An analytically solvable model of probabilistic network dynamics

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur

Condensation oscillations in the peptidization of phenylglycine

In earlier studies, we showed that certain low-molecular-weight carboxylic acids (profens, amino acids, hydroxy acids) can undergo spontaneous in vitro chiral conversion accompanied by condensation to from oligomers, and we proposed two simple models to describe these processes. Here, we present the results of investigations using non-chiral high-performance liquid chromatography with diode array detector (HPLC-DAD) and mass spectrometry (MS) on the dynamics of peptidization of S-, R-, and rac-phenylglycine dissolved in 70% aqueous ethanol and stored for times up to one year. The experimental results demonstrate that peptidization of phenylglycine can occur in an oscillatory fashion. We also describe, and carry out simulations with, three models that capture key aspects of the oscillatory condensation and chiral conversion processes

Fronts and patterns in a spatially forced CDIMA reaction

We use the CDIMA chemical reaction and the Lengyel–Epstein model of this reaction to study resonant responses of a pattern-forming system to time-independent spatial periodic forcing. We focus on the 2:1 resonance, where the wavenumber of a one-dimensional periodic forcing is about twice the wavenumber of the natural stripe pattern that the unforced system tends to form. Within this resonance, we study transverse fronts that shift the phase of resonant stripe patterns by π. We identify phase fronts that shift the phase discontinuously, and pairs of phase fronts that shift the phase continuously, clockwise and anti-clockwise. We further identify a front bifurcation that destabilizes the discontinuous front and leads to a pair of continuous fronts. This bifurcation is the spatial counterpart of the nonequilibrium Ising–Bloch (NIB) bifurcation in temporally forced oscillatory systems. The spatial NIB bifurcation that we find occurs as the forcing strength is increased, unlike earlier studies of the NIB bifurcation. Furthermore, the bifurcation is subcritical, implying a range of forcing strength where both discontinuous Ising fronts and continuous Bloch fronts are stable. Finally, we find that both Ising fronts and Bloch fronts can form discrete families of bound pairs, and we relate arrays of these front pairs to extended rectangular and oblique patterns