The present work is a statistical analysis of the COVID-19 pandemic. As the number of cases worldwide overtakes one million, data reveals closed outbreaks in Hubei and South Korea, with a new slight increase in the number of infected people in the latter. Both of these countries have reached a plateau in the number of Total Confirmed Cases per Million (TCCpM) residents, suggesting a trend to be followed by other affected regions. Using Hubei’s data as a basis of analysis, we have studied the spreading ...
Tópico(s): COVID-19 epidemiological studies
1959 - Yale University | American Journal of Science
Tópico(s): Advanced Topics in Algebra
2006 - Springer Nature | Algorithms and computation in mathematics
Abstract We present a mathematical model for the flow of a partial melt through its solid phase. The model is based on the conservation laws of two-phase flow, which reduce to a generalization of porous flow in a permeable medium, when the solid matrix deforms very slowly. The continuity equation for the melt contains a source term (due to melting), which is determined by the energy equation. In addition, the melt fraction is unknown, and a new equation, representing conservation of pore space, is ...
Tópico(s): Navier-Stokes equation solutions
1985 - Taylor & Francis | Geophysical & Astrophysical Fluid Dynamics
A. A. Papin, Margarita A. Tokareva,
The local solvability of initial-boundary value problem for the system of the equations of non stationary motion of magma is proved.
Tópico(s): Differential Equations and Boundary Problems
2017 - | Journal of Siberian Federal University Mathematics & Physics
We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general Las Vegas algorithm for computing the head and the constituents of a module with simple head in characteristic zero which we develop here theoretically. This algorithm is very successful when applied to Verma modules for restricted rational Cherednik algebras and ...
Tópico(s): Advanced Topics in Algebra
2015 - London Mathematical Society | LMS Journal of Computation and Mathematics
Donald L. Turcotte, J. L. Ahern,
It is generally accepted that a large fraction of the earth's volcanism is due to pressure release melting of mantle rock in the ascending limbs of mantle convection cells. A problem that remains largely unsolved is the migration of the melt from the asthenosphere to the earth's surface. We have modeled the early stages of this process by treating the asthenosphere as a porous medium. We assume that mantle rock is moving upward at a constant velocity. The onset of partial melting provides liquid; ...
Tópico(s): Advanced Mathematical Modeling in Engineering
1978 - American Geophysical Union | Journal of Geophysical Research Atmospheres
Shirley E. Harris, Peter A. Clarkson,
In this paper, we examine a generalized magma equation for rational values of two parameters, m and n.Firstly, the similarity reductions are found using the Lie group method of infinitesimal transformations.The Painlevé ODE test is then applied to the travelling wave reduction, and the pairs of m and n which pass the test are identified.These particular pairs are further subjected to the ODE test on their other symmetry reductions.Only two cases remain which pass the ODE test for all such symmetry ...
Tópico(s): Algebraic structures and combinatorial models
2006 - National Academy of Sciences of Ukraine | Symmetry Integrability and Geometry Methods and Applications
Motivated to understand the process of melt migration in the earth’s mantle, we have studied a generalised form of Darcy’s law that describes porous flow in a matrix that can deform by creep. We find a remarkable richness of phenomena, including a new class of solitons. These consist of shape‐preserving waves of high liquid fraction which buoyantly ascend through a stationary matrix. This may have important implications for the morphology and geochemistry of primary igneous processes, and applicability ...
Tópico(s): Heat and Mass Transfer in Porous Media
1984 - American Geophysical Union | Geophysical Research Letters
Finite‐amplitude solutions to subcritical, time‐dependent, double‐diffusive convection (D.D.C.) applicable for magma chambers are obtained by a two‐dimensional, finite‐element method based on stream‐function, temperature and compositional fields. Grid‐refinement is used for resolving the disparately‐scaled thermal and chemical boundary layers present for large ratios of the thermal to chemical diffusivity (Lewis number) characteristic of magmas. The occurrence of layered convection depends strongly ...
Tópico(s): Phase Equilibria and Thermodynamics
1987 - American Geophysical Union | Geophysical Research Letters
Dia Zeidan, R. Touma, A. Slaouti,
SUMMARY This paper reports on the application and development of a fully hyperbolic and fully conservative two‐phase flow model for the simulation of gas and magma flow within volcanic processes. The model solves a set of mixture conservation equations for the gas and magma two‐phase flow with velocity non‐equilibrium. In this model, the effect of the relative velocity is introduced by a kinetic constitutive equation with other equations for volume and mass fractions of the gas phase. The model ...
Tópico(s): Particle Dynamics in Fluid Flows
2014 - Wiley | International Journal for Numerical Methods in Fluids
Andrea Parmigiani, Christian Huber, Olivier Bachmann,
Abstract Reactivation and eruption of upper crustal crystal‐rich magma reservoirs (“crystal mushes”) following recharge has recently been invoked in numerous volcanic systems worldwide. Over the last few years, several models have been proposed for the reactivation of such mushes prior to or during eruptions. These models vary significantly in terms of predicted timescales associated with reactivation, because they assume that different physical mechanisms control the dynamics of this process. A common ...
