Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

Diffusion Limitations and Translocation Barriers in Atomically Thin Biomimetic Pores

Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore can be critical in determining the transport properties of the channel due to several commensurate length scales, such as the effective membrane thickness, radii of the first and the second hydration layers, pore radius, and Debye length. In particular, for biomimetic pores, such as the graphene crown ether we examine here, there are regimes where transport is highly sensitive to the pore size due to the interplay of dehydration and interaction with pore charge. Picometer changes in the size, e.g., due to a minute strain, can lead to a large change in conductance. Outside of these regimes, the small pore size itself gives a large resistance, even when electrostatic factors and dehydration compensate each other to give a relatively flat—e.g., near barrierless—free energy landscape. The permeability, though, can still be large and ions will translocate rapidly after they arrive within the capture radius of the pore. This, in turn, leads to diffusion and drift effects dominating the conductance. The current thus plateaus and becomes effectively independent of pore-free energy characteristics. Measurement of this effect will give an estimate of the magnitude of kinetically limiting features, and experimentally constrain the local electromechanical conditions.     

Solvent‐free Liquid Crystals and Liquids from DNA

As DNA exhibits persistent structures with dimensions that exceed the range of their intermolecular forces, solid‐state DNA undergoes thermal degradation at elevated temperatures. Therefore, the realization of solvent‐free DNA fluids, including liquid crystals and liquids, still remains a significant challenge. To address this intriguing issue, we demonstrate that combining DNA with suitable cationic surfactants, followed by dehydration, can be a simple generic scheme for producing these solvent‐free DNA fluid systems. In the anhydrous smectic liquid crystalline phase, DNA sublayers are intercalated between aliphatic hydrocarbon sublayers. The lengths of the DNA and surfactant are found to be extremely important in tuning the physical properties of the fluids. Stable liquid‐crystalline and liquid phases are obtained in the ?20 °C to 200 °C temperature range without thermal degradation of the DNA. Thus, a new type of DNA‐based soft biomaterial has been achieved, which will promote the study and application of DNA in a much broader context.     

High Ethene/Ethane Selectivity in 2,2′‐Bipyridine‐Based Silver(I) Complexes by Removal of Coordinated Solvent

Following removal of coordinated CH₃CN, the resulting complexes [Ag^I(2,2′‐bipyridine)][BF₄] ( 1 ) and [Ag^I(6,6′‐dimethyl‐2,2′‐bipyridine)][OTf] ( 2 ) show ethene/ethane sorption selectivities of 390 and 340, respectively, and corresponding ethene sorption capacities of 2.38 and 2.18 mmol g^?1 when tested at an applied gas pressure of 90 kPa and a temperature of (20±1) °C. These ethene/ethane selectivities are 13 times higher than those reported for known solid sorbents for ethene/ethane separation. For 2 , ethene sorption reached 90 % of equilibrium capacity within 15 minutes, and this equilibrium capacity was maintained over the three sorption/desorption cycles tested. The rates of ethene sorption were also measured. To our knowledge, these are the first complexes, designed for olefin/paraffin separations, which have open silver(I) sites. The high selectivities arise from these open silver(I) sites and the relatively low molecular surface areas of the complexes.     

A study of ignition and combustion of liquid hydrocarbon droplets in premixed fuel/air mixtures in a rapid compression machine

The combustion of two fuels with disparate reactivity such as natural gas and diesel in internal combustion engines has been demonstrated as a means to increase efficiency, reduce fuel costs and reduce pollutant formation in comparison to traditional diesel or spark-ignited engines. However, dual fuel engines are constrained by the onset of uncontrolled fast combustion (i.e., engine knock) as well as incomplete combustion, which can result in high unburned hydrocarbon emissions. To study the fundamental combustion processes of ignition and flame propagation in dual fuel engines, a new method has been developed to inject single isolated liquid hydrocarbon droplets into premixed methane/air mixtures at elevated temperatures and pressures. An opposed-piston rapid compression machine was used in combination with a newly developed piezoelectric droplet injection system that is capable of injecting single liquid hydrocarbon droplets along the stagnation plane of the combustion chamber. A high-speed Schlieren optical system was used for imaging the combustion process in the chamber. Experiments were conducted by injecting diesel droplet of various diameters (50 µm < d_o < 400 µm), into methane/air mixtures with varying equivalence ratios (0 < ϕ < 1.2) over a range of compressed temperatures (700 K < T_c < 940 K). Multiple autoignition modes was observed in the vicinity of the liquid droplets, which were followed by transition to propagating premixed flames. A computational model was developed with CONVERGE™, which uses a 141 species dual-fuel chemical kinetic mechanism for the gas phase along with a transient, analytical droplet evaporation model to define the boundary conditions at the droplet surface. The simulations capture each of the different ignition modes in the vicinity of the injected spherical diesel droplet, along with bifurcation of the ignition event into a propagating, premixed methane/air flame and a stationary diesel/air diffusion flame.     

