A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis

This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non-linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single- and double-front simulations for two- and three-phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non-linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non-zero value for the repulslive force to avoid development of an ill-conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.     

Subtle differences in structural transitions between poly-L- and poly-D-amino acids of equal length in water

Mirror-image asymmetric molecules, i.e., chiral isomers or enantiomers, are classically considered as chemically identical. Recent studies, however, have indicated that parity violation by the nuclear weak force induces a tiny energy difference between chiral isomers. Upon combination with a massive amplification process, expansion of this difference to a detectable macroscopic level may be achieved. Yet, experimental tests of this possibility, where one enantiomer is compared to the other in solution, are hampered by the possible presence of undetectable impurities. In this study we have overcome this problem by comparing structural and dynamic features of synthetic D- and L-polyglutamic acid and polylysine molecules each of 24 identical residues. In these water-soluble polypeptides helix formation is an intramolecular autocatalytic process amplified by each turn, which is actually unaffected by low level of putative impurities in the solvent. The helix and random coil configurations and their transition were determined in this study by circular dichroism (CD) and isothermal titration calorimetry (ITC) in water and deuterium oxide. Distinct differences in structure and transition energies between the enantiomeric polypeptides were detected by both CD and ITC when dissolved in water. Intriguingly, these differences were by and large abolished in deuterium oxide. Our findings suggest that deviation from physical invariance between the D- and L-polyamino acids is induced in part by different hydration in water which is eliminated in deuterium oxide. Based on the recent findings by Tikhonov and Volkov (V. I. Tikhonov and A. A. Volkov, Science 2002, 296, 2363) we suggest that ortho-H(2)O, which constitutes 75% of bulk H(2)O, has a preferential affinity to L-enantiomers. Differential hydration of enantiomers may have played a role in the selection of L-amino acids by early forms of life.     

Black Hole Evaporation Entails an Objective Passage of Time

Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We prove that any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. It is only determinism that enables time reversal, whether theoretical or experimental, of any entropy-increasing process. A contradiction therefore arises between Hawking's [1] argument that physical law is time-symmetric and his controversial claim [2] that black-hole evaporation introduces a fundamental unpredictability into the physical world. The latter claim forcibly entails an intrinsic time-arrow independent of boundary conditions. A simulation of a simple system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even the slightest failure of determinism occurs. This proof is then extended to the classical behavior of black holes. We conclude with pointing out the affinity between time's arrow and its apparent passage.     

A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets

A theoretical quantum neural network model is proposed using a nonlinear Schrödinger wave equation. The model proposes that there exists a nonlinear Schrödinger wave equation that mediates the collective response of a neural lattice. The model is used to explain eye movements when tracking moving targets. Using a recurrent quantum neural network(RQNN) while simulating the eye tracking model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical neural network, a wave packet is triggered in the quantum neural network.This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of ‘jumps’ and ‘rests’. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter.     

Synthesis and Stereochemical Studies of Derivatives of 1,4-Dimethyl-2-phosphabicyclo[2.2.1]heptane

Abstract

1,4-Dimethyl-2-phenyl-2-phosphabicyclo[2.2.1]heptane 2-oxide 1 was prepared by the reaction of 2,5-dimethyl-1,5-hexadiene with PhPCl₂-AlCl₃: stereo-assignments of the exo and endo isomers were established by ¹³C NMR spectroscopy (using lanthanide shift reagents) and by x-ray crystal structures. The isomers of 1 were separately reduced (phenylsilane) to give the phosphine derivative; in turn the phosphines were thermally equilibrated at 190°C to give a predominance (70%) of the exo-phenyl isomer.     

Interaction-Free Effects Between Distant Atoms

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former’s half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the “no exchange” result, apparently precluding entanglement, is non-locally established between the atoms by this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell’s theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework.     

The Effect of Gadolinium Doping in [13C6,2H7]Glucose Formulations on 13C Dynamic Nuclear Polarization at 3.35 T

The promise of hyperpolarized glucose as a non-radioactive imaging agent capable of reporting on multiple metabolic routes has led to recent advances in its dissolution-DNP (dDNP) driven polarization using UV-light induced radicals and trityl radicals at high field (6.7 T) and 1.1 K. However, most preclinical dDNP polarizers operate at the field of 3.35 T and 1.4–1.5 K. Minute amounts of Gd³⁺ complexes have shown large improvements in solid-state polarization, which can be translated to improved hyperpolarization in solution. However, this Gd³⁺ effect seems to depend on magnetic field strength, metal ion concentration, and sample formulation. The effect of varying Gd³⁺ concentrations at 3.35 T has been described for ¹³C-labeled pyruvic acid and acetate. However, it has not been studied for other compounds at this field. The results presented here suggest that Gd³⁺ doping can lead to various concentration and temperature dependent effects on the polarization of [¹³C₆,²H₇]glucose, not necessarily similar to the effects observed in pyruvic acid or acetate in size or direction. The maximal polarization for [¹³C₆,²H₇]glucose appears to be at a Gd³⁺ concentration of 2 mM, when irradiating for more than 2 h at the negative maximum of the DNP intensity profile. Surprisingly, for shorter irradiation times, higher polarization levels were determined at 1.50 K compared to 1.45 K, at a [Gd³⁺]=1.3 mM. This was explained by the build-up time constant and maximum at these temperatures.