Related papers: Collapse of 4D random geometries
In this paper, we study the progressive collapse of 3D framed structures made of reinforced concrete after the sudden loss of a column. The structures are represented by elasto-plastic Euler Bernoulli beams with elongation-rotation failure…
Granular systems confined in vertically vibrated shallow horizontal boxes (quasi two-dimensional geometry) present a liquid to solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains…
Rigidity percolation provides an important basis for understanding the onset of mechanical stability in disordered materials. While most studies on the triangular lattice have focused on static properties at fixed bond~(site) occupation…
(2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian Chern-Simons gauge field theory (E Witten 1988). Regarding this as the topological phase of quantum gravity in (2+1)d, we suggest a topological symmetry breaking by…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a…
When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the…
We present an updated analysis of the first-order phase transition associated with symmetry breaking in the early Universe in a classically scale-invariant model extended with a new SU(2) gauge group. Including recent developments in…
We present a numerical model for a two dimensional (2D) granular assembly, falling in a rectangular container when the bottom is removed. We observe the occurrence of cracks splitting the initial pile into pieces, like in experiments. We…
We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions showing the…
The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a…
We introduce a 2-dimensional lattice model of granular matter. We use a combination of proof and simulation to demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close…
The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the…
We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global…
By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high…
We study a class of models of i.i.d.~random environments in general dimensions $d\ge 2$, where each site is equipped randomly with an environment, and a parameter $p$ governs the frequency of certain environments that can act as a barrier.…
We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular periodic function $f$. We give a sufficient condition on the second derivative of $f$ giving…