Related papers: A note on instantaneous gelation for coagulation k…
We analyze greying of the dark soliton in a Bose-Einstein condensate in the limit of weak interaction between atoms. The condensate initially prepared in the excited dark soliton state is loosing atoms because of spontaneous quantum…
This paper deals with nonnegative solutions of the one dimensional degenerate parabolic equations with zero homogeneous Dirichlet boundary condition. To obtain an existence result, we prove a sharp gradient estimate of |u_x|. Besides, we…
Paradigm shift in gauge topology at finite temperatures, from the instantons to their constituents -- instanton-dyons -- has recently lead to studies of their ensembles and very significant advances. Like instantons, they have fermionic…
The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels.…
We present a path-integral Monte Carlo study of dissociation in dense hydrogen ($1.75 \leq r_s \leq 2.2$, with $r_s$ the Wigner sphere radius). As temperature is lowered from $10^5$ to 5000 K, a molecular hydrogen gas forms spontaneously…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
We present molecular dynamics simulations of the homogeneous (mechanical) melting transition of a bcc metal, vanadium. We study both the nominally perfect crystal as well as one that includes point defects. According to the Born criterion,…
We show that in a uniform medium, the vanishing of a particular condensate along with spontaneously broken symmetry imply the existence of an anomalously light pseudo-Goldstone mode. The consequences for a vanishing chiral condensate in…
Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…
Consider a complex line bundle over a compact complex manifold equipped with an infinitely differentiable metric with strictly positive curvature form. Assign to positive tensor powers of this bundle the associated product metrics and…
One or two negative mass singularities are found to occur in static inhomogeneous spatially closed solutions to the Einstein equations. The singularities produce a positive Komar mass, and this decreases the size of the cosmological…
We consider a homogenization problem for the diffusion equation $-\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f$ when the coefficient $a_{\varepsilon}$ is a non-local perturbation of a periodic coefficient. The…
We consider a gauge/gravity dual model of thermalization which consists of a collapsing thin matter shell in asymptotically Anti-de Sitter space. A central aspect of our model is to consider a shell moving at finite velocity as determined…
Differential equations of the form $\ddot R=-kR^\gamma$, with a positive constant $k$ and real parameter $\gamma$, are fundamental in describing phenomena such as the spherical gravitational collapse ($\gamma=-2$), the implosion of…
We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional…
The thermal and chemical evolution of gravitationally collapsing protostellar clouds is investigated, focusing attention on their dependence on metallicity. Calculations are carried out for a range of metallicities spanning the local…
The instanton approach to spontaneous chiral symmetry breaking is reviewed, with emphasis on the connection to chiral random matrix theory. We extend the approach to discuss the finite density, zero-temperature behaviour of quark matter.…
In this paper we show how the method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation for arbitrary homogeneous kernel. The resulting massdistributions are of Kolmogorov…
We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring…