Modular Forms on the Double Half-Plane

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.Comment: 17 pages: Minor corrections in text (due to a helpful referee), updated affiliations. Accepted for publication in the International Journal for Number Theory (IJNT

Water does partially dissociate on the perfect TiO2(110) surface : a quantitative structure determination

There has been a long-standing controversy as to whether water can dissociate on perfect areas of a TiO2(110) surface; most early theoretical work indicated this dissociation was facile, while experiments indicated little or no dissociation. More recently the consensus of most theoretical calculations is that no dissociation occurs. New results presented here, based on analysis of scanned-energy mode photoelectron diffraction data from the OH component of O 1s photoemission, show the coexistence of molecular water and OH species in both atop (OHt) and bridging (OHbr) sites. OHbr can arise from reaction with oxygen vacancy defect sites (Ovac), but OHt have only been predicted to arise from dissociation on the perfect areas of the surface. The relative concentrations of OHt and OHbr sites arising from these two dissociation mechanisms are found to be fully consistent with the initial concentration Ovac sites, while the associated Ti-O bondlengths of the OHt and OHbr species are found to be 1.85±0.08Å and 1.94±0.07 Å, respectively

Noncompact sigma-models: Large N expansion and thermodynamic limit

Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for ``criticality'' and ``triviality'' of the theories in the SO(1,N) invariant sector are discussed.Comment: 46 pages, 2 figure

Circuit Synthesis of Electrochemical Supercapacitor Models

This paper is concerned with the synthesis of RC electrical circuits from physics-based supercapacitor models describing conservation and diffusion relationships. The proposed synthesis procedure uses model discretisation, linearisation, balanced model order reduction and passive network synthesis to form the circuits. Circuits with different topologies are synthesized from several physical models. This work will give greater understanding to the physical interpretation of electrical circuits and will enable the development of more generalised circuits, since the synthesized impedance functions are generated by considering the physics, not from experimental fitting which may ignore certain dynamics

Adsorbate structure determination using energy scanned photoelectron diffraction

Energy-scanned photoelectron diffraction was used to determine the local adsorption site of several molecular species on well defined single crystal surfaces. Cytosine and uracil on Cu(110) were found to adsorb with their molecular planes perpendicular to the surface and mostly aligned along the close packed [110] direction. Both molecules were found to adsorb through their constituent oxygen atom(s) and a deprotonated nitrogen atom. The associated Cu-O and Cu-N bond lengths were found to be 1.94 (+0.06/-0.04)Å and 1.94 (+0.07 / -0.03) Å, respectively, for cytosine and 1.96 ± 0.04 / 1.93 ± 0.04 Å and 1.96 ± 0.04 Å, respectively, for uracil. The mono- and bi- tartrate phases of tartaric acid on Cu(110) were found to adsorb via deprotonated carboxylic acid groups with the oxygen atoms in different near-atop sites. The associated Cu-O bond lengths were found to be 1.92 ± 0.08 Å / 1.93 ± 0.06 Å and 1.93 – 1.97 ± 0.06 – 0.09 Å respectively. Glycine on Cu(111) was found to adsorb via both its nitrogen and oxygen constituent atoms, though three competing models were found for the local adsorption site of the oxygen atoms. The nitrogen atom was found to adsorb in a near-atop site with an associated Cu-N bond length of 2.02 ± 0.03 Å. The oxygen adsorption site was found to at least have some near-atop characteristics, with the near-atop site having an associated Cu-O bond length of 2.00 – 2.02 ± 0.04 – 0.07 Å. Reanalysis of the C 1s PhD data of the hydrocarbon remnant from the decomposition of furan on Pd(111) found that the lowest energy model predicted by DFT does not occur, at least in large quantities, on the surface. The most likely structure was found to be CH–C–CH2. On the Ru(0001) surface, dehydrogenation of methanol was not observed in the temperature range around 150 K, with no evidence for the strong modulations in the O 1s PhD spectra predicted for a methoxy species. A reexamination of water adsorption of the rutile TiO2(110) surface found that water does, at least partially, dissociate on the perfect surface as well as at defect sites – in contrast to previously published experimental results. The associated Ti-O bond lengths for the resulting atop and bridging hydroxyl species were found to be 1.85 ± 0.08 Å and 1.94 ±0.07 Å respectively. Finally vanadyl phthalocyanine was found to adsorb upright (with the oxygen atom further from the surface than the vanadium atom) on the Au(111) surface. The V=O bond length was found to be 1.60 ± 0.04 Å

Identifiability and parameter estimation of the single particle lithium-ion battery model

This paper investigates the identifiability and estimation of the parameters of the single particle model (SPM) for lithium-ion battery simulation. Identifiability is addressed both in principle and in practice. The approach begins by grouping parameters and partially non-dimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that, excluding open circuit voltage, there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearised SPM is unique. It is found that the model is unique provided that the electrode open circuit voltage functions have a known non-zero gradient, the parameters are ordered, and the electrode kinetics are lumped into a single charge transfer resistance parameter. We then demonstrate the practical estimation of model parameters from measured frequency-domain experimental electrochemical impedance spectroscopy (EIS) data, and show additionally that the parametrised model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between model and experiment over a 10 minute dynamic discharge.Comment: 16 pages, 9 figures, pre-print submitted to the IEEE Transactions on Control Systems Technolog