3,406 research outputs found
Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions
We present a new criterion for the weighted boundedness of
multiplier operators for Laguerre and Hermite expansions that arise from a
Laplace-Stieltjes transform. As a special case, we recover known results on
weighted estimates for Laguerre and Hermite fractional integrals with a unified
and simpler approach.Comment: 22 pages; new section added, corrected typos, new references adde
The dune size distribution and scaling relations of barchan dune fields
Barchan dunes emerge as a collective phenomena involving the generation of
thousands of them in so called barchan dune fields. By measuring the size and
position of dunes in Moroccan barchan dune fields, we find that these dunes
tend to distribute uniformly in space and follow an unique size distribution
function. We introduce an analyticalmean-field approach to show that this
empirical size distribution emerges from the interplay of dune collisions and
sand flux balance, the two simplest mechanisms for size selection. The
analytical model also predicts a scaling relation between the fundamental
macroscopic properties characterizing a dune field, namely the inter-dune
spacing and the first and second moments of the dune size distribution.Comment: 6 pages, 4 figures. Submitted for publicatio
Deep learning as closure for irreversible processes: A data-driven generalized Langevin equation
The ultimate goal of physics is finding a unique equation capable of
describing the evolution of any observable quantity in a self-consistent way.
Within the field of statistical physics, such an equation is known as the
generalized Langevin equation (GLE). Nevertheless, the formal and exact GLE is
not particularly useful, since it depends on the complete history of the
observable at hand, and on hidden degrees of freedom typically inaccessible
from a theoretical point of view. In this work, we propose the use of deep
neural networks as a new avenue for learning the intricacies of the unknowns
mentioned above. By using machine learning to eliminate the unknowns from GLEs,
our methodology outperforms previous approaches (in terms of efficiency and
robustness) where general fitting functions were postulated. Finally, our work
is tested against several prototypical examples, from a colloidal systems and
particle chains immersed in a thermal bath, to climatology and financial
models. In all cases, our methodology exhibits an excellent agreement with the
actual dynamics of the observables under consideration
- …