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Computational Cardiac Safety Testing (2023)
Book Chapter
Mirams, G. R. (2023). Computational Cardiac Safety Testing. In F. J. Hock, M. R. Gralinski, & M. K. Pugsley (Eds.), Drug Discovery and Evaluation: Safety and Pharmacokinetic Assays (1-33). Springer. https://doi.org/10.1007/978-3-030-73317-9_137-1

In recent years, computational cardiac electrophysiology simulations using mathematical models have begun to be used in industrial and regulatory assessment of the proarrhythmic risk of candidate drug compounds. The aim of this chapter is to equip th... Read More about Computational Cardiac Safety Testing.

Dynamical Survival Analysis for Epidemic Modeling (2023)
Book Chapter
Rempała, G. A., & KhudaBukhsh, W. R. (2023). Dynamical Survival Analysis for Epidemic Modeling. In Handbook of Visual, Experimental and Computational Mathematics: Bridges through Data (1-17). Springer. https://doi.org/10.1007/978-3-030-93954-0_31-1

This chapter describes the dynamical survival analysis (DSA) method for modeling infectious diseases. This method provides a powerful framework for analyzing compartmental models of large epidemics, such as the popular susceptible-infected-recovered... Read More about Dynamical Survival Analysis for Epidemic Modeling.

Word and Multiword Processing (2022)
Book Chapter
Conklin, K., & Thul, R. (2022). Word and Multiword Processing. In A. Godfroid, & H. Hopp (Eds.), The Routledge Handbook of Second Language Acquisition and Psycholinguistics (203-215). Routledge. https://doi.org/10.4324/9781003018872-20

When we encounter linguistic input, both spoken and written, we need to identify words and multiword sequences (e.g., “spill the beans” meaning “to reveal a secret”), ascertain their meaning, and integrate them into our unfolding understanding of a s... Read More about Word and Multiword Processing.

Compensated Convex-Based Transforms for Image Processing and Shape Interrogation (2022)
Book Chapter
Orlando, A., Crooks, E., & Zhang, K. (2022). Compensated Convex-Based Transforms for Image Processing and Shape Interrogation. In K. Chen, C. Schönlieb, X. Tai, & L. Younces (Eds.), Handbook of mathematical models and algorithms in computer vision and imaging (1-60). Cham: Springer. https://doi.org/10.1007/978-3-030-03009-4_106-1

This paper reviews some recent applications of the theory of the compensated convex trans-forms or of the proximity hull as developed by the authors to image processing and shape inter-rogation with special attention given to the Hausdorff stability... Read More about Compensated Convex-Based Transforms for Image Processing and Shape Interrogation.

Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching (2022)
Book Chapter
Pinel, G. D., Horder, J. L., King, J. R., McIntyre, A., Mongan, N. P., López, G. G., & Benest, A. V. (2022). Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching. In A. V. Benest (Ed.), Angiogenesis: Methods and Protocol (369-426). Springer. https://doi.org/10.1007/978-1-0716-2059-5_29

RNA-seq is a common approach used to explore gene expression data between experimental conditions or cell types and ultimately leads to information that can shed light on the biological processes involved and inform further hypotheses. While the prot... Read More about Endothelial Cell RNA-Seq Data: Differential Expression and Functional Enrichment Analyses to Study Phenotypic Switching.

High-Order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations (2021)
Book Chapter
Antonietti, P., Facciola, C., Houston, P., Mazzieri, I., Pennesi, G., & Verani, M. (2021). High-Order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations. In D. Di Pietro, L. Formaggia, & R. Masson (Eds.), Polyhedral methods in geosciences (159-225). Springer

Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows (2020)
Book Chapter
Zee, K. G. D., Zee, K. G. V. D., Miles, C., van der Zee, K. G., Hubbard, M. E., & MacKenzie, R. (2020). Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical methods for flows: FEF 2017 selected contributions (121-129). Springer Verlag. https://doi.org/10.1007/978-3-030-30705-9_11

© Springer Nature Switzerland AG 2020. We use phase-field techniques coupled with a Coleman–Noll type procedure to derive a family of thermomechanically consistent models for predicting the evolution of a non-volatile thin liquid film on a flat subst... Read More about Thermomechanically-Consistent Phase-Field Modeling of Thin Film Flows.

Upscaling Flow and Transport Processes (2019)
Book Chapter
Icardi, M., Boccardo, G., & Dentz, M. (2019). Upscaling Flow and Transport Processes. In F. Toschi, & M. Sega (Eds.), Flowing Matter, 137-176. Springer International Publishing. https://doi.org/10.1007/978-3-030-23370-9_5

This chapter deals with flow, transport and reaction processes in porous and heterogeneous media characterised by multiple spatial scales. Although the governing equations, at the micro-scale, are simple (and often linear), complex upscaled (effectiv... Read More about Upscaling Flow and Transport Processes.

Combining Modeling and Measurements to Predict Crystal Morphology in Material Extrusion (2019)
Book Chapter
McIlroy, C., Seppala, J. E., & Kotula, A. P. (2019). Combining Modeling and Measurements to Predict Crystal Morphology in Material Extrusion. In Polymer-Based Additive Manufacturing: Recent Developments (85-113). American Chemical Society. https://doi.org/10.1021/bk-2019-1315.ch006

Semicrystalline polymer melts are commonly used in material extrusion (MatEx) for 3D printing. Although flows have a profound effect on polymer crystallization, the relationship between typical MatEx deformation rates and printed-part crystal morphol... Read More about Combining Modeling and Measurements to Predict Crystal Morphology in Material Extrusion.

