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At least 73 records · Page 4

Smallest matrix black hole model in the classical limit

We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2×2 traceless hermitian matrices with a commutator squared potential and an SU(2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an SO(2) angular momentum is tuned to a critical value. Finally, we compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

Unified continuum damage model for matrix cracking in composite rotor blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic load.

36 MATERIALS SCIENCE↗

Development of a novel type of hybrid non-symmetric flexure hinges

A novel type of hybrid non-symmetric flexure hinges (NSFHs) is developed for higher motion precision in this paper, then the finite beam based matrix modeling (FBMM) method is employed to describe elastic deformation behaviors, model compliance matrix, and define non-dimensional precision factors of the hybrid NSFHs. Influences of the dimensional parameters on the dominant compliances and motion accuracies of the NSFHs are analytically investigated based on the FBMM models, while an asymmetry ratio is introduced and its influences on performances of the NSFHs are well revealed. Moreover, making comparisons of the main performances between the proposed NSFHs and symmetric flexure hinges, the obtained results indicate that the hybrid NSFHs can greatly improve the motion accuracy and suppress the adverse inherent motions. Finally, performances of the NSFHs and modeling accuracies are investigated by experimental tests, and making comparison with other flexure hinges.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗

Shell model nuclear matrix elements for competing mechanisms contributing to double beta decay

Recent progress in the shell model approach to the nuclear matrix elements for the double beta decay process are presented. This includes nuclear matrix elements for competing mechanisms to neutrionless double beta decay, a comparison between closure and non-closure approximation for {sup 48}Ca, and an updated shell model analysis of nuclear matrix elements for the double beta decay of {sup 136}Xe.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Impact of Limited Degree of Freedom Drag Coefficients on a Floating Offshore Wind Turbine Simulation

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

17 WIND ENERGY↗

Towards an “$\mathrm{AdS}_1$/$\mathrm{CFT}_0$” correspondence from the $\mathrm{D}$(-1)/$\mathrm{D}$7 system?

We argue that a type IIB Euclidean supergravity solution of the form $\mathbb{R}$ x S 1 x $\mathbb{T}$ 8 with imaginary self-dual F 1 flux through $\mathbb{R}$ x S 1 belongs to the chain of AdS d x S d x $\mathbb{T}$ 10-2d vacua with (imaginary) self-dual Fd flux, where d ≤ 5. Such vacua come from the near-horizon of D(d - 2)/D(8 - d) branes and are supersymmetric for odd values of d. For d = 1 we speculate that the hallmark of conformal symmetry for the matrix model dual is a vanishing free energy. The matrix dual was recently constructed by [1] by adding matrix interactions coming from strings stretching between the D(-1) and D7 branes to the IKKT matrix model. We find that the corresponding supergravity solution indeed has vanishing on-shell action. Specific F 5 fluxes need to be switched on as a consequence of (a T-dual version of) the Hanany-Witten effect.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved semiclassical model for real-time evaporation of matrix black holes

In this paper, we study real-time classical matrix mechanics of a simplified 2 × 2 matrix model inspired by the black hole evaporation problem. This is a step towards making a quantitative model of real-time evaporation of a black hole, which is realized as a bound state of D0-branes in string theory. The model we study is the reduction of Yang–Mills in 2 + 1 dimension to 0 + 1 dimensions, which has been corrected with an additional potential that can be interpreted as a zero-point energy for fermions. Our goal is to understand the lifetime of such a classical bound state object in the classical regime. To do so, we pay particular attention to when D-particles separate to check that the “off-diagonal modes” of the matrices become adiabatic and use that information to improve on existing models of evaporation. It turns out that the naive expectation value of the lifetime with the fermionic correction is infinite. This is a logarithmic divergence that arises from very large excursions in the separation between the branes near the threshold for classical evaporation. The adiabatic behavior lets us get some analytic control of the dynamics in this regime to get this estimate. This divergence is cutoff in the quantum theory due to quantization of the adiabatic parameter, resulting in a long lifetime of the bound state, with a parametric dependence of order log(1/ℏ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fuel Matrix Degradation Model Development Update: Alloy Corrosion Rates and Hydrogen Generation

