Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states

We show that the nearest neighbour entanglement in a mixture of ground and first excited states - the subjacent state - of the J1-J2 Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to introduction of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point.Comment: 14 pages, 9 figure

Theory and simulation of electrokinetic fluctuations in electrolyte solutions at the mesoscale

Electrolyte solutions play an important role in energy storage devices, whose performance highly relies on the electrokinetic processes at sub-micron scales.\ Although fluctuations and stochastic features become more critical at small scales, the long-range Coulomb interactions pose a particular challenge for both theoretical analysis and simulation of fluid systems with fluctuating hydrodynamic and electrostatic interactions. Here, we present a theoretical framework based on the Landau-Lifshitz theory to derive closed-form expressions of fluctuation correlations in electrolyte solutions, indicating significantly different decorrelation processes of ionic concentration fluctuations from hydrodynamic fluctuations, which provides insights for understanding transport phenomena of coupled fluctuating hydrodynamics and electrokinetics. Furthermore, we simulate fluctuating electrokinetic systems using both molecular dynamics (MD) with explicit ions and mesoscopic charged dissipative particle dynamics (cDPD) with semi-implicit ions, from which we identify that the spatial probability density functions of local charge density follow Gamma distribution at sub-nanometer scale (i.e., 0.3 nm) and converge to Gaussian distribution above nanometer scales (i.e., 1.55 nm), indicating the existence of a lower limit of length scale for mesoscale models using Gaussian fluctuations. The temporal correlation functions of both hydrodynamic and electrokinetic fluctuations are computed from all-atom MD and mesoscale cDPD simulations, showing a good agreement with the theoretical predictions based on the linearized fluctuating hydrodynamics theory.Comment: 19 pages, 6 figure

Thermochemistry of Calcium-Magnesium-Aluminum-Silicate (CMAS) and Components of Advanced Thermal and Environmental Barrier Coating Systems

There is increasing interest in the degradation mechanism studies of thermal and environmental barrier coatings (TEBCs) of gas turbines by molten CaO-MgO-Al(exp. 2)O(exp. 3)-SiO(exp. 2) CMAS). CMAS minerals are usually referred as silicon-containing sand dust and volcano ash materials that are carried by the intake air into gas turbines, e.g. in aircraft engines, and their deposits often react at high temperatures (greater than 1200 degrees C) with the engine turbine coating systems and components. The high temperature reactions causes degradation and accelerated failure of the static and rotating components of the turbine engines. We discuss some results of the reactions between the CMAS and Rare-Earth (RE = Y, Yb, Dy, Gd, Nd and Sm) - oxide stabilized ZrO(exp. 2) or HfO(exp. 2) systems, and the stability of the resulting oxides and silicates. Plasma sprayed hollow tube samples (outside diameter = 4.7 mm, wall thickness = 0.76 mm and = 26 mm height) were half filled with CMAS powder, wrapped and sealed with platinum foil, and heat treated at 1310 degrees C for 5h. Samples were characterized by differential scanning calorimetry (DSC), X-ray diffraction, and cross-section electron microscopy analysis and energy dispersive X-ray spectroscopy. It was found that CMAS penetrated the samples at the grain boundaries and dissolved the TEBC materials to form silicate phases containing the rare-earth elements. Furthermore, it was found that apatite crystalline phases were formed in the samples with total rare-earth content higher than 12 mol% in the reaction zone for the ZrO(exp. 2) system. In general, samples with the nominal compositions (30YSZ), HfO(exp. 2)-7Dy(exp. 2)O(exp. 2) and ZrO(exp. 2)-9.5Y(exp. 2)O(exp. 3)-2.25Gd(exp. 2)O(exp. 3)-2.25Yb(exp. 2)O(exp. 3) exhibited lower reactivity or more resistance to CMAS than the other coating compositions of this work

Comparative Study of Vibration Condition Indicators for Detecting Cracks in Spur Gears

