18,254 research outputs found
Quasi-periodic solutions of completely resonant forced wave equations
We prove existence of quasi-periodic solutions with two frequencies of
completely resonant, periodically forced nonlinear wave equations with periodic
spatial boundary conditions. We consider both the cases the forcing frequency
is: (Case A) a rational number and (Case B) an irrational number.Comment: 25 pages, 1 figur
The LHCf experiment: present status and physics results
The main aim of the LHCf experiment is to provide precise measurements of the
production spectra relative to neutral particle produced by high energy
proton-ion collisions in the very forward region. This information is necessary
in order to test and tune hadronic interaction models used by ground-based
cosmic rays experiments. In order to reach this goal, LHCf makes use of two
small sampling calorimeters installed in the LHC tunnel at m from
IP1, able to detect neutral particles having pseudo-rapidity . In
this paper we will present the current status of the LHCf experiment, regarding
in particular the first analysis results from data taking relative to p-p
collisions at 13 TeV
Periodic solutions of nonlinear wave equations with general nonlinearities
We prove the existence of small amplitude periodic solutions, with strongly
irrational frequency \om close to one, for completely resonant nonlinear
wave equations. We provide multiplicity results for both monotone and
nonmonotone nonlinearities. For \om close to one we prove the existence of
a large number N_\om of 2 \pi \slash \om -periodic in time solutions : N_\om \to + \infty as \om \to 1 . The minimal
period of the -th solution is proved to be 2 \pi \slash n \om . The
proofs are based on a Lyapunov-Schmidt reduction and variational arguments.Comment: 29 page
Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential
We prove the existence of quasi-periodic solutions for wave equations with a
multiplicative potential on T^d, d \geq 1, and finitely differentiable
nonlinearities, quasi-periodically forced in time. The only external parameter
is the length of the frequency vector. The solutions have Sobolev regularity
both in time and space. The proof is based on a Nash-Moser iterative scheme as
in [5]. The key tame estimates for the inverse linearized operators are
obtained by a multiscale inductive argument, which is more difficult than for
NLS due to the dispersion relation of the wave equation. We prove the
"separation properties" of the small divisors assuming weaker non-resonance
conditions than in [11]
Temperature estimation and slip-line force analytical models for the estimation of the radial forming force in the RARR process of flat rings
open2noIn this study, a mathematical model for the prediction of the temperature evolution in the ring during the radial-axial ring rolling process is developed and used, together with the authors’ previous results, to determine analytically the flow stress of the material during process. These results, combined with Hill's slip-line field solution adapted to the RARR process, allow a fast and reasonably precise calculation of the radial forming force, a key parameter at the preliminary stage of the process design. The approach is validated by applying the proposed model to a case available in the literature and comparing the analytical results with those of the laboratory experiment and FEM simulation. Following the successful comparison, the models were applied to a large variety of flat rings, comparing analytical predictions with the results of FEM simulations. The accuracy of the analytical calculation and the reliability of the proposed models, for different ring configuration and process parameters, are presented and discussed.embargoed_20190501Quagliato, Luca; Berti, GuidoQuagliato, Luca; Berti, Guid
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