Browsing by Author "Haataja, M."

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Dynamics of driven interfaces in algebraically correlated random media
(1999) Kuittu, M.-P.; Haataja, M.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
In this work we consider the dynamics of interfaces embedded in algebraically correlated two-dimensional random media. We study the isotropic percolation and the directed percolation lattice models away from and at their percolation transitions. Away from the transition, the kinetic roughening of an interface in both of these models is consistent with the power-law correlated Kardar-Parisi-Zhang universality class. Moreover, the scaling exponents are found to be in good agreement with existing renormalization-group calculations. At the transition, however, we find different behavior. In analogy to the case of a uniformly random background, the scaling exponents of the interface can be related to those of the underlying percolation transition. For the directed percolation case, both the growth and roughness exponents depend on the strength of correlations, while for the isotropic case the roughness exponent is constant. For both cases, the growth exponent increases with the strength of correlations. Our simulations are in good agreement with theory.
Dynamics of driven interfaces near isotropic percolation transition
(1998) Kuittu, M.-P.; Haataja, M.; Provatas, N.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete “forest fire” lattice models through Monte Carlo simulations in two and three spatial dimensions. An interface generated in the models is found to display complex behavior. Away from the percolation transition, the interface is self-affine with asymptotic dynamics consistent with the Kardar-Parisi-Zhang universality class. However, in the vicinity of the percolation transition, there is a different behavior at earlier times. By scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster. Our numerical results are in good agreement with theory. However, we demonstrate that at the depinning transition, the interface as defined in the models is no longer self-affine. Finally, we compare these results with those obtained from a more realistic reaction-diffusion model of slow combustion.
Quartz tuning fork as a probe of surface oscillations
(2017-02-13) Todoshchenko, I.; Savin, A.; Haataja, M.; Kaikkonen, J. P.; Hakonen, P. J.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Quartz tuning forks are high-quality mechanical oscillators widely used in low temperature physics as viscometers, thermometers, and pressure sensors. We demonstrate that a fork placed in liquid helium near the surface of solid helium is very sensitive to the oscillations of the solid-liquid interface. We developed a double-resonance read-out technique, which allowed us to detect oscillations of the surface with an accuracy of 1 Å in 10 s. Using this technique, we have investigated crystallization waves in 4He down to 10 mK. In contrast to previous studies of crystallization waves, our measurement scheme has very low dissipation, on the order of 20 pW, which allows us to carry out experiments even at sub-mK temperatures. We propose to use this scheme in the search for crystallization waves in 3He, which exist only at temperatures well below 0.5 mK. The suggested technique can also be used for accurate displacement detection in a large variety of systems.