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We consider the model of viscous compressible multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which…
We study the cosmology of models with four space and one time dimension where our universe is a 3-brane and report a few results which extend existing work in several directions. Assuming a stable fifth dimension, we obtain a solution for…
We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly…
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
A general framework for studying a large class of cosmological solutions of the low-energy limit of type II string theory and of M-theory, with non-trivial Ramond form fields excited, is presented. The framework is applicable to spacetimes…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…
We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…
Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence…
Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the…
We review a few off-the-beaten-track ideas in cosmology. They solve a variety of fundamental problems; also they are fun. We start with a description of non-singular dilaton cosmology. In these scenarios gravity is modified so that the…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
An extension of the Standard Model by extra scalar singlets was considered. Theoretical (unitarity, vacuum stability, triviality) and cosmological (dark matter relic abundance, direct detection experiments, constraints on dark matter…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the electrostatic and mechanical energies, the governing evolution…
A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
A semiclassical linear response theory based on the Vlasov equation is reviewed. The approach discussed here differs from the classical one of Vlasov and Landau for the fact that the finite size of the system is explicitly taken into…
We consider a universe with an arbitrary number of extra dimensions, $N$. We present a new method for constructing the cosmological equations of motion and find analytic solutions with an explicit dependence on $N$. When we take the…