Tópico(s): Advanced Mathematical Modeling in Engineering
2014 - Wiley | Journal of Geophysical Research Solid Earth
Wieb Bosma, John Cannon, Catherine Playoust,
In the first of two papers onMAGMA, a new system for computational algebra, we present theMAGMAlanguage, outline the design principles and theoretical background, and indicate its scope and use. Particular attention is given to the constructors for structures, maps, and sets.
Tópico(s): Algebraic structures and combinatorial models
1997 - Elsevier BV | Journal of Symbolic Computation
CQF is a free, open-source Magma package for doing computations in quadratic forms theory. We present some selected ingredients of the package.
Tópico(s): Finite Group Theory Research
2020 - SIGSAM | ACM communications in computer algebra
Martina Ulvrová, S. Labrosse, Nicolas Coltice, Peter Råback, Paul Tackley,
Melting and solidification are fundamental to geodynamical processes like inner core growth, magma chamber dynamics, and ice and lava lake evolution. Very often, the thermal history of these systems is controlled by convective motions in the melt. Computing the evolution of convection with a solid–liquid phase change requires specific numerical methods to track the phase boundary and resolve the heat transfer within and between the two separate phases. Here we present two classes of method to model ...
Tópico(s): Geological and Geochemical Analysis
2012 - Elsevier BV | Physics of The Earth and Planetary Interiors
The flow of a fluid in a pipe was treated by Poiseuille and one may find in Landau and Lifshitz a generalization of Poiseuille's solution for a fluid the temperature of which varies in a section. Platten and Legros treat a flow with a variable viscosity, but the expression for the viscosity they use, does not describe the viscosity of a liquid. The solution we propose here concerns the flow of magma, the viscosity of which is a rapidly changing function of temperature. The example we calculate numerically ...
Tópico(s): Enhanced Oil Recovery Techniques
1989 - Elsevier BV | International Journal of Heat and Mass Transfer
Lothar Gerritzen, Ralf Holtkamp,
Generalizations of the series exp and log to noncommutative non-associative and other types of algebras were considered by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp( x ) in one non-associative variable x such that exp( x )exp( x )=exp(2 x ), exp′(0)=1. We call the unique series H = H ( x , y ) in two non-associative variables satisfying exp( H )=exp( x )exp( y ) the non-associative Hausdorff series, and we show that the homogeneous components H n of H are primitive elements ...
Tópico(s): Homotopy and Cohomology in Algebraic Topology
2003 - Elsevier BV | Journal of Algebra
M. Bottiglieri, C. Godano, G. Lauro,
In this paper we perform a linear stability analysis of the equilibrium solution of a suitable Korteweg model for a two-phase fluid modeling a magma transport in a volcanic conduit. By perturbing the fluid at rest and applying the principle of exchange of stabilities, we prove that at the onset of instability, a stationary cellular convection of bubbles prevails. This behavior could be a reasonable description of the transition from the two-phase system magma-dissolved gas in the chamber to the ...
Tópico(s): Geological formations and processes
2012 - Institute of Physics | EPL (Europhysics Letters)
This paper describes a model representing the process of partial melting of deforming mantle rock, and the associated melt migration due to differential buoyancy. The model is a double free-boundary problem of degenerate type, and is typical of such slow, reactive two-phase flows. Prescription of boundaryconditions is problematical, but in some sense the model picks its own; a realistic asymptotic solution involving rather novel boundary layer behaviour is presented, for the case of two fixed boundaries, ...
Tópico(s): Heat and Mass Transfer in Porous Media
1989 - Society for Industrial and Applied Mathematics | SIAM Journal on Applied Mathematics
Miglena N. Koleva, Lubin G. Vulkov,
In this paper, we present numerical treatment for a compaction-driven Darcian flow viscoelastic rock magma model. This problem is a strongly coupled system of one quasi-linear parabolic equation and one integro-differential equation for the density and the porosity of the flow. The numerical discretization uses cell-centered finite difference method, combined with semi-implicit and implicit time stepping. Implicit–explicit schemes, as well as implicit–explicit iterative algorithms have been developed ...
Tópico(s): Differential Equations and Numerical Methods
2019 - Elsevier BV | Journal of Computational and Applied Mathematics
Juliane Dannberg, René Gassmöller, Ryan R. Grove, Timo Heister,
Many open problems in the Earth sciences can only be understood by modelling the porous flow of melt through a viscously deforming solid rock matrix. However, the system of equations describing this process becomes mathematically degenerate in the limit of vanishing melt fraction. Numerical methods that do not consider this degeneracy or avoid it solely by regularising specific material properties generally become computationally expensive as soon as the melt fraction approaches zero in some part ...
