Related papers: Some Additional Solutions of Conformal Turbulence
A new form of the well known Lin equation for the energy balance in isotropic turbulence is given which takes account of the filtered-partitioned transfer spectra which were used to resolve the scale paradox. It is argued that this new…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
Enstrophy, half the integral of the square of vorticity, plays a role in 2D turbulence theory analogous to that played by kinetic energy in the Kolmogorov theory of 3D turbulence. It is therefore interesting to obtain a description of the…
We give some new results related to the directional short-time Fourier transform (DSTFT) and extend them on the spaces $\mathcal K_{1}(\mathbb R^{n})$ and $\mathcal K_{1}({\mathbb R})\widehat{\otimes}\mathcal U(\mathbb C^n)$ and their…
Particle-laden turbulence involves complex interactions between the dispersed and continuous phases. Given that particles can exhibit a wide range of properties, such as varying density, size, and shape, their interplay with the flow can…
In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with…
We propose a new parametrization of 2D turbulence based on generalized thermodynamics and Brownian theory. Explicit relaxation equations are obtained that should be easily implementable in numerical simulations for three typical types of…
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little…
We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a…
A real-space representation of the current response of many-electron systems with possible applications to x-ray nonlinear spectroscopy and magnetic susceptibilities is developed. Closed expressions for the linear, quadratic and third-order…
We demonstrate the importance of relativistic corrections for the study of the stability of $(2+1)$-dimensional non-topological solitons with quartic self-interaction in the low-energy limit. This result is explained by the restoration of…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…
We survey a collection of recent results on center Lyapunov exponents of partially hyperbolic diffeomorphisms. We explain several ideas in simplified setups and formulate the general versions of results. We also pose some open questions.
By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy and attractor…
In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that…
Density functional theory (DFT) calculation has had huge success as a tool capable of predicting important physical and chemical properties of condensed matter systems. We calculate the electric dipole moment of a molecule by using the…