of their microenvironment. Simulations show complex
internal flows and motions of nutrients, metabolites and cells, that are
otherwise unobservable with current experimental techniques, and give novel
clues on tumor development and strong hints for future therapies.Comment: 20 pages, 10 figures. Accepted for publication in PLOS One. The
published version contains links to a supplementary text and three video
file
Sign rank versus VC dimension
This work studies the maximum possible sign rank of sign
matrices with a given VC dimension . For , this maximum is {three}. For
, this maximum is . For , similar but
slightly less accurate statements hold. {The lower bounds improve over previous
ones by Ben-David et al., and the upper bounds are novel.}
The lower bounds are obtained by probabilistic constructions, using a theorem
of Warren in real algebraic topology. The upper bounds are obtained using a
result of Welzl about spanning trees with low stabbing number, and using the
moment curve.
The upper bound technique is also used to: (i) provide estimates on the
number of classes of a given VC dimension, and the number of maximum classes of
a given VC dimension -- answering a question of Frankl from '89, and (ii)
design an efficient algorithm that provides an multiplicative
approximation for the sign rank.
We also observe a general connection between sign rank and spectral gaps
which is based on Forster's argument. Consider the adjacency
matrix of a regular graph with a second eigenvalue of absolute value
and . We show that the sign rank of the signed
version of this matrix is at least . We use this connection to
prove the existence of a maximum class with VC
dimension and sign rank . This answers a question
of Ben-David et al.~regarding the sign rank of large VC classes. We also
describe limitations of this approach, in the spirit of the Alon-Boppana
theorem.
We further describe connections to communication complexity, geometry,
learning theory, and combinatorics.Comment: 33 pages. This is a revised version of the paper "Sign rank versus VC
dimension". Additional results in this version: (i) Estimates on the number
of maximum VC classes (answering a question of Frankl from '89). (ii)
Estimates on the sign rank of large VC classes (answering a question of
Ben-David et al. from '03). (iii) A discussion on the computational
complexity of computing the sign-ran
MGOS: A library for molecular geometry and its operating system
The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)'' as a theoretical framework accompanied by "MG Operating System (MGOS)'' which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. (C) 2019 The Author(s). Published by Elsevier B.V
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