Full Potential Electronic Structure Calculations and the Concept of Stress Fields and Energy Densities for Total Energy Calculations

1991 ◽  
Vol 253 ◽  
Author(s):  
P. Ziesche
Keyword(s):  
Energy Density ◽  
Stress Field ◽  
Stress Tensor ◽  
Particle Density ◽  
Local Stress ◽  
Full Potential ◽  
Many Body ◽  
Tensor Fields ◽  
Defect Energies ◽  
Total Energies

ABSTRACTWith the availability of reliable full atomic cell orbitals the possibility arises to calculate pressure or stress, restoring or relaxation driving Hellmann -Feynman forces, and total energies (especially of defects) alternatively and directly via stress tensor fields and energy densities, two local quantities. Although quantum mechanical stress field and energy density can not be defined uniquely, there is a recent interest in these quantities, because integrals with physical meaning are gauge invariant.The mentioned fields can be defined (i) for the full many-body description with the exact one-particle density matrix and pair distribution function as well as (ii) for the Kohn-Sham one-particle description with LDA or beyond (gradient expansion approximation). If the local stress field for a special system once is constructed, then the global stress tensor and /or forces on nuclei can be calculated via the stress theorem and the force theorem by means of unit cell surface integrals. The energy density can be derived from the terms of the stress field by taking the trace and can be used to calculate defect energies without bothering about the thermodynamic limit.

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

2021 ◽  
Author(s):  
O. Andersen ◽  
M. Kelley ◽  
V. Smith ◽  
S. Raziperchikolaee
Keyword(s):  
Stress Field ◽  
Stress Tensor ◽  
Co2 Storage ◽  
Measurement Data ◽  
Automatic Calibration ◽  
Storage Site ◽  
Tensor Fields ◽  
Geomechanical Model ◽  
Fully Automatic

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US CO2 storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending point-wise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego Country, Michigan, as our case study. Input data consists of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs and processing of seismic data. A static earth model of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results to observations. Results were interpreted through a Bayesian framework. The focus of this article is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained but does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to non-invasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters, in order to produce results optimally agreeing with available measurements and thus extend partial point-wise estimates to full tensor fields compatible with the physics of the site.

scholarly journals Many-body localization of spinless fermions with attractive interactions in one dimension

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Sheng-Hsuan Lin ◽  
Björn Sbierski ◽  
Florian Dorfner ◽  
Christoph Karrasch ◽  
Fabian Heidrich-Meisner
Keyword(s):  
Phase Diagram ◽  
Energy Density ◽  
Ground State ◽  
Intermediate Phase ◽  
Particle Density ◽  
Luttinger Liquid ◽  
Finite Size ◽  
Finite Energy ◽  
One Dimension ◽  
Many Body

We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

scholarly journals Pole skipping away from maximal chaos

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changha Choi ◽  
Márk Mezei ◽  
Gábor Sárosi
Keyword(s):  
Lyapunov Exponent ◽  
Energy Density ◽  
Stress Tensor ◽  
Diffusion Constant ◽  
Special Point ◽  
Many Body ◽  
Point Function ◽  
Strongly Coupled ◽  
Universal Bound ◽  
Subtle Effect

Abstract Pole skipping is a recently discovered subtle effect in the thermal energy density retarded two point function at a special point in the complex (ω, p) planes. We propose that pole skipping is determined by the stress tensor contribution to many-body chaos, and the special point is at (ω, p)p.s. = $$ i{\lambda}^{(T)}\left(1,1/{u}_B^{(T)}\right) $$ i λ T 1 1 / u B T , where λ(T) = 2π/β and $$ {u}_B^{(T)} $$ u B T are the stress tensor contributions to the Lyapunov exponent and the butterfly velocity respectively. While this proposal is consistent with previous studies conducted for maximally chaotic theories, where the stress tensor dominates chaos, it clarifies that one cannot use pole skipping to extract the Lyapunov exponent of a theory, which obeys λ ≤ λ(T). On the other hand, in a large class of strongly coupled but non-maximally chaotic theories $$ {u}_B^{(T)} $$ u B T is the true butterfly velocity and we conjecture that uB ≤ $$ {u}_B^{(T)} $$ u B T is a universal bound. While it remains a challenge to explain pole skipping in a general framework, we provide a stringent test of our proposal in the large-q limit of the SYK chain, where we determine λ, uB, and the energy density two point function in closed form for all values of the coupling, interpolating between the free and maximally chaotic limits. Since such an explicit expression for a thermal correlator is one of a kind, we take the opportunity to analyze many of its properties: the coupling dependence of the diffusion constant, the dispersion relations of poles, and the convergence properties of all order hydrodynamics.

