A new trust region technique for the maximum weight clique problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n³), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.     

Effect of interactions on molecular fluxes and fluctuations in the transport across membrane channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients, the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, where transition states are equally distant from the neighboring binding sites, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that, in this case, the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.     

Conformational changes of a polyelectrolyte in mixtures of water and acetone

Samples of a polyelectrolyte poly(methacryloylethyl trimethylammonium methylsulfate), PMETMMS, with molar masses M_w = 22−25 × 10⁶ were examined with viscosity, static light scattering, and conductivity measurements in a water–acetone solvent. Because acetone is a nonsolvent for this polymer the measurements were performed to determine the influence of the solvent composition, the polymer concentration, and the presence of added ions on the conformation of the polyelectrolyte in mixed solvents. The possible influence of a hydrodynamic field on the polymer conformation was also studied. The viscosity of the polymer solutions as a function of polymer concentration, as well as of the solvent composition, was studied using a broad range of shear rates. When the mass fraction of acetone in the solvent, γ, is below 0.5, the solutions show a usual polyelectrolyte behavior. When γ ≥ 0.80, the polymer adopts a compact conformation. This is observed as a decrease of the radius of gyration, R_g, second virial coefficient, A₂, the viscosity, and also as a change in the conductivity of the solution. The change in the polymer conformation may be induced also by dilution. When 0.60 ≤ γ < 0.80, a gradual decrease in the polymer concentration leads to a sudden decrease of the reduced viscosity, which indicates a decrease in the particle size. The values of M_w measured by static light scattering were constant in all experiments. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1107–1114, 1998     

Metallopyrrole-capped carbon nanocones

We design nickel-doped and nitrogen-doped carbon nanocones with various amounts of buckling that feature square-planar, (approximate) tetrahedral, and octahedral coordination. The optimized geometries and electronic structures of these novel metallocarbon complexes are calculated by using the B3LYP (Gaussian03) and GGA-BLYP (ADF) exchange-correlation functionals. We analyze buckling and stability of the nanocones, and discuss their potential for additional functionalization at the metallic site.     

Preparation, crystallographic characterization and theoretical study of two isomers of C70(CF3)12

Two isomers of C70(CF3)12 have been isolated from a mixture obtained by trifluoromethylation of C70 with CF3I; their molecular structures determined by X-ray crystallography are in good agreement with the results of theoretical DFT calculations for the most stable C70(CF3)12 isomers.     

Electrophoresis of soft particles at high electrolyte concentrations: an interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.     

Ab initio calculation of structure and transport properties of He…X (X = Zn, Cd, Hg) van der Waals complexes

The ground state ab initio CCSD(T) potential curves using various basis sets (aug-cc-pVXZ-PP (X = D, T, Q, 5)) is obtained for the dimers of helium with IIb group metals. The effect of the position of the (mid) bond-functions on the interaction energy is discussed. A Symmetry Adapted Perturbation Theory decomposition of the interaction energy is provided and the trends in the dimer stabilizing and destabilizing contributions are depicted. The spline fitted potential curves are applied together with rigorous statistical formulae in order to obtain the transport coefficients (viscosity coefficients, diffusion coefficients) and the second virial coefficient both for pure constituents and mixtures. The obtained theoretical results are compared with available experimental data. Molecular dynamics is used to obtain reliable values of the diffusion coefficients for all the systems under study.     

Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure

The effect of a finite size model for both the nuclear charge and magnetic moment distributions on calculated EPR hyperfine structure have been studied using a relativistic four-component method based on density functional theory. This approach employs a restricted kinetically balanced basis (mDKS-RKB) and includes spin-polarization using noncollinear spin-density exchange-correlation functionals in the unrestricted fashion. Benchmark calculations have been carried out for a number of small molecules containing Zn, Cd, Ag, and Hg. The present results are compared with those obtained at the Douglas-Kroll-Hess second order (DKH-2) method. The dependence of the results on the quality of the orbital and auxiliary basis sets has been studied. It was found that some basis sets contain irregularities that deteriorate the results. Especial care has to be taken also on the construction of the auxiliary basis for fitting the total electron and spin-densities.     

Photochemistry of dithiocarbamate Cu(II) complex in CCl4

Laser pulse photolysis was used to study the nature and reactions of intermediates in the photochemistry of the flat dithiocarbamate complex Cu(Et(2)dtc)(2) in CCl(4). A nanosecond laser pulse (355 nm) is shown to induce intermediate absorption bands of bivalent copper complex whose coordination sphere contains a dithiocarbamate radical Et(2)dtc(?) and a chloride ion at the axial position ([(Et(2)dtc)Cu(Et(2)dtc(?))Cl(a)]). At room temperature during some microseconds after the laser pulse, this intermediate interacts with the initial complex to form presumably a dimer [Cu(2)(Et(2)dtc)(3)(Et(2)dtc(?))Cl]. The latter vanishes in the second-order reaction. Analysis of kinetic and spectral features gives the arguments for the formation of a cluster [Cu(2)(Et(2)dtc)(3)Cl-tds-Cu(2)(Et(2)dtc)(3)Cl], which produces a new absorption band at 345 nm. The cluster decomposes in ～5 ms into final products, a binuclear complex [Cu(2)(Et(2)dtc)(3)Cl] and tetraethylthiuramdisulfide (Et(4)tds).     

Experimental Study of Pulse Polarity and Magnetic Field on Ozone Production of the Dielectric Barrier Discharge in Air

We studied the combined effect of the pulse or sinusoidal driving voltage and magnetic field on electrical characteristics and ozone production of a dielectric barrier discharge in air. These effects were studied for both polarities of the pulse. We found that the pulse polarity, as well as the magnetic field, affects discharge ozone production only for higher powers. The discharge driven by sinusoidal voltage produces higher ozone concentration than the discharge driven by voltage pulses of negative polarity. The discharge driven by the voltage pulses of negative polarity produces higher ozone concentrations than the discharge driven by positive voltage pulses. Ozone production yield for the voltage pulses of negative polarity is similar to that of sinusoidal driving voltage. For the positive polarity of voltage pulses, the yield is lower. Magnetic field slightly increases the concentration of ozone produced by the discharge and ozone production yield only for the discharge driven by positive voltage pulses. For the discharge driven by the sinusoidal voltage or by the pulses of the negative polarity magnetic field has only small effect on the concentration of ozone produced by the discharge.