1,267 research outputs found
Behavior of a Model Dynamical System with Applications to Weak Turbulence
We experimentally explore solutions to a model Hamiltonian dynamical system
derived in Colliander et al., 2012, to study frequency cascades in the cubic
defocusing nonlinear Schr\"odinger equation on the torus. Our results include a
statistical analysis of the evolution of data with localized amplitudes and
random phases, which supports the conjecture that energy cascades are a generic
phenomenon. We also identify stationary solutions, periodic solutions in an
associated problem and find experimental evidence of hyperbolic behavior. Many
of our results rely upon reframing the dynamical system using a hydrodynamic
formulation.Comment: 22 pages, 14 figure
Syrian Refugees and the Digital Passage to Europe: Smartphone Infrastructures and Affordances
This research examines the role of smartphones in refugees’ journeys. It traces the risks and possibilities afforded by smartphones for facilitating information, communication, and migration flows in the digital passage to Europe. For the Syrian and Iraqi refugee respondents in this France-based qualitative study, smartphones are lifelines, as important as water and food. They afford the planning, navigation, and documentation of journeys, enabling regular contact with family, friends, smugglers, and those who help them. However, refugees are simultaneously exposed to new forms of exploitation and surveillance with smartphones as migrations are financialised by smugglers and criminalized by European policies, and the digital passage is dependent on a contingent range of sociotechnical and material assemblages. Through an infrastructural lens, we capture the dialectical dynamics of opportunity and vulnerability, and the forms of resilience and solidarity, that arise as forced migration and digital connectivity coincide
Singularites in the Bousseneq equation and in the generalized KdV equation
In this paper, two kinds of the exact singular solutions are obtained by the
improved homogeneous balance (HB) method and a nonlinear transformation. The
two exact solutions show that special singular wave patterns exists in the
classical model of some nonlinear wave problems
Steady State Solutions of a Mass-Conserving Bistable Equation with a Saturating Flux
We consider a mass-conserving bistable equation with a saturating flux on an
interval. This is the quasilinear analogue of the Rubinstein-Steinberg
equation, suitable for description of order parameter conserving solid-solid
phase transitions in the case of large spatial gradients in the order
parameter. We discuss stationary solutions and investigate the change in
bifurcation diagrams as the mass constraint and the length of the interval are
varied.Comment: 26 pages, 14 figure
Machine Learning Can Predict the Timing and Size of Analog Earthquakes
Despite the growing spatiotemporal density of geophysical observations at subduction zones, predicting the timing and size of future earthquakes remains a challenge. Here we simulate multiple seismic cycles in a laboratory‐scale subduction zone. The model creates both partial and full margin ruptures, simulating magnitude M_w 6.2–8.3 earthquakes with a coefficient of variation in recurrence intervals of 0.5, similar to real subduction zones. We show that the common procedure of estimating the next earthquake size from slip‐deficit is unreliable. On the contrary, machine learning predicts well the timing and size of laboratory earthquakes by reconstructing and properly interpreting the spatiotemporally complex loading history of the system. These results promise substantial progress in real earthquake forecasting, as they suggest that the complex motion recorded by geodesists at subduction zones might be diagnostic of earthquake imminence
Ill-posedness of degenerate dispersive equations
In this article we provide numerical and analytical evidence that some
degenerate dispersive partial differential equations are ill-posed.
Specifically we study the K(2,2) equation and
the "degenerate Airy" equation . For K(2,2) our results are
computational in nature: we conduct a series of numerical simulations which
demonstrate that data which is very small in can be of unit size at a
fixed time which is independent of the data's size. For the degenerate Airy
equation, our results are fully rigorous: we prove the existence of a compactly
supported self-similar solution which, when combined with certain scaling
invariances, implies ill-posedness (also in )
Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2d K\"ahler-Ricci Soliton
We consider some aspects of the curved BPS domain walls and their
supersymmetric Lorentz invariant vacua of the four dimensional N=1 supergravity
coupled to a chiral multiplet. In particular, the scalar manifold can be viewed
as a two dimensional K\"ahler-Ricci soliton generating a one-parameter family
of K\"ahler manifolds evolved with respect to a real parameter, . This
implies that all quantities describing the walls and their vacua indeed evolve
with respect to . Then, the analysis on the eigenvalues of the first
order expansion of BPS equations shows that in general the vacua related to the
field theory on a curved background do not always exist. In order to verify
their existence in the ultraviolet or infrared regions one has to perform the
renormalization group analysis. Finally, we discuss in detail a simple model
with a linear superpotential and the K\"ahler-Ricci soliton considered as the
Rosenau solution.Comment: 19 pages, no figures. Typos corrected. Published versio
Symmetries of a class of nonlinear fourth order partial differential equations
In this paper we study symmetry reductions of a class of nonlinear fourth
order partial differential equations \be u_{tt} = \left(\kappa u + \gamma
u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2,
\ee where , , , and are constants. This
equation may be thought of as a fourth order analogue of a generalization of
the Camassa-Holm equation, about which there has been considerable recent
interest. Further equation (1) is a ``Boussinesq-type'' equation which arises
as a model of vibrations of an anharmonic mass-spring chain and admits both
``compacton'' and conventional solitons. A catalogue of symmetry reductions for
equation (1) is obtained using the classical Lie method and the nonclassical
method due to Bluman and Cole. In particular we obtain several reductions using
the nonclassical method which are no} obtainable through the classical method
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