On a periodic vehicle routing problem

This paper deals with a study on a variant of the Periodic Vehicle Routing Problem (PVRP). As in the traditional Vehicle Routing Problem, customer locations each with a certain daily demand are given, as well as a set of capacitated vehicles. In addition, the PVRP has a horizon, say T days, and there is a frequency for each customer stating how often within this T-day period this customer must be visited. A solution to the PVRP consists of T sets of routes that jointly satisfy the demand constraints and the frequency constraints. The objective is to minimize the sum of the costs of all routes over the planning horizon. We develop different algorithms solving the instances of the case studied. Using these algorithms we are able to realize considerable cost reductions compared to the current situation.     

Methyl side-chain dynamics in proteins using selective enrichment with a single isotopomer

13C relaxation studies on side-chain methyl groups in proteins typically involve measurements on (13)CHD(2) isotopomers, where the (13)C relaxation mechanism is particularly straightforward in the presence of a single proton. While such isotopomers can be obtained in proteins overexpressed in bacteria by use of (13)C enriched and fractionally deuterated media, invariably all possible (2)H isotopomers are obtained. This results in a loss of both resolution and sensitivity, which becomes particularly severe for larger proteins. We describe an approach that overcomes this problem by chemical synthesis of amino acids containing a pure (13)CHD(2) isotopomer. We illustrate the benefits of this approach in (13)C side-chain relaxation measurements on the mouse major urinary protein selectively enriched with [gamma(1),gamma(2)-(13)C(2),alpha,beta,gamma(1),gamma(1),gamma(2),gamma(2)-(2)H(6)] valine. Relaxation measurements in the absence and presence of pyrazine-derived ligands suggest that valine side-chain dynamics do not contribute significantly to binding entropy.     

Theoretical study on the group 2 atoms + N2O reactions

The electronic structure aspects of the M (1S,3P) + N2O(X 1sigma+) (M = Be, Mg, Ca) reactions are investigated using the CASSCF/MRMP2 (complete active space SCF and the multireference M?ller-Plesset perturbation theory of the second order) computational methodology. The lowest adiabatic 1 1A' and 1 3A' potential energy surfaces (PESs) favor the bending dissociation mechanism of N2O in all studied cases. The rate-limiting channels are determined by the classical barriers that decrease in the series Be (8.9) > Mg (7.0) > Ca (1.2) kcal/mol, whereas the spin-forbidden reaction channels are found to be less important. A comparison with elaborated kinetic results (Plane et al. J. Phys. Chem. 1990, 94, 5255; Gas-Phase Metal Reactions; Elsevier: Amsterdam, 1992; Vinckier et al. J. Phys. Chem. A 1999, 103, 5328) on the Ca (1S) + N2O(X 1sigma+) reaction is presented, and the differences in the kinetic behavior of the title reactions are discussed. Our results also indicate that the techniques based on the multiconfigurational wave functions are unavoidable if a correct topology of the PESs governing these reactions is needed.     

The E x e dynamic Jahn-Teller problem: a new insight from the strong coupling limit

Correct boundary conditions for the E x e dynamic Jahn-Teller problem are considered explicitly for the first time to obtain approximate analytical solutions in the strong coupling limit. Numerical solutions for the decoupled equations using the finite difference method are also presented. The numerical solutions for the decoupled equations exhibit avoided crossings in the weak coupling region, which explains the oscillating behavior of the solutions obtained by Longuet-Higgins et al. for the coupled equations. The obtained analytical energy expressions show improved agreement with the numerical calculations as compared with the previous treatment in which the potentials were assumed to be harmonic. We demonstrate that the pseudorotational energy j(2)/(2g(2)), where g is the dimensionless vibronic coupling constant, and j total angular momentum: j=+/-1/2,+/-3/2,..., in the conventional strong coupling expression for the vibronic levels of the lower sheet is exact. Non-Hermitian first-order perturbation theory gives the energy which is correct up to 1/g(4). The asymptotic behavior of the wave function at the origin does not influence the corrected energy up to order of 1/g(4). At the same time the treatment of the upper sheet with correct boundary conditions gives solutions which are entirely different from the corresponding Slonczewski's solutions. Besides, the correct boundary conditions enable us to evaluate the nonadiabatic coupling between the lower and upper potential sheets. The energy correction due to the nonadiabatic coupling is estimated to be of order 1/g(6).     

Multiquanta vortex entry and vortex-antivortex pattern expansion in a superconducting microsquare with a magnetic dot

We investigate the nucleation of superconductivity in a microsquare with a magnetic dot on top. The cusplike behavior of the calculated normal-superconducting phase boundaries, T(c)(H), shows a transition between short-period to long-period oscillations when going from positive to negative applied fields, H. Vorticity changes by more than 1, indicating multiquanta vortex entries, have been detected along this asymmetric T(c)(H) boundary. The dot also expands dramatically the symmetry-consistent vortex-antivortex patterns, thus facilitating their experimental observation.     

Band formation in mixtures of oppositely charged colloids driven by an ac electric field

We present experiments on pattern formation in a Brownian system of oppositely charged colloids driven by an ac electric field. Using confocal laser scanning microscopy we observe complete segregation of the two particle species into bands perpendicular to a field of sufficient strength when the frequency is in a well-defined range. Because of its Brownian nature the system spontaneously returns to the equilibrium mixture after the field is turned off. We show that band formation is linked to the time scale associated with collisions between particles moving in opposite directions.     

Ring currents in boron and carbon buckyballs, B80 and C60

The ipsocentric method at the coupled Hartree-Fock level is used for the calculation of magnetically induced ring currents in the boron buckyball B(80), for both I(h) and distorted T(h) geometries. A close similarity between the current patterns in boron and carbon buckyballs is noted, but with a higher current density in B(80). Paratropic currents on the pentagons are predominant in the boron buckyball, and the central NICS value is positive. These observations support the conclusion that B(80) should be considered (weakly) anti-aromatic. The largest orbital contributions to the ring currents in both molecules are identified and related to specific excitations in the frontier orbital region.