Related papers: Harmonic moment dynamics in Laplacian growth
In this study, we investigate the behavior of inertial active Brownian particles in a $d$-dimensional harmonic trap in the presence of translational diffusion. While the solution of the Fokker-Planck equation is generally challenging, it…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows one to distinguish a class of exact…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field…
We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible magnetohydrodynamics (MHD), while the electric and magnetic…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of…
We consider the nonlinear dynamics of inflaton fragmentation during and after preheating in the simplest model of chaotic inflation. While the earlier regime of parametric resonant particle production and the later turbulent regime of…
Harmonic balls are domains which satisfy the mean-value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum gravity (LQG) surfaces using the obstacle problem formulation of…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We characterize the existence of the $L^1$ solutions of the truncated moments problem in several real variables on unbounded supports by the existence of the maximum of certain concave Lagrangian functions. A natural regularity assumption…
The dynamics of typical phase transitions is studied out of equilibrium in weakly coupled inflaton-type scalar field theories in Minkowski space. The shortcomings of the effective potential and equilibrium descriptions are pointed out. A…
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple…
Large field inflation is arguably the simplest and most natural variant of slow-roll inflation. Axion monodromy may be the most promising framework for realising this scenario. As one of its defining features, the long-range polynomial…
The coherent interband dynamics of optically excited two-dimensional lateral surface superlattices driven by an in-plane static electric field has been investigated. The linear absorption, the spectrally-resolved pump-probe four-wave mixing…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary.…
A dynamic concordia discors, a finely tuned equilibrium between opposing forces, is hypothesized to drive historical transformations. Similarly, a precise interplay of excitation and inhibition, often approximated by an 80:20 ratio,…