Related papers: Harmonic moment dynamics in Laplacian growth
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and…
The dynamics of hybrid models is usually approximated by the evolution of a scalar field slowly rolling along a nearly flat valley. Inflation ends with a waterfall phase, due to a tachyonic instability. This final phase is usually assumed…
We propose a method to obtain the equilibrium distribution for positions and velocities of a one-dimensional particle via time-averaging and Laplace transformations. We apply it to the case of a damped harmonic oscillator in contact with a…
We consider several mathematical issues regarding models that simulate forces exerted by cells. Since the size of cells is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta…
It is shown that the efficiency of the universe heating by an inflaton field depends not only on the possible presence of parametric resonance in the production of scalar particles but also strongly depends on the character of the inflaton…
The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We…
Since the tension instability was discovered in updated Lagrangian smoothed particle hydrodynamics (ULSPH) at the end of the 20th century, researchers have made considerable efforts to suppress its occurrence. However, up to the present…
In analogy to the harmonic analysis for the Poincar\'e group with its irreducible representations characterizing free particles, the harmonic analysis for a nonlinear spacetime model as homogenous space of the extended Lorentz group GL(C^2)…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…
A new selection phenomenon in nonlinear interface dynamics is predicted. A generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw cell is presented. These solutions show that the case where the asymptotic bubble…
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
We study a one-dimensional hamiltonian chain of masses perturbed by an energy conserving noise. The dynamics is such that, according to its hamiltonian part, particles move freely in cells and interact with their neighbors through…
This manuscript concerns the stability conditions for the well-posedness of the two-dimensional plasma-vacuum interface problems for ideal incompressible magnetohydrodynamics (MHD) equations, which describe the dynamics of conducting…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We establish a thermodynamic limit and Gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces. The results hold for the standard ballistic deposition model as well as…
Studying the topology of spatiotemporal media poses a fundamental challenge: their remarkable properties stem from breaking spatial and temporal symmetries, yet this same breaking obscures their topological characterization. Here, we show…
The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a…
Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and…