Projection of diffusions on submanifolds: Application to mean force computation

We consider the problem of sampling a Boltzmann‐Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold Σ of ?ⁿ implicitly defined by N constraints q₁(x) = ? = q_N(x) = 0 (N < n). This problem arises, for example, in systems subject to hard constraints or in the context of free energy calculations. We prove that the constrained stochastic differential equations (i.e., diffusions) proposed in [7, 13] are ergodic with respect to this restricted distribution. We also construct numerical schemes for the integration of the constrained diffusions. Finally, we show how these schemes can be used to compute the gradient of the free energy associated with the constraints. © 2007 Wiley Periodicals, Inc.     

Synthesis of 2′-C-methyl-branched isonucleosides

Novel regioisomers of 2′-methyl-branched nucleosides were designed and synthesized to mimic potent anti-viral drugs like Valopicitabine. The short and efficient synthesis of the targets involves a one-pot tosylation/cyclization step that leads to an activated furan scaffold on which the isonucleosides were built.     

Waves on vortex cores

Here we discuss the types of waves which can be supported on compact regions of vorticity. This is a subject first studied by Lord Kelvin for waves propagating along the vortex lines of the Rankine and hollow-core vorticity distributions. Kelvin's major interest was in the stability of vortex rings and the numerous resurgencies in interest have usually been driven by practically important phenomena, e.g., the observations of vortex breakdown and waves on tornado and aircraft vortices in the early 1960's and more recently in technologically and geophysically significant flows and on the quantised vortices of super fluid HeII.

The major wave-types of interest are of varicose, helicoidal and fluted form and represent a periodic swelling and contraction, a bending and a “krinkling” of the core, respectively. The first two propagate along and the third around the vortex lines. All have been studied theoretically, experimentally and numerically in the limit of small wave amplitude and their major characteristics are now clear. Of particular interest is the extension of these results to the non-linear regime in which case the two first types are known to exhibit solitary wave or soliton characteristics in certain parameter ranges. It is these non-linear waves which often dominate observations of vortex flows both in nature and in technological applications and which have caused much controversy in the interpretation of results found under complex circumstances of flow and apparatus geometry.     

A computational investigation of the nitrogen-boron interaction in o-(N,N-dialkylaminomethyl)arylboronate systems

o-(N,N-Dialkylaminomethyl)arylboronate systems are an important class of compounds in diol-sensor development. We report results from a computational investigation of fourteen o-(N,N-dialkylaminomethyl)arylboronates using second-order M?ller-Plesset (MP2) perturbation theory. Geometry optimizations were performed at the MP2/cc-pVDZ level and followed by single-point calculations at the MP2/aug-cc-pVDZ(cc-pVTZ) levels. These results are compared to those from density functional theory (DFT) at the PBE1PBE(PBE1PBE-D)/6-311++G(d,p)(aug-cc-pVDZ) levels, as well as to experiment. Results from continuum PCM and CPCM solvation models were employed to assess the effects of a bulk aqueous environment. Although the behavior of o-(N,N-dialkylaminomethyl) free acid and ester proved to be complicated, we were able to extract some important trends from our calculations: (1) for the free acids the intramolecular hydrogen-bonded B-O-H···N seven-membered ring conformers 12 and 16 are found to be slightly lower in energy than the dative-bonded N→B five-membered ring conformers 10 and 14 while conformers 13 and 17, with no direct boron-nitrogen interaction, are significantly higher in energy than 12 and 16; (2) for the esters where no intramolecular B-O-H···N bonded form is possible, the N→B conformers 18 and 21 are significantly lower in energy than the no-interaction forms 20 and 23; (3) H(2)O insertion reactions into the N→B structures 10, 14, 18, and 21 leading to the seven-membered intermolecular hydrogen-bonded B···OH(2)···N ring structures 11, 15, 19, and 22 are all energetically favorable.     

Diols and anions can control the formation of an exciplex between a pyridinium boronic acid with an aryl group connected via a propylene linker

The exciplex formation between a pyridinium boronic acid and phenyl group connected via a propylene linker can be monitored using fluorescence. Addition of pinacol affords a cyclic boronate ester with enhanced Lewis acidity that increases the strength of its cation-π stacking interaction causing a four-fold fluorescence enhancement.     

Ultrasonication-assisted spray ionization mass spectrometry for on-line monitoring of organic reactions

A straightforward on-line monitoring of organic reactions by ultrasonication-assisted spray ionization mass spectrometry (UASI MS) is demonstrated in this work.     

Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.