Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

Self-condensation of a thiazole-peptide bearing a 21-membered loop into a library of giant macrocycles with multiple orthogonal loops

Tetrapeptide analogue H-[Glu-Ser-Lys(Thz)]-OH, containing a turn-inducing thiazole constraint, was used as a template to produce a 21-membered structurally characterized loop by linking Glu and Lys side chains with a Val-Ile dipeptide. This template was oligomerized in one pot to a library (cyclo-[1](n), n = 2-10) of giant symmetrical macrocycles (up to 120-membered rings), fused to 2-10 appended loops that were carried intact through multiple oligomerization (chain extension) and cyclization (chain terminating) reactions of the template. A three-dimensional solution structure for cyclo-[1](3) shows all three appended loops projecting from the same face of the macrocycle. This is a promising approach to separating pepticle motifs over large distances.

Organic reactions in ionic liquids:ionic liquids ethylammonium nitrate promoted Knoevenagel condensation of aromatic aldehydes with active methylene compounds

The Knoevenagel condensation of aromatic aldehydes with active methylene compounds proceeded efficiently in a reusable ionic liquid, ethylammonium nitrate, at room temperature in the absence of any catalyst with high yields.

Organic reactions in ionic liquids: Ionic liquid-promoted three-component condensation of benzotriazole with aldehyde and alcohol

1-(alpha-Alkoxyalkyl)benzotriazoles are readily synthesized from three-component condensation of benzotriazole with aldehyde and alcohol in ionic liquid [Bmim]PF6.

Organic reactions in ionic liquids:Ionic liquid promoted Knoevenagel condensation of aromatic aldehydes with (2-thio)barbituric acid

The Knoevenagel condensation of aromatic aldehydes with (2-thio)barbituric acid proceeded efficiently in reusable ionic liquids, EAN, BmimBF4, and BmimPF6 at room temperature in the absence of any catalyst with high yields.

Organic reactions in ionic liquids: Knoevenagel condensation catalyzed by ethylenediammonium diacetate

The moisture and air stable ionic liquids 1-butyl-3-methylimidazonium tetrafluoroborate [bmim]BF4 and 1-butyl-3-methylimidazonium hexafluorophosphate [bmim]PF6 were used as ‘green' recyclable alternatives to volatile organic solvents (VOCs) for ethylenediammonium diacetate (EDDA) catalyzed Knoevenagel condensation between aldehydes or ketones with active methylene compounds. Both aldehydes and ketones gave satisfactory results. The ionic liquids containing catalyst EDDA were recycled several times with no decreases in yields and reaction rates. In the case of 2-hydroxybenzaldehyde, the reactions led to the formation of 3-substituted coumarins under standard reaction conditions.

Reentrant condensation of proteins in solution induced by multivalent counterions

Negatively charged globular proteins in solution undergo a condensation upon adding trivalent counterions between two critical concentrations C* and C**, C*condensation behavior above C** is caused by short-ranged electrostatic interactions between multivalent cations and acidic residues, mechanistically different from the case of DNA. Small-angle x-ray scattering indicates a short-ranged attraction between counterion-bound proteins near C* and C**. Monte Carlo simulations (under these strong electrostatic coupling conditions) support an effective inversion of charge on surface side chains through binding of the multivalent counterions.

Symbol synchronization exploiting the symmetric property in optical fast OFDM

We propose a new simple method to achieve precise symbol synchronization using one start-of-frame (SOF) symbol in optical fast orthogonal frequency-division multiplexing (FOFDM) with subchannel spacing equal to half of the symbol rate per sub-carrier. The proposed method first identifies the SOF symbol, then exploits the evenly symmetric property of the discrete cosine transform in FOFDM, which is also valid in the presence of chromatic dispersion, to achieve precise symbol synchronization. We demonstrate its use in a 16.88-Gb/s phase-shifted-keying-based FOFDM system over a 124-km field-installed single-mode fiber link and show that this technique operates well in automatic precise symbol synchronization at an optical signal-to-noise ratio as low as 3 dB and after transmission.

Multilevel amplitude regeneration of 256-symbol constellation

We propose a novel scheme for multilevel (9 and more) amplitude regeneration based on nonlinear optical loop mirror and demonstrate its efficiency and cascadability on 256-symbol constellation. © 2014 OSA.

Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.