Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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Results for “Matrix models”
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Matrix Approach to Land Carbon Cycle Modeling
Land ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin-up of land carbon cycle models by tens of times. The accelerated spin-up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever-increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.
54 ENVIRONMENTAL SCIENCES↗
PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method
Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.
36 MATERIALS SCIENCE↗
Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model
To study quantum properties of the hadron wavefunction at small x, we derived the reduced density matrix for soft gluons in the CGC framework. We explicitly showed that the reduced density matrix is not diagonal in the particle number basis. The off-diagonal components are usually ignored in the conventional parton model. We thus defined the density matrix of ignorance by keeping only the part of the reduced density matrix which can be probed in a limited set of experimental measurements. We calculated Von Neumann entropy for both the reduced and ignorance density matrices. The entropy of ignorance is always greater than the entanglement entropy (computed drom the reduced density matrix) of gluons. Finally, we showed that the CGC reduced density matrix for soft gluons can be diagonalized in a thermal basis with Boltzmann weights suggesting thermalization of new quasi-particle states which we dubbed entangolons.
Duan, Haowu↗
Piezo-Antenna: An Electromagnetic-Ultrasonic Data Transfer System
Electronic systems contained within sealed metallic enclosures, such as nuclear waste containers where wire penetration is not an option, require a through-wall data transfer technology to communicate. One such technology utilizes piezoelectric ultrasonic transducers to communicate through the barrier using elastic waves. Currently demonstrated ultrasonic through-wall data communication techniques have relied on having a direct interface with the ultrasonic transducers on either side. Here, this work studies the coupling of an antenna to such an ultrasonic communication system. A computationally efficient model of a piezobarrier ultrasonic communication system and antenna using a simplified antenna model and a transfer matrix piezobarrier model is utilized to perform a representative parameter space search. The system efficiency and bandwidth trends are shown for the system parameters as well as operating frequency. The tradeoff between efficiency and bandwidth is also presented. A system configuration within the parameter space is fabricated and demonstrated to achieve a data rate of up to 100 kb/s.
Antenna↗
Finite Element Modeling of the Fiber-Matrix Interface in Polymer Composites
Polymer composites are used in numerous industries due to their high specific strength and high specific stiffness. Composites have markedly different properties than both the reinforcement and the matrix. Of the several factors that govern the final properties of the composite, the interface is an important factor that influences the stress transfer between the fiber and matrix. The present study is an effort to characterize and model the fiber-matrix interface in polymer matrix composites. Finite element models were developed to study the interfacial behavior during pull-out of a single fiber in continuous fiber-reinforced polymer composites. A three-dimensional (3D) unit-cell cohesive damage model (CDM) for the fiber/matrix interface debonding was employed to investigate the effect of interface/sizing coverage on the fiber. Furthermore, a two-dimensional (2D) axisymmetric model was used to (a) analyze the sensitivity of interface stiffness, interface strength, friction coefficient, and fiber length via a parametric study; and (b) study the shear stress distribution across the fiber-interface-matrix zone. It was determined that the force required to debond a single fiber from the matrix is three times higher if there is adequate distribution of the sizing on the fiber. The parametric study indicated that cohesive strength was the most influential factor in debonding. Moreover, the stress distribution model showed the debonding mechanism of the interface. It was observed that the interface debonded first from the matrix and remained in contact with the fiber even when the fiber was completely pulled out.
36 MATERIALS SCIENCE↗
Mobile Sensing for Wind Field Estimation in Wind Farms: Preprint
This paper introduces a novel approach for estimating the wind field over an entire wind farm using a mobile sensor to collect limited amounts of data. The proposed method estimates the boundary conditions of a simplified turbine wake model by computing the model sensitivity matrix and using a recursive least-squares algorithm to recover the model parameters from the wind field measurements. To address the fact that it is not practical to take measurements across the entire wind farm, the proposed method classifies each area on the map based on its sensitivity to parameter variations. This classification is then used to generate a suitable path for a mobile sensor, which is charged with collecting data for the recursive least-squares algorithm. The proposed framework can successfully estimate the model boundary conditions using just the measurements collected along the path of the mobile sensor. This preliminary result paves the way for using real-time wind field estimates for the coordinated control of all the turbines within a wind farm.
