Related papers: Wave Arithmetic: A Smooth Integral Representation …
In this note I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics it plays a very important role in…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial conditions pose significant challenges, often leading to a…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Set theory brought revolution to philosophy of mathematics and it can bring revolution to philosophy of physics too. All that stands in the way is the intuition that sets of physical objects cannot themselves be physical objects, which…
High-order wave-making theories are becoming available but are limited to certain ranges of waves and wavemaker types in their applicability. Alternatively, machine learning can be considered to find nonlinear functional relationships.…
Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for…
We report a numerical evolution of axisymmetric Brill waves. The numerical algorithm has new features, including (i) a method for keeping the metric regular on the axis and (ii) the use of coordinates that bring spatial infinity to the edge…
Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems.…
We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly…
Clarithmetics are number theories based on computability logic (see http://www.csc.villanova.edu/~japaridz/CL/ ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Gravitational waves are produced by orbiting massive binary objects, such as black holes and neutron stars, and propagate as ripples in the very fabric of spacetime. As the waves carry off orbital energy, the two bodies spiral into each…
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
We present, in the same vein as in [20] and [21], some results of the so-called "Smooth (or $\mathcal{C}^\infty$) Commutative Algebra", a version of Commutative Algebra of $\mathcal{C}^{\infty}-$rings instead of ordinary commutative unital…