Related papers: New explicit spike solution -- non-local component…
The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a…
The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a…
In this paper we expand upon our previous work [1] by using the entire family of Bianchi type V stiff fluid solutions as seed solutions of the Stephani transformation. Among the new exact solutions generated, we observe a number of…
We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of…
According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an…
A modified semi-classical method is used to construct both ground and excited state solutions to the canonically quantized vacuum Bianchi IX (Mixmaster) cosmological models. Employing a modified form of the semi-classical Ansatz we solve…
We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as Ho\v{r}ava-Lifshitz, $\lambda$-$R$ or $f(R)$ gravity), which are expected to describe generic spacelike singularities for these…
Non-singular Bianchi type I solutions are found from the effective action with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular solutions evolve from the asymptotic Minkowski region, subsequently super-inflate, and…
We produce numerical evidence that spikes in the Mixmaster regime of G_2 cosmologies are transient and recurring, supporting the conjecture that the generalized Mixmaster behavior is asymptotically non-local where spikes occur. Higher order…
We use a conformal transformation to find solutions to the generalised scalar-tensor theory, with a coupling constant dependent on a scalar field, in an empty Bianchi type I model. We describe the dynamical behaviour of the metric functions…
We report some new exact instantons in general relativity. These solutions are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0, with matter content of a stiff fluid. The qualitative behaviour of the solutions is…
We generalize the orthogonally transitive (OT) $G_2$ spike solution to the non-OT $G_2$ case. This is achieved by applying Geroch's transformation on a Kasner seed. The new solution contains two more parameters than the OT $G_2$ spike…
Numerical simulations of classical pattern forming reaction-diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady-state consisting of a spatially repeating pattern of localized spikes. In…
We consider the most cosmologically interesting and relevant case of scalar-tensor theory (STT) and derive new normal and phantom, dynamical and static, solutions. We determine the Bianchi I Kasner exponents and show that the dynamical…
Localized solutions are known to arise in a variety of singularly perturbed reaction-diffusion systems. The Gierer-Meinhardt (GM) system is one such example and has been the focus of numerous rigorous and formal studies. A more recent focus…
The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which exponentially…
The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…
We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. Surprisingly few facts are known about the `Mixmaster' dynamics of these models, while…
We introduce a generalized excitable system in which spikes can happen in a continuum of directions, therefore drastically enriching the expressivity and control capability of the spiking dynamics. In this generalized excitable system,…
We construct black hole attractor solutions for a wide class of N=2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as…