Macroscopic and microscopic properties of solutions of aromatic compounds in an ionic liquid

Molecular dynamics simulations of binary mixtures of benzene, 1,3,5-trifluorobenzene and hexafluorobenzene with dimethylimidazolium hexafluorophosphate were carried out to examine their macroscopic and microscopic properties. The energies and volumes of mixing of these mixtures correlate well with observed microscopic properties including coordination number about the aromatic compound. The local ordering of the ions about an aromatic molecule was found to depend on the quadrupole moment of the aromatic species and to remain qualitatively the same on varying the mole fraction of the aromatic species. Interaction energies showed the most significant interactions to be between the aromatic molecule and the ions located about its equator. These findings have implications for the practical use of ionic liquids as solvents for chemical processes.     

The projective dimension of three cubics is at most 5

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\le 5$. In the present paper we prove this conjectured sharp bound.     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.     

Experimental study of hydraulic engine mounts using multiple inertia tracks and orifices: Narrow and broad band tuning concepts

Hydraulic engine mount tuning concepts with one inertia track and one decoupler are well understood. However, the dynamic response with multiple tracks or orifices is not. To overcome this void in the literature, dynamic tuning concepts of hydraulic engine mounts, with emphasis on multiple (n-)inertia tracks/orifices, are experimentally examined. A new prototype mount concept is designed, built, and experimentally evaluated in a controlled manner. Refined linear time-invariant models of fixed decoupler-type designs are developed to critically assess the dynamic stiffness measurements and to explore a family of alternate designs. Three narrowband devices are investigated for accurately predicting the frequencies corresponding to peak loss angles for the first time, in addition to examining and validating an n = 3 track mount. Two broadband devices are also successfully evaluated by tuning damping introduced by orifice-type tracks. A special broad-tuned design utilizing a controlled ‘leakage’ path flow area is then suggested, and the role of fluid resistance in achieving the desired performance is clarified. Finally, a production mount with unknown configuration is diagnosed using the proposed models with n tracks.     

A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip

This paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically use a non‐physical equation of state in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi‐component systems containing gases of differing molecular masses. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. The new model developed for multi‐component gases avoids the pitfalls of some other LB models. A single computational grid is shared by all the species, and the diffusivity is independent of the viscosity. The Navier–Stokes equation for the mixture and the Stefan–Maxwell diffusion equation are both recovered by the model. Diffusion slip, the non‐zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one‐dimensional model for channel flow. To increase the accuracy of the scheme, a second‐order numerical implementation is needed. This may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Origin of Primitive Cells: From Nutrient Intake to Elongation of Encapsulated Nucleotides

Recent major discoveries in membrane biophysics hold the key to a modern understanding of the origin of life on Earth. Membrane bilayer vesicles have been shown to provide a multifaceted microenvironment in which protometabolic reactions could have developed. Cell‐membrane‐like aggregates of amphiphilic molecules capable of retaining encapsulated oligonucleotides have been successfully created in the laboratory. Sophisticated laboratory studies on the origin of life now show that elongation of the DNA primer takes place inside fatty acid vesicles when activated nucleotide nutrients are added to the external medium. These studies demonstrate that cell‐like vesicles can be sufficiently permeable to allow for the intake of charged molecules such as activated nucleotides, which can then take part in copying templates in the protocell interior. In this Review we summarize recent experiments in this area and describe a possible scenario for the origin of primitive cells, with an emphasis on the elongation of encapsulated nucleotides.     

Novel Copolymers of Styrene and Alkyl and Alkoxy Ring‐Trisubstituted Methyl 2‐Cyano‐3‐phenyl‐2‐propenoates

Electrophilic trisubstituted ethylene monomers, akyl and alkoxy ring‐trisubstituted methyl 2‐cyano‐3‐phenyl‐2‐propenoates, RC₆H₂CH[dbnd]C(CN)CO₂CH_3, (where R is 2,3‐dimethyl‐4‐methoxy, 2,5‐dimethyl‐4‐methoxy‐, 2,3,4‐trimethoxy‐, 2,4,5‐trimethoxy, 2,4,6‐trimethoxy, and 2,4‐dimethoxy‐3‐methyl), were synthesized by the piperidine catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and methyl cyanoacetate, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (AIBN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 283–306°C range.