Renormalization Group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media

Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a new technique based on Mode-Elimination Renormalization-Group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly so due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner that we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.Comment: 15 pages, 7 figures, Physical Review

Magnetization Properties of Some Quantum Spin Ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second order terms give corrections to the XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.Comment: Revtex, 26 pages including 17 epsf figures; a few minor changes; this is the final published versio

Electron correlation effects in electron-hole recombination in organic light-emitting diodes

We develop a general theory of electron--hole recombination in organic light emitting diodes that leads to formation of emissive singlet excitons and nonemissive triplet excitons. We briefly review other existing theories and show how our approach is substantively different from these theories. Using an exact time-dependent approach to the interchain/intermolecular charge-transfer within a long-range interacting model we find that, (i) the relative yield of the singlet exciton in polymers is considerably larger than the 25% predicted from statistical considerations, (ii) the singlet exciton yield increases with chain length in oligomers, and, (iii) in small molecules containing nitrogen heteroatoms, the relative yield of the singlet exciton is considerably smaller and may be even close to 25%. The above results are independent of whether or not the bond-charge repulsion, X_perp, is included in the interchain part of the Hamiltonian for the two-chain system. The larger (smaller) yield of the singlet (triplet) exciton in carbon-based long-chain polymers is a consequence of both its ionic (covalent) nature and smaller (larger) binding energy. In nitrogen containing monomers, wavefunctions are closer to the noninteracting limit, and this decreases (increases) the relative yield of the singlet (triplet) exciton. Our results are in qualitative agreement with electroluminescence experiments involving both molecular and polymeric light emitters. The time-dependent approach developed here for describing intermolecular charge-transfer processes is completely general and may be applied to many other such processes.Comment: 19 pages, 11 figure

Electron correlation effects in electron–hole recombination and triplet–triplet scattering in organic light emitting diodes

Using a time-dependent model many-body formulation, we follow the electron–hole recombination between a pair of oppositely charged polyene chains and triplet–triplet (T–T) scattering in $\pi$-conjugated systems. Electron correlations reduce the overall yields and also lead to large differences between the singlet and triplet yields. External electric field has a strong influence on the recombination products. The fraction of singlet yield, η, increases with the chain length. Heteroatoms also change this ratio significantly, as has been observed experimentally. The outcome of the triplet–triplet scattering is also significantly affected by electron correlations

Electron correlation effects in electron–hole recombination and triplet–triplet scattering in organic light emitting diodes

Using a time-dependent model many-body formulation, we follow the electron–hole recombination between a pair of oppositely charged polyene chains and triplet–triplet (T-T) scattering in π-conjugated systems. Electron correlations reduce the overall yields and also lead to large differences between the singlet and triplet yields. External electric field has a strong influence on the recombination products. The fraction of singlet yield, η, increases with the chain length. Heteroatoms also change this ratio significantly, as has been observed experimentally. The outcome of the triplet–triplet scattering is also significantly affected by electron correlations

Symmetrized DMRG studies of low-energy electronic states of poly-para-phenylene (PPP) and poly-para-phenylenevinylene (PPV) systems

Symmetrized DMRG calculations on long oligomers of poly- para-phenylene (PPP) and poly-para-phenylene vinylene (PPV) systems within a `U-V' model have been carried out to obtain the one-photon, two-photon and singlet-triplet gaps in these systems. The extrapolated gaps (in eV) are 2.89, 3.76 and 2.72 in PPP and 3.01, 3.61 and 2.23 in PPV for the one- photon, two-photon and spin gaps respectively. By studying doped systems, we have obtained the exciton binding energies. The larger exciton binding energies, compared to strongly dimerized linear chains emphasizes the role of topology in these polymers. Bond orders, charge and spin correlations in the low-lying states bring out the similarities between the lowest one-photon, the lowest triplet and the lowest bipolaronic states in these systems. The two-photon state bond orders show evidence for strong localization of this excitation in both PPP and PPV systems

Formation cross-sections of singlet and triplet excitons in pi-conjugated polymers

Electroluminescence in organic light-emitting diodes arises from a charge-transfer reaction between the injected positive and negative charges by which they combine to form singlet excitons that subsequently decay radiatively. The quantum yield of this process (the number of photons generated per electron or hole injected) is often thought(1) to have a statistical upper limit of 25 per cent. This is based on the assumption that the formation cross-section of singlet excitons, sigma (s), is approximately the same as that of any one of the three equivalent non-radiative triplet exciton states, sigma (T); that is, sigma (S)/sigma (T) approximate to 1. However, recent experimental(2) and theoretical(3) work suggests that sigma (S)/sigma (T) may be greater than 1. Here we report direct measurements of sigma (S)/sigma (T) for a large number of pi -conjugated polymers and oligomers. We have found that there exists a strong systematic, but not monotonic, dependence of sigma (S)/sigma (T) on the optical gap of the organic materials. We present a detailed physical picture of the charge-transfer reaction for correlated pi -electrons, and quantify this process using exact valence bond calculations. The calculated sigma (S)/sigma (T) reproduces the experimentally observed trend. The calculations also show that the strong dependence of sigma (S)/sigma (T) on the optical gap is a signature of the discrete excitonic energy spectrum, in which higher energy excitonic levels participate in the charge recombination process

Method of Moments for Computational Microemulsion Analysis and Prediction in Tertiary Oil Recovery

We discuss the application of Helfrich’s surface torque density concept to microemulsion design and analysis from three different angles: (i) from the point of view of coarse-grained molecular simulations, using Dissipative Particle Dynamics, including charge interactions and added salt, (ii) using an approximate double-film model for the surface, and (iii) comparison with formulation approaches. The simulations use that the surface torque can be calculated unambiguously from the stress profile, provided the surface is tensionless. Very good agreement is found on predicting optimal salinity (or the absence of that) for a range of surfactants: dioctyl sodium sulfosuccinate, various twin-tailed sulfonates and sodium dodecyl sulfate. The simulations are very fast, on par with times for experiments, thus they could lead to a practical tool for discovery of more efficient surfactants, although much remains to be done with respect to other important variables: oil composition, surfactant mixtures, aggregation in solution, and so on. The microscopic model (second approach) is highly approximate: it is essentially based on two opposing swelling tendencies, that are both of osmotic nature. In accordance with the model, the tails are swollen by the oil and the charged head groups are confined in a salty layer in Donnan equilibrium with the salt solution. In this way, the surface interactions are purely entropic. The comparison of the film model with existing formulation approaches (third approach) covers the interfacial tension minimum, Winsor R theory, quantitative structure property relations (QSPR), hydrophilic–lipophilic deviation (HLD), HLD-net average curvature, and temperature coefficients. Using the surface torque analysis, we succeed in deriving in an ab initio way QSPR empirical coefficients that have been known for decades, but until now, have been obscure in origin