284 research outputs found
Interior over-penalized enriched Galerkin methods for second order elliptic equations
In this paper we propose a variant of enriched Galerkin methods for second
order elliptic equations with over-penalization of interior jump terms. The
bilinear form with interior over-penalization gives a non-standard norm which
is different from the discrete energy norm in the classical discontinuous
Galerkin methods. Nonetheless we prove that optimal a priori error estimates
with the standard discrete energy norm can be obtained by combining a priori
and a posteriori error analysis techniques. We also show that the interior
over-penalization is advantageous for constructing preconditioners robust to
mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical
results are included to illustrate the convergence and preconditioning results.Comment: preconditioning for anisotropic cases is improve
Optimal design of chemoepitaxial guideposts for directed self-assembly of block copolymer systems using an inexact-Newton algorithm
Directed self-assembly (DSA) of block-copolymers (BCPs) is one of the most
promising developments in the cost-effective production of nanoscale devices.
The process makes use of the natural tendency for BCP mixtures to form
nanoscale structures upon phase separation. The phase separation can be
directed through the use of chemically patterned substrates to promote the
formation of morphologies that are essential to the production of semiconductor
devices. Moreover, the design of substrate pattern can formulated as an
optimization problem for which we seek optimal substrate designs that
effectively produce given target morphologies.
In this paper, we adopt a phase field model given by a nonlocal
Cahn--Hilliard partial differential equation (PDE) based on the minimization of
the Ohta--Kawasaki free energy, and present an efficient PDE-constrained
optimization framework for the optimal design problem. The design variables are
the locations of circular- or strip-shaped guiding posts that are used to model
the substrate chemical pattern. To solve the ensuing optimization problem, we
propose a variant of an inexact Newton conjugate gradient algorithm tailored to
this problem. We demonstrate the effectiveness of our computational strategy on
numerical examples that span a range of target morphologies. Owing to our
second-order optimizer and fast state solver, the numerical results demonstrate
five orders of magnitude reduction in computational cost over previous work.
The efficiency of our framework and the fast convergence of our optimization
algorithm enable us to rapidly solve the optimal design problem in not only
two, but also three spatial dimensions.Comment: 35 Pages, 17 Figure
Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data
Identifying parameters of computational models from experimental data, or
model calibration, is fundamental for assessing and improving the
predictability and reliability of computer simulations. In this work, we
propose a method for Bayesian calibration of models that predict morphological
patterns of diblock copolymer (Di-BCP) thin film self-assembly while accounting
for various sources of uncertainties in pattern formation and data acquisition.
This method extracts the azimuthally-averaged power spectrum (AAPS) of the
top-down microscopy characterization of Di-BCP thin film patterns as summary
statistics for Bayesian inference of model parameters via the pseudo-marginal
method. We derive the analytical and approximate form of a conditional
likelihood for the AAPS of image data. We demonstrate that AAPS-based image
data reduction retains the mutual information, particularly on important length
scales, between image data and model parameters while being relatively agnostic
to the aleatoric uncertainties associated with the random long-range disorder
of Di-BCP patterns. Additionally, we propose a phase-informed prior
distribution for Bayesian model calibration. Furthermore, reducing image data
to AAPS enables us to efficiently build surrogate models to accelerate the
proposed Bayesian model calibration procedure. We present the formulation and
training of two multi-layer perceptrons for approximating the
parameter-to-spectrum map, which enables fast integrated likelihood
evaluations. We validate the proposed Bayesian model calibration method through
numerical examples, for which the neural network surrogate delivers a fivefold
reduction of the number of model simulations performed for a single calibration
task
Rapid turnover of T cells in acute infectious mononucleosis.