On the low-temperature chemistry of 1,3-butadiene

In this paper, species versus temperature profiles were measured during the oxidation of 1,3-butadiene in a jet-stirred reactor (JSR) at 1 atm, at different equivalence ratios (φ = 0.5, 1.0 and 2.0), in the temperature range 600 – 1020 K. Both synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) and gas chromatography (GC) methods were used to analyze the species. The experimental results show that a large proportion of the products are aldehydes (formaldehyde, acetaldehyde, acrolein, etc.) and ketenes (ketene, methyl-ketene), with acrolein being one of the major products. Moreover, furan, 1,3-cyclopentadiene and benzene are also present as intermediates in significant amounts. The reaction pathways leading to the formation of these species are discussed in detail. A new detailed mechanism, NUIGMech1.3, was developed to simulate these new data as well as other experimental data available in the literature. The validation results indicate that quantum calculations are also needed to explore the formation of some important species formed in the oxidation of 1,3-butadiene. Overall, the new 1,3-butadiene mechanism agrees well with various experimental data in the low- to high-temperature regimes and at different pressures. Flux and sensitivity analyses show that 1,3-butadiene shares some common reaction chemistry pathways with 1- and 2-butene via Ḣ atom and HȮ₂ radical addition to the C = C double bond in 1,3-butadiene, reactions which are important for both systems. The low temperature chemistry of 1,3-butadiene is mainly controlled by the reaction pathways of ȮH radical addition to the C = C double bond of the fuel molecule. The 1-buten-4-ol-3-yl radicals so formed subsequently add to O₂ and react via the Waddington mechanism, which is important in accurately simulating the oxidation and auto-ignition of 1,3-butadiene at engine relevant conditions.     

Poroelastodynamic potential method for transversely isotropic fluid-saturated poroelastic media

By introduction of two scalar potentials, an analytical method is developed for the solution of poroelastodynamic boundary value problems in transversely isotropic fluid-saturated poroelastic media. The governing equations of motion are considered in the framework of Biot's complete model without any assumption or simplification. As a case of application, solutions in three dimensions for a transversely isotropic fluid saturated porous half space loaded by an arbitrary distribution of time harmonic tractions at the free surface is derived. The free surface of the half space may be considered either permeable or impermeable. As a particular solution, Green's functions for uniform vertical and horizontal circular patch loads are presented as semi-infinite integrals which may be evaluated by means of an appropriate numerical method proposed. The accuracy of the solutions is verified both analytically and numerically against the preceding solutions. Some numerical results are also presented to clarify the influence of different degrees of anisotropy and frequency of excitation on the response of the medium.     

Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate

Heat and mass transfer along a semi-infinite vertical flat plate under the combined buoyancy force effects of thermal and species diffusion is investigated in the presence of a strong non-uniform magnetic field and the Hall currents are taken into account. The induced magnetic field due to the motion of the electrically conducting fluid is negligible. This assumption is valid for a small magnetic Reynolds number. The similarity solutions are obtained using the scale group of transformations. These are the only symmetry transformations admitted by the field equations. The non-linear boundary layer equations with the boundary conditions are transferred to a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the magnetic parameter M in the range of 0-1 with the Hall parameter m taking the values 0.5, 1, 2, and 3.     

The effect of rotation on conical wave beams in a stratified fluid

Experiments are conducted to test extant theory on the effect of uniform rotation on the angle of conical beam wave propagation excited by a sphere vertically oscillating at frequency in a density stratified fluid. The near-constant Brunt–Väisälä frequency stratification N produced in situ in a rotating cylindrical tank exhibits no effect of residual motion for the range of Froude numbers investigated. Good agreement between experiment and theory is found over the range of angles 15°<<65° using the synthetic schlieren visualization technique. In particular, the cut-off for wave propagation at =2, below which waves do not propagate, is clearly observed.