8,775 research outputs found
Solving the flow fields in conduits and networks using energy minimization principle with simulated annealing
In this paper, we propose and test an intuitive assumption that the pressure
field in single conduits and networks of interconnected conduits adjusts itself
to minimize the total energy consumption required for transporting a specific
quantity of fluid. We test this assumption by using linear flow models of
Newtonian fluids transported through rigid tubes and networks in conjunction
with a simulated annealing (SA) protocol to minimize the total energy cost. All
the results confirm our hypothesis as the SA algorithm produces very close
results to those obtained from the traditional deterministic methods of
identifying the flow fields by solving a set of simultaneous equations based on
the conservation principles. The same results apply to electric ohmic
conductors and networks of interconnected ohmic conductors. Computational
experiments conducted in this regard confirm this extension. Further studies
are required to test the energy minimization hypothesis for the non-linear flow
systems.Comment: 11 pages, 2 figures, 1 tabl
The LBFGS Quasi-Newtonian Method for Molecular Modeling Prion AGAAAAGA Amyloid Fibrils
Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance)
spectroscopy, dual polarization interferometry, etc are indeed very powerful
tools to determine the 3-Dimensional structure of a protein (including the
membrane protein); theoretical mathematical and physical computational
approaches can also allow us to obtain a description of the protein 3D
structure at a submicroscopic level for some unstable, noncrystalline and
insoluble proteins. X-ray crystallography finds the X-ray final structure of a
protein, which usually need refinements using theoretical protocols in order to
produce a better structure. This means theoretical methods are also important
in determinations of protein structures. Optimization is always needed in the
computer-aided drug design, structure-based drug design, molecular dynamics,
and quantum and molecular mechanics. This paper introduces some optimization
algorithms used in these research fields and presents a new theoretical
computational method - an improved LBFGS Quasi-Newtonian mathematical
optimization method - to produce 3D structures of Prion AGAAAAGA amyloid
fibrils (which are unstable, noncrystalline and insoluble), from the potential
energy minimization point of view. Because the NMR or X-ray structure of the
hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the
model constructed by this paper can be used as a reference for experimental
studies on this region, and may be useful in furthering the goals of medicinal
chemistry in this field
Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation
Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach
Shape optimization of Stokesian peristaltic pumps using boundary integral methods
This article presents a new boundary integral approach for finding optimal
shapes of peristaltic pumps that transport a viscous fluid. Formulas for
computing the shape derivatives of the standard cost functionals and
constraints are derived. They involve evaluating physical variables (traction,
pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction
with a boundary integral approach for solving forward and adjoint problems, we
completely avoid the issue of volume remeshing when updating the pump shape as
the optimization proceeds. This leads to significant cost savings and we
demonstrate the performance on several numerical examples
Intrinsic Frequency Analysis and Fast Algorithms
Intrinsic Frequency (IF) has recently been introduced as an ample signal
processing method for analyzing carotid and aortic pulse pressure tracings. The
IF method has also been introduced as an effective approach for the analysis of
cardiovascular system dynamics. The physiological significance, convergence and
accuracy of the IF algorithm has been established in prior works. In this
paper, we show that the IF method could be derived by appropriate mathematical
approximations from the Navier-Stokes and elasticity equations. We further
introduce a fast algorithm for the IF method based on the mathematical analysis
of this method. In particular, we demonstrate that the IF algorithm can be made
faster, by a factor or more than 100 times, using a proper set of initial
guesses based on the topology of the problem, fast analytical solution at each
point iteration, and substituting the brute force algorithm with a pattern
search method. Statistically, we observe that the algorithm presented in this
article complies well with its brute-force counterpart. Furthermore, we will
show that on a real dataset, the fast IF method can draw correlations between
the extracted intrinsic frequency features and the infusion of certain drugs.
In general, this paper aims at a mathematical analysis of the IF method to show
its possible origins and also to present faster algorithms
Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids
The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'
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