Related papers: Spike behavior in the approach to spacetime singul…
An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an…
We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\] for general linear operators $R$ in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localized…
A timely combination of new theoretical ideas and observational discoveries has brought about significant advances in our understanding of cosmic evolution. Computer simulations have played a key role in these developments by providing the…
We study the formation of singularities for the Euler-Alignment system with influence function $\psi=\frac{k_\alpha}{|x|^\alpha}$ in 1D. As in [20] the problem is reduced to the analysis of a nonlocal 1D equation. We show the existence of…
New Planck scale physics may solve the singularity problems of classical general relativity and may lead to interesting consequences for very early Universe cosmology. Two approaches to these questions are reviewed in this article. The…
An Euclidean approach for investigating quantum aspects of a scalar field living on a class of D-dimensional static black hole space-times, including the extremal ones, is reviewed. The method makes use of a near horizon approximation of…
This paper is a continuation of the paper Berestycki, Wei and Winter \cite{Berestycki2014}. In \cite{Berestycki2014}, the existence of multiple symmetric and asymmetric spike solutions of a chemotaxis system modeling crime pattern…
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
An overview over the current status of modeling galaxies by means of numerical simulations is given. After a short description of how galaxies form in hierarchically clustering scenarios, success and failures of current simulations are…
The approach of a quantum state to a cosmological singularity is studied through the evolution of its moments in a simple version of a Bianchi I model. In spite of the simplicity, the model exhibits several instructive and unexpected…
Modeling spike firing assumes that spiking statistics are Poisson, but real data violates this assumption. To capture non-Poissonian features, in order to fix the inevitable inherent irregularity, researchers rescale the time axis with…
We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are…
The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time…
Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant…
We simulate the transformation of a classical fluid into a quantum-like (super)-fluid by the application of a generalized quantum potential through a retro-active loop. This numerical experiment is exemplified in the case of a non-spreading…
One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms…
In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the…
I review recent results from numerical simulations on the structure and dynamics of the ISM, and attempt to put together a coherent dynamical scenario. In particular, I discuss results on 1) the spatial distribution of the gas components,…
The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the…