This work is being performed as part of the DOE NE Spent Fuel and Waste Science and Technology Campaign, Argillite and Crystalline Rock R&D work packages: SF-19AN01030101 and SF-19AN01030201. This document meets the milestone M4SF-19AN010301013 for Argillite R&D and the milestone M4SF-19AN010302013 for Crystalline R&D. The fuel matrix degradation (FMD) model calculates the degradation rate of spent UO2 fuel based on fundamental electrochemical theory and thermodynamics. The model provides the quantitative basis for radionuclide source term predictions in the generic disposal system analysis (GDSA) performance assessment (PA) model. The FMD model has been implemented in a manner that facilitates its integration with the GDSA-PA code and a preliminary, integrated FMD-GDSA model has been successfully tested (Jerden et al., 2017). The specific focus of on-going work is to accurately and quantitatively represent the generation of H2 in a breached waste package and its effect on the spent fuel degradation rate so that this key process can be accurately represented in PA models. It has been shown experimentally that millimolar concentrations of dissolved H2 in contact with spent fuel will inhibit oxidative dissolution and decrease the fuel degradation rates by as much as three orders of magnitude (e.g., Röllin et al., 2001, Ollila, 2008). This will lead to a significant decrease in the radionuclide source term values used in repository PA models. Sensitivity studies using the FMD model have shown that the dissolved H2 concentration is the dominant environmental variable affecting the UO2 spent fuel dissolution rate as long as a source of H2 persists in the breached waste package (Jerden et al., 2015). Therefore, on-going experimental and modeling efforts focus on H2 production, accumulation and interfacial reactions within a breached waste package. The anoxic corrosion of metallic engineering materials within a breached waste package will be the main source of H2 in crystalline and argillite rock repository systems. The most important H2-producing alloys present within a waste package include stainless steel, carbon steel, and aluminum alloys and the Zircaloy fuel cladding. A steel corrosion module was added to the FMD model to account for these H2 sources and couple the H2 generation rate with fuel degradation processes (Jerden et al., 2017). As discussed below, there is a need for experimental data from electrochemical corrosion tests to quantify the H2 generation rates due to the corrosion of these waste package alloys as a function of key environmental variables (Eh, pH, groundwater chemistry). This report presents results from series of electrochemical corrosion tests with materials present in waste packages that provide information needed to parameterize and validate the FMD model. The alloys tested include 316L stainless steel (316SS), AISI 4320 carbon steel (C-steel) and Zircaloy-4 fuel cladding (unirradiated). Potentiodynamic polarization and potentiostatic polarization tests were performed in buffer solutions at pH 4, 7 and 10 with NaCl concentrations of 0, 4 and 100 millimolar (mM). The potentiostatic tests were performed at voltages varying from 0.5 volts down to -0.66 volts, vs the standard hydrogen electrode (SHE), and all tests were performed at laboratory ambient temperatures (~22 °C). The corrosion rates measured during the electrochemical tests were used as direct input to a new FMD/in-package chemistry model that is being developed to provide accurate long-term spent fuel degradation rates as chemical conditions (Eh, pH, speciation) evolve within a breached waste package. This new model was developed by coupling the FMD model with the reactive transport code X1t, which is a module within the Geochemist’s Workbench (GWB) reaction path modeling code (Jerden et al., 2019). The reactive transport model consists of a 1D domain discretized with 21 reaction diffusion cells and includes a single waste packag

Jerden, James↗

Topological order in matrix Ising models

We study a family of models for an N_1 \times N_2 N 1 × N 2 matrix worth of Ising spins S_{aB} S a B . In the large N_i N i limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) O ( N 1 , ℤ ) × O ( N 2 , ℤ ) symmetry. The models can undergo topological large N N phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} S a B becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Loop equation and exact soft anomalous dimension in $ \mathcal{N} $ = 4 super Yang-Mills

BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in $ \mathcal{N} $ = 4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N, and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W-bosons in the Coulomb branch.

't Hooftand Polyakov loops↗

Real-time monitoring of trace noble gases using laser-induced breakdown spectroscopy—An investigation of the impact of bulk gas on plasma properties and sensitivity

The impact of Ar and He bulk gases on laser-induced breakdown spectroscopy (LIBS) real-time monitoring of trace Xe and Kr was assessed. LIBS is being developed as a monitoring tool for measuring noble gas transport in molten salt systems, in which traditional sensors may face challenges associated with radiation, corrosive materials, and/or mixed phases. The plasma temperature and electron densities of LIBS plasmas were measured in both static and various flowing Ar and He streams (0–5 L min −1 ). The use of an Ar bulk gas resulted in higher plasma temperature, greater electron densities by an order of magnitude, and extended plasma lifetime compared with when He bulk gas was used. Gas flow rate was found to have little impact on plasma temperature; however, its effect on electron density was significant, indicating the need to consider flow rate–specific models. Matrix effects on emission peaks were reported for both bulk gases. Due to these matrix effects, multivariate models were developed for Xe and Kr ranging from 0 to 700 ppm in both bulk gases. Although the predictive behavior was similar (root mean square error of prediction ranging from 11.1 to 20.6 ppm), the limits of detection were superior in He (Xe: 22.9 ppm, Kr: 30.4 ppm). Furthermore, these models were employed in demonstrative real-time tests (>1 h), which showed strong predictive precision (relative standard deviation <5 %) regardless of the bulk gas. Ultimately, this study provides a guide for the considerations required when developing gaseous LIBS models for real-time monitoring.

