SEARCH · Search NASA

Results for “oscillation cases”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

DOE OSTI2022

A Novel Fault Diagnosis Approach for Rolling Bearing Based on CWT and Adaptive Sparse Representation

Extraction and enhancement of weak impulse signature is the key of rolling bearing fault prognostics in which case the features are often weak and covered by noise. Tunable Q-factor wavelet transform (TQWT), as an emerging wavelet construction theory developed in a frequency domain explicitly, has the advantages of matching with the specific oscillation behavior of signal components. In this article, an adaptive sparse representation (ASR) method is proposed, which integrates the sparse code shrinkage (SCS) and parameter optimization into TQWT. However, direct application of ASR is difficult to extract fault signatures at the early stage or low-speed operation due to weak fault symptoms and background noise. A novel fault diagnosis strategy based on continuous wavelet transform (CWT) and ASR is investigated. CWT owns significant advantages on multiscale subdivision and weak signal detection. The results of simulated and experimental vibration signal analyses verify the effectiveness of the proposed method in accurately extracting weak impulse features from the noise environment.

Yuan, Xing↗

DOE OSTI2024

Performance Assessment of Photovoltaic Panels Using Impedance Spectroscopy

The goal of this project was to develop a technique for measuring internal characteristics of a PV module using light modulation under a fixed voltage bias while measuring the resulting alternating current. This technique, light-intensity modulated impedance spectroscopy (LIMIS), has the promise of detecting early signs of panel aging and degradation that could be used for example by solar farm operators to have early warnings to repair or replace panels to maintain reliability of the overall PV array. LIMIS would be complementary with the previously developed electrochemical impedance spectroscopy (EIS), which uses an alternating voltage applied electrically to a solar cell with a similar alternating current measurement. EIS has mostly been developed for individual PV cells rather than whole modules. The project was intended to assess what different information could be revealed by LIMIS, which may in some cases be more scalable to larger modules and potentially more practical to apply in field measurements without needing to electrically disconnect PV modules. We began with small 10 W PV modules and built a testbed capable of oscillating the light intensity with frequencies up to 50 kHz. In parallel, we built a large testbed for testing large 250 W PV modules. Meanwhile, we developed procedures for established measurement techniques: current–voltage (I–V), EIS, and electroluminescence (EL) imaging, where panels are subjected to forward bias while their infrared emission is recorded using a camera modified to be sensitive to IR wavelengths. In addition, we developed protocols for accelerated aging of PV modules in two ways. Thermal cycling from –40°C to +90°C simulates the diurnal temperature cycles on a rooftop. Mechanical stress by dropping a 227 g ball from a height of 1 m simulates damage such as that due to hail impacts.

14 SOLAR ENERGY↗

DOE OSTI2023

Evaluating skill in predicting the Interdecadal Pacific Oscillation in initialized decadal climate prediction hindcasts in E3SMv1 and CESM1 using two different initialization methods and a small set of start years

Abstract It is a daunting challenge to conduct initialized hindcasts with enough ensemble members and associated start years to form a drifted climatology from which to compute the anomalies necessary to quantify the skill of the hindcasts when compared to observations. This limits the ability to experiment with case studies and other applications where only a few initial years are needed. Here we run a set of hindcasts with CESM1 and E3SMv1 using two different initialization methods for a limited set of start years and use the respective uninitialized free-running historical simulations to form the model climatologies. Since the drifts from the observed initial states in the hindcasts toward the uninitialized model state are large and rapid, after a few years the drifted initialized models approach the uninitialized model climatological errors. Therefore, hindcasts from the limited start years can use the uninitialized climatology to represent the drifted model states after about lead year 3, providing a means to compute forecast anomalies in the absence of a large hindcast sample. There is comparable skill for predicting spatial patterns of multi-year Pacific sea surface temperature anomalies in the domain of the Interdecadal Pacific Oscillation using this method compared to the conventional methodology with a large hindcast data set, though there is a model dependence to the drifts in the two initialization methods.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Vibronic Coupling and Exciton Chirality: Electronic and Structural Rearrangement between Helical to Zero Momentum Molecular Exciton States

