We study the master equation with time-dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate ...

This technical note presents the experimental validation of a hybrid fire testing coordination algorithm recently developed by some authors. For first time, is applied to solve static response multiple-degrees-of-freedom model.

A method is presented to partially transfer nuclear spin polarization from one isotope S to another isotope I by the way of heteronuclear spin couplings, while minimizing the loss of spin order to other degrees of freedom. The desired I spin polarization to be detected is a design parameter, while the sequence of pulses at the two Larmor frequencies is optimized to store the greatest unused S s...

Mathematical models of phase transitions in solids lead to the variational problem, minimize R W (Du)dx where W has a multi-well structure: W = 0 on a multi-well set K and W > 0 otherwise. We study this problem in two dimensions in the case of equal determinant, i.e., for K = denotes the (3 2)-matrix formed with the rst two columns of U i. We characterize generalized convex hulls, including the...

We present dynamical properties of spin crossover compounds with photomagnetization, proposing a new model in which the spin-crossover phenomena and magnetic ordering are incorporated in a unified way. By using this model, the novel characteristics observed in Prussian blue analogs are qualitatively well reproduced. We investigate the time evolution of the magnetization and high spin fraction t...

Several single-scan experiments for the measurement of the longitudinal relaxation time (T1) are proposed. These experiments result in fast and accurate determinations of the relaxation rate, are relatively robust to pulse imperfections, and preserve information about the chemical shift. The method used in these experiments is to first encode the T1 values as a spatial variation of the magnetiz...

For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive cha...