estimation↗
Microstructure in matrix elements
We investigate the simple model of Pennington, Shenker, Stanford and Yang for modeling the density matrix of Hawking radiation, but further include dynamics for EOW branes behind the horizon. This allows interactions that scatter one interior state to another, and also allows EOW loops. At strong coupling, we find that EOW states are no longer random; the ensemble has collapsed, and coupling constants encode the microscopic matrix elements of Hawking radiation. This suggests strong interior dynamics are important for understanding evaporating black holes, without any ensemble average. In this concrete model the density matrix of the radiation deviates from the thermal state, small off-diagonal fluctuations encode equivalences between naively orthogonal states, and bound the entropy from above. For almost evaporated black holes the off-diagonal terms become as large as the diagonal ones, eventually giving a pure state. We also find the unique analytic formula for all Renyi entropies.
2D gravity↗
An ICME Modeling Framework for Titanium/Tungsten-Carbide Metal Matrix Composites
This report describes a collaborative project to develop a validated, predictive model for the high temperature mechanical properties of a titanium-matrix, tungsten-carbide/cobalt-reinforced metal matrix composite. The modeling approach was to first develop a detailed, microstructural model linking the material structure and the interfacial debonding properties to the effective properties of the material. The project then completed a throughput simulation campaign to generate a large number of simulations for discrete microstructures and different debonding parameters. Finally, the project trained a fast, Gaussian process surrogate model against this simulation database to provide a quick model linking the material compositions, structure, and processing parameters to the resulting material properties. This model was validated against high temperature tensile test data on a few particular composite compositions. The tests validate the model predictions for ultimate tensile strength and uniform elongation/ductility, meaning the final surrogate model can now be used to tune the material composition and processing parameters to identify optimal composite compositions for particular applications.
36 MATERIALS SCIENCE↗
Direct Feed High-Level Waste APPS Model Glass Testing (DFHLW APPS) Matrix
This report summarizes the data collected during the batching and melting of the Direct Feed High-Level Waste APPS Model Glass Matrix (DFHLW APPS) to serve as a quality-assured validation of the Aspen Process Performance Simulation (APPS) formulation method. Of 15 glasses tested, 12 satisfied all target property constraints. Two glasses, APPS-05 and -06, formed nepheline on canister centerline cooling heat-treatment and failed the Product Consistency Test response limits. Glass APPS-07-2 formed unacceptably high concentrations of crystals (primarily Na3Nd(PO4)2) when heat treated at 950 °C. All other glasses were found to be satisfactory. The measured property values were compared to predicted values from a set of current models. In many cases the current models were found to be inadequate for design of DFHLW glasses. These models are being adjusted to correct for mispredictions. Other models, e.g., density, toxicity characteristic leaching procedure, and sulfur solubility, are adequate for formulation of DFHLW glasses.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Fast matrix algebra for Bayesian model calibration
In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. Here, we also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation
97 MATHEMATICS AND COMPUTING↗
Model predictive control for matrix converter operating in current control mode with load current estimation
A matrix converter system operating in current control mode is provided. The matrix converter includes a switching matrix coupled between a low voltage side and a high voltage side, wherein the matrix converter is coupled at its low voltage side to a generator for receiving an input power including an input current and transforming the input power into an output power at its high voltage side, wherein a load is coupled to the high voltage side. The control system includes a load observer and a model predictive controller (MPC). The load observer is configured to estimate a load current that flows to the load from the high voltage side of the matrix converter as a function of a switching state of the switching matrix, an output voltage output at the high voltage side of the matrix converter, and the input current. The MPC is configured to select the switching state of the switching matrix to meet one or more control objectives defined by minimization of a multi-objective function that tracks the output voltage and the input current using the estimated load current.
