Related papers: Rolling G_2 Moduli
Two-component (normal and degenerate stars) models are the simplest realization of clusters with a mass spectrum because high mass stars evolve quickly into degenerates, while low mass stars remain on the main-sequence for the age of the…
We investigated the evolution of clusters of galaxies using self-consistent N-body simulations. We varied the initial model of galaxies and clusters, and studied the dependence of evolution on initial conditions. We found that the growth…
We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
In this paper I focus on three topics related to the dynamical evolution of small galaxy groups, for which the input of N-body simulations has been decisive. These are the merging rates in compact groups, the properties of remnants of…
We study the change of moduli spaces of Gieseker-semistable torsion free rank-$2$ sheaves on algebraic surfaces as we vary the polarizations. When the surfaces are rational with an effective anti-canonical divisor, the moduli spaces are…
We produce new non-K\"ahler, non-Einstein, complete expanding gradient Ricci solitons with conical asymptotics and underlying manifold of the form $\R^2 \times M_2 \times \cdots \times M_r$, where $r \geq 2$ and $M_i$ are arbitrary closed…
We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric $G_2$ model) filled with a tilted perfect fluid undergoing velocity diffusion on a scalar field. Considered are two types of fluid: dust and radiation. We solve…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
We develop a generalization of the time-varying Drude model, treating carrier density, effective mass, and collision rate as explicit functions of time. We derive expressions for polarization, susceptibility, displacement, and permittivity…
In this article we study a one dimensional model for Magnetic Relaxation. This model was introduced by Moffatt and describes a low resistivity viscous plasma, in which the pressure and the inercia are much smaller than the magnetic…
Star clusters - open and globulars - experience dynamical evolution on time scales shorter than their age. Consequently, open and globular clusters provide us with unique dynamical laboratories for learning about two-body relaxation, mass…
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.
Some dynamical properties of a bouncing ball model under the presence of an external force modeled by two nonlinear terms are studied. The description of the model is made by use of a two dimensional nonlinear measure preserving map on the…
We analyze the blowup (finite-time singularity) in inviscid shell models of convective turbulence. We show that the blowup exists and its internal structure undergoes a series of bifurcations under a change of shell model parameter. Various…
We consider evolutions of linear fluctuations as the background Friedmann world model goes from contracting to expanding phases through smooth and non-singular bouncing phases. As long as the gravity dominates over the pressure gradient in…
The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the \textit{scale-invariant case} and time derivative nonlinearity with small initial data. Under appropriate initial…
We survey the implications of our joint work with E. Bru\`e and A. Pigati on the structure of blow-downs for a smooth, complete, Riemannian $4$-manifold with nonnegative Ricci curvature and Euclidean volume growth. Very imprecisely, any…
Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperk\"ahler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their…
We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension 1, multiplicity 4, Euler characteristic 2, and first Chern class (2, 2), is the blow-up at two points of a certain hypersurface in a weighted…