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DOE OSTI2022

A Thermogravimetric Temperature-Programmed Thermal Redox Protocol for Rapid Screening of Metal Oxides for Solar Thermochemical Hydrogen Production

As combinatorial and computational methods accelerate the identification of potentially suitable thermochemically-active oxides for use in solar thermochemical hydrogen production (STCH), the onus shifts to quickly evaluating predicted performance. Traditionally, this has required an experimental setup capable of directly carrying out a two-stage thermochemical water-splitting process. But this can be a difficult endeavor, as most off-the-shelf equipment cannot adequately deal simultaneously with the high temperatures, varying oxygen partial pressures, and high H 2 O partial pressures required; achieving sufficient temporal sensitivity to accurately quantify the kinetics is also a major challenge. However, as proposed here, a less complicated experiment can be used as a first screening for thermochemical water splitting potential. Temperature-Programmed Thermal Redox (TPTR) using thermogravimetry evaluates the thermal reduction behavior of materials. This technique does not require water splitting or CO 2 -splitting analogs but can nonetheless predict water-splitting performance. Three figures of merit are obtained from the TPTR experiment: reduction onset temperature, extent of reduction, and extent of recovery upon reoxidation. These metrics can collectively be used to determine if a material is capable of thermochemical water-splitting, and, to good approximation, predict whether the thermodynamics are favorable for use under more challenging high-conversion conditions. This paper discusses the pros and cons of using TPTR and proposes a protocol for use within the STCH community.

08 HYDROGEN↗

NASA NTRSDate not supplied

TPSAS-NF1676L-17800-DND

Currently, there are two national challenge problems that guide much of the research in durability and damage tolerance at NASA Langley. The first, Airframe Digital Twin, is a concept that combines as-built vehicle components, as-experienced loads and environments, and other vehicle-specific characteristics to enable ultrahigh fidelity modeling of aircraft and spacecraft throughout their service lives. The second, Materials Genome Initiative, is an analog to the Human Genome Project, and is intended to improve the rate at which materials scientists can discover, understand fundamental physics, and improve material systems. This presentation will highlight several research projects ongoing at NASA Langley that are in support of the above challenge problems. Two of those topics will be the subject of detailed discussion. First, investigations of microstructurally-small fatigue cracking (MSFC) in Al-2Cu and Al-4Cu, fabricated in-house, will be presented. Single- and oligo-crystals of Al-Cu specimens were loaded in uniaxial fatigue, while high-resolution in-situ measurements of deformation were made using image correlation (IC) in a scanning-electron microscope (SEM). The Al-Cu specimens were then replicated as crystal plasticity finite element models (CPFEM), where evolution of slip localization near grain boundaries was computed. Comparison among experiment and CPFEM is made. In addition, XRay diffraction measurements of the as-fabricated specimens were carried out, where direct measurements of the embedded copper precipitates were made, and their influence on growing MSFCs were directly observed. The second main topic will illustrate ongoing work in the area of so-called damage-sensing particles. In this work, shape-memory alloys are embedded in an aluminum alloy matrix. Upon the propagation of a fatigue crack, these particles undergo a strain-induced phase transformation which is detected using an acoustic sensor, providing real-time information on propagating cracks. Experiments and simulations regarding the development of this system will also be detailed.

Jacob Hochhalter↗

NASA NTRS1986

Short time Fourier analysis of the electromyogram - Fast movements and constant contraction

Short-time Fourier analysis was applied to surface electromyograms (EMG) recorded during rapid movements, and during isometric contractions at constant forces. A portion of the data to be transformed by multiplying the signal by a Hamming window was selected, and then the discrete Fourier transform was computed. Shifting the window along the data record, a new spectrum was computed each 10 ms. The transformed data were displayed in spectograms or 'voiceprints'. This short-time technique made it possible to see time-dependencies in the EMG that are normally averaged in the Fourier analysis of these signals. Spectra of EMGs during isometric contractions at constant force vary in the short (10-20 ms) term. Short-time spectra from EMGs recorded during rapid movements were much less variable. The windowing technique picked out the typical 'three-burst pattern' in EMG's from both wrist and head movements. Spectra during the bursts were more consistent than those during isometric contractions. Furthermore, there was a consistent shift in spectral statistics in the course of the three bursts. Both the center frequency and the variance of the spectral energy distribution grew from the first burst to the second burst in the same muscle. The analogy between EMGs and speech signals is extended to argue for future applicability of short-time spectral analysis of EMG.

