Related papers: Nonlinear Criterion for the Stability of Molecular…
It has been recently discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with the cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the 1D version…
Magnetic fields play a fundamental role in protostellar collapse and disk formation, yet direct measurements of magnetic field strength in deeply embedded protostellar envelopes remain difficult. We present a new method to estimate both the…
We study the magnetic field to density ($B-\rho$) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a…
We review recent advances in the analytical and numerical modeling of the star formation rate in molecular clouds and discuss the available observational constraints. We focus on molecular clouds as the fundamental star formation sites,…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
The mass-to-magnetic flux ratio of molecular clouds is a parameter of central importance as it quantifies the dynamical significance of the magnetic field with respect to gravitational forces. Therefore, it can provide invaluable…
We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' or partial viscosity. The main result is the establishment of…
We have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with…
Stars form in highly-magnetised, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments…
Independent tests aiming to constrain the value of the cosmological constant $\Lambda$ are usually difficult because of its extreme smallness $\left(\Lambda \simeq 1\times 10^{-52}~\textrm{m}^{-2},~\textrm{or}~2.89\times…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
Isolated low-mass stars are formed in dense cores of molecular clouds. In the standard picture, the cores are envisioned to condense out of strongly magnetized clouds through ambipolar diffusion. Most previous calculations based on this…
We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of…
A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously…
We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear…
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
Based on simple physical and geometric assumptions, we have calculated the mean surface molecular density of spiral galaxies at the threshold between star formation induced by cloud-cloud collision and spontaneous gravitational collapse.…
The ac response of a slab of material with electrodynamic characteristics $E\sim j^{\kappa+1}$, $\kappa\geq0$, is studied numerically. From the solutions of the nonlinear diffusion equation, the fundamental and higher-order components of…