Related papers: Wavy spirals and their fractal connection with chi…
The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
We use hydrodynamical simulations to investigate the response of geometrically thin, self-gravitating, singular isothermal disks of gas to imposed rigidly rotating spiral potentials. By minimizing reflection-induced feedback from…
This study investigates the dynamics of Strato-Rotational Instability (SRI) in a stratified, rotating fluid, focusing on the interaction between axial modes and spiral components. Through numerical analysis, we find that SRI induces…
We study several fractal properties of the Weierstrass-type function \[ W(x)=\sum_{n=0} ^\infty \lambda (x) \lambda(\tau x) \cdots \lambda (\tau ^{n-1}x)\, g(\tau ^n x), \] where $\tau :[0,1)\to[0,1)$ is a cookie cutter map with possibly…
We find a new Tully-Fisher-like relation for spiral galaxies holding at different galactocentric radii. This Radial Tully-Fisher (RTF) relation allows us to investigate the distribution of matter in the optical regions of spiral galaxies.…
We study the velocity autocorrelations in an experimental configuration of confined two-dimensional active rotors (disks). We report persistent small scale oscillations in both rotational and translational velocity autocorrelations, with…
We study a heretofore ignored class of spiral patterns for oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of $r$, thereby turning off the…
Stars in the Galactic disk have mean radial velocities $\overline{v}_R$ that oscillate as a function of angular momentum $J_\varphi$. This `$J_\varphi$-${\overline{v}}_R$ wave' signal also exhibits a systematic phase shift when stars are…
This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in…
Spirals are common in Nature: the snail's shell and the ordering of seeds in the sunflower are amongst the most widely-known occurrences. While these are static, dynamic spirals can also be observed in excitable systems such as heart…
In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity…
Spiral perturbations in a gravitationally unstable accretion disk regulate disk evolution through angular-momentum transport and heating and provide an observational signature of gravitational instability (GI). We use global 3D simulations…
In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…
Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we…
We construct first a class of Moran fractals in R^d with countably many generators and non-stationary contraction rates; at each step n, the contractions depend on n-truncated sequences, and are related to asymptotic letter frequencies. In…
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…
Spiral density waves dominate several facets of accretion disc dynamics --- planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, their…
Spiral arms are the defining features of broad morphological classes of disc galaxies, but their nature and influence on galaxy evolution is still under debate. A key diagnostic for their nature is the spiral arm pattern speed: the radial…