44,861 research outputs found
A numerical method for junctions in networks of shallow-water channels
There is growing interest in developing mathematical models and appropriate
numerical methods for problems involving networks formed by, essentially,
one-dimensional (1D) domains joined by junctions. Examples include hyperbolic
equations in networks of gas tubes, water channels and vessel networks for
blood and lymph in the human circulatory system. A key point in designing
numerical methods for such applications is the treatment of junctions, i.e.
points at which two or more 1D domains converge and where the flow exhibits
multidimensional behaviour. This paper focuses on the design of methods for
networks of water channels. Our methods adopt the finite volume approach to
make full use of the two-dimensional shallow water equations on the true
physical domain, locally at junctions, while solving the usual one-dimensional
shallow water equations away from the junctions. In addition to mass
conservation, our methods enforce conservation of momentum at junctions; the
latter seems to be the missing element in methods currently available. Apart
from simplicity and robustness, the salient feature of the proposed methods is
their ability to successfully deal with transcritical and supercritical flows
at junctions, a property not enjoyed by existing published methodologies.
Systematic assessment of the proposed methods for a variety of flow
configurations is carried out. The methods are directly applicable to other
systems, provided the multidimensional versions of the 1D equations are
available
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
This work introduces a number of algebraic topology approaches, such as
multicomponent persistent homology, multi-level persistent homology and
electrostatic persistence for the representation, characterization, and
description of small molecules and biomolecular complexes. Multicomponent
persistent homology retains critical chemical and biological information during
the topological simplification of biomolecular geometric complexity.
Multi-level persistent homology enables a tailored topological description of
inter- and/or intra-molecular interactions of interest. Electrostatic
persistence incorporates partial charge information into topological
invariants. These topological methods are paired with Wasserstein distance to
characterize similarities between molecules and are further integrated with a
variety of machine learning algorithms, including k-nearest neighbors, ensemble
of trees, and deep convolutional neural networks, to manifest their descriptive
and predictive powers for chemical and biological problems. Extensive numerical
experiments involving more than 4,000 protein-ligand complexes from the PDBBind
database and near 100,000 ligands and decoys in the DUD database are performed
to test respectively the scoring power and the virtual screening power of the
proposed topological approaches. It is demonstrated that the present approaches
outperform the modern machine learning based methods in protein-ligand binding
affinity predictions and ligand-decoy discrimination
A Multiscale Thermo-Fluid Computational Model for a Two-Phase Cooling System
In this paper, we describe a mathematical model and a numerical simulation
method for the condenser component of a novel two-phase thermosyphon cooling
system for power electronics applications. The condenser consists of a set of
roll-bonded vertically mounted fins among which air flows by either natural or
forced convection. In order to deepen the understanding of the mechanisms that
determine the performance of the condenser and to facilitate the further
optimization of its industrial design, a multiscale approach is developed to
reduce as much as possible the complexity of the simulation code while
maintaining reasonable predictive accuracy. To this end, heat diffusion in the
fins and its convective transport in air are modeled as 2D processes while the
flow of the two-phase coolant within the fins is modeled as a 1D network of
pipes. For the numerical solution of the resulting equations, a Dual
Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for
2D heat diffusion and convection while a Primal Mixed Finite Element
discretization method with upwind stabilization is used for the 1D coolant
flow. The mathematical model and the numerical method are validated through
extensive simulations of realistic device structures which prove to be in
excellent agreement with available experimental data
Single-image Tomography: 3D Volumes from 2D Cranial X-Rays
As many different 3D volumes could produce the same 2D x-ray image, inverting
this process is challenging. We show that recent deep learning-based
convolutional neural networks can solve this task. As the main challenge in
learning is the sheer amount of data created when extending the 2D image into a
3D volume, we suggest firstly to learn a coarse, fixed-resolution volume which
is then fused in a second step with the input x-ray into a high-resolution
volume. To train and validate our approach we introduce a new dataset that
comprises of close to half a million computer-simulated 2D x-ray images of 3D
volumes scanned from 175 mammalian species. Applications of our approach
include stereoscopic rendering of legacy x-ray images, re-rendering of x-rays
including changes of illumination, view pose or geometry. Our evaluation
includes comparison to previous tomography work, previous learning methods
using our data, a user study and application to a set of real x-rays
A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling
Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK âOctopusâ, EPSRC âReactor Core-Structure Re-location Modelling for Severe Nuclear Accidentsâ) and Horizon 2020 âIn-Vessel Melt Retentionâ. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC âMulti-Scale Exploration of Multi-phase Physics in Flowsâ. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD
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