24 POWER TRANSMISSION AND DISTRIBUTION↗
An ICME Modeling Framework for Metal Matrix Composites Focusing on Ultrahigh Temperature Matrix Material and Tungsten Carbide Reinforcement Particulate (Final CRADA Report)
Ultra High Temperature Metal Matrix Composites (UHT-MMCs) are of interest to the due to their potential defense and aerospace applications. These materials consist of a metal matrix reinforced with a stiff ceramic or cermet. Based on a preliminary literature survey, this project will focused on a pure titanium (Ti) matrix reinforced with tungsten carbide-cobalt (WC-Co). UHT-MMC technology is still at a nascent stage of development and requires extensive experimental work to optimize the structure and resulting material properties of a particular UHT-MMC material system. An accurate and complete high-performance computing (HPC) model of the Ti/WC-Co material system could greatly accelerate the development and deployment Ti/WC-Co materials by connecting processing parameters to material properties. This type of model could then be used in an integrated computational materials engineering approach to optimize the material structure to achieve a targeted level of performance.
36 MATERIALS SCIENCE↗
Phase-Field Modeling of Mechanical Damages in Ceramic Matrix Composites
Developed a phase-field model for mechanical damages in CMCs, which incorporates the CMC microstructures, matrix cracking, fiber breakage, and interfacial sliding. Two types of mechanisms, fiber bridging and fiber pull-out, are considered. The obtained simulation results agree with experimental observations and an analytical solution. Simulation results suggest that the performance of CMCs would be enhanced with thicker fibers, longer fibers, and higher fiber density. Opposite trends of interfacial sliding resistances are suggested for the two types of situations. In reality, a mixture of the two situations may exist, and then an intermediate interfacial sliding resistance may be optimal.
Xue, Fei↗
The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.
54 ENVIRONMENTAL SCIENCES↗
Osteoporosis Treatments Affect Bone Matrix Maturation in a Rat Model of Induced Cortical Remodeling
ABSTRACT To test how osteoporosis drugs affect bone matrix maturation during cortical bone remodeling, 72 pregnant rats were switched from a 0.4% to a 0.01% calcium diet at parturition for a 23‐day lactation period. At weaning, eight dams were sacrificed to establish baseline values, while the remaining dams were returned to 0.4% calcium and treated with vehicle (saline), sodium fluoride (NaF), zoledronic acid (ZA), or sclerostin antibody (Scl‐Ab) for either 7 or 28 days (eight animals per group per time point). Femora were examined by μCT, dynamic histomorphometry, Fourier transform infrared imaging, and three‐point bending of notched specimens. Cortical porosity decreased in all groups from baseline to day 28. Intracortical mineralizing surface (MS/BS) and mineral apposition rate (MAR), as well as the mineral‐to‐matrix ratio were unaffected by treatment, but intracortical crystallinity was increased in the ZA group at day 10 compared with vehicle. Cortical area increased in all groups over 28 days mainly because of an addition of bone at the endocortical surface. Endocortical MS/BS did not vary among the groups, but endocortical MAR was suppressed in the NaF group at day 2 and elevated in the Scl‐Ab group at day 4 compared with vehicle. Endocortical mineral‐to‐matrix ratio was increased at days 5 and 10 following NaF treatment and endocortical crystallinity was increased at day 5 following ZA treatment compared with vehicle. Fracture toughness did not differ among the groups. Thus, the treatments affected matrix maturation more strongly at the endocortical then intracortical envelope. In this model of induced remodeling, the bone formation phase is synchronized at multiple sites, facilitating study of the effects of drugs or other bone‐targeting agents on matrix maturation independent of their effects on the initiation of remodeling. © 2020 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research.
59 BASIC BIOLOGICAL SCIENCES↗
On time-dependent backgrounds in 1 + 1 dimensional string theory
In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1 + 1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string
Although the energy spectrum of the Heisenberg spin chain on a circle defined by H = 1 4 Σ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether Mϵ 4N + r, where r = -1,0,1,2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M 1 < M and M - M 1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case Δ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R 0 . We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for Δ ≠ 0 is a change in the compactification radius R 0 → R Δ . As Δ→ -1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