An integrable evolution equation for surface waves in deep water

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution.Comment: LaTex file, 16 pages, 4 figure

The theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in propagation of light beams through photore- fractive media is developed. Full one-dimensional analytical theory based on the Whitham modu- lation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is con¯rmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed

Hydrothermal Surface-Wave Instability and the Kuramoto-Sivashinsky Equation

We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient, and a basic nonlinear bulk velocity profile. In the limit of long-wavelength and large nondimensional surface tension, we show that hydrothermal surface-wave instabilities may give rise to disturbances governed by the Kuramoto-Sivashinsky equation. A possible connection to hot-wire experiments is also discussed.Comment: 11 pages, RevTex, no figure

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps.Comment: 8 pages, 3 figure

Modelling the impact of school reopening and contact tracing strategies on Covid-19 dynamics in different epidemiologic settings in Brazil

This study was funded by the Brazilian National Council for Scientific and Technological Development (CNPq) [grant number 402834/2020-8]. MEB received a technological and industrial scholarship from CNPq [grant number 315854/2020-0]. LSF received a master's scholarship from Coordination for the Improvement of Higher Education Personnel (CAPES) [finance code 001]. SP was supported by São Paulo Research Foundation (FAPESP) [grant number 2018/24037-4]. AMB received a technological and industrial scholarship from CNPq [grant number 402834/2020-8]. CF was supported by FAPESP [grant numbers 2019/26310-2 and 2017/26770-8]. MQMR received a postdoctoral scholarship from CAPES [grant number 305269/2020-8]. LMS received a technological and industrial scholarship from CNPq [grant number 315866/2020-9]. RSK has been supported by CNPq [grant number 312378/2019-0]. PIP has been supported by CNPq [grant number 313055/2020-3]. JAFD-F has been supported by CNPq productivity fellowship and the National Institutes for Science and Technology in Ecology, Evolution and Biodiversity Conservation (INCT-EEC), supported by MCTIC/CNPq [grant number 465610/2014-5] and Goiás Research Foundation (FAPEG) [grant number 201810267000023]. RAK has been supported by CNPq [grant number 311832/2017-2] and FAPESP [grant number 2016/01343-7]. CMT has been supported by CNPq productivity fellowship and the National Institute for Health Technology Assessment (IATS) [grant number 465518/2014-1].Peer reviewedPublisher PD

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation,without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.Comment: 7 figure

Model-based estimation of transmissibility and reinfection of SARS-CoV-2 P.1 variant

Acknowledgements We are grateful for the collaborative work of the reviewers and the entire group of the Observatório COVID-19 BR. In particular, we thank Verônica Coelho for critical inputs. We also thank the research funding agencies: the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brazil (Finance Code 001 to F.M.D.M., L.S.F. and T.P.P.), Conselho Nacional de Desenvolvimento Científico e Tecnológico—Brazil (grant number: 315854/2020-0 to M.E.B., 141698/2018-7 to R.L.P.S., 313055/2020-3 to P.I.P., 312559/2020-8 to M.A.S.M.V., 311832/2017-2 to R.A.K., 305703/2019-6 to A.A.M.S.) and Fundação de Amparo à Pesquisa do Estado de São Paulo—Brazil (grant number: 2019/26310-2 and 2017/26770-8 to C.F., 2018/26512-1 to O.C., 2018/24037-4 to S.P. and contract number: 2016/01343-7 to R.A.K.). The findings and conclusions in this article are those of the authors and do not necessarily represent the official position of the Centers of Disease Control and Prevention.Peer reviewe

Potential health and economic impacts of dexamethasone treatment for patients with COVID-19

Acknowledgements We thank all members of the COVID-19 International Modelling Consortium and their collaborative partners. This work was supported by the COVID-19 Research Response Fund, managed by the Medical Sciences Division, University of Oxford. L.J.W. is supported by the Li Ka Shing Foundation. R.A. acknowledges funding from the Bill and Melinda Gates Foundation (OPP1193472).Peer reviewedPublisher PD

An optimal Boussinesq model for shallow water wave-microstructure interaction

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