First steps towards modeling a multi-scale Earth system

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

A multi-scaling approach to predict hydraulic damage of poromaterials

The purpose of this paper is to introduce the concept of hydraulic damage and its numerical integration. Unlike the common phenomenological continuum damage mechanics approaches, the procedure introduced in this paper relies on mature concepts of homogenization, linear fracture mechanics, and thermodynamics. The model is applied to the problem of fault reactivation within resource reservoirs. The results show that propagation of weaknesses is highly driven by the contrasts of properties in porous media. In particular, it is affected by the fracture toughness of host rocks. Hydraulic damage is diffused when it takes place within extended geological units and localized at interfaces and faults.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Entropic bounds for multi-scale and multi-physics coupling in earth sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

Multiscale coupling and multiphysics approaches in earth sciences : applications

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

Deep geothermal: The ‘Moon Landing’ mission in the unconventional energy and minerals space

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Complex solitons in Bose-Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

Ductile deformation of single inclusions in simple shear with a finite-strain hyperelastoviscoplastic rheology

We examine the 2D plane-­strain deformation of initially round, matrix-­bonded, deformable single inclusions in isothermal simple shear using a recently introduced hyperelastoviscoplastic rheology. The broad parameter space spanned by the wide range of effective viscosities, yield stresses, relaxation times, and strain rates encountered in the ductile lithosphere is explored systematically for weak and strong inclusions, the effective viscosity of which varies with respect to the matrix. Most inclusion studies to date focused on elastic or purely viscous rheologies. Comparing our results with linear-­viscous inclusions in a linear-­viscous matrix, we observe significantly different shape evolution of weak and strong inclusions over most of the relevant parameter space. The evolution of inclusion inclination relative to the shear plane is more strongly affected by elastic and plastic contributions to rheology in the case of strong inclusions. In addition, we found that strong inclusions deform in the transient viscoelastic stress regime at high Weissenberg numbers (≥0.01) up to bulk shear strains larger than 3. Studies using the shapes of deformed objects for finite-­strain analysis or viscosity-­ratio estimation should establish carefully which rheology and loading conditions reflect material and deformation properties. We suggest that relatively strong, deformable clasts in shear zones retain stored energy up to fairly high shear strains. Hence, purely viscous models of clast deformation may overlook an important contribution to the energy budget, which may drive dissipation processes within and around natural inclusions.

The origin of degeneracies and crossings in the 1d Hubbard model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyse in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter-independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter-independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wavefunctions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter-independent symmetry.

A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.

Relatos de viajes medievales : una historia de taxonomías literarias (1849-2007)

Número monográfico: El viaje y sus discursos

Letras, Nº 71, 2015

Contenido: El azaroso viaje de la hispanidad en nuestra Argentina de hoy / Javier Roberto González -- Viajes en palabras : entre historias de vidas y de culturas / Sofía Carrizo Rueda -- "Fuesse paral Papa et contól la sua fazienda" : la escritura ejemplar del viaje en el Conde Lucanor / Juan Paredes -- La poética del libro de viaje entre la Edad Media y el siglo XXI / Julio Peñate Rivero -- Relatos de viaje y paradigmas culturales / Luis Alburquerque García -- Espacio y desplazamiento en el viaje de Santa Oria / Javier Roberto González -- El inédito Ms. BNM 17.806 y los itinerarios de la Sagrada Escritura : edición y estudio de un texto ignorado / María Mercedes Rodríguez Temperley -- Dilemas del paraíso : viaje, utopía y mundanidad en la literatura árabe / Daniel Del Percio -- El viaje dantesco y su funcionalidad metapoética en El sueño y el Infierno de los enamorados del Marqués de Santillana / Cinthia Hamlin -- La aventura no cumplida : el camino del caballero andante hacia el ocaso / Mónica Nasif -- Benjamín de Tudela y los motivos del viaje : la educación del judío y el encuentro con la propia identidad a través del otro / María Gabriela Pauer -- El motivo del viaje en la literatura de sentencias / Alicia Esther Ramadori -- La travesía del caballero andante : mapas e itinerarios en el Amadis de Gaula / María del Rosario Valenzuela Munguía -- El viaje del héroe en el Libro del caballero Zifar, el caso de Zifar y Roboán / Simón Andrés Villegas -- La dinámica del viaje en el contexto del Ms. Esc. K-III-4 : Libro de Apolonio, Vida de Santa María Egipciaca, Libro de los tres reyes de Oriente -- Reseñas

