Pore Space Microstructure Evolution of Regular Sphere Packings Undergoing Compaction and Cementation

We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths (l _c). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in l _c. This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which l _c is non-monotonic exhibiting a kink at ${\phi \approx 0.1452}$ , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in l _c as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability?Cporosity relation as porosity decreases. The consequences are great; clearly l _c is not a constant unless the diagenetic process is mild. A l _c function of compaction/cementation advancement should be used above a transition and a different l _c function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a l _c function of compaction/cementation advancement is mandatory if we are to capture all significant flow features.     

Dielectric response of frustrated water down to a single‐molecule contribution

A theory of dielectric response of water under nanoscale confinement was long overdue. This work addresses the problem by establishing a relation between dielectric response and hydrogen‐bond frustration subsumed in a non‐Debye polarization term. The results hold down to the single‐molecule contribution and are validated vis‐à‐vis experimental measurements on a system where dielectric modulation entails removal of a single water molecule. The frustrated dielectric response down to molecular scales is assessed by contrasting two enantiomeric ligands in association with the same protein, with the complexes differing in the removal of a single interfacial water molecule.

     

Lowering Energy Barriers in Surface Reactions through Concerted Reaction Mechanisms

Any technologically important chemical reaction typically involves a number of different elementary reaction steps consisting of bond‐breaking and bond‐making processes. Usually, one assumes that such complex chemical reactions occur in a step‐wise fashion where one single bond is made or broken at a time. Using first‐principles calculations based on density functional theory we show that the barriers of rate‐limiting steps for technologically relevant surface reactions are significantly reduced if concerted reaction mechanisms are taken into account.     

Energetic and spectral properties of triple photon downconversion in a phase-matched KTiOPO4 crystal

We measured the spectrum and energy of infrared triple photons generated in a phase-matched KTiOPO4 crystal pumped by picosecond beams at 532 and 1662 nm. The experimental data are in good agreement with our model, taking into account the spectral linewidths of the incident beams as well as a parasitic Kerr effect.     

Four NiII complexes with the new cyclam–methylimidazole ligand 1‐[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane

Although it has not proved possible to crystallize the newly prepared cyclam–methylimidazole ligand 1‐[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane (L^Im1), the trans and cis isomers of an Ni^II complex, namely trans‐aqua{1‐[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane}nickel(II) bis(perchlorate) monohydrate, [Ni(C₁₅H₃₀N₆)(H₂O)](ClO₄)₂·H₂O, (1), and cis‐aqua{1‐[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane}nickel(II) bis(perchlorate), [Ni(C₁₅H₃₀N₆)(H₂O)](ClO₄)₂, (2), have been prepared and structurally characterized. At different stages of the crystallization and thermal treatment from which (1) and (2) were obtained, a further two compounds were isolated in crystalline form and their structures also analysed, namely trans‐{1‐[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane}(perchlorato)nickel(II) perchlorate, [Ni(ClO₄)(C₁₅H₃₀N₆)]ClO₄, (3), and cis‐{1,8‐bis[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane}nickel(II) bis(perchlorate) 0.24‐hydrate, [Ni(C₂₀H₃₆N₆)](ClO₄)₂·0.24H₂O, (4); the 1,8‐bis[(1‐methyl‐1H‐imidazol‐2‐yl)methyl]‐1,4,8,11‐tetraazacyclotetradecane ligand is a minor side product, probably formed in trace amounts in the synthesis of L^Im1. The configurations of the cyclam macrocycles in the complexes have been analysed and the structures are compared with analogues from the literature.     

Application of the multi-standard methodology for calculating 1H NMR chemical shifts

Gauge including atomic orbitals (GIAO) (1)H NMR chemical shift calculations have been performed for 66 organic compounds at 72 different levels of theory using the multi-standard approach (MSTD) previously developed for (13)C NMR. This straightforward computational technique involves the combination of methanol and benzene as standards. The studied methodology has been shown to predict (1)H NMR chemical shifts efficiently at different levels of theory.     

Increasing the output length of zero‐error dispersers

Let $\cal{C}$ be a class of probability distributions over a finite set Ω. A function $D : \Omega \mapsto\{0,1\}^{m}$ is a disperser for $\cal{C}$ with entropy threshold $k$ and error $\epsilon$ if for any distribution X in $\cal{C}$ such that X gives positive probability to at least $2^{k}$ elements we have that the distribution $D(X)$ gives positive probability to at least $(1-\epsilon)2^{m}$ elements. A long line of research is devoted to giving explicit (that is polynomial time computable) dispersers (and related objects called “extractors”) for various classes of distributions while trying to maximize m as a function of k. For several interesting classes of distributions there are explicit constructions in the literature of zero‐error dispersers with “small” output length m. In this paper we develop a general technique to improve the output length of zero‐error dispersers. This strategy works for several classes of sources and is inspired by a transformation that improves the output length of extractors (which was given by Shaltiel (CCC'06; Proceedings of the 21st Annual IEEE Conference on Computational Complexity, (2006) 46–60.) building on earlier work by Gabizon, Raz and Shaltiel (SIAM J Comput 36 (2006) 1072–1094). Our techniques are different than those of Shaltiel (CCC'06; Proceedings of the 21st Annual IEEE Conference on Computational Complexity (2006) 46–60) and in particular give non‐trivial results in the errorless case. Using our approach we construct improved zero‐error 2‐source dispersers. More precisely, we show that for any constant $\delta >0$ there is a constant $\eta >0$ such that for sufficiently large n there is a poly‐time computable function $D :\{0,1\}^{n}\times\{0,1\}^{n}\mapsto\{0,1\}^{\eta n}$ such that for every two independent distributions $X_1,X_2$ over $\{0,1\}^{n}$ each with support size at least $2^{\delta n}$ , the output distribution $D(X_1,X_2)$ has full support. This improves the output length of previous constructions by Barak, Kindler, Shaltiel, Sudakov and Wigderson (Proceedings of the 37th Annual ACM Symposium on Theory of Computing (2005) 1–10) and has applications in Ramsey theory and in improved constructions of certain data structures from the work of Fiat and Naor [SIAM J Comput 22 (1993)]. We also use our techniques to give explicit constructions of zero‐error dispersers for bit‐fixing sources and affine sources over polynomially large fields. These constructions improve the best known explicit constructions due to Rao (unpublished data) and Gabizon and Raz [Combinatorica 28 (2008)] and achieve $m=\Omega(k)$ for bit‐fixing sources and $m=k-o(k)$ for affine sources over polynomial size fields. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

The singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale ℓ from a crack's tip, significant logr displacements and 1/r displacement-gradient contributions arise. Whereas in LEFM the 1/r singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As ℓ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.     

Quantum Information Entropies on Hyperbolic Single Potential Wells

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies Sx and Sp with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.     

Surface reconstruction of chiral glassy oligomers under the action of volatile organic compounds (VOCs)

The response of chiral polymers to volatile organic compounds (VOCs) was studied by atomic force microscopy. It was found that under the influence of toluene vapour, the focal conic domains on the surface of chiral polymer undergo remarkable reconstruction that is at least partially reversible. This opens new ways for building VOC sensors and using surface reconstruction in creating new surface patterns for nanotechnology.