At equilibrium, Bloch walls are chiral interfaces between domains with different magnetization. Far from equilibrium, a set of forced oscillators can exhibit walls between states with different phases. In this Letter, we show that when these walls become chiral, they move with a velocity simply related to their chirality. This surprising behavior is a straightforward consequence of nonvariational effects, which are typical of nonequilibrium systems.PACS numbers: 47.10.+g, 05.45.+b, 47.20.Ky Domain walls exhibit phase transitions, where Ising walls become Bloch walls,' and which have been related to spontaneous breaking of chirality, 2,3 in the frame of an anisotropic X-Y model. In this Letter, we investigate the nonequilibrium analog of these transitions. Namely, we consider the parametric forcing of an assembly of self-oscillators. In such a system, "phase anisotropy," induced by the forcing, provides a natural counterpart to crystalline anisotropy which allows the existence of walls. We show that spontaneous breaking of chirality is accompanied by the motion of chiral interfaces. A simple analysis allows us to describe this behavior. Since this motion is due to nonvariational effects, it is generic to nonequilibrium systems. The occurrence of such effects has been recently emphasized, 4 " 8 and here is another manifestation of these phenomena. In conclusion, we suggest an experiment where these phenomena are likely to be observed.We consider a one-dimensional system which undergoes a spatially homogeneous Hopf bifurcation, 9 with temporal frequency coo. Such a system can be seen as a continuous assembly of oscillators, which auto-oscillate above the Hopf bifurcation threshold. Now, we parametrically force this system at twice its natural frequency too. Let A be the complex order parameter which measures the amplitude of oscillations. It is assumed to vary slowly in space and time and obeys the following Ginzburg-Landau equation:where p measures the distance from the oscillatory instability threshold, v is the detuning parameter, V stands for d/dx, and y > 0 is the forcing amplitude.When the real parameters v, a, and j3 vanish, Eq. (1) can be cast into a variational form:bt 8Awhere 7 -J {-p CY 2 + v 2 ) + \vx\ 2 + |vr| 2 + HX 2 +Y 2 ) 2 -r (X 2 -Y 2 )}dx and A =X + iY. The quantity J turns out to be the free energy of the X-Y model in the presence of weak anisotropy whose amplitude is controlled by 7. In this limit, Eq.(1) exhibits spontaneous breaking of chirality. 2 Namely, Eq. (2) possesses stationary kinklike solutions 1,10 which connect stable homogeneous solutions (X=± VAI + 7, F=0). They read X I = ±Jp + ytanh{[{(p + y)] {/2 x}, r,=0, A-fl = ±v^T7tanh(V27x), Y B -±
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We describe a turbulent state characterized by the presence of topological defects. This "topological turbulence" is likely to be experimentally observed in nonequilibrium systems.
Significance This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the United States. Results show high variation in accuracy between and within stand-alone models and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public-health action.
Brief Reports are short papers which report on completed research which, while meeting the usual Physical Review standards of scientific quality, does not warrant a regular article (A. ddenda to papers previously published in the Physical Review by the same authors are included in Brief Reports )A. Brief Report may be no longer than 3g printed pages and must be accompanied by an abstract. The same publication schedule as for regular articles is followed, and page proofs are sent to authors We study some statistical properties of a turbulent state described by a generalized Ginzburg-Landau equation and characterized by topological defects.
Since 2013, the Centers for Disease Control and Prevention (CDC) has hosted an annual influenza season forecasting challenge. The 2015–2016 challenge consisted of weekly probabilistic forecasts of multiple targets, including fourteen models submitted by eleven teams. Forecast skill was evaluated using a modified logarithmic score. We averaged submitted forecasts into a mean ensemble model and compared them against predictions based on historical trends. Forecast skill was highest for seasonal peak intensity and short-term forecasts, while forecast skill for timing of season onset and peak week was generally low. Higher forecast skill was associated with team participation in previous influenza forecasting challenges and utilization of ensemble forecasting techniques. The mean ensemble consistently performed well and outperformed historical trend predictions. CDC and contributing teams will continue to advance influenza forecasting and work to improve the accuracy and reliability of forecasts to facilitate increased incorporation into public health response efforts.
The defects of a system where hexagons and rolls are both stable solutions are considered. On the basis of topological arguments we show that the unstable phase is present in the core of the defects. This means that a roll is present in the penta-hepta defect of hexagons and that a hexagon is found in the core of a grain boundary connecting rolls with different orientations. These results are verified in an experiment of thermal convection under non-Boussinesq conditions. PACS numbers: 47.20. Bp, 47.25.Qv Defects play an important role in the dynamics of pattern-forming systems. Specifically, dislocations and grain boundaries in convective patterns of rolls, and spirals and centered defects in chemical reactions, have been the object of several studies. ! However, the structure of defects has not been carefully analyzed in systems where two different symmetries coexist. This is a very important case that appears very often in nature, a typical example being the transition between hexagons and rolls in thermal convection. The competition between patterns associated with different symmetries has recently been discussed on the basis of general arguments. 2 The purpose of this Letter is to study defect properties when hexagons and rolls are stable solutions in a nonequilibrium pattern-forming system.The competition between hexagons and rolls can be described by means of three coupled Ginzburg-Landau equations (GLH), which determine the behavior of the three complex amplitudes A t of the sets of rolls describing the hexagonal structure. Each of them makes an angle of 2;r/3 with each of the others. A qualitative description of the nature of the cores of the various defects which may be observed in this problem can be deduced 3 from an elementary study of the following sixdimensional dynamical system, obtained from GLH, in the limit of homogeneous patterns: 4 d
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