Related papers: Cross-over in scaling laws: A simple example from …
We study the depinning transition of driven interfaces in thin ferromagnetic films driven by external magnetic fields. Approaching the transition point the correlation length increases with decreasing driving. If the correlation length…
Near the Curie temperature of a ferromagnet the form of a domain wall changes from the Bloch type to (asymptotically) the linear Zhirnov wall. Unlike the simple 180 degree rotation of the magnetization vector in a Bloch wall, its absolute…
Using a combination of analytic arguments and numerical simulations, we determine lower and upper bounds for the energy barriers to the motion of a defect line in a random potential at low temperatures. We study the cases of magnetic flux…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with non-linear couplings…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review…
We present an analysis of edge domain walls in exchange-biased ferromagnetic films appearing as a result of a competition between the stray field at the film edges and the exchange bias field in the bulk. We introduce an effective…
Shearing transitions of multi-layer molecularly thin-film lubrication systems in variations of the film-substrate coupling strength and the load are studied by using a multiscale method. Three kinds of the interlayer slips found in…
Motivated by the observed thickness-scaling of the coercive field in ferroelectric films over five decades, we develop a statistical approach towards understanding the conceptual underpinnings of this behavior. Here the scaling exponent is…
We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin film (Tanner's law regime) to that of a…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
Turbulent flows are observed in low-Reynolds active fluids. They are intrinsically different from the classical inertial turbulence and behave distinctively in two- and three-dimensions. Understanding the behaviors of this new type of…
The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…
The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy…
Nearly magnetic metals often have layered lattice structures, consisting of coupled planes. In such a situation, physical properties will display, upon decreasing temperature or energy, a dimensional crossover from two-dimensional (2d) to…
In this paper, we perform a detailed study of the scaling properties of a ferromagnetic thin film model. Recently, interest has increased in the scaling properties of the magnetic domain wall (MDW) motion in disordered media when an…
Hydrated granular packings often crack into discrete clusters of grains when dried. Despite its ubiquity, accurate prediction of cracking remains elusive. Here, we elucidate the previously overlooked role of individual grain shrinkage---a…