Preprints

Filtering by Subject: Applied Mathematics

A damage model for the frictional shear failure of brittle materials in compression

Simon Philip Gill

Published: 2021-05-13
Subjects: Applied Mathematics, Computational Engineering, Earth Sciences, Engineering, Geology, Materials Science and Engineering, Physical Sciences and Mathematics

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces [...]

Utilizing Random Forest Machine Learning Models to Determine Water Table Flood Levels through Volunteered Geospatial Information

Raghav Sriram

Published: 2021-04-27
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Environmental Sciences, Physical Sciences and Mathematics

Many people use smartphone cameras to record their living environments through captured images, and share aspects of their daily lives on social networks, such as Facebook, Instagram, and Twitter. These platforms provide volunteered geographic information (VGI), which enables the public to know where and when events occur. At the same time, image-based VGI can also indicate environmental changes [...]

Dilatancy and compaction of a rate-and-state fault in a poroelastic medium: Linearized stability analysis

Elias Rafn Heimisson, John Rudnicki, Nadia Lapusta

Published: 2021-04-06
Subjects: Applied Mathematics, Geophysics and Seismology, Tectonics and Structure

Faults in the crust at seismogenic depths are embedded in a fluid-saturated, elastic, porous material. Slip on such faults may induce transient pore pressure changes through dilatancy or compaction of the gouge or host rock. However, the poroelastic nature of the crust and the full coupling of inelastic gouge processes and the host rock have been largely neglected in previous analyses. Here, we [...]

An idealized 1.5-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

Onno Bokhove, Luca Cantarello, Steven Tobias

Published: 2021-01-22
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

In this part II paper we present the analytical derivation of the isentropic 1.5-layer shallow water model described and used in part I of this study. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis. The scaling assumptions throughout the paper are supported by real observations based on radiosonde data. Eventually, a fully consistent [...]

An idealized 1.5-layer isentropic model with convection and precipitationfor satellite data assimilation research. Part I: model dynamics

Luca Cantarello, Onno Bokhove, Steven Tobias

Published: 2021-01-22
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

An isentropic 1.5-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic [...]

Assessing erosion and flood risk in the coastal zone through the application of the multilevel Monte Carlo method

Mariana C A Clare, Matthew Piggott, Colin J Cotter

Published: 2021-01-07
Subjects: Applied Mathematics, Earth Sciences, Geomorphology, Hydrology, Numerical Analysis and Computation, Risk Analysis, Statistics and Probability

The risk from erosion and flooding in the coastal zone has the potential to increase in a changing climate. The development and use of coupled hydro-morphodynamic models is therefore becoming an ever higher priority. However, their use as decision support tools suffers from the high degree of uncertainty associated with them, due to incomplete knowledge as well as natural variability in the [...]

Determination of vulnerability areas from the simulated deposition of atmospheric pollutants using LOTOS-EUROS chemical transport model in North-West South-America

Andres Yarce Botero, Santiago Lopez-Restrepo, Arjo Segers, et al.

Published: 2021-01-06
Subjects: Applied Mathematics, Bioresource and Agricultural Engineering, Civil and Environmental Engineering, Computer Sciences, Engineering, Physical Sciences and Mathematics, Planetary Sciences

This work presents the implementation of the LOTOS-EUROS regional atmospheric Chemical Transport Model (CTM) on Northwestern South America. The impact of land use and orography update in the model was analyzed to identify potential vulnerable natural areas by quantifying atmospheric deposition pollutants. CTMs allow simulating the physical dynamics of trace gasses and aerosols, including [...]

Urban Air Quality Modeling Using Low-Cost Sensor Network and Data Assimilation in the Aburra Valley, Colombia

Santiago Lopez-Restrepo, Andres Yarce, Nicolas Pinel, et al.

