104 research outputs found
An embedding technique for the solution of reaction-fiffusion equations on algebraic surfaces with isolated singularities
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry.\ud
We create a family of smooth curves in higher dimensional space that correspond to the original curve by projection. Following this, we pose the analogous reaction-diffusion PDE on each member of this family and show that the solutions (their projection onto the original domain) approximate the solution of the original problem. Finally, we compute these approximants numerically by applying the Closest Point Method which is an embedding technique for solving PDEs on smooth surfaces of arbitrary dimension or codimension, and is thus suitable for our situation. In addition, we discuss the potential to generalize the techniques presented for higher-dimensional surfaces with multiple singularities
A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
The closest point method (Ruuth and Merriman, J. Comput. Phys.
227(3):1943-1961, [2008]) is an embedding method developed to solve a variety
of partial differential equations (PDEs) on smooth surfaces, using a closest
point representation of the surface and standard Cartesian grid methods in the
embedding space. Recently, a closest point method with explicit time-stepping
was proposed that uses finite differences derived from radial basis functions
(RBF-FD). Here, we propose a least-squares implicit formulation of the closest
point method to impose the constant-along-normal extension of the solution on
the surface into the embedding space. Our proposed method is particularly
flexible with respect to the choice of the computational grid in the embedding
space. In particular, we may compute over a computational tube that contains
problematic nodes. This fact enables us to combine the proposed method with the
grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024,
[2009]) to obtain a numerical method for approximating PDEs on moving surfaces.
We present a number of examples to illustrate the numerical convergence
properties of our proposed method. Experiments for advection-diffusion
equations and Cahn-Hilliard equations that are strongly coupled to the velocity
of the surface are also presented
Spatially partitioned embedded Runge-Kutta Methods
We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory
Genetic algorithm for finding a good first integer solution for MILP
The paper proposes a genetic algorithm based method for nding a good rst integer solu- tion to mixed integer programming problems (MILP). The objective value corresponding to this solution can be used to e ciently prune the search tree in branch and bound type algorithms for MILP. Some preliminary computational results are also presented which support the view that this approach deserves some attention
A multiobjective dynamic nonlinear robot assignment problem
Robots will be used under rapidly changing and highly dangerous circumstances such as rescue operations in a radioactive environment or a fire as well as military operations. The robots are sent to several targets in order to carry out various tasks. The robots we are considering here are able to send and receive messages to and from each other as well as solve nonlinear assignment problems. When the robot salvo is en-route to their targets several events may happen. A number of co- operative robots may get jammed as a consequence of disturbances. Some robots may already have reached their targets. Some robots may not be able to reach all targets. The system being investigated enables the surviving robots to work together in real time and change their pre-set tasks if necessary in order to maximize their effectiveness. In this paper we present a method which solves the reallocation problem using a piecewise linear network algorithm. Experimental results up to 493 targets and 500 robots show that the reallocation of the robots can be done in real time
Low-density lipoprotein aggregation predicts adverse cardiovascular events in peripheral artery disease
Background and aims: Peripheral artery disease (PAD) is a systemic manifestation of atherosclerosis that is associated with a high risk of major adverse cardiovascular events (MACE). LDL aggregation contributes to atherosclerotic plaque progression and may contribute to plaque instability. We aimed to determine if LDL aggregation is associated with MACE in patients with PAD undergoing lower extremity revascularization (LER). Methods: Two hundred thirty-nine patients with PAD undergoing LER had blood collected at baseline and were followed prospectively for MACE (myocardial infarction, stroke, cardiovascular death) for one year. Nineteen age, sex and LDL-C-matched control subjects without cardiovascular disease also had blood drawn. Subject LDL was exposed to sphingomyelinase and LDL aggregate size measured via dynamic light scattering. Results: Mean age was 72.3 10.9 years, 32.6% were female, and LDL-cholesterol was 68 +/- 25 mg/dL. LDL aggregation was inversely associated with triglycerides, but not associated with demographics, LDL-cholesterol or other risk factors. Maximal LDL aggregation occurred significantly earlier in subjects with PAD than in control subjects. 15.9% of subjects experienced MACE over one year. The 1st tertile (shortest time to maximal aggregation) exhibited significantly higher MACE (25% vs. 12.5% in tertile 2 and 10.1% in tertile 3, p = 0.012). After multivariable adjustment for demographics and CVD risk factors, the hazard ratio for MACE in the 1st tertile was 4.57 (95% CI 1.60-13.01; p = 0.004) compared to tertile 3. Inclusion of LDL aggregation in the Framingham Heart Study risk calculator for recurrent coronary heart disease events improved the c-index from 0.57 to 0.63 (p = 0.01). Conclusions: We show that in the setting of very well controlled LDL-cholesterol, patients with PAD with the most rapid LDL aggregation had a significantly elevated MACE risk following LER even after multivariable adjustment. This measure further improved the classification specificity of an established risk prediction tool. Our findings support broader investigation of this assay for risk stratification in patients with atherosclerotic CVD.Peer reviewe
Lessons Learnt in Implementation of Coordinated Voltage Control Demonstration
publishedVersionPeer reviewe
Differential evolution for the offline and online optimization of fed-batch fermentation processes
The optimization of input variables (typically feeding trajectories over
time) in fed-batch fermentations has gained special attention, given the economic impact
and the complexity of the problem. Evolutionary Computation (EC) has been a
source of algorithms that have shown good performance in this task. In this chapter,
Differential Evolution (DE) is proposed to tackle this problem and quite promising
results are shown. DE is tested in several real world case studies and compared with
other EC algorihtms, such as Evolutionary Algorithms and Particle Swarms. Furthermore,
DE is also proposed as an alternative to perform online optimization, where the
input variables are adjusted while the real fermentation process is ongoing. In this case,
a changing landscape is optimized, therefore making the task of the algorithms more
difficult. However, that fact does not impair the performance of the DE and confirms
its good behaviour.(undefined
High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: application to cardiac electrophysiology
We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the compu- tational cost of anatomically-realistic models can be reduced through the surface representation. We describe and validate our discretisation and provide a demonstration of its application to modeling electrochemical propagation across a human left atrium
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