Overcomplete Free Energy Functional for D = 1 Particle Systems with Next Neighbor Interactions

We deduce an overcomplete free energy functional for D=1 particle systems with next neighbor interactions, where the set of redundant variables are the local block densities _i of i interacting particles. The idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture. This mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system. Thus it identifies the local particle density of component i of the mixture with the local block density _i of the given system. Consequently, our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities _i representing the sequence of partition functions of the local aggregates of particle numbers i. The system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of . Analoguous to the uniform isothermal-isobaric technique, all our results are expressible in terms of effective pressures. We illustrate the theory with two standard examples, the adhesive interaction and the square-well potential. For the uniform case, our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer (Hardy-Ramanujan formula) and on Varadhan's theorem on the asymptotics of a class of integrals.     

Numerical investigation of taper parameters for high Q infiltrated nanobeam slot microcavities

Photonic nanobeam microcavities are devices for applications where strong light–matter-interaction is needed. They are characterized by a strong field enhancement in a small volume, which can be used for nonlinear optical applications. To enhance such effects, a solid microcavity can be replaced by a slot, that can be infiltrated with a material of choice (e.g. chalcogenide glasses or nonlinear polymers). Here, the parameters needed to create high quality nanobeam slot microcavities are numerically investigated. Design rules for the minimization of scattering losses and thus the enhancement of the Q factor are reviewed and discussed.     

Semiclassical calculations of half-widths and line shifts for transitions in the 30012←00001 and 30013←00001 bands of CO2 II: Collisions with O2 and air

The complex Robert–Bonamy (CRB) formalism was used to calculate the half-width, its temperature dependence, and the line shift for CO₂ for transitions in the 30012←00001 and 30013←00001 bands with O₂ as the perturbing gas. The calculations were done for rotational quantum numbers from J=0 to J=120 with no ad hoc scaling of the line shape equations. The intermolecular potential parameters are adjusted on accurate experimental measurements of the half-widths, its temperature dependence, and the pressure-induced line shifts so that a single intermolecular potential reproduces all three parameters. Using the results of this work and previous results for N₂-broadening, air-broadening line shape parameters were also determined. The comparison of the CRB calculations with the experimental data available in the literature for the three line shape coefficients demonstrates the quality of the present calculations for the both bands under study.     

Separation of Anisotropy and Exchange Broadening Using N CSA–N–H Dipole–Dipole Relaxation Cross-Correlation Experiments

Based on the measurement of cross-correlation rates between ¹⁵N CSA and ¹⁵N–¹H dipole–dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R₂ = 1/T₂) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T₁/T₂ ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T₁/T₂ ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N–H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or β-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T₁/T₂ ratios. The ¹⁵N CSA tensor of the residues for this β-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T₂ relaxation times for several residues could be mistaken as indications for exchange processes.     

On the Classification of q-Algebras

The problem is the classification of the ideals of free differential algebras, or the associated quotient algebras, the q-algebras; being finitely generated, unital C-algebras with homogeneous relations and a q-differential structure. This family of algebras includes the quantum groups, or at least those that are based on simple (super) Lie or Kac–Moody algebras. Their classification would encompass the so far incompleted classification of quantized (super) Kac–Moody algebras and of the (super) Kac–Moody algebras themselves. These can be defined as singular limits of q-algebras, and it is evident that to deal with the q-algebras in their full generality is more rational than the examination of each singular limit separately. This is not just because quantization unifies algebras and superalgebras, but also because the points q=1 and q=–1 are the most singular points in parameter space. In this Letter, one of two major hurdles in this classification program has been overcome. Fix a set of integers n ₁,...,n _k, and consider the space of homogeneous polynomials of degree n ₁ in the generator e ₁, and so on. Assume that there are no constants among the polynomials of lower degree, in any one of the generators; in this case all constants in the space have been classified. The task that remains, the more formidable one, is to remove the stipulation that there are no constants of lower degree.     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

Experimental and modeling assessment of sulfur release from coal under low and high heating rates

Coal combustion releases elevated amounts of pollutants to the atmosphere including SO_X. During the pyrolysis step, sulfur present in the coal is released to the gas phase as many different chemical species such as H₂S, COS, SO₂, CS₂, thiols and larger tars, also called SO_X precursors, as they form SO_X during combustion. Understanding the sulfur release process is crucial to the development of reliable kinetic models, which support the design of improved reactors for cleaner coal conversion processes. Sulfur release from two bituminous coals, Colombian hard coal (K1) and American high sulfur coal (U2), were studied in the present work. Low heating rate (LHR) experiments were performed in a thermogravimetric analyzer coupled with mass spectrometry (TG-MS), allowing to track the mass loss and the evolution of many volatile species (CO, CO₂, CH₄, SO₂, H₂S, COS, HCl and H₂O). High heating rate (HHR) experiments were performed in an entrained flow reactor (drop-tube reactor – DTR), coupled with MS and nondispersive infrared sensor (NDIR). HHR experiments were complemented with CFD simulation of the multidimentional reacting flow field. A kinetic model of coal pyrolysis is employed to reproduce the experiments allowing a comprehensive assessment of the process. The suitability of this model is confirmed for LHR. The combination of HHR experiments with CFD simulations and kinetic modeling revealed the complexity of sulfur chemistry in coal combustion and allowed to better understand of the individual phenomena resulting in the formation of the different SO_X precursors. LHR and HHR operating conditions lead to different distribution of sulfur species released, highly-dependent on the gas-phase temperature and residence time. Higher retention of total sulfur in char is observed at LHR (63%) when compared to HHR (37–44%), at 1273 K. These data support the development of reliable models with improved predictability.