Helical porphyrin aggregates are attractive macromolecular nanostructures for biomimetic light-harvesting and energy transfer in solar energy technology due to their large light absorbing cross sections and promising energy conservation benefits from chiral-induced spin selectivity. However, with these soft materials, it is imperative that we understand how the nuclear degrees of freedom impact the excitonic energy landscape and dynamics, particularly pertaining to how it influences the chiral angular momentum of the excitons. To this end, we have measured time-resolved depolarization ratios using femtosecond stimulated Raman spectroscopy to uncover the vibronic coupling guided by molecular vibrations between excitons of different angular momentum in helical tetra(sulfonatophenyl)porphyrin aggregates. We find that while transient absorption anisotropy reveals rapid (1 ps lifetime) exciton rotation from helical to achiral states in the Q-band, time-resolved vibrational depolarization ratios evolve on remarkably faster time scales (<500 fs lifetime) for the totally symmetric 1530 cm –1 vibration and the nontotally symmetric 1540 cm –1 vibration. The time-resolved depolarization ratios of the 1540 cm –1 vibration, in particular, show strong evidence of vibronic coupling and nonadiabatic exciton behavior that mediates the nonradiative transition between chiral and achiral excitons. Furthermore, our study shows that for rational design of helical molecular aggregates for exciton transport, the vibronic coupling between excitons of different angular momenta driven by molecular vibrations must be considered especially in the case where chiral-induced spin selectivity is desired.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Effect of Inlet Throttling on Thermohydraulic Instability in a Large Scale Waterbased RCCS: A System-Level Analysis with RELAP5-3D

This paper presents results from system -level modeling of a water -based reactor cavity cooling system using RELAP5-3D. The computational model is benchmarked with experimental data from a half -scale RCCS test facility at Argonne National Laboratory. The model prediction is first compared with a two-phase oscillatory baseline experimental case where mixed accuracy is obtained. The model shows reasonable prediction of mass flow rate, pressure, and temperature but significant overprediction of void fraction. The model prediction is then compared with a fault case where the inlet of the risers is gradually reduced using a throttling valve. As the valve is closed, the model is able to predict some major flow phenomena observed in the experiment such as the dampening of oscillations, the reintroduction of oscillations, as well as boiling, flashing, and geysering in the risers. However, the timeline of these events are not well captured by the model. The model is also used to investigate the evolution of flow regime in the chimney. This work highlights that the semiempirical constitutive relations used in RELAP-3D could have a strong influence on the accuracy of the model in two-phase oscillatory flows.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

“Magic” Orientation Angles to Suppress Spin-Driven Hall Currents in Anisotropic 2D Materials with an Ideal Skyrmion Gas

The Hall effect depending on conduction electron spin projection becomes very different for anisotropic 2D crystals. In this case the spin-dependent electron current strongly determined by the orientation angle, θ, of the sample with respect to an applied electric eld. The spin-up and -down components of the direct and Hall charge currents oscillate with the angle 2θ. The direct and Hall components of the current have the structure where there are the angle-independent part, oscillation amplitude, and phase shift. All three quantitates strongly depend on the electron spin projection, electron mass ratio, and skyrmion size. We nd that there are "magic" orientation angles where the spin-up, spin-down, and total Hall currents vanish. There is a great interest in computations based on 2D materials with skyrmions. Such properties can be useful for computer logic operations based on skyrmions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Programmable soft valves for digital and analog control

In soft devices, complex actuation sequences and precise force control typically require hard electronic valves and microcontrollers. Existing designs for entirely soft pneumatic control systems are capable of either digital or analog operation, but not both, and are limited by speed of actuation, range of pressure, time required for fabrication, or loss of power through pull-down resistors. Using the nonlinear mechanics intrinsic to structures composed of soft materials—in this case, by leveraging membrane inversion and tube kinking—two modular soft components are developed: a piston actuator and a bistable pneumatic switch. These two components combine to create valves capable of analog pressure regulation, simplified digital logic, controlled oscillation, nonvolatile memory storage, linear actuation, and interfacing with human users in both digital and analog formats. Three demonstrations showcase the capabilities of systems constructed from these valves: 1) a wearable glove capable of analog control of a soft artificial robotic hand based on input from a human user’s fingers, 2) a human-controlled cushion matrix designed for use in medical care, and 3) an untethered robot which travels a distance dynamically programmed at the time of operation to retrieve an object. This work illustrates pathways for complementary digital and analog control of soft robots using a unified valve design.

