Topological localization in out-of-equilibrium dissipative systems

In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of principle that notions of topological protection, established in the context of electronic and mechanical systems, do indeed extend generically to processes that operate out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.Comment: 11 pages, 4 figures (SI: 8 pages 3 figures

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions

The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials.Comment: 21 pages, 7 figure

Uncertainty quantification Of performance and stability of high-speed axial compressors

Geometrical uncertainties in a compressor (due to manufacturing tolerance and/or in-service degradation) often result in flow asymmetry around the annulus of a compressor that jeopardises compressor stability and performance. Usually, sensitivity of compressor stability and performance for any parametric variation is arrived at by considering all blades to have same dimension. In reality, an inherent blade-to-blade variation causes the blades to have a probability distribution. These blades can be redistributed circumferentially resulting in adjacent passage areas between different blades to be completely random and hence the performance variation. Surrogate model is preferred for quantifying the effects of parametric variation on compressor stability and performance given its quick turnaround time vis-a-vis CFD and experiments. In this thesis, uncertainties for three test cases were considered: each representative of fans on military aircraft engines, fans on civil aircraft engines and a 1-stage transonic compressor used in industrial gas turbine. This research establishes a rule of thumb to arrange blades of differing dimensions around the compressor to eke out maximum performance and stability margin. The parameters tip gap and stagger angle represent manufacturing tolerance while in-service degradation was represented by leading edge damage. For both random tip gap variation (0.15% to 0.94% span) and random leading edge damage (4% to 18% chord), the compressor performance and stability boundaries were found to be best with a zigzag pattern of blade arrangement and worst with a sinusoidal pattern of arrangement. The converse was found to be true for blades having random stagger angle variation (± 2.25% change in nominal stagger angle). The best/worst arrangement of blades with differing dimensions was ascertained using a mix of CFD and travelling salesman (TSP) analogy. The TSP analogy is handy for determining the best arrangement when two or more parameters vary simultaneously. Generalised surrogate model was developed to accurately predict the performance of compressors undergoing random tip gap and stagger angle variation. Due to its robustness, the surrogate model was combined with Monte Carlo technique to gauge the impact of parametric variation on quantities of interest (QoI). The mean absolute percentage error between CFD and surrogate models of stagger angle and tip gap (for different QoI) were found to be less than 0.14% and 1.5% respectively. This de novo analysis considers only the aerodynamic effect from geometric variations while neglecting the associated aeroelastic effects. Detailed analyses based on past experience and physical reasoning were used to validate the numerical simulations.Open Acces

Design for quality manufacturability analysis for common assembly process

The globalization of market economy has precipitated a dramatic increase in competition necessitating the need for higher quality products at lower cost in shorter time periods. Shorter life cycles and proliferation of products has made companies integrate all the phases of manufacturing to bring about a superior design. Design for Quality Manufacturability (DFQM) provides a technique to invoke manufacturing and assembly considerations while designing a product. The DFQM architecture identifies factors consisting of several variables that are influenced by certain error catalysts to cause one or more specific defects. A methodology is suggested to identify and quantify these error catalysts to be able to estimate the quality of the design. Some of the assembly processes that are widely used are insertion, riveting, welding, fastening, press-fit, and snap-fit. A detailed study of each of these processes is done to analyze the techniques, capabilities, and limitations. Using the DFQM architecture defect classes and specific defects are identified and analyzed. A correlation matrix is formed to identify the processes that are associated with each specific defect. Cause-Effect analysis using Ishikawa diagrams provide a means of analyzing the characteristics of the relevant processes attributing to each specific defect. These characteristics are grouped to identify the error catalysts that influence the occurrence of the specific defect