Congruences for overpartitions with restricted odd differences

The Ramanujan Journal - In a recent work, Bringmann, Dousse, Lovejoy, and Mahlburg defined the function $$\overline{t}(n)$$ to be the number of overpartitions of weight n where (i) the difference...     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional manganese dioxide-functionalized carbon nanotube electrodes for electrochemical supercapacitors

Three-dimensional manganese dioxide (MnO₂)-functionalized multiwalled carbon nanotube (MWCNT) electrodes have been produced by a simple and scalable thermal decomposition process. The electrodes are prepared by treating planar MWCNT sheets with manganese(II) nitrate (Mn(NO₃)₂) solution and annealing at low temperature (200–300 °C) and ambient pressure. The morphology, chemical composition, and structure of the resulting matrices have been investigated with scanning electron microscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, and X-ray diffraction. Supercapacitors assembled with three-dimensional electrodes exhibit a 14-fold increase in specific capacitance (C _sp) in comparison to those containing pristine, two-dimensional MWCNT electrodes. C _sp varies linearly with Mn(NO₃)₂ thermal decomposition temperature (from 100 to 61 F/g at 0.2 A/g), a trend that is discussed in the context of nitrate reaction chemistry and MWCNT structure. This efficient and promising approach allows for simultaneous enhancement of electrode–electrolyte contact area and incorporation of redox-based charge storage within electrochemical capacitors.     

Unique Path Partitions: Characterization and Congruences

We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.     

Detection of halogenated organic compounds using immobilized thermophilic dehalogenase

Environmental pollutants containing halogenated organic compounds can cause a plethora of health problems. Detection, quantification, and eventual remediation of halogenated pollutants in the environment are important to human well-being. Toward this end, we previously identified a haloacid dehalogenase, L-HAD_ST, from the thermophile Sulfolobus tokodaii. This thermophilic enzyme is extremely stable and catalyzes, stereospecifically, the dehalogenation of l-2-haloacids. In the current study, we covalently linked L-HAD_ST to an N-hydroxysuccinimidyl Sepharose resin to construct a highly specific sensor with long shelf life for the detection of l-2-haloacids. The enzyme-modified resin was packed into disposable columns. Samples containing l-2-haloacids were first incubated in the column, and were then collected to quantify the chloride produced through the breakdown of the substrate. The optimum pH of the immobilized enzyme is around 9.5, similar to that of the soluble protein. Its catalytic activity increased with temperature up to the highest temperature measured (50 °C). The resin could be fully regenerated after multiple reaction cycles and retained 70% of the initial activity after being stored at 4 °C for 6 months. The L-HAD_ST-modified resin could be used to breakdown and quantify l-2-haloacids spiked in the simulated environmental samples, indicating dehalogenases from extremophiles can potentially be employed in the detection and decontamination of l-2-haloacids.     

Ab initio studies of structural features not easily amenable to experiment: the molecular structures of some hydrogenfluoride clusters

The completely relaxed ab initio structures of some forms of H₂F₂ and H₃F₃ reflect the cooperative nature of hydrogen bonding and can be used to estimate the order of magnitude of the variations in local geometry which are neglected when interactive potentials for HF in clusters or in the liquid state are evaluated with constrained geometries.     

Bis(fluoroalkyl)acrylic and methacrylic phosphate monomers, their polymers and some of their properties

Ten fluoromonomers of structure (R_FO)₂P(O)OCH₂CH₂OC(O)CRCH₂ were made in 30-64% yield by treating the chloridates (R_FO)₂P(O)Cl with HOCH₂CH₂OC(O)CRCH₂ in chloroform in the presence of triethylamine [R_F=CF₃CH₂, C₂F₅CH₂, C₃F₇CH₂, C₄F₉CH₂, C₄F₉CH₂CH₂ or C₆F₁₃CH₂CH₂; R  H or Me]. The chloromonomer (CCl₃CH₂O)₂P(O)OCH₂CH₂OC(O)CHCH₂ was obtained analogously in 29% yield. Polymerisation of the acrylate monomers, but not the methacrylate monomers, could be effected using α-azoisobutyronitrile as a radical initiator. Acrylic polymers having CF₃CH₂O, CCl₃CH₂O and C₆F₁₃CH₂CH₂O side-chains were obtained as translucent rubbers. Specimens of cotton fabric were treated with solutions of the polymers, and average water and oil repellency ratings measured. Fabric coated with the polymer with the C₆F₁₃CH₂CH₂O side-chain afforded protection from penetration of the test liquids. Treated fabrics were subjected to the limiting oxygen index (LOI) test according to BS EN ISO 4589-2 (1999): this test determines the point at which a material just burns in a volumetric flow of oxygen and nitrogen. The treated fabrics were more fire-resistant (LOI 22-29%) than the untreated fabric (LOI 18%). Fabric coated with the CCl₃CH₂O-based polymer can be considered fire-retardant (LOI 29%). The fluoromonomers were tested for anti-acetylcholinesterase activity and were found to be poor enzyme inhibitors; they are predicted to possess low acute toxicity.     

A Monte Carlo simulation of energy transfer processes in thermal unimolecular reactions. II. An applications to polyatomic dissociation

The Monte Carlo method has been used to provide a numerical solution to the ro-vibrational master equation for the low pressure unimolecular decomposition of a polyatomic molecule. This type of solution is made possible through the use of a simple exponential transition probability function, that represents the efficiency with which energy transfer takes place between the reactant molecule and an unspecified heat bath gas. The Monte Carlo technique is used to generate random variables that are distributed in a manner prescribed by the transition probability function. In the case of the present simulation, these variables correspond to random energy jumps induced in the molecule through single collision events. In order to account for the energy dependence of the vibrational state densities, we have proposed that vibrational relaxation in the polyatomic takes place from a single vibrational mode. Under equilibrium conditions we are able to show that with this assumption, the Monte Carlo model is capable of reproducing molecular quantities, such as the average vibrational energy per molecule and the vibrational specific heat, that compare favourable with the corresponding values calculated from equilibrium statistical mechanics. The model has been applied to a study of the low pressure unimolecular decomposition of a series of polyatomics. For three of the molecules, CH₄, CD₄, and C₂H₆ the agreement between the calculated and the high temperature experimental rate constants is very good. The calculations indicate that a significant proportion of the molecules that dissociate are rotationally as well as vibrationally excited. Very few of the reactive molecules have a vibrational energy content equal to or greater than E₀, the dissociation energy. The extent of rotational excitation is found to be temperature dependent.