Gas flow effects↗

Recent progress in molecular engineering to tailor organic–inorganic interfaces in composite membranes

Organic-inorganic composite membranes are of great interest in modern water treatment processes because they offer potentially superior separation efficiency and advanced funtionality by integrating the properties of polymers and inorganics. The biggest challenge in the fabrication and applications of organic-inorganic composite membranes is the incompatibility of organic-inorganic interfaces. In this minireview, we summarize the most recent advances in molecular engineering to tailor the properties of interfaces in composite membranes. Three typical models (i.e. mixed matrix model, interface composite model, and dual-layer composite model) are presented to demonstrate how to regulate these interfaces via molecular engineering and how the interfacial properties ultimately affect the membrane performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

2D gravity↗

Random matrix approach to three-dimensional QCD with a Chern-Simons term

We propose a random matrix theory for QCD in three dimensions with a Chern-Simons term at level k which spontaneously breaks the flavor symmetry according to U(2Nf) → U(Nf+k)×U(Nf-k). This random matrix model is obtained by adding a complex part to the action for the k = 0 random matrix model. We derive the pattern of spontaneous symmetry breaking from the analytical solution of the model. Additionally, we obtain explicit analytical results for the spectral density and the spectral correlation functions for the Dirac operator at finite matrix dimension, that become complex. In the microscopic domain where the matrix size tends to infinity, they are expected to be universal, and give an exact analytical prediction to the spectral properties of the Dirac operator in the presence of a Chern-Simons term. Here, we calculate the microscopic spectral density. It shows exponentially large (complex) oscillations which cancel the phase of the k = 0 theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evaluation of the accuracy of an offline seasonally-varying matrix transport model for simulating ideal age

Newton-Krylov solvers for ocean tracers have the potential to greatly decrease the computational costs of spinning up deep-ocean tracers, which can take several thousand model years to reach equilibrium with surface processes. One version of the algorithm uses offline tracer transport matrices to simulate an annual cycle of tracer concentrations and applies Newton’s method to find concentrations that are periodic in time. Here we present the impact of time-averaging the transport matrices on the equilibrium values of an ideal-age tracer. We compared annually-averaged, monthly-averaged, and 5-day-averaged transport matrices to an online simulation using the ocean component of the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels. We found that increasing the time resolution of the offline transport model reduced a low age bias from 12% for the annually-averaged transport matrices, to 4% for the monthly-averaged transport matrices, and to less than 2% for the transport matrices constructed from 5-day averages. The largest differences were in areas with strong seasonal changes in the circulation, such as the Northern Indian Ocean. As a result, for many applications the relatively small bias obtained using the offline model makes the offline approach attractive because it uses significantly less computer resources and is simpler to set up and run.

54 ENVIRONMENTAL SCIENCES↗

Atomic Layer Deposition of Vanadium Oxide to Reduce Parasitic Absorption and Improve Stability in n-i-p Perovskite Solar Cells for Tandems

Two critical issues associated with semi-transparent, n-i-p perovskite solar cells for 2-terminal tandem devices are parasitic absorption and long-term instability associated with the widely used spiro-OMeTAD and MoOx hole transport and buffer layers, respectively. In this work, we present an alternative hole contact bilayer that consists of a 30 nm undoped layer of spiro-TTB in conjunction with 9 nm of air-stable vanadium oxide (VOx) deposited via atomic layer deposition. The low absorption of UV and visible light in this bilayer results in the fabrication of a semi-transparent perovskite cell with 18.9 mA cm-2 of photocurrent, a 14% increase compared to the 16.6 mA cm-2 generated in a control device with 150 nm of doped spiro-OMeTAD. The ALD VOx buffer layer shows promise as a stable alternative to MoOx; an unencapsulated Cs0.17FA0.83Pb(Br0.17I0.83)3 device with ALD VOx and ITO as the top contact maintains its efficiency following 1000 hours at 85 degrees C in a N2 environment. Lastly, we use transfer matrix modeling of the optimized perovskite stack to predict its optical performance in a monolithic tandem cell with heterojunction silicon.

14 SOLAR ENERGY↗

A note on the Bayesian analysis of experiments with correlated multiple responses using a matrix-logarithmic covariance model

In the literature, analysis of multiple responses from experiments with replicates has modeled the covariance matrix directly as linear models of the transformed variances and correlations, i.e., covariance modeling. This article considers models based on the matrix- logarithm of the covariance matrix. This so-called log-covariance modeling is illustrated with data from actual experiments and compared with the traditional covariance modeling.

97 MATHEMATICS AND COMPUTING↗