Continuum Mechanics in the Earth Sciences

Published on Apr 23, 2012
William I. Newman1
Estimated H-index: 1
Preface Acknowledgements 1. Some mathematical essentials 2. Stress principles 3. Deformation and motion 4. Fundamental laws and equations 5. Linear elastic solids 6. Classical fluids 7. Geophysical fluid dynamics 8. Computation in continuum mechanics 9. Nonlinearity in the Earth References Index.
  • References (0)
  • Citations (6)
📖 Papers frequently viewed together
102 Citations
78% of Scinapse members use related papers. After signing in, all features are FREE.
#1Paul SegallH-Index: 69
240 Citations
#1Geoffrey K. VallisH-Index: 37
Part I. Fundamentals of Geophysical Fluid Dynamics: 1. Equations of motion 2. Effects of rotation and stratification 3. Shallow water systems and isentropic coordinates 4. Vorticity and potential vorticity 5. Simplified equations for ocean and atmosphere Part II. Instabilities, Waves and Turbulence: 6. Barotropic and baroclinic instability 7. Wave-mean flow interaction 8. Turbulence: basic theory 9. Geostrophic turbulence and baroclinic eddies 10. Turbulent diffusion and eddy transport Part III....
512 Citations
#1W. I. Newman (UCLA: University of California, Los Angeles)H-Index: 1
#2Donald L. Turcotte (Cornell University)H-Index: 72
Abstract. We have studied a hybrid model combining the forest-fire model with the site-percolation model in order to better understand the earthquake cycle. We consider a square array of sites. At each time step, a "tree" is dropped on a randomly chosen site and is planted if the site is unoccupied. When a cluster of "trees" spans the site (a percolating cluster), all the trees in the cluster are removed ("burned") in a "fire." The removal of the cluster is analogous to a characteristic earthqua...
25 CitationsSource
#1Gerald SchubertH-Index: 88
#2Donald L. TurcotteH-Index: 72
Last. Peter OlsonH-Index: 53
view all 3 authors...
Preface 1. Historical background 2. Plate tectonics 3. Structure and composition of the mantle 4. Mantle temperatures and thermodynamic properties 5. Viscosity of the mantle 6. Basic equations 7. Linear stability 8. Approximate solutions 9. Calculations of convection in two dimensions 10. Numerical models of three-dimensional convection 11. Hotspots and mantle plumes 12. Chemical geodynamics 13. Thermal history of the Earth 14. Convection in the interiors of solid planets and moons 15. Nature of...
715 Citations
#1Martin H. MüserH-Index: 30
#2Ludgar WenningH-Index: 1
Last. Mark O. Robbins (Johns Hopkins University)H-Index: 53
view all 3 authors...
A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons' laws. However the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficie...
164 CitationsSource
#1Andrei Gabrielov (Purdue University)H-Index: 29
#2Ilya ZaliapinH-Index: 25
Last. Vladimir I. Keilis-borok (UCLA: University of California, Los Angeles)H-Index: 27
view all 4 authors...
A wide set of premonitory seismicity patterns is reproduced on a numerical model of seismicity, and their performance in the prediction of major model earthquakes is evaluated. Seismicity is generated by the colliding cascades model, recently developed by the authors. The model has a hierarchical structure. It describes the interaction of two cascades: a direct cascade of loading, which is applied to the top (largest) element and transfers down the hierarchy, and an inverse cascade of failures, ...
49 CitationsSource
#1Andrei Gabrielov (Purdue University)H-Index: 29
#2Vladimir I. Keilis-borok (UCLA: University of California, Los Angeles)H-Index: 27
Last. William I. Newman (UCLA: University of California, Los Angeles)H-Index: 26
view all 4 authors...
We consider here the interaction of direct and inverse cascades in a hierarchical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarchy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail ~i.e., break down! under the load. The smallest elements fail first. The failures gradually expand up the hierarchy to the larger elements, thus forming an inverse cascade...
46 CitationsSource
#1William I. Newman (UCLA: University of California, Los Angeles)H-Index: 26
Burgers equation is employed as a pedagogical device for analytically demonstrating the emergence of a form of inverse cascade to the lowest wavenumber in a flow. The transition from highly nonlinear mode–mode coupling to an ordered preference for large scale structure is shown, both analytically (revealing the presence of a global attractor) and via a numerical example.
1 CitationsSource
#1Roger PeyretH-Index: 1
About the basic numerical methods, A. Dervieux Navier-Stokes equations for incompressible flows - finite-difference and finite-volume methods, G.B. Deng et al Navier-Stokes equations for incompressible laminar flow - finite-element methods, M.D. Gunzburger euler and Navier-Stokes equations for compressible laminar flows - finite-volume methods, F. Grasso and C. Meola turbulent flows - direct numerical simulation and large-eddy simulation, C. Hartel turbulent flows - model equations and solution ...
94 Citations
Cited By6
#1Mingliang Xiong (Tongji University)H-Index: 2
#2Mingqing Liu (Tongji University)H-Index: 2
Last. Pengfei Xia (Tongji University)H-Index: 19
view all 6 authors...
Resonant beam charging (RBC) can realize wireless power transfer (WPT) from a transmitter to multiple Internet of Things devices via resonant beams. The adaptive RBC (ARBC) can effectively improve its energy utilization. In order to support multiuser WPT in the ARBC system, we propose the time-division multiple access (TDMA) method and design the TDMA-based WPT scheduling algorithm. Our TDMA WPT method has the features of concurrently charging, continuous charging current, individual user power ...
3 CitationsSource
#1Narayan Bose (IITB: Indian Institute of Technology Bombay)H-Index: 3
#2Dripta Dutta (IITB: Indian Institute of Technology Bombay)H-Index: 2
Last. Soumyajit Mukherjee (IITB: Indian Institute of Technology Bombay)H-Index: 25
view all 3 authors...
Abstract Brittle Y- and P-planes exist in an exposure of greywacke in the Garhwal Lesser Himalaya, India. Although, Y-planes are well developed throughout, the P-planes are prominent only in some parts (domain-A), and not elsewhere (domain-B). To investigate why the P-planes developed selectively, the following studies were undertaken: 1. Clay-separated XRD analyses: clinochlore and illite are present in both the domains. 2. Strain analyses by Rf-φ method: it deduces strain magnitudes of ∼1.8 fo...
11 CitationsSource
#1Ke Gao (U of T: University of Toronto)H-Index: 6
#2John P. Harrison (U of T: University of Toronto)H-Index: 5
Abstract In situ stress is an important parameter in rock mechanics, but localised measurements of stress often display significant variability. For improved understanding of in situ matrices that satisfy both Eq. stress it is important that this variability be correctly characterised, and for this a robust statistical distribution model – one that is faithful to the tensorial nature of stress – is essential. Currently, variability in stress measurements is customarily characterised using separa...
11 CitationsSource
#1Qingwen LiuH-Index: 13
#2Jun Wu (Tongji University)H-Index: 1
Last. Lajos Hanzo (University of Southampton)H-Index: 75
view all 7 authors...
Increasing the battery-recharge period of smartphones is becoming a challenge since their power consumption is increased as a result of enhanced functions that require sophisticated multimedia signal processing. An attractive solution is constituted by wireless charging, which is capable of replenishing the battery over the ether. Given this motivation, we present the fundamental physics and the related system structure of a promising wireless charging technique, i.e., distributed laser charging...
33 CitationsSource