Published: 2020-10-29
Subjects: Applied Mathematics, Atmospheric Sciences, Environmental Monitoring

The use of low air quality networks has been increasing in recent years to study urban pollution dynamics. Here we show the evaluation of the operational Aburra Valley's low-cost network against the official monitoring network. The results show that the PM2.5 low-cost measurements are very close to those observed by the official network. Additionally, the low-cost allows a higher spatial [...]

Multi-scale hydro-morphodynamic modelling using mesh movement methods.

Mariana C A Clare, Joseph Gregory Wallwork, Stephan C Kramer, et al.

Published: 2020-10-22
Subjects: Applied Mathematics, Geomorphology, Mathematics, Numerical Analysis and Computation, Partial Differential Equations

Hydro-morphodynamic models are an important tool that can be used in the protection of coastal zones. They can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement [...]

Dynamical analysis of a reduced model for the North Atlantic Oscillation

Courtney Quinn, Dylan Harries, Terence J. O'Kane

Published: 2020-10-21
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

The dynamics of the North Atlantic Oscillation (NAO) are analyzed through a data-driven model obtained from atmospheric reanalysis data. We apply a regularized vector autoregressive clustering technique to identify recurrent and persistent states of atmospheric circulation patterns in the North Atlantic sector (110W-0E, 20N-90N). In order to analyze the dynamics associated with the resulting [...]

An analytical solution to the Navierâ€“Stokes equation for incompressible flow around a solid sphere

Published: 2020-08-25
Subjects: Applied Mathematics, Earth Sciences, Engineering, Fluid Dynamics, Mechanical Engineering, Other Mechanical Engineering, Partial Differential Equations, Physical Sciences and Mathematics, Physics, Special Functions

This paper is concerned with obtaining a formulation for the flow past a sphere in a viscous and incompressible fluid, building upon previously obtained well-known solutions that were limited to small Reynolds numbers. Using a method based on a summation of separation of variables, we develop a general analytical solution to the Navier--Stokes equation for the special case of axially symmetric [...]

Robust Q estimation using surface seismic data

Joakim Oscar Blanch

Published: 2020-07-30
Subjects: Applied Mathematics, Computational Engineering, Earth Sciences, Engineering, Geophysics and Seismology, Numerical Analysis and Computation, Physical Sciences and Mathematics

Direct wave arrivals are the most robust signals to determine velocity and consequently they have been used for almost a century in hydrocarbon exploration. The reason is simple as the arrivaltime is explicitly available and provide a direct measurement of the average velocity of the sub-surface ray-path. These signals have not been extensively used to estimate attenuation or Q. One reason may [...]

Modelling an energetic tidal strait: investigating implications of common numerical configuration choices

Lucas Mackie, Paul Evans, Magnus Harrold, et al.

Published: 2020-07-16
Subjects: Applied Mathematics, Civil and Environmental Engineering, Civil Engineering, Engineering, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Characterising tidal hydrodynamics in the vicinity of submerged features can be demanding given the hostility of the marine environment. Logistical challenges in the measurement of such flows has promoted research on wake studies through physical and numerical modelling. In this study, site measurements and modelled data are combined to provide an insight into the regional hydrodynamics within a [...]

Adjoint-based sensitivity analysis for a numerical storm surge model

Simon Charles Warder, Kevin Horsburgh, Matthew Piggott

Published: 2020-06-29
Subjects: Applied Mathematics, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which will carry uncertainty, and an awareness and understanding of the sensitivity of the model outputs with respect to those uncertain inputs is necessary when interpreting model results. Here, we use an [...]

A comparison of Bayesian inference and gradient-based approaches for friction parameter estimation

Simon Charles Warder, Athanasios Angeloudis, Stephan C Kramer, et al.

Published: 2020-06-29
Subjects: Applied Mathematics, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Numerical tidal models are essential to the study of a variety of coastal ocean processes, but typically rely on uncertain inputs, including a bottom friction parameter which can in principle be spatially varying. Here we employ an adjoint-capable numerical ocean model, Thetis, and apply it to the Bristol Channel and Severn Estuary, using a spatially varying Manning coefficient within the bottom [...]

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