Related papers: Scale Holography
Two-dimensional diffeomorphism symmetry can be described by an operator algebra extension of the well-known Virasoro algebra description of conformal symmetry. Utilizing this extension, this note explains why the conformal symmetry that…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
A supersolid is a system that presents long-range order and shear rigidity as a solid but which also supports a non-dissipative superflow as a superfluid. From an effective perspective, supersolids are identified with phases of matter that…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
An experimental study on how reconstructed image signal and noise scale with acquisition and reconstruction parameters is proposed. Monte-carlo simulation is performed to emphasize that the measured noise is shot-noise.
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson and Wei) we describe precise necessary and sufficient conditions for…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…
We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…
The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of…
The consequences of holography hypothesis are investigated for the Pre-big-bang string cosmological models. The evolution equations are obtained from the tree level string effective action. It is shown that $S/A$ is bounded by a constant in…
We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a…
Gravitational holography is argued to render the cosmological constant stable against divergent quantum corrections. This provides a technically natural solution to the cosmological constant problem. Evidence for quantum stability of the…
A holographic microscope captures interference patterns, or holograms, that encode three-dimensional (3D) information about the object being viewed. Computation is essential to extracting that 3D information. By wrapping low-level…
We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…
Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…