Related papers: Unparticle signals with a few particles
Propagation of extremely short unipolar pulses of electromagnetic field ("videopulses") is considered in the framework of a model in which the material medium is represented by anharmonic oscillators (approximating bound electrons) with…
We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear-optical response. Size effects are removed by normalizing all nonlinearities to…
Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
Optical parametric amplification is a second-order nonlinear process whereby an optical signal is amplified by a pump via the generation of an idler field. It is the key ingredient of tunable sources of radiation that play an important role…
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
The problem of detecting new signals in the presence of an unknown background is ubiquitous in scientific discoveries and is especially prominent in the physical sciences. Most solutions proposed thus far to address the problem focus on…
In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability…
The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…
We propose a simple formula for multichannel resonant scattering with parameters related to physical resonant properties. It can be used to predict residue phase from other resonant parameters and describe the shape of scattering amplitudes…
The transmission of a wave through a randomly chosen `pile of plates' typically decreases exponentially with the number of plates, a phenomenon closely related to Anderson localisation. In apparent contradiction we construct disordered…
We compare the HEIDI models with the unparticle models. We show that the unparticle models are a limiting case of the HEIDI models. We discuss consistency conditions.
After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasi-particles in non-commutative supersymmetric gauge theories at finite temperature. In particular we discuss the…
We study one particle subspaces for two particles of different masses with ultra local interaction on a lattice of arbitrary dimension.