Tópico(s): Advanced Numerical Methods in Computational Mathematics
2019 - Oxford University Press | Geophysical Journal International
Óscar J. Falcón, Raúl Manuel Falcón Ganfornina, Juan Núñez Valdés,
The set of n ‐dimensional Malcev magma algebras over a finite field can be identified with algebraic sets defined by zero‐dimensional radical ideals for which the computation of their reduced Gröbner bases makes feasible their enumeration and distribution into isomorphism and isotopism classes. Based on this computation and the classification of Lie algebras over finite fields given by De Graaf and Strade, we determine the mentioned distribution for Malcev magma algebras of dimension n ≤4. We also ...
Tópico(s): Polynomial and algebraic computation
2016 - Wiley | Mathematical Methods in the Applied Sciences
Ester Piegari, Rosa Di Maio, Roberto Scandone, L. Milano,
Volcanoes are complex dynamical systems that manifest their activity in a wide range of eruptions with different explosivity. In this paper, we propose a cellular automaton model aimed at capturing the key features of the magma ascent dynamics that reproduces the great variability of volcanic explosivity. The novelty of our approach consists in considering an eruption not as an event caused by overpressure in the magma chamber but as the result of transport of discrete magma batches from the reservoir ...
Tópico(s): Complex Systems and Time Series Analysis
2011 - Elsevier BV | Journal of Volcanology and Geothermal Research
Sage is a free, open source, self-contained distribution of mathematical software, including a large library that provides a unified interface to the components of this distribution. This library also builds on the components of Sage to implement novel algorithms covering a broad range of mathematical functionality from algebraic combinatorics to number theory and arithmetic geometry.
Tópico(s): Polynomial and algebraic computation
2010 - Springer Science+Business Media | Lecture notes in computer science
Christine Andersen, Philipp Weis,
Abstract Magma flow, heat conduction, and hydrothermal fluid flow control the heat transfer through the upper crust. Magmatic‐hydrothermal activity is essential for the utilization of geothermal energy, formation of ore deposits, and predictions of volcanic hazards, but the interplay between magmatic and hydrothermal processes is not well constrained due to the lack of adequate scientific tools. Simulation results from our novel coupled numerical model resolving both magma (Navier‐Stokes) and hydrothermal ( ...
Tópico(s): Heat and Mass Transfer in Porous Media
2020 - American Geophysical Union | Geophysical Research Letters
Kyle R. Mayborn, Charles E. Lesher,
Mass balance calculation is a fundamental approach in geosciences. In petrology and geochemistry, it is widely used for quantitative characterization of phase transition and mass transfer. In a routine petrological practice, this method is commonly used to calculate proportions of the minerals formed from initial or parental bulk composition, or to quantify the reaction coefficients for minerals involved in a chemical reaction that achieves equilibria. In this paper, we present a new mass balance ...
Tópico(s): Statistical and numerical algorithms
2011 - Elsevier BV | Computers & Geosciences
Gideon Simpson, Marc Spiegelman, Michael I. Weinstein,
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Two proposed methods for this transport are percolation through porous rock and flow up conduits. Under reasonable assumptions and simplifications, both means of transport can be described by a class of degenerate nonlinear dispersive partial differential equations of the form: where ϕ(z, 0) > 0 and ϕ(z, t) → 1 as z → ±∞.
Tópico(s): Navier-Stokes equation solutions
2006 - IOP Publishing | Nonlinearity
G. Capaldi, Edoardo Del Pezzo, R. Pece, R. Scarpa,
Mount Vesuvius is emplaced on a regional NE-SW-trending fault that accommodates the stretching of the lithosphere caused by a backward retreat of the Calabrian arc. The dynamics of the Calabrian arc controls the temporal occurrence of earthquakes in the Southern Apennines and in Sicily.By means of a detailed statistical approach, we identified a significant correlation between seismic events occurring in different subsets of this geodynamic domain: seismicity changes in the Southern Apennines follow ...
Tópico(s): Geological Studies and Exploration
1976 - Elsevier BV | Journal of Volcanology and Geothermal Research
Onno Bokhove, Andrew W. Woods, A. de Boer,
A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the characteristic dike width are considered. The model emerges when nonlinear inertia terms in the momentum equation are neglected in a viscous, low-speed approximation of a magma flow model coupled to the elastic ...
Tópico(s): Computational Fluid Dynamics and Aerodynamics
2005 - Springer Science+Business Media | Theoretical and Computational Fluid Dynamics
Sander Rhebergen, Garth N. Wells, Richard F. Katz, Andrew J. Wathen,
This article considers the iterative solution of a finite element discretisation of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyse and numerically test a Elman, Silvester and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters ...
Tópico(s): Matrix Theory and Algorithms
2014 - Society for Industrial and Applied Mathematics | SIAM Journal on Scientific Computing
Sander Rhebergen, Garth N. Wells, Andrew J. Wathen, Richard F. Katz,
For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field formulation can be obtained, the construction of preconditioners that are uniform with respect to model parameters is difficult. This limits the applicability of two-field preconditioners in certain regimes of practical interest. We address this issue by reformulating ...
Tópico(s): Matrix Theory and Algorithms
2015 - Society for Industrial and Applied Mathematics | SIAM Journal on Scientific Computing