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Bayesian inversion in resin transfer molding (2018)
Journal Article
Iglesias, M., Park, M., & Tretyakov, M. (2018). Bayesian inversion in resin transfer molding. Inverse Problems, 34(10), Article 105002. https://doi.org/10.1088/1361-6420/aad1cc

We study a Bayesian inverse problem arising in the context of Resin Transfer Molding (RTM), which is a process commonly used for the manufacturing of fiber- reinforced composite materials. The forward model is described by a moving boundary problem i... Read More about Bayesian inversion in resin transfer molding.

Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations (2018)
Journal Article
Bailey, N., Hibberd, S., Power, H., & Tretyakov, M. (2018). Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations. Journal of Engineering Mathematics, 112(1), 17–35. https://doi.org/10.1007/s10665-018-9963-9

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing... Read More about Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions (2017)
Journal Article
Davidchack, R., Ouldridge, T., & Tretyakov, M. (in press). Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions. Journal of Chemical Physics, 147(22), Article 224103. https://doi.org/10.1063/1.4999771

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevi... Read More about Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.

Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability (2017)
Journal Article
Matveev, M. Y., Ball, F. G., Jones, I. A., Long, A. C., Schubel, P. J., & Tretyakov, M. V. (2018). Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability. Journal of Composite Materials, 52(16), 2255-2269. https://doi.org/10.1177/0021998317741951

© 2017, The Author(s) 2017. Resin transfer moulding is one of several processes available for manufacturing fibre-reinforced composites from dry fibre reinforcement. Recently, dry reinforcements made with Automated Dry Fibre Placement have been intro... Read More about Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability.

Stochastic resin transfer molding process (2017)
Journal Article
Park, M., & Tretyakov, M. (in press). Stochastic resin transfer molding process. SIAM/ASA Journal on Uncertainty Quantification, 5(1), https://doi.org/10.1137/16M1096578

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in t... Read More about Stochastic resin transfer molding process.

Layer methods for stochastic Navier–Stokes equations using simplest characteristics (2016)
Journal Article
Milstein, G., & Tretyakov, M. (2016). Layer methods for stochastic Navier–Stokes equations using simplest characteristics. Journal of Computational and Applied Mathematics, 302, https://doi.org/10.1016/j.cam.2016.01.051

We propose and study a layer method for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploit... Read More about Layer methods for stochastic Navier–Stokes equations using simplest characteristics.

A recursive sparse grid collocation method for differential equations with white noise (2014)
Journal Article
Zhang, Z., Tretyakov, M., Rozovskii, B., & Karniadakis, G. E. (2014). A recursive sparse grid collocation method for differential equations with white noise. SIAM Journal on Scientific Computing, 36(4), A1652–A1677. https://doi.org/10.1137/130938906

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first an... Read More about A recursive sparse grid collocation method for differential equations with white noise.

On the long-time integration of stochastic gradient systems (2014)
Journal Article
Leimkuhler, B., Matthews, C., & Tretyakov, M. (2014). On the long-time integration of stochastic gradient systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2170), Article 20140120. https://doi.org/10.1098/rspa.2014.0120

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic (stepsize... Read More about On the long-time integration of stochastic gradient systems.