Structural relaxation in Ag-Ni nanoparticles: Atomistic modeling away from equilibrium

The out-of-equilibrium structural relaxation of Ag-Ni nanoparticles containing about 1000--3000 atoms was investigated computationally by means of molecular dynamics trajectories in which the temperature is decreased gradually over hundreds of nanoseconds. At low silver concentration of 10--30\%, the evolution of chemical ordering in Ni$_{\rm core}$Ag$_{\rm shell}$ nanoparticles with different surface arrangements is found to proceed spontaneously and induce some rounding of the nickel core and its partial recristallization. Fast cooling of an initially hot metal vapor mixture was also considered, and it is shown to disfavor silver aggregation at the surface. Silver impurities are also occasionally produced but remain rare events under the conditions of our simulations.

Rare roll event modeling of unmanned catamaran

Статья посвящена вопросу моделирования редких событий, которые возникают при качке катамарана. Система управления автономного катамарана должна уметь распознавать нежелательные ситуации, которые могут привести к осуществлению редких событий. В данной статье приводится несколько методов, позволяющих проводить моделирование редких событий и делать оценку риска возникновения редкого события. Методы основываются на теории больших уклонений. Первый метод позволяет оценить возможные «ожидаемые потери» при достижении редкого события путём оценки скорости убывания вероятности компонентов вектора состояния в редком состоянии. Оценка осуществляется путём расчёта квазипотенциалов из аттрактора до порогового значения состояния. Второй метод позволяет оценить вероятность движения вдоль наиболее вероятной траектории к редкому событию. Оценка осуществляется путём сравнения вектора состояния с состояниями на наиболее вероятной траектории к редкому событию. Точность оценок зависит от вектора состояния. Приводится сравнение с результатами, полученными с помощью метода Монте-Карло. Указанные методы могут быть использованы для создания систем супервизорного управления и систем поддержки принятия решений при оценке рискованности совершения морских переходов. The article is devoted to the issue of modeling rare events that occur when a catamaran is pitching. The control system of an autonomous catamaran should be able to recognize undesirable situations that can lead to the rare events. This article provides several methods for modeling rare events and making estimation of risk of a rare event occurrence. The methods are based on the large deviations theory for dynamical systems. The first method allows to estimate possible losses via calculation of the probability decreasing rate of the state vector components in a rare state. The estimation is carried out by calculating the quasipotential from the state close to the attractor to the threshold state. The second method allows to estimate the probability of moving along the most likely trajectory to a rare event. The evaluation is carried out by comparing the studied state vector with the states on the most likely trajectory. The accuracy of the estimates depends on the studied state vector. A comparison with the results obtained using the Monte Carlo method. These methods can be used to create supervisory control systems and decision support systems when assessing the riskiness of sea navigation.

On the ROC Area of Ensemble Forecasts for Rare Events

The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g. probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g. precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known bi-normal fitting model, we discuss a new approach which embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.

Collapse of transitional wall turbulence captured using a rare events algorithm

This text presents one of the first successful applications of a rare events sampling method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow, and their probability and rate of occurrence are systematically computed using adaptive multilevel splitting (AMS). The AMS computations are performed in a system of size $L_x\times L_z=24\times 18$ at Reynolds number $R=370$ with an acceleration by a factor ${O}(10)$ with respect to direct numerical simulations (DNS) and in a system of size $L_x\times L_z=36\times 27$ at Reynolds number $R=377$ with an acceleration by a factor ${O}(10^3)$ . The AMS results are validated by a comparison with DNS in the smaller system. Visualisations indicate that turbulence collapses because the self-sustaining process of turbulence fails locally. The streamwise vortices decay first in streamwise elongated holes, leaving streamwise invariant streamwise velocity tubes that experience viscous decay. These holes then extend in the spanwise direction. The examination of more than a thousand trajectories in the $(E_{k,x}=\int u_x^2/2\,\textrm {d}^3\boldsymbol {x},E_{k,y-z}=\int (u_y^2/2+u_z^2/2)\,\textrm {d}^3\boldsymbol {x})$ plane in the smaller system confirms the faster decay of streamwise vortices and shows concentration of trajectories. This hints at an instanton phenomenology in the large size limit. The computation of turning point states, beyond which laminarisation is certain, confirms the hole formation scenario and shows that it is more pronounced in larger systems. Finally, the examination of non-reactive trajectories indicates that both the vortices and the streaks reform concomitantly when the laminar holes close.