Computational phase-field modeling (2017)
Book Chapter
Gomez, H., & van der Zee, K. G. (2017). Computational phase-field modeling. In E. Stein, R. de Borst, & T. J. Hughes (Eds.), Encyclopedia of Computational Mechanics, Second Edition. John Wiley & Sons, Ltd

Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domai... Read More about Computational phase-field modeling.

Theory and numerical modelling of parity-time symmetric structures in photonics: boundary integral equation for coupled microresonator structures (2017)
Book Chapter
Phang, S., Vukovic, A., Gradoni, G., Sewell, P., Benson, T. M., & Creagh, S. C. (2017). Theory and numerical modelling of parity-time symmetric structures in photonics: boundary integral equation for coupled microresonator structures. In Recent Trends in Computational Photonics. Springer Nature

The spectral behaviour and the real-time operation of Parity-Time (PT) symmetric coupled resonators are investigated. A Boundary Integral Equation (BIE) model is developed to study these structures in the frequency domain. The impact of realistic gai... Read More about Theory and numerical modelling of parity-time symmetric structures in photonics: boundary integral equation for coupled microresonator structures.

Relativistic Quantum Clocks (2017)
Book Chapter
Lock, M. P. E., & Fuentes, I. (2017). Relativistic Quantum Clocks. In Time in Physics: Tutorials, Schools, and Workshops in the Mathematical Sciences, 51-68. Springer. doi:10.1007/978-3-319-68655-4_5

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The resul... Read More about Relativistic Quantum Clocks.

Adjoint error estimation and adaptivity for hyperbolic problems (2017)
Book Chapter
Houston, P. (2017). Adjoint error estimation and adaptivity for hyperbolic problems. In R. Abgrall, & C. Shu (Eds.), Handbook of Numerical Methods for Hyperbolic Problems. Applied and Modern Issues. Elsevier / North Holland

In this article we present an overview of a posteriori error estimation and adaptive mesh design for hyperbolic/nearly-hyperbolic problems. In particular, we discuss the question of error estimation for general target functionals of the solution; typ... Read More about Adjoint error estimation and adaptivity for hyperbolic problems.

Microstructural Influences on Growth and Transport in Biological Tissue-A Multiscale Description (2017)
Book Chapter
Irons, L., Collis, J., & O'Dea, R. D. (2017). Microstructural Influences on Growth and Transport in Biological Tissue-A Multiscale Description. In S. M. Becker (Ed.), Modeling of microscale transport in biological processes (311-334). Academic Press. https://doi.org/10.1016/B978-0-12-804595-4.00012-2

The detailed understanding of growth and transport dynamics within biological tissue is made particularly challenging by the complex and multiscale nature of this medium. For this reason so-called effective descriptions are frequently sought. These o... Read More about Microstructural Influences on Growth and Transport in Biological Tissue-A Multiscale Description.

Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension (2016)
Book Chapter
Phang, S., Benson, T. M., Susanto, H., Creagh, S. C., Gradoni, G., Sewell, P. D., & Vukovic, A. (2016). Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension. In A. Agrawal, T. M. Benson, R. De La Rue, & G. Wurtz (Eds.), Recent trends in computational photonics (161-205). Springer. https://doi.org/10.1007/978-3-319-55438-9_6

A class of structures based on PT PT-symmetric Bragg gratings in the presence of both gain and loss is studied. The basic concepts and properties of parity and time reversal in one-dimensional structures that possess idealised material properties are... Read More about Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension.

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains (2016)
Book Chapter
Antonietti, P. F., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E. H., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. R. Barrenechea, F. Brezzi, A. Cangiani, & E. H. Georgoulis (Eds.), Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations (281-310). Cham: Springer Publishing Company. https://doi.org/10.1007/978-3-319-41640-3_9

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of st... Read More about Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains.

Nonparametric Statistical Methods on Manifolds (2016)
Book Chapter
Dryden, I. L., Le, H., Preston, S. P., & Wood, A. T. A. (2016). Nonparametric Statistical Methods on Manifolds. In M. Denker, & E. C. Waymire (Eds.), Rabi N. Bhattacharya: Selected Papers (587-597). Springer. https://doi.org/10.1007/978-3-319-30190-7_17

One of the many fundamental contributions that Rabi Bhattacharya, together with his coauthors, has made is the development of a general nonparametric theory of statistical inference on manifolds, in particular related to both intrinsic and extrinsic... Read More about Nonparametric Statistical Methods on Manifolds.

Variational water wave modelling: from continuum to experiment (2016)
Book Chapter
Bokhove, O., & Kalogirou, A. (2016). Variational water wave modelling: from continuum to experiment. In Lectures on the Theory of Water Waves (226-260). Cambridge University Press. https://doi.org/10.1017/CBO9781316411155.012

© Cambridge University Press 2016. Variational methods are investigated asymptotically and numerically to model water waves in tanks with wave generators. As a validation, our modelling results using (dis)continuous Galerkin finite element methods wi... Read More about Variational water wave modelling: from continuum to experiment.

Vanishing of some Galois cohomology groups for elliptic curves (2016)
Book Chapter
Lawson, T., & Wuthrich, C. (2016). Vanishing of some Galois cohomology groups for elliptic curves. In D. Loeffler, & S. L. Zerbes (Eds.), Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H1(G;E[p] does not v... Read More about Vanishing of some Galois cohomology groups for elliptic curves.

Mathematical neuroscience: from neurons to networks (2015)
Book Chapter
Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. T... Read More about Mathematical neuroscience: from neurons to networks.