During acute infectious mononucleosis (AIM), large clones of Epstein-Barr virus-specific T lymphocytes are produced. To investigate the dynamics of clonal expansion, we measured cell proliferation during AIM using deuterated glucose to label DNA of dividing cells in vivo, analyzing cells according to CD4, CD8 and CD45 phenotype. The proportion of labeled CD8(+)CD45R0(+) T lymphocytes was dramatically increased in AIM subjects compared to controls (mean 17.5 versus 2.8%/day; p<0.005), indicating very rapid proliferation. Labeling was also increased in CD4(+)CD45R0(+) cells (7.1 versus 2.1%/day; p<0.01), but less so in CD45RA(+) cells. Mathematical modeling, accounting for death of labeled cells and changing pool sizes, gave estimated proliferation rates in CD8(+)CD45R0(+) cells of 11-130% of cells proliferating per day (mean 47%/day), equivalent to a doubling time of 1.5 days and an appearance rate in blood of about 5 x 10(9) cells/day (versus 7 x 10(7) cells/day in controls). Very rapid death rates were also observed amongst labeled cells (range 28-124, mean 57%/day),indicating very short survival times in the circulation. Thus, we have shown direct evidence for massive proliferation of CD8(+)CD45R0(+) T lymphocytes in AIM and demonstrated that rapid cell division continues concurrently with greatly accelerated rates of cell disappearance
Success and Failure in the Simulation of an Accident and Emergency Department
Healthcare simulation has the potential to offer many benefits but the implementation is often problematic. This paper describes the development of a simulation of an Accident and Emergency Department in an NHS hospital. The early experience of the client provoked great enthusiasm but ultimately the simulation failed to meet all expectations. The simulation delivered a number of benefits, notably in terms of stimulating constructive debate and helping the stakeholders appreciate the complete Accident and Emergency system. The project produced a technically proficient tool that was delivered too late to have the desired impact. This mixed record of success appears typical of many simulations. Important lessons were learned, both technically and in the management of client expectations, which have contributed to subsequent successful implementation in other departments of the hospital. The experience suggests that both potential clients and analysts need to establish realistic expectations and appreciate the particular challenges of simulation in a healthcare environment
Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems
We explore using neural operators, or neural network representations of
nonlinear maps between function spaces, to accelerate infinite-dimensional
Bayesian inverse problems (BIPs) with models governed by nonlinear parametric
partial differential equations (PDEs). Neural operators have gained significant
attention in recent years for their ability to approximate the
parameter-to-solution maps defined by PDEs using as training data solutions of
PDEs at a limited number of parameter samples. The computational cost of BIPs
can be drastically reduced if the large number of PDE solves required for
posterior characterization are replaced with evaluations of trained neural
operators. However, reducing error in the resulting BIP solutions via reducing
the approximation error of the neural operators in training can be challenging
and unreliable. We provide an a priori error bound result that implies certain
BIPs can be ill-conditioned to the approximation error of neural operators,
thus leading to inaccessible accuracy requirements in training. To reliably
deploy neural operators in BIPs, we consider a strategy for enhancing the
performance of neural operators, which is to correct the prediction of a
trained neural operator by solving a linear variational problem based on the
PDE residual. We show that a trained neural operator with error correction can
achieve a quadratic reduction of its approximation error, all while retaining
substantial computational speedups of posterior sampling when models are
governed by highly nonlinear PDEs. The strategy is applied to two numerical
examples of BIPs based on a nonlinear reaction--diffusion problem and
deformation of hyperelastic materials. We demonstrate that posterior
representations of the two BIPs produced using trained neural operators are
greatly and consistently enhanced by error correction
Dynamic Data Driven Methods for Self-aware Aerospace Vehicles
A self-aware aerospace vehicle can dynamically adapt the way it performs missions by gathering information about itself and its surroundings and responding intelligently. Achieving this DDDAS paradigm enables a revolutionary new generation of self-aware aerospace vehicles that can perform missions that are impossible using current design, flight, and mission planning paradigms. To make self-aware aerospace vehicles a reality, fundamentally new algorithms are needed that drive decision-making through dynamic response to uncertain data, while incorporating information from multiple modeling sources and multiple sensor fidelities.In this work, the specific challenge of a vehicle that can dynamically and autonomously sense, plan, and act is considered. The challenge is to achieve each of these tasks in real time executing online models and exploiting dynamic data streams–while also accounting for uncertainty. We employ a multifidelity approach to inference, prediction and planning an approach that incorporates information from multiple modeling sources, multiple sensor data sources, and multiple fidelities
Synthesis and characterization of [Fe(BPMEN)-ACC]SbF 6 : a structural and functional mimic of ACC-oxidase â€
International audienceA mononuclear Fe(II) complex bearing 1-aminocyclopropane-1-carboxylic acid (ACCH) was synthesized and characterized. X-ray crystallography demonstrated that ACC binds to the Fe(II) ion in a bidentate mode constituting the first structural mimic of the expected binding of ACC to the Fe(II) center of the ethylene forming enzyme ACC-oxidase (ACCO). [Fe(BPMEN)ACC]SbF 6 also constitutes a functional biomimetic complex of ACCO, as it reacts with hydrogen peroxide producing ethylene
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