Model order reduction for stochastic dynamical systems with continuous symmetries

Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order reduction techniques and a large number of modes is typically necessary for an accurate solution. In this work, we introduce a new methodology for efficient order reduction of such systems by combining (i) the method of slices, a symmetry reduction tool, with (ii) any standard order reduction technique, resulting in efficient mixed symmetry-dimensionality reduction schemes. In particular, using the Dynamically Orthogonal (DO) equations in the second step, we obtain a novel nonlinear Symmetry-reduced Dynamically Orthogonal (SDO) scheme. We demonstrate the performance of the SDO scheme on stochastic solutions of the 1D Korteweg-de Vries and 2D Navier-Stokes equations.Comment: Minor revision

The first inherited retinal disease registry in Iran: Research protocol and results of a pilot study

Background: To describe the protocol for developing a national inherited retinal disease (IRD) registry in Iran and present its initial report. Methods: This community-based participatory research was approved by the Ministry of Health and Medical Education of Iran in 2016. To provide the minimum data set (MDS), several focus group meetings were held. The final MDS was handed over to an engineering team to develop a web-based software. In the pilot phase, the software was set up in two referral centers in Iran. Final IRD diagnosis was made based on clinical manifestations and genetic findings. Ultimately, patient registration was done based on all clinical and non-clinical manifestations. Results: Initially, a total of 151 data elements were approved with Delphi technique. The registry software went live at www.IRDReg.org based on DHIS2 open source license agreement since February 2016. So far, a total of 1001 patients have been registered with a mean age of 32.41±15.60 years (range, 3 months to 74 years). The majority of the registered patients had retinitis pigmentosa (42, 95 CI: 38.9 to 45). Genetic testing was done for approximately 20 of the registered individuals. Conclusion: Our study shows successful web-based software design and data collection as a proof of concept for the first IRD registry in Iran. Multicenter integration of the IRD registry in medical centers throughout the country is well underway as planned. These data will assist researchers to rapidly access information about the distribution and genetic patterns of this disease. © 2020 The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Control of linear instabilities by dynamically consistent order reduction on optimally time-dependent modes

Abstract Identification and control of transient instabilities in high-dimensional dynamical systems remain a challenge because transient (non-normal) growth cannot be accurately captured by reduced-order modal analysis. Eigenvalue-based methods classify systems as stable or unstable on the sole basis of the asymptotic behavior of perturbations and therefore fail to predict any short-term characteristics of disturbances, including transient growth. In this paper, we leverage the power of the optimally time-dependent (OTD) modes, a set of time-evolving, orthonormal modes that capture directions in phase space associated with transient and persistent instabilities, to formulate a control law capable of suppressing transient and asymptotic growth around any fixed point of the governing equations. The control law is derived from a reduced-order system resulting from projecting the evolving linearized dynamics onto the OTD modes and enforces that the instantaneous growth of perturbations in the OTD-reduced tangent space be nil. We apply the proposed reduced-order control algorithm to several infinite-dimensional systems, including fluid flows dominated by normal and non-normal instabilities, and demonstrate unequivocal superiority of OTD control over classical modal control

Particle size selection in capillary instability of locally heated coaxial fiber

Harnessing fluidic instabilities to produce structures with robust and regular properties has recently emerged as a new fabrication paradigm. This approach is exemplified in the work of Gumennik et al. [Nat. Commun. 4, 2216 (2103)], in which the authors fabricated silicon spheres by feeding a silicon-in-silica coaxial fiber into a flame. Following the localized melting of the silicon, a capillary instability of the silicon-silica interface induced the formation of uniform silicon spheres. Here we investigate the physical mechanisms at play in selecting the size of these particles, which was notably observed by Gumennik et al. to vary monotonically with the speed at which the fiber is fed into the flame. Using a simplified model derived from standard long-wavelength approximations, we show that linear stability analysis strikingly fails at predicting the selected particle size. Nonetheless, nonlinear simulations of the simplified model do recover the particle size observed in experiments, without any adjustable parameters. This result demonstrates that the formation of the silicon spheres in this system is an intrinsically nonlinear process that has little in common with the loss of stability of the underlying base flow solution