A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale “source” fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress- and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation

General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera

Nonlocal Gate Of Quantum Network Via Cavity Quantum Electrodynamics

We propose an experimentally feasible scheme to realize the nonlocal gate between two different quantum network nodes. With an entanglement-qubit (ebit) acts as a quantum channel, our scheme is resistive to actual environment noise and can get high fidelity in current cavity quantum electrodynamics (C-QED) system.Comment: 5 pages, 3 figures, 1 tabl

Low energy physical properties of high-Tc superconducting Cu oxides: A comparison between the resonating valence bond and experiments

In a recent review by Anderson and coworkers\cite{Vanilla}, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high temperature superconducting (SC) Cu-oxides. Here we extend previous calculations \cite{anderson87,FC Zhang,Randeria} to study more systematically low energy physical properties of the plain vanilla d-wave RVB state, and to compare results with the available experiments. We use a renormalized mean field theory combined with variational Monte Carlo and power Lanczos methods to study the RVB state of an extended $t-J$ model in a square lattice with parameters suitable for the hole doped Cu-oxides. The physical observable quantities we study include the specific heat, the linear residual thermal conductivity, the in-plane magnetic penetration depth, the quasiparticle energy at the antinode $(\pi, 0)$, the superconducting energy gap, the quasiparticle spectra and the Drude weight. The traits of nodes (including $k_{F}$, the Fermi velocity $v_{F}$ and the velocity along Fermi surface $v_{2}$), as well as the SC order parameter are also studied. Comparisons of the theory and the experiments in cuprates show an overall qualitative agreement, especially on their doping dependences.Comment: 12 pages, 14 figures, 1 tabl

Demonstration of Temporal Distinguishability in a Four-Photon State and a Six-Photon State

An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multi-photon interference scheme in a recent discovered NOON-state projection measurement. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and thus quantitatively determine the degree of temporal (in)distinguishability of a multi-photon state

Role of natural fractures in damage evolution around tunnel excavation in fractured rocks

This paper studies the role of pre-existing fractures in the damage evolution around tunnel excavation in fractured rocks. The length distribution of natural fractures can be described by a power law model, whose exponent a defines the relative proportion of large and small fractures in the system. The larger a is, the higher proportion of small fractures is. A series of two-dimensional discrete fracture networks (DFNs) associated with different length exponent a and fracture intensity P21 is generated to represent various scenarios of distributed pre-existing fractures in the rock. The geomechanical behaviour of the fractured rock embedded with DFN geometry in response to isotropic/anisotropic in-situ stress conditions and excavation-induced perturbations is simulated using the hybrid finite-discrete element method (FEMDEM), which can capture the deformation of intact rocks, the interaction of matrix blocks, the displacement of natural fractures, and the propagation of new cracks. An excavation damaged zone (EDZ) develops around the man-made opening as a result of reactivation of pre-existing fractures and propagation of wing cracks. The simulation results show that when a is small, the system which is dominated by large fractures can remain stable after excavation given that P21 is not very high; however, intensive structurally-governed kinematic instability can occur if P21 is sufficiently high and the fracture spacing is much smaller than the tunnel size. With the increase of a, the system becomes more dominated by small fractures, and the EDZ is mainly created by the coalescence of small fractures near the tunnel boundary. The results of this study have important implications for designing stable underground openings for radioactive waste repositories as well as other engineering facilities that are intended to generate minimal damage in the host rock mass

Theory for Nonlinear Spectroscopy of Vibrational Polaritons

Molecular polaritons have gained considerable attention due to their potential to control nanoscale molecular processes by harnessing electromagnetic coherence. Although recent experiments with liquid-phase vibrational polaritons have shown great promise for exploiting these effects, significant challenges remain in interpreting their spectroscopic signatures. In this letter, we develop a quantum-mechanical theory of pump-probe spectroscopy for this class of polaritons based on the quantum Langevin equations and the input-output theory. Comparison with recent experimental data shows good agreement upon consideration of the various vibrational anharmonicities that modulate the signals. Finally, a simple and intuitive interpretation of the data based on an effective mode-coupling theory is provided. Our work provides a solid theoretical framework to elucidate nonlinear optical properties of molecular polaritons as well as to analyze further multidimensional spectroscopy experiments on these systems

Electron quantum interference in epitaxial antiferromagnetic NiO thin films

The electron reflectivity from NiO thin films grown on Ag(001) has been systematically studied as a function of film thickness and electron energy. A strong electron quantum interference effect was observed from the NiO film, which is used to derive the unoccupied band dispersion above the Fermi surface along the Γ-X direction using the phase accumulation model. The experimental bands agree well with first-principles calculations. A weaker electron quantum interference effect was also observed from the CoO film