This paper reports the results of an empirical study on the tooth breakage failure mode in spur gears. Of four dominant gear failure modes (breakage, wear, pitting, and scoring), tooth breakage is the most precipitous and often leads to catastrophic failures. The cracks were initiated using a fatigue tester and a custom-designed single-tooth bending fixture to simulate over-load conditions, instead of traditional notching using wire electrical discharge machining (EDM). The cracks were then propagated on a dynamometer. The ground truth of damage level during crack propagation was monitored with crack-propagation sensors. Ten crack propagations have been performed to compare the existing condition indicators (CIs) with respect to their: ability to detect a crack, ability to assess the damage, and sensitivity to sensor placement. Of more than thirty computed CIs, this paper compares five commonly used: raw RMS, FM0, NA4, raw kurtosis, and NP4. The performance of combined CIs was also investigated, using linear, logistic, and boosted regression trees based feature fusion

An interactive geometry modeling and parametric design platform for isogeometric analysis

In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples—an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA

Optimizing Gas-Turbine Operation using Finite-Element CFD Modeling

Gas turbine engines are generally optimized to operate at nearly a fixed speed with fixed blade geometries for the design operating condition. The performance of gas turbine reduces when operated at different operating condition. In this work, we present a parametric study to optimize gas-turbine performance under off-design conditions by articulating the rotor blades in both clockwise and counterclockwise directions. Articulating the pitch angle of turbine blades in coordination with adjustable nozzle vanes can improve performance by maintaining flow incidence angles within the optimum range at certain off-design conditions. To observe the effect of rotor pitching on the performance of the gas turbine, a computational fluid dynamics (CFD) study is performed using the finite element formulation for compressible flows with moving domain. Results obtained from the CFD simulation for different rotor pitch angles are presented in this paper

Experimental Analysis and Material Characterization of Ultra High Temperature Composites

Proceedings of ASME Turbo Expo 2021 Turbomachinery Technical Conference and Exposition GT2021Ultra high temperature ceramic (UHTC) materials have attracted attention for hypersonic applications. Currently there is significant interest in possible gas turbine engine applications of UHTC composites as well. However, many of these materials, such as hafnium carbide, zirconium carbide, and zirconium diboride, have significant oxidation resistance and toughness limitations. In addition, these materials are very difficult to manufacture because of their high melting points. In many cases, SiC powder is incorporated into UHTCs to aid in processing and to enhance fracture toughness. This can also improve the materials’ oxidation resistance at moderately high temperatures due to a crack-healing borosilicate phase. ZrB₂-SiC composites show very good oxidation resistance up to 1700 °C, due to the formation of SiO₂ and ZrO₂ scales in numerous prior studies. While this may limit its application to hypersonic applications (due to reduced thermal conductivity and oxidation resistance at higher temperatures), these UHTC-SiC composites may find applications in turbomachinery, as either stand-alone parts or as a component in a multi-layer system.This research was supported in part by an appointment to the Postdoctoral Research Participation Program at the U.S. Army Research Laboratory administered by the Oak Ridge Associated Universities through an interagency agreement between the U.S. Department of Energy and DEVCOM ARL. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-16-2-0008. The first author would like to acknowledge the support of DoD Laboratory University Collaborative Initiative (LUCI) Fellowship [2016-2019]. The UHTC specimen fabrication via Spark Plasma Sintering processing was done at UCSD by UCSD and DEVCOM ARL. The ablation experimental testing was conducted at DEVCOM ARL. The microstructure analysis and characterization were performed at NPS.W911NF-16-2-000

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand, a mixture of calcia, magnesia, alumina, and silicate, known as CMAS, is characterized by its high viscosity, density, and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics (mDPD) simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a coarse parametric ordinary differential equation (ODE) that captures the spreading radius behavior of the CMAS droplets. The ODE parameters are then identified based on the Physics-Informed Neural Network (PINN) framework. Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modeling and state-of-the-art machine learning techniques

c=1 Matrix Models: Equivalences and Open-Closed String Duality

We give an explicit demonstration of the equivalence between the Normal Matrix Model (NMM) of c=1 string theory at selfdual radius and the Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic loop expectation values in the NMM to condensates of the closed string tachyon, and discuss the implications for open-closed duality. As in c<1, the Kontsevich-Miwa transform between the parameters of the two theories appears to encode open-closed string duality, though our results also exhibit some interesting differences with the c<1 case. We also briefly comment on two different ways in which the Kontsevich model originates.Comment: 27 pages, latex, 1 figure, typos, discussion added, acknowledgements update