42 ENGINEERING↗

DOE OSTI2023

Modified Virtual Oscillator Based Operation of Grid Forming Converters with Single Voltage Sensor

Virtual oscillator based control architecture for grid forming converter with inner current control loop for additional objective accomplishments is proposed in this paper. In general, virtual oscillator is based on Lienard type of oscillator equation with a cubic nonlinearity. Virtual oscillator alone cannot accommodate unbalanced or harmonic mitigation while operating converters in grid forming mode. Therefore, to accomplish better tracking performance, incorporating the provision for nonlinear and/or unbalanced loads, an inner current control loop is utilized which is based upon Lyapunov energy function type control architecture due to its advantages. To reduce the overall cost of implementation and ensure proper phase difference in the generated voltages, the implemented virtual oscillator operates with only one voltage feedback from the point of common coupling as presented in this paper. To verify the effectiveness of the proposed approach, the overall system has been modeled in MATTLAB/Simulink and PLECS domain and case studies showing the successful production of low harmonic load voltages under nonideal loading condition along with other important results are presented in this paper.

dual second order generalized integrator↗

DOE OSTI2021

Novel usage of deep learning and high-performance computing in long-baseline neutrino oscillation experiments

Mención Internacional en el título de doctorDeep-learning methods are playing a crucial role in numerous scientific and industrialapplications. Over the past two decades, these techniques have helped in the collection,reconstruction, and analysis of large data samples in particle physics experiments. Themain topic of this PhD research is the study of deep-learning techniques in long-baselineneutrino oscillation experiments. Neutrinos are mysterious light elementary particles,and their investigation is essential to shed light on some of the remaining open questionsin physics. The work presented here describes an algorithm based on a convolutionalneural network developed to provide highly accurate and efficient selections of electronneutrino and muon neutrino interactions in the Deep Underground Neutrino Experiment(DUNE). With this algorithm, the electron neutrino (antineutrino) selection efficiencypeaks at 90% (94%) and exceeds 85% (90%) for reconstructed neutrino energies between2-5 GeV. The selection efficiency for muon neutrino (antineutrino) interactions is foundto have a maximum of 96% (97%) and exceeds 90% (95%) efficiency for reconstructedneutrino energies above 2 GeV. When considering all electron neutrino and antineutrinointeractions as signal (both those appearing from oscillations and those intrinsic tothe beam), a selection purity of 90% is achieved. These event selections are criticalto maximise the sensitivity of the experiment to CP-violating effects, key to furtherunderstand the matter-antimatter asymmetry of the Universe.In high-energy physics experiments, deep learning has also been explored for producingfast simulations and physically-motivated manipulations of simulated images. Some ofthose simulations, such as the light production and detection, are very computationallyexpensive and require novel methods to produce the necessary samples while controllingthe varied underlying physics model parameters. To do so, we invented the model-assistedgenerative adversarial network (MAGAN), first validated on simple generic case studiesand then successfully applied to the DUNE photon-detector simulation.Moreover, we also developed graph neural networks for 3D-voxel classification ofambiguities and optical crosstalk for a different particle physics experiment, most preciselyfor the proposed SuperFGD. This novel 3D-granular plastic-scintillator neutrino detectorwill be used to upgrade the near detector of the T2K neutrino oscillation experiment, and our method reports efficiencies and purities of 94-96% per event in the classificationof particle track voxels.Due to the growth and complexity of deep neural networks, researchers have beeninvestigating techniques to train those networks in a more computationally-efficient way.Many efforts have been made by the community to optimise deep-learning models byparallelising or distributing their training computation across multiple devices. In thisthesis, we study an approach based on data locality for those neural networks that cannotbenefit from scaling their computation due to a significant bottleneck in the data I/O.The research also includes a detailed study on the performance of deep neural networkson hardware accelerator boards.Los métodos de aprendizaje profundo son cada vez más utilizados en numerosas aplicacionescientíficas e industriales hoy en día. Durante las dos últimas décadas, estastécnicas se han empleado en la recolección, reconstrucción y análisis de la gran cantidadde datos generados por experimentos de física de partículas. El tema principal de estatesis doctoral es el uso de estos modelos de aprendizaje profundo en experimentos defísica de neutrinos, en concreto en los experimentos de larga distancia DUNE y T2K. Losneutrinos, partículas fundamentales neutras, de las más ligeras del Universo, pueden serclave para explicar algunas de las cuestiones todavía sin resolver en física fundamental.Entre las diferentes contribuciones que esta tesis ha hecho a su estudio, cabe destacar eldesarrollo de un algoritmo basado en una red de neuronas convolucional para seleccionarcon gran eficiencia y precisión las interacciones de neutrinos electrónicos y muónicos enel Deep Underground Neutrino Experiment (DUNE). La eficiencia de selección obtenidapara neutrinos (antineutrinos) electrónicos alcanza un máximo del 90% (94%) y supera el85% (90%) para neutrinos con energías reconstruidas en el rango 2-5 GeV. La selección deneutrinos (antineutrinos) muónicos tiene una eficiencia máxima del 96% (97%) y excedeel 90% (95%) para neutrinos con energías reconstruidas de más de 2 GeV. Considerandocomo señal todas las interacciones de neutrinos y antineutrinos electrónicos (procedentestanto de oscilaciones como intrínsecos en el haz inicial), se logra una pureza en la seleccióndel 90%. Dichas selecciones de eventos son fundamentales para maximizar la sensibilidaddel experimento a los efectos de violació...

