J. Timonen

Kinetic roughening in slow combustion of paper.

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To obtain a more detailed picture of the strong-coupling fixed point, characteristic of the KPZ universality class, universal amplitude ratios, and the universal coupling constant are computed from the data and found to be in good agreement with theory. Below the spatial and temporal scales at which a crossover takes place to the standard KPZ behavior, the fronts display higher apparent exponents and apparent multiscaling. In this regime the interface velocities are spatially and temporally correlated, and the distribution of the magnitudes of the effective noise has a power-law tail. The relation of the observed short-range behavior and the noise as determined from the local velocity fluctuations is discussed.

Temporal and spatial persistence of combustion fronts in paper.

The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior.

Stiffness of compressed fiber mats

We investigate, using an analytical and a numerical model, the in-plane stiffness of fiber mats. A mat is modeled by randomly depositing thin linear-elastic fibers on top of each other under the influence of an external pressure. The external pressure has the effect of bending the fibers over each other. The fibers are assumed rigidly bonded at contacts. For a low external pressure the stiffness of the mat deviates from that of its two-dimensional projection only by a geometrical factor, and the effective Poisson contraction is close to zero. For higher pressures, stiffness is governed by two competing effects and a maximum appears in the stiffness. The effective Poisson ratio is clearly negative in this range. An approximative analytical description is developed for the stiffness of mats formed under low external pressure. The stiffness is given as a function of only a few parameters: the degree of bonding, the dimensions of the fibers, the elastic constants of the fiber material, and the density of fibers.