相关论文: High-Acceleration Patterns in Thin Vibrated Granul…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…
The self-organization processes of nanopattern formation on semiconductor surfaces under low energy ion beam bombardment is considered. The new mathematical model based on nonlinear evolution equation of the sixth order is presented. The…
We study the three-dimensional Ginzburg-Landau model of superconductivity for strong applied magnetic fields varying between the second and third critical fields. In this regime, it is known from physics that superconductivity should be…
A system consisting of the cubic complex Ginzburg-Landau equation which is linearly coupled to an additional linear dissipative equation, is considered. The model was introduced earlier in the context of dual-core nonlinear optical fibers…
Certain dissipative Ginzburg-Landau models predict existence of planar interfaces moving with constant velocity. In most cases the interface solutions are hard to obtain because pertinent evolution equations are nonlinear. We present a…
We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent…
We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial inhomogeneity moving with constant speed. In the comoving…
We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary…
A generalization of the de Gennes-Alexander micronetworks theory is presented. In this framework, the phase transition of synthetic networks of superconducting islands is described by means of a Ginzburg-Landau approach adapted to the case…
We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first…
When a primary order breaks multiple symmetries, partially ordered phases that only break a subset of those symmetries, known as vestigial phases, may onset at a higher temperature. This concept has been applied to a wide range of systems,…
We study an experimental system of hard granular squares in two dimensions, energized by vibration. The interplay of order in the orientations and positions of anisotropic particles allows for a rich set of phases. We measure the structure…
Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective…
Magnetic properties of layered high temperature superconductors with a weak interlayer coupling in the region of the critical fluctuations are investigated in the framework of the Ginzburg--Landau approach. The sample magnetization is…
We study the onset of patterns in vertically oscillated layers of frictionless dissipative particles. Using both numerical solutions of continuum equations to Navier-Stokes order and molecular dynamics (MD) simulations, we find that…