Theoretical studies of solute vibrational energy relaxation at liquid interfaces

Recent advances in the theoretical understanding of solute vibrational energy relaxation at liquid interfaces and surfaces are described. Non-equilibrium molecular dynamics simulations of the relaxation of an initially excited solute molecule are combined with equilibrium force autocorrelation calculations to gain insight into the factors that influence the vibrational relaxation rate. Diatomic and triatomic nonpolar, polar, and ionic solute molecules adsorbed at the liquid/vapor interface of several liquids as well as at the water/CCl(4) liquid/liquid interface are considered. In general, the vibrational relaxation rate is significantly slower (a factor of 3 to 4) at the liquid/vapor and liquid/liquid interface than in the bulk due to the reduced density, which gives rise to a reduced contribution of the repulsive solvent-solute forces on the vibrational mode. The surface effects on the ionic solutes are much smaller (50% or less slower relaxation relative to the bulk). This is due to the fact that ionic solutes at the interface are able to keep part of their solvation shell to a degree that depends on their size. Thus, a significant portion of the repulsive forces is maintained. A high degree of correlation is found between the peak height of the solvent-solute radial distribution function and the vibrational relaxation rate. The relaxation rate at the liquid/liquid interface strongly depends on the location of the solute across the interface and correlates with the change in the density and polarity profile of the interface.     

Electron beam emission from a diamond-amplifier cathode

The diamond amplifier (DA) is a new device for generating high-current, high-brightness electron beams. Our transmission-mode tests show that, with single-crystal, high-purity diamonds, the peak current density is greater than 400 mA/mm2, while its average density can be more than 100 mA/mm2. The gain of the primary electrons easily exceeds 200, and is independent of their density within the practical range of DA applications. We observed the electron emission. The maximum emission gain measured was 40, and the bunch charge was 50 pC/0.5 mm2. There was a 35% probability of the emission of an electron from the hydrogenated surface in our tests. We identified a mechanism of slow charging of the diamond due to thermal ionization of surface states that cancels the applied field within it. We also demonstrated that a hydrogenated diamond is extremely robust.     

Observation of the second harmonic in Thomson scattering from relativistic electrons

A free relativistic electron in an electromagnetic field is a pure case of a light-matter interaction. In the laboratory environment, this interaction can be realized by colliding laser pulses with electron beams produced from particle accelerators. The process of single photon absorption and reemission by the electron, so-called linear Thomson scattering, results in radiation that is Doppler shifted into the x-ray and gamma-ray regions. At elevated laser intensity, nonlinear effects should come into play when the transverse motion of the electrons induced by the laser beam is relativistic. In the present experiment, we achieved this condition and characterized the second harmonic of Thomson x-ray scattering using the counterpropagation of a 60 MeV electron beam and a subterawatt CO2 laser beam.     

Catalytic Enantioselective Cyclopropenation of Internal Alkynes: Access to Difluoromethylated Three‐Membered Carbocycles

Herein we described an efficient Rh^II‐catalyzed enantioselective cyclopropenation reaction of internal alkynes with a masked difluorodiazoethane reagent (PhSO₂CF₂CHN₂, Ps‐DFA). This asymmetric transformation offers efficient access to a broad range of enantioenriched difluoromethylated cyclopropenes (40 examples, up to 99 % yield, 97 % ee). The synthetic utility of obtained strained carbocycles is demonstrated by subsequent stereodefined processes, including cross‐couplings, hydrogenation, Diels–Alder reaction, and Pauson–Khand reaction.     

Endomorphisms of stable continuous-trace -algebras

We classify -endomorphisms of stable continuous-trace -algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite-dimensional vector bundles over the spectrum. Specializing to automorphisms, this gives a different approach to results of Lance, Smith, Phillips and Raeburn.

     

Diastereoselective reduction of alkenylboronic esters as a new method for controlling the stereochemistry of up to three adjacent centers in cyclic and acyclic molecules

[reaction: see text] cis-Boronates are readily available via a diastereoselective Pd-catalyzed reduction of tetrasubstituted alkenylboronic esters using H2. Applying the reaction conditions presented to unsaturated open-chain boronic esters allows the stereochemistry of up to three adjacent centers to be controlled.     

Budding and tubulation in highly oblate vesicles by anchored amphiphilic molecules

We studied local budding and tubulation induced in highly oblate lipid vesicles by the anchoring of either polymers having a hydrophilic backbone and grafted hydrophobic anchor groups, or by oleoyl-coenzyme A, an amphiphilic molecule important in lipid metabolism. The dynamics of bud formation, shrinkage, and readsorption is consistent with an induced spontaneous curvature coupled with local amphiphile diffusion on the membrane. We report a novel metastable state prior to bud readsorption.     

An implementation of Karmarkar's algorithm for linear programming

This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational advantage. Implementation issues particular to this family of algorithms, such as treatment of dense columns, are discussed. The code is tested on several standard linear programming problems and compares favorably with the simplex codeMinos 4.0.     

Four-component reactions for a new diastereoselective synthesis of chiral quaternary centers

The one-pot preparation of chiral homoallylic alcohol and amine derivatives was easily achieved by carbocupration of alkynyl sulfoxides followed by an in situ zinc homologation and reaction with aldehydes or imines. In this process, three new carbon-carbon bonds were created as well as quaternary and tertiary chiral centers with excellent diastereo- and enantioselectivities.     

A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio

We extend Clarkson's randomized algorithm for linear programming to a general scheme for solving convex optimization problems. The scheme can be used to speed up existing algorithms on problems which have many more constraints than variables. In particular, we give a randomized algorithm for solving convex quadratic and linear programs, which uses that scheme together with a variant of Karmarkar's interior point method. For problems withn constraints,d variables, and input lengthL, ifn = (d ²), the expected total number of major Karmarkar's iterations is O(d ²(logn)L), compared to the best known deterministic bound of O( L). We also present several other results which follow from the general scheme.