Self-avoiding walks on random fractal environments

Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimensionD _saw is affected by disorder is introduced. Using this method, it is found that for some lattices,D _saw is unaffected by weak disorder; while for othersD _saw changes even for infinitestimal disorder. A weak disorder exponent is defined and calculated analytically [ measures the dependence of the variance in the partition function (or in the effective fugacity per step)vL on the end-to-end distance of the SAW,L]. For lattices which are stable against weak disorder (<0) a phase transition exists at a critical valuev=v ^* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of are discussed.     

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, δ, is comparable to the diffusion time, Δ. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Δ/δ, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Δ/δ  1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long δ the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Δ/δ  1 the diffraction peaks are shifted to even higher q-values, even when δ is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Δ/δ  1.     

Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.     

Microscopic irreversibility in the neutral kaon system and the thermodynamical arrow of time I. CPT symmetric case

The master equation for the reduced density matrix of the neutral kaon system interacting with a (low temperature) boson gas is derived. The equation is transformed under time reversal (assuming CPT conservation) and the equations of motion in the direct and inverted time schemes are compared. The equations of motion are solved, in a perturbation method, and the explicit approach to thermodynamical equilibrium is described. The entropy production function for the kaonic decaying system is defined and calculated. It is shown that although the equilibrium state and the total entropy change during the approach to it are the same in both time schemes, the details of the entropy time dependence of a coherent initial state are different, thus suggesting a relation between microscopic and macroscopic arrows of time.     

p-adic Arakelov theory

We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the metric on the determinant of its cohomology in the style of Faltings. We also prove analogues of the Adjunction formula and the Riemann-Roch formula.     

Modeling of one-dimensional smoldering of polyurethane in microgravity conditions

Results are presented from a model of forward smoldering combustion of polyurethane foam in microgravity. The transient one-dimensional numerical-model is based on that developed at the University of Texas at Austin. The conservation equations of energy, species, and mass in the porous solid and in the gas phases are numerically solved. The solid and the gas phases are not assumed to be in thermal or in chemical equilibrium. The chemical reactions modeled consist of foam oxidation and pyrolysis reactions, as well as char oxidation. The model has been modified to account for new polyurethane kinetics parameters and radial heat losses to the surrounding environment. The kinetics parameters are extracted from thermogravimetric analyses published in the literature and using Genetic Algorithms as the optimization technique. The model results are compared with previous tests of forward smoldering combustion in microgravity conducted aboard the NASA Space Shuttle. The model calculates well the propagation velocities and the overall smoldering characteristics. Direct comparison of the solution with the experimental temperature profiles shows that the model predicts well these profiles at high temperature, but not as well at lower temperatures. The effect of inlet gas velocity is examined, and the minimum airflow for ignition is identified. It is remarkable that this one-dimensional model with simplified kinetics is capable of predicting cases of smolder ignition but with no self-propagation away from the igniter region. The model is used for better understanding of the controlling mechanisms of smolder combustion for the purpose of fire safety, both in microgravity and normal gravity, and to extend the unique microgravity data to wider conditions avoiding the high cost of space-based experiments.     

Can Substituted Cyclopentadiene Become Aromatic or Antiaromatic?

Cyclopentadiene derivatives with electronegative (F, Cl) or electropositive (H(3)Si, Me(3)Si) bis-5,5-substituents were studied at the B3LYP/6-311G* level of theory. It was found that there is no special stabilization or destabilization for any of the derivatives; the energetic effects that were previously attributed to aromatic stabilization or antiaromatic destabilization are the result of interactions in the reference systems. A nucleus-independent chemical shift (NICS) scan study at the HF-GIAO/6-311+G* theoretical level of these and similar derivatives suggest that they all show different magnitudes of diamagnetic ring current. None of the derivatives shows a paramagnetic ring current. Thus, cyclopentadienes are neither aromatic nor antiaromatic. It is also concluded that a diamagnetic ring current is perhaps necessary but certainly not a sufficient condition for aromaticity. The NICS scan procedure describes the type of ring current in the system, whereas a single isotropic NICS value (i.e., NICS(1)) may wrongly assign the type of ring current. It is shown that neither NICS(1) nor the NICS scan procedure can be used as a single aromaticity criterion.     

Propellanes. Part LXXXI. Why are tetrakis[organoboranediylbis(oxy)]cyclobutanes formed without a trace of the isomeric tetrakis-dioxabora[3.3.2]propellanes?

MNDO and STO-3G calculations rationalize the relative instability of the title propellanes vis-à-vis the title products that are formed exclusively.