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Understanding the negative triangularity ELM trigger and ELM free state on DIII-D with ECE-imaging

Here, the Electron Cyclotron Emission Imaging (ECEI) diagnostic was used to observe a finite-n interchange mode structure in the edge of negative triangularity shaped plasmas on DIII-D. At a small negative triangularity (δ u = -0.2), the plasma is in the H-mode with ELMs that are triggered by a low-n interchange mode. At a larger negative triangularity (δ u = -0.4) and low NBI power (2 MW), a dithering oscillation is observed that is triggered by a low-n interchange mode, whereas at higher NBI power (>2 MW), the edge reverts to L-mode and the low-n interchange mode is present continuously. In all cases, the edge pressure gradient is clamped when the interchange mode is present. It is concluded that the low-n interchange mode prevents the plasma from transitioning to H-mode at a large negative triangularity. This agrees with linear BOUT++ simulations which suggest that the interchange-type MHD can be a resistive ballooning mode whereby resistivity can significantly increase the finite-n ballooning mode growth rate. The absence of H-mode at large negative triangularity can, thus, be explained by the excitation of low-n pressure driven resistive ballooning modes in the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Bulk Power System Dynamics with Varying Levels of Synchronous Generators and Grid-Forming Power Inverters

Inverters using phase-locked loops for control depend on voltages generated by synchronous machines to operate. This might be problematic if much of the conventional generation fleet is displaced by inverters. To solve this problem, grid-forming control for inverters has been proposed as being capable of autonomously regulating grid voltages and frequency. Presently, the performance of bulk power systems with massive penetration of grid-forming inverters has not been thoroughly studied as to elucidate benefits. Hence, this paper presents inverter models with two grid-forming strategies: virtual oscillator control and droop control. The two models are specifically developed to be used in positive-sequence simulation packages and have been implemented in PSLF. The implementations are used to study the performance of bulk power grids incorporating inverters with gridforming capability. Specifically, simulations are conducted on a modified IEEE 39-bus test system and the microWECC test system with varying levels of synchronous and inverter-based generation. The dynamic performance of the tested systems with gridforming inverters during contingency events is better than cases with only synchronous generation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Neutrino mass and mass ordering: no conclusive evidence for normal ordering

The extraction of the neutrino mass ordering is one of the major challenges in particle physics and cosmology, not only for its implications for a fundamental theory of mass generation in nature, but also for its decisive role in the scale of future neutrinoless double beta decay experimental searches. It has been recently claimed that current oscillation, beta decay and cosmological limits on the different observables describing the neutrino mass parameter space provide robust decisive Bayesian evidence in favor of the normal ordering of the neutrino mass spectrum. We further investigate these strong claims using a rich and wide phenomenology, with different sampling techniques of the neutrino parameter space. Contrary to the findings of Jimenez et al., no decisive evidence for the normal mass ordering is found. Neutrino mass ordering analyses must rely on priors and parameterizations that are ordering-agnostic: robust results should be regarded as those in which the preference for the normal neutrino mass ordering is driven exclusively by the data, while we find a difference of up to a factor of 33 in the Bayes factors among the different priors and parameterizations exploited here. An ordering-agnostic prior would be represented by the case of parameterizations sampling over the two mass splittings and a mass scale, or those sampling over the individual neutrino masses via normal prior distributions only. In this regard, we show that the current significance in favor of the normal mass ordering should be taken as 2.7σ (i.e. moderate evidence), mostly driven by neutrino oscillation data. Let us stress that, while current data favor NO only mildly, we do not exclude the possibility that this may change in the future. Eventually, upcoming oscillation and cosmological data may (or may not) lead to a more significant exclusion of IO.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The role of vectors in reheating