scholarly journals Driving stress and seismotectonic implications of the 2013 Mw5.8 Awaji Island earthquake, southwestern Japan, based on earthquake focal mechanisms before and after the mainshock

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Kazutoshi Imanishi ◽  
Makiko Ohtani ◽  
Takahiko Uchide
Keyword(s):  
Stress Field ◽  
Stress Tensor ◽  
Nankai Trough ◽  
Source Region ◽  
Local Scale ◽  
Southwest Japan ◽  
Stress Tensor Inversion ◽  
Earthquake Fault ◽  
Reverse Faulting ◽  
Before And After

Abstract A driving stress of the Mw5.8 reverse-faulting Awaji Island earthquake (2013), southwest Japan, was investigated using focal mechanism solutions of earthquakes before and after the mainshock. The seismic records from regional high-sensitivity seismic stations were used. Further, the stress tensor inversion method was applied to infer the stress fields in the source region. The results of the stress tensor inversion and the slip tendency analysis revealed that the stress field within the source region deviates from the surrounding area, in which the stress field locally contains a reverse-faulting component with ENE–WSW compression. This local fluctuation in the stress field is key to producing reverse-faulting earthquakes. The existing knowledge on regional-scale stress (tens to hundreds of km) cannot predict the occurrence of the Awaji Island earthquake, emphasizing the importance of estimating local-scale (< tens of km) stress information. It is possible that the local-scale stress heterogeneity has been formed by local tectonic movement, i.e., the formation of flexures in combination with recurring deep aseismic slips. The coseismic Coulomb stress change, induced by the disastrous 1995 Mw6.9 Kobe earthquake, increased along the fault plane of the Awaji Island earthquake; however, the postseismic stress change was negative. We concluded that the gradual stress build-up, due to the interseismic plate locking along the Nankai trough, overcame the postseismic stress reduction in a few years, pushing the Awaji Island earthquake fault over its failure threshold in 2013. The observation that the earthquake occurred in response to the interseismic plate locking has an important implication in terms of seismotectonics in southwest Japan, facilitating further research on the causal relationship between the inland earthquake activity and the Nankai trough earthquake. Furthermore, this study highlighted that the dataset before the mainshock may not have sufficient information to reflect the stress field in the source region due to the lack of earthquakes in that region. This is because the earthquake fault is generally locked prior to the mainshock. Further research is needed for estimating the stress field in the vicinity of an earthquake fault via seismicity before the mainshock alone.

A SOLVABLE MODEL OF INTERACTING MANY BODY SYSTEMS EXHIBITING A BREAKDOWN OF THE BOLTZMANN EQUATION

2014 ◽  
Vol 28 (03) ◽  
pp. 1450046
Author(s):  
B. H. J. McKELLAR
Keyword(s):  
Boltzmann Equation ◽  
Time Dependence ◽  
Single Particle ◽  
Density Operator ◽  
Particle Density ◽  
Solvable Model ◽  
Many Body ◽  
Single Particle Density ◽  
The Boltzmann Equation ◽  
Many Body Systems

In a particular exactly solvable model of an interacting system, the Boltzmann equation predicts a constant single particle density operator, whereas the exact solution gives a single particle density operator with a nontrivial time dependence. All of the time dependence of the single particle density operator is generated by the correlations.

scholarly journals Local stress fields in solids estimated by acoustical emission method

2021 ◽  
Vol 2103 (1) ◽  
pp. 012064
Author(s):  
V L Hilarov ◽  
E E Damaskinskaya
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Stress Field ◽  
Estimation Method ◽  
Local Stress ◽  
Stress Fields ◽  
Emission Method ◽  
Macroscopic Fracture ◽  
Stress Estimation ◽  
Kinetic Concept

Abstract Based on the Zhurkov’s kinetic concept of solids’ fracture a local internal stress estimation method is introduced. Stress field is computed from the time series of acoustic emission intervals between successive signals. For the case of two structurally different materials the time evolution of these stresses is examined. It is shown that temporal changes of these stresses’ accumulation law may serve as a precursor of incoming macroscopic fracture.

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