# LogLatt: A computational library for the calculus and flows on logarithmic lattices

@article{Campolina2020LogLattAC, title={LogLatt: A computational library for the calculus and flows on logarithmic lattices}, author={Ciro S. Campolina}, journal={arXiv: Computational Physics}, year={2020} }

We introduce LogLatt, an efficient MATLAB library for the calculus and operations between functions on multi-dimensional lattices of logarithmically distributed nodes in Fourier space. The computational applicabilities are available in one, two and three dimensions and include common differential operators, norms and functional products, which are local convolutions in Fourier space. All operations are encoded as MATLAB function handles, so their implementations result in elegant and intuitive…

## References

SHOWING 1-10 OF 13 REFERENCES

### Fluid dynamics on logarithmic lattices

- Mathematics
- 2020

Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc, are related to multi-scale structure and…

### Chaotic Blowup in the 3D Incompressible Euler Equations on a Logarithmic Lattice.

- MathematicsPhysical review letters
- 2018

This model clarifies the present controversy at the scales of existing DNS and provides the unambiguous evidence of the following transition to the blowup, explained as a chaotic attractor in a renormalized system.

### Turbulence: The Legacy of A. N. Kolmogorov

- Physics
- 1995

Preface 1. Introduction 2. Symmetries and conservation laws 3. Why a probabilistic description of turbulence? 4. Probabilistic tools: a survey 5. Two experimental laws of fully developed turbulence…

### Quantum mechanics: Non-relativistic theory,

- Physics
- 1958

The basic concepts of quantum mechanics Energy and momentum Schrodinger's equation Angular momentum Perturbation theory Spin The identity of particles The atom The theory of symmetry Polyatomic…

### Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space

- Mathematics
- 2016

A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a…

### The MATLAB ODE Suite

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 1997

This paper describes mathematical and software developments for a suite of programs for solving ordinary differential equations in MATLAB.

### Hamiltonian structure of the Sabra shell model of turbulence: Exact calculation of an anomalous scaling exponent

- Physics
- 1999

We show that the Sabra shell model of turbulence, which was introduced recently, displays a Hamiltonian structure for given values of the parameters. The requirement of scale independence of the flux…

### Continuous representation for shell models of turbulence

- Mathematics
- 2015

In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models…