arXiv subjects

Edgar Knobloch

Publications and source records attributed to Edgar Knobloch.

58 records · Page 4Linked to original sources

arXiv2011

Modelling fluids and crystals using a two-component modified phase field crystal model

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where modulated and uniform phases are formed and also regions where localised states are formed. We investigate the effectiveness of the phase field crystal model for describing fluids and crystals with defects. We further consider a two component model and elucidate how the structure transforms from hexagonal crystalline ordering to square ordering as the concentration changes. Our conclusion contains a discussion of possible interpretations of the order parameter field.

cond-mat.soft↗

arXiv2008

Generation of finite wave trains in excitable media

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.

nlin.PS↗

arXiv2006

Drops on an inclined heterogeneous substrate: onset of sliding motion

Pinning and depinning of drops on an inclined heterogeneous substrate is studied as a function of the inclination and heterogeneity amplitude. Two types of heterogeneity are considered: a hydrophobic defect that blocks the droplet in front, and a hydrophilic one that holds it at the back. Two different types of depinning leading to sliding motion are identified, and the resulting stick-slip motion is studied numerically.

physics.flu-dyn↗

arXiv1997

Amplitude equations for coupled electrostatic waves in the limit of weak instability

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order terms. The nonlinear coefficients are singular in the limit in which the linear growth rates vanish together. These singularities are analyzed using techniques developed in previous studies of a single unstable wave. In addition to the singularities familiar from the one mode problem, there are new singularities in coefficients coupling the modes. The new singularities are most severe when the two waves have the same linear phase velocity and satisfy the spatial resonance condition $k_2=2k_1$. As a result the short wave mode saturates at a dramatically smaller amplitude than that predicted for the weak growth rate regime on the basis of single mode theory. In contrast the long wave mode retains the single mode scaling. If these resonance conditions are not satisfied both modes retain their single mode scaling and saturate at comparable amplitudes.

patt-sol↗