Related papers: Harmonic moment dynamics in Laplacian growth
We consider the evolution of homogeneous cosmologies towards the future in a dynamical systems formulation. Using a variational equation approach, we show that there is a short period in which transient solutions between the end of a…
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc., is known to be integrable and to…
A Lagrangian is introduced which includes the coupling between magnetic moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the…
We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of scalar potential is highly constrained by the discrete shift symmetries of the…
We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
We study the non-linear dynamics of an inflationary phase transition in a quartically self coupled inflaton model within the framework of a de Sitter background. Large N and Hartree non-perturbative approximations combined with…
Dirac-Born-Infeld type effective actions reproduce many aspects of string theory classical tachyon dynamics of unstable Dp-branes. The inhomogeneous tachyon field rolling from the top of its potential forms topological defects of lower…
We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency…
Consider the wave propagation in a two-layered medium consisting of a homogeneous compressible air or fluid on top of a homogeneous isotropic elastic solid. The interface between the two layers is assumed to be an unbounded rough surface.…
We study the time correlation functions of coupled linear Langevin dynamics without and with inertia effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three…
Conformal mapping models are used to study competition of noise and anisotropy in Laplacian growth. For that, a new family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a…
A special class of conformal gravity theories is proposed to solve the long standing problem of the fine-tuned cosmological constant. In the proposed model time evolution of the inflaton field leaves behind a nearly vanishing, but finite…
In this article we study different extensions of the celebrated Hopf's boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the…
We point out the existence of a consistency relation involving the 3-point function of scalar perturbations which is valid in any inflationary model, independently of the inflaton Lagrangian under the assumption that the inflaton is the…
Supersymmetric hybrid inflation is an exquisite framework to connect inflationary cosmology to particle physics at the scale of grand unification. Ending in a phase transition associated with spontaneous symmetry breaking, it can naturally…