Preprints
Filtering by Subject: Applied Mathematics
From Magma Chambers to Magma Oceans: A Unified Model for the Thermo-chemical-mechanical Evolution of Magma Bodies
Published: 2025-02-06
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Physical Sciences and Mathematics, Planetary Sciences
Magma bodies play a critical role in Earth's geological evolution, influencing volcanic activity, crustal differentiation, and planetary-scale processes. Understanding their thermo-chemical and mechanical evolution requires models that integrate fluid dynamics, phase changes, and chemical transport. This study presents a new numerical model that couples these processes using a multi-phase, [...]
Joint effects of submesoscale lateral dispersion and biological reactions on biogeochemical flux
Published: 2024-12-11
Subjects: Applied Mathematics, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics
Submesoscale dynamics, operating at spatial scales of O(1−10 km) and temporal scales of O(1 day), are particularly important for marine ecosystems as they occur on similar timescales as phytoplankton growth, enabling biophysical feedbacks. While submesoscale dynamics are known to impact biological fluxes by modifying nutrient upwelling, horizontal transport has traditionally been assumed to only [...]
Guidelines for Sensitivity Analyses in Process Simulations for Solid Earth Geosciences
Published: 2024-09-18
Subjects: Applied Mathematics, Earth Sciences, Education, Partial Differential Equations, Physical Sciences and Mathematics, Science and Mathematics Education, Tectonics and Structure
Numerical simulations are widely used as tools to understand processes or to make predictions about states and their evolution in time. However, in the process of a simulation setup, a multitude of choices and simplifications have to be made - beginning from the definition of the implemented physical laws, over model discretization and spatial parameterisation, to the definition of initial and [...]
A global C-staggered composite model for shallow water equations 1 with latitude-longitude grid and reductions in the polar regions
Published: 2024-08-07
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics
To develop a numerical method for global geophysical fluids, we usually need to choose a spherical grid and numerical approximations to represent the partial derivative equations. Some alternatives include the use of finite differences or finite volumes with latitude-longitude or reduced grids. Each of these cases has some advantages and also some limitations. This paper presents a comparison [...]
Modeling sediment compaction beneath ice lenses during frost heave
Published: 2024-07-13
Subjects: Applied Mathematics, Earth Sciences, Glaciology, Hydrology, Physical Sciences and Mathematics, Soil Science
Frost heave occurs when the ground swells during freezing conditions due to the growth of ice lenses in the subsurface. The mechanics of ice-infiltrated sediment, or frozen fringe, influences the formation and evolution of ice lenses. As the frozen fringe thickens during freezing, progressive unloading can result in dilation of the pore space and the formation of new ice lenses. Compaction can [...]
A study of extreme water waves using a hierarchy of models based on potential-flow theory
Published: 2023-12-02
Subjects: Applied Mathematics, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Partial Differential Equations, Physical Sciences and Mathematics
The formation of extreme waves arising from the interaction of three line-solitons with equal far-field amplitudes is examined through a hierarchy of water-wave models. The Kadomtsev-Petviashvili equation (KPE) is first used to prove analytically that its exact three-soliton solution has a ninefold maximum amplification that is achieved in the absence of spatial divergence. Reproducing this [...]
Progression of the surge in the Negribreen Glacier System from two years of ICESat-2 measurements
Published: 2023-10-08
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics
The unique measurement capabilities of ICESat-2 allow high spatiotemporal resolution of complex ice-dynamic processes that occur during a surge. Detailed and precise mapping of height changes on surge glaciers has previously escaped observations from space due to limited resolution of space-borne altimeter data and the surface characteristics of glaciers during surge such as heavy crevassing. [...]
Omnivariant Generalized Least Squares Regression: Theory, Geochronological Applications, and Making the Case for Reconciled Δ47 calibrations
Published: 2023-09-22
Subjects: Applied Mathematics, Earth Sciences, Geochemistry
Least-squares regression methods are mathematically powerful, conceptually and computationally simple, and widely used in many fields. However, none of the commonly-used flavors of least-squares regression, such as York regression or Generalized Least Squares (GLS), take into account the full set of covariances between all observed (x,y) values. Here we describe the Omnivariant Generalized Least [...]
Linear analysis of ice-shelf topography response to basal melting and freezing
Published: 2023-04-28
Subjects: Applied Mathematics, Dynamic Systems, Earth Sciences, Fluid Dynamics, Glaciology, Physical Sciences and Mathematics, Physics
Floating ice shelves in Antarctica and Greenland limit land-ice contributions to sea level rise by resisting the flow of grounded ice. Melting at the surface and base of ice shelves can lead to destabilisation by promoting thinning and fracturing. Basal melting often results in channelised features that manifest as surface topography due to buoyancy. The assumption of hydrostatic flotation [...]
Numerical simulation of meteorite impact on basaltic lavas at Lonar Crater, India
Published: 2023-01-28
Subjects: Applied Mathematics, Astrophysics and Astronomy, Planetary Sciences
Lonar lake is a hypervelocity impact crater formed in a basaltic terrain of Deccan Traps in the state of Maharashtra, India. The crater has an approximate radius of 915 m and an average depth of about 137 m. Here we report the results of our numerical investigations aimed to elucidate the physical characteristics of incoming asteroid. For realistic simulation, we not only consider [...]
Estimating the Occurrence of Slow Slip Events and Earthquakes with an Ensemble Kalman Filter
Published: 2022-08-07
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics
Our ability to forecast earthquakes and slow slip events is hampered by limited information on the current state of stress on faults. Ensemble data assimilation methods permit estimating the state by combining physics-based models and observations, while considering their uncertainties. We employ an Ensemble Kalman Filter (EnKF) to estimate shear stresses, slip rates, and the state theta acting [...]
A High-order Accurate Summation-by-Parts Finite Difference Method for Fully-dynamic Earthquake Sequence Simulations within Sedimentary Basins
Published: 2022-08-06
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics
We present a computationally efficient numerical method for earthquake sequences that incorporates wave propagation during rupture. A vertical strike-slip fault governed by rate-and-state friction is embedded in a heterogeneous elastic half-space discretized using a high-order accurate Summation-by-Parts finite difference method. We develop a two solver approach: Adaptive time-stepping is [...]
A computational framework for time dependent deformation in viscoelastic magmatic systems
Published: 2022-04-01
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Mathematics
Time-dependent ground deformation is a key observable in active magmatic systems, but is challenging to characterize. Here we present a numerical framework for modeling transient deformation and stress around a subsurface, spheroidal pressurized magma reservoir within a viscoelastic half-space with variable material coefficients, utilizing a high-order finite-element method and explicit [...]
Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk
Published: 2022-03-14
Subjects: Applied Mathematics, Earth Sciences, Hydrology, Risk Analysis, Statistical Methodology, Statistics and Probability
When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficiency of low fidelity models. Here, we apply the [...]
Diapycnal Displacement, Diffusion, and Distortion of Tracers in the Ocean
Published: 2022-01-07
Subjects: Applied Mathematics, Fluid Dynamics, Non-linear Dynamics, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics
Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Indirect microstructure measurements of in situ turbulence suggest that mixing is bottom enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. Tracer release experiments (TREs), in which inert tracers are purposefully [...]