Letras, 1999-2000, nº 40-41 (número completo)

Contenido: Nota preliminar – Poesía mariana en Gonzalo de Berceo / Lía N. Uriarte Rebaudi – El judío y el diablo como “otro” en los Milagros de Nuestra Señora de Berceo / Heanon M. Wilkins – “Intellectum tibi dabo et instruam te” / Eric Naylor – Descripción, narración, argumentación y crisis de la oralidad en el Libro del Buen Amor / Sofía M. Carrizo Rueda – El poema de Alfonso XI: ¿Un eco priscilianista, sabeliano, patripasiano? / Jorge Norberto Ferro – El vino en el refranero español; concordancias / Dolly M. Lucero Ontiveros – Una propuesta de clasificación de la Literatura Sapiencial Hispánica en el siglo XIII / Alicia E. Ramadori – Fray Juan García de Castrojeriz receptor de Aristóteles / Hugo Oscar Bizzarri – La especificidad de la prosa alfonsí; el caso del Lapidario / Mirta G. Aguayo – Alfonso el Sabio y Brunetto Latini: convergencias / Gretchem Arnstedt de Magneres – La figura autoral de Alfonso X en las Cantigas de Santa María / Santiago Aníbal Disalvo – La historia del rey Guillermo de Inglaterra: del relato del siglo XIV a la crónica quinientista / Carina Alejandra Zubillaga – El prólogo de “El Victorial”: heterogeneidad y orden a favor de una adecuada recepción / María Mercedes Rodríguez Temperley – A propósito del prólogo de la Confesión del amante / María Cristina Balestrini – Función de la “ekprhasis” en los relatos caballerescos / Lilia Elda Ferrario de Orduna – Una nueva fuente del Amadís de Gaula primitivo: la Waltbarii poesis del abad Ekkehard I. de Saint Gall / Aquilino Suárez Pallasá – Profecía mesiánica y profecía apocalíptica: la cuestión constantinopolitana en las Sergas de Esplandián y Primaleón / Javier Roberto González – Dos romances sefardíes de incógnito en una colección de romances. Aporte de nuevas versiones / Eleonora Angélica Alberti de Kleinbort – Conjeturas acerca del original manuscrito de la Comedia de Fernando Rojas / Germán Orduna – Fernando de Rojas, ¿autor? / Joseph Thomas Snow – El fondo medieval de la colección Foulché-Delbosc / Georgina Olivetto – Nómina de todos los congresistas

El inédito Ms. BNM 17.806 y los itinerarios de la Sagrada Escritura : edición y estudio de un texto ignorado

Resumen: El Ms. 17.806 de la Biblioteca Nacional de Madrid, titulado Descripción y destrucion de la ciudad y templo de Jerusalem. Los viajes y caminos que hizieron los Santos Patriarcas, Profetas, Reyes, Cristo Señor Nuestro, su Madre Santissima y los Apostoles mencionados en la Sagrada Escritura; con una breue declaracion de los pesos, medidas y monedas antiguas hebreas, griegas y romanas reduzidas a las nuestras, es un curioso libro de viajes que permanece inédito y del que casi nada se sabe. Presentamos en esta oportunidad las características generales del texto, las particularidades de la edición que estamos realizando y los posibles modelos literarios subyacentes.

Viel, así en el cielo como en el canon : un lugar en el corpus de la poesía argentina

Resumen: Para analizar cuál es el lugar de Héctor Viel Temperley en las letras argentinas tomamos el movimiento editorial en torno de él, sobre todo la edición y reedición de sus obras y, por otro lado, relevamos antologías poéticas. En la labor, sorpresivamente, aparecen rasgos reveladores que desmienten el supuesto acerca de su haber sido ignoto; por otro lado, hemos hallado elementos que iluminan áreas no estudiadas, las que en nuestra investigación —aún en marcha— se van mostrando fundantes. Asimismo, consideramos su papel como ícono motivador en algunas obras recientes, movilizador, afectiva y conceptualmente, de cierto cúmulo de contenidos.