Related papers: How does the supercritical GMC converge?
Observations show that galaxies and their interstellar media are pervaded by strong magnetic fields with energies in the diffuse component being at least comparable to the thermal and even as large or larger than the turbulent energy. Such…
Using the apparatus of correlation Gamma-function (``conditional density''), we have analyzed spatial clustering of objects from several different samples of galaxies, clusters and superclusters. On small scales the distribution of objects…
Critical phenomena in gravitational collapse opened a new mathematical vista into the theory of general relativity and may ultimately entail fundamental physical implication in observations. However, at present, the dynamics of critical…
The anisotropy due to a magnetic field is shown to result in significant changes in Langmuir collapse. Using a variational approach, the quasi-classical collapse phenomenon is investigated analytically. A hierarchy of quasi-classical…
We study the nature of the instability of the homogeneous steady states of the subcritical Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by…
I study type II critical collapse in the spherically symmetric gravitating magnetic monopole system. This is an Einstein-Yang-Mills-Higgs system with two matter fields: a field parametrizing the scalar field gauged under SU(2) and a field…
Consider the conjugation action of the general linear group $\operatorname{GL}_{2}(K)$ on the polynomial ring $K[X_{2 \times 2}]$. When $K$ is an infinite field, the ring of invariants is a polynomial ring generated by the trace and the…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it is positive semi-definite along the complexified orbit, and…
We study real left-invariant spin Gaussian fields on $SO(3)$, a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leveraging recent results from "New chaos decomposition of…
The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…
The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide…
We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…
A simplicial framework for the gerbe-theoretic modelling of supercharged-loop dynamics in the presence of worldsheet defects is discussed whose equivariantisation with respect to global supersymmetries of the bulk theory and subsequent…
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in…
The gas-stars instability criterion for infinitesimally thin disc was applied to the galaxy NGC 628. Instead of using the azimuthally averaged profiles of data the maps of the gas surface densities (THINGS, HERACLES), of the velocity…
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering…
The behaviour of the magnetic field inside the superconducting quark matter core of a neutron star is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate…
We investigate the dynamical state of superclusters in Lambda cold dark matter ($\Lambda$CDM) cosmological models, where the density parameter $\Omega_0=0.2-0.4$ and $\sigma_8$ (the rms fluctuation on the $8h^{-1}$Mpc scale) is $0.7-0.9$.…
One of the most puzzling properties of observed galaxies is the universality of the empirical correlation between the star formation rate and average gas surface density on kiloparsec scales (the Schmidt law). In this study I present…