Abstract An interparticle interaction potential has been recently proposed in studies of condensate-like systems described by logarithmically nonlinear equations, such as the superfluid helium-4 and Korteweg-type melts. It shape a Gaussian multiplied linear function can switch between attraction repulsion regimes distance varies. We consider classical fluid model with discretized version this M...

We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of boundary layers through displacement-strain curves. Most prominently, we distinguish wavenumber-selecting and phase-selecting boundary conditions and show how they...

Failure of economic models to anticipate the global financial crisis illustrates the need for modeling to better capture complex real-world dynamics. Conventional models—in which economic variables evolve toward equilibria or fluctuate about equilibria in response to exogenous random shocks—are ill-equipped to portray complex realworld dynamics in which economic variables may cycle aperiodicall...

A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However,...