We explore various aspects concerning the role of vector bosons during the reheating process. Generally, reheating occurs during the period of oscillations of the inflaton condensate and the evolution of the radiation bath depends on the inflaton equation of state. For oscillations about a quadratic minimum, the equation of state parameter, w = p/ρ = 0, and the evolution of the temperature, T(a) with respect to the scale factor is independent of the spin of the inflaton decay products. However, for cases when w > 0, there is a dependence on the spin, and here we consider the evolution when the inflaton decays or scatters to vector bosons. We also investigate the gravitational production of vector bosons as potential dark matter candidates. Gravitational production predominantly occurs through the longitudinal mode. We compare these results to the gravitational production of scalars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Self-interacting neutrinos, the Hubble parameter tension, and the cosmic microwave background

Here, we perform a comprehensive study of cosmological constraints on nonstandard neutrino self-interactions using cosmic microwave background and baryon acoustic oscillation data. We consider different scenarios for neutrino self-interactions distinguished by the fraction of neutrino states allowed to participate in self-interactions and how the relativistic energy density, N eff , is allowed to vary. Specifically, we study cases in which all neutrino states self-interact and N eff varies; two species free-stream, which we show alleviates tension with laboratory constraints, while the energy in the additional interacting states varies; and a variable fraction of neutrinos self-interact with either the total N eff fixed to the Standard Model value or allowed to vary. In no case do we find compelling evidence for new neutrino interactions or nonstandard values of N eff . In several cases, we find additional modes with neutrino decoupling occurring at lower redshifts z dec ~ 10 3–4 . We do a careful analysis to examine whether new neutrino self-interactions solve or alleviate the so-called H 0 tension and find that, when all Planck 2018 CMB temperature and polarization data are included, none of these examples eases the tension more than allowing a variable N eff comprised of free-streaming particles. Although we focus on neutrino interactions, these constraints are applicable to any light relic particle.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

Highlights: • Equivalence of a harmonic oscillator to a free particle is considered. • The Eisenhart lift is applied to most general harmonic and linear potentials. • In geometric language, equivalence is the result of the conformal flatness of the Eisenhart metric. It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein’s principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Exploring entanglement and spectral split correlations in three-flavor collective neutrino oscillations

In environments with prodigious numbers of neutrinos, such as core-collapse supernovae, neutron star mergers, or the early Universe, neutrino-neutrino interactions are dynamically significant. They can dominate neutrino flavor evolution and force it to be nonlinear, causing collective neutrino oscillations. Such collective oscillations have been studied numerically, for systems with up to millions of neutrinos, using mean-field or one-particle effective approximations. However, such a system of interacting neutrinos is a quantum many-body system, wherein quantum correlations could play a significant role in the flavor evolution—thereby motivating the exploration of many-body treatments that follow the time evolution of these correlations. In many-body flavor evolution calculations with two neutrino flavors, the emergence of spectral splits in the neutrino energy distributions has been found to be correlated with the degree of quantum entanglement across the spectrum. In this work, for the first time, we investigate the emergence of spectral splits in the three-flavor many-body collective neutrino oscillations. We find that the emergence of spectral splits resembles the number and location found in the mean-field approximation but not in the width. Moreover, unlike in the two-flavor many-body calculations, we find that additional degrees of freedom make it more difficult to establish a correlation between the location of the spectral splits and the degree of quantum entanglement across the neutrino energy spectrum. The observation from the two-flavor case, that neutrinos nearest to the spectral split frequency exhibit the highest level of entanglement, is more difficult to ascertain in the three-flavor case because of the presence of multiple spectral splits across different pairwise combinations of flavor and/or mass states. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