Biomedical subjects
Publications and source records attributed to Im Kim.
We introduce a simple self-organized growth model mimicking the dynamics of a driven tensionless interface in a random medium near the depinning threshold. The roughness and growth exponents for the model are obtained as zeta approximately 1.93 and beta approximately 0.96, respectively. We discuss the possible continuum equation describing the motion of a driven interface in our model.
We study an anisotropic nonlocal Kardar-Parisi-Zhang (KPZ) equation with spatially correlated noise by using the dynamic renormalization group method. When the signs of nonlinear terms in parallel and perpendicular directions are opposite, the correlated noise coupled with the long ranged nature of interaction produces a stable non-KPZ fixed point for d<d(c). For the uncorrelated noise, the roughness and dynamic exponents associated with the stable fixed point are different from those of the isotropic nonlocal KPZ equation, while for the correlated noise the exponents are the same as those of the isotropic case.
By using the dynamic renormalization group approach, we analyze a nonlocal conserved Kardar-Parisi-Zhang equation with spatially correlated conservative noise in order to study the effect of the long-range nature of interactions coupled with spatially correlated noise on the dynamics of a volume conserving surface. The roughness of the surface depends on both the long-range interaction strength and the spatial correlation parameter. The surface becomes less rough by the long-range interaction, while it becomes more rough by the spatial correlation of noise. We also study the nonlocal conserved Kardar-Parisi-Zhang equation with spatially correlated nonconservative noise.
We study the morphologies of river networks on various landscapes. In general, the probability density distribution of drainage area a of the river network scales as P(a) approximately a(-tau). We consider a slope-slope correlation function G(r) and define the persistent length R where G(r=R) becomes zero. In our restricted solid on solid network model, R is independent of the system size L and tau is close to 4/3, which is the value of the Scheidegger's river network model with random walk process. We also consider an avalanche model, where R is proportional to L. There is a large slope-slope correlation length and the river network does not follow the directed random walk process with tau approximately 1.42.
We introduce a simple growth model for a driven interface in random media, exhibiting a smoothing (roughening) transition as well as a pinning-depinning transition in a nonequilibrium (1+1)-dimensional system. At both transition points, the scaling exponents belong to the directed percolation universality class. The rough interface at the pinning-depinning transition point belongs to the quenched Kardar-Parisi-Zhang universality class. The two transitions are second order phase transitions. We also introduce a modified growth model exhibiting the pinning-depinning transition. In the modified model, the pinning-depinning transition is a first order phase transition in the directed percolation universality class.
We introduce a simple stochastic model for a driven interface in a random medium, in which we can control the degree of the anisotropy of a random medium. When there is no anisotropy of a random medium, the motion of a growing interface in our model can be well described by the quenched Edwards-Wilkinson equation. When there is anisotropy of a random medium, however, the motion of a growing interface can be described by the quenched Kardar-Parisi-Zhang (KPZ) equation. In the two interfaces, apart from one growing in an isotropic medium and the other growing in an anisotropic medium, the growth rule of our model is the same. Our results support the fact that the anisotropy of a random medium is a source of the KPZ nonlinearity.
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