Hannaford, Blake↗

NASA NTRS2018

Building Reliable Printed Circuit Boards - the Lessons Learned

"Printed circuit boards (PCBs) are the baseline for electronics manufacturing upon which electronic components are mounted and formed into electronic systems. PCBs are used in a variety of electronic circuits from simple one-transistor amplifiers to large super computers. A PCB serves three main functions: 1) it provides the necessary mechanical support for the components in the circuit 2) it provides the necessary electrical interconnections, and 3) it bears some form of legend which identifies the components it carries. The failure modes on the PCBs can be categorized in a hierarchical structure, in which the mechanisms and causes are site or location dependant. This one day workshop will discuss a variety of failure mechanisms that effect the functionality of PCBs. These mechanisms can be related to how PCB materials are selected, PCBs are designed, manufactured, tested and used in the field conditions. The workshop will begin with an overview of PCB manufacturing, materials and processes. With the help of examples and case studies, a wide range of failure mechanisms will be discussed, case studies are focused on digital circuits, however some failures in analog, double sided boards are also presented. The workshop then provides the guideline for selection of methodologies for identifying potential failure mechanisms based on the failure history and how a systematic root cause failure analysis of the PCB can result in prevention of future issues."

Sood, Bhanu↗

NASA NTRSDate not supplied

Multi-Domain Routing in Delay Tolerant Networks

The goal of Delay Tolerant Networking (DTN) is to provide the missing ingredient for the ever-growing collection of communicating nodes in our solar system to become a Solar System Internet (SSI). Great strides have been made in modeling particular types of DTNs, such as schedule- or discovery-based. Now, analogously to the Internet, these smaller DTNs can be considered routing domains which must be stitched together to form the overall SSI. In this paper, we propose a framework for cross-domain routing in DTNs as well as methodologies for detecting these sub-domains. Example time-varying networks are given to demonstrate the techniques proposed. A basic component is the mathematical theory of sheaves, which unifies the underlying model of DTN routing algorithms, by giving rise to routing sheaves – these can be defined for the dynamic and scheduled networks as noted above, and can also be used to define the interfaces between these domains in order to route across them. An immediate application would be routing across discovery-based networks connected by scheduled networks. These DTN subdomains remain elusive, however, and need to become well-defined and properly sized for tractable computability. In particular, a balance must be determined between areas that are too large (i.e. large matrix computations) versus areas that are too small (i.e. “many” single-noded domains). Moreover, the connections between the domains should, at least locally, be chosen to optimize data flow and connectivity: we address this in three ways. First, tools from persistent homology are given to understand underlying structures, reminiscent of hierarchies in the Internet Protocol (IP) addressing. Second, we construct a notion of temporal graph curvature based on network geometry to analyze flows induced by dynamical processes on these networks. Finally, Schrodinger Bridges, a tool arising from statistical physics, are proposed as a method of constructing flows on time-evolving networks with desirable properties such as speed, robustness, and load sensitivity. We construct an approach to temporal hypergraphs to simultaneously model unicast, multicast, and broadcast, using the language of scheme theory, and then consider DTN network coding as a way to achieve network-level computation and organization. The paper concludes with a discussion and ideas for future work.

Alan Hylton↗

NASA NTRSDate not supplied

A Proposed Clock Synchronization Method for the Solar System Internet

Networked communications in space are necessary to achieve scalability in terms of the number of communicating nodes but also in terms of the overall system complexity. A key component to such a system is the ability to synchronize clocks, which is the focus of this paper. The so-called Solar System Internet (SSI) will be built upon Delay Tolerant Networking (DTN), which, in analogy to the Internet Protocol (IP), can be considered a suite of protocols necessary for networking in the space domain. Therefore, our goal is to extend this suite to include a DTN clock synchronization capability, analogous to the Network Time Protocol (NTP) used in the Internet. A motivating example of a network in space is NASA’s LunaNet, a vision for a multi-hop multi-path network extending to the moon wherein not all nodes will have direct connections to an authoritative reference clock. In this paper, we propose a general clock synchronization methodology and algorithm that could be used for LunaNet as well as more elaborate time-varying networks. In recent years, DTN has benefited from modeling efforts founded on the mathematical tool of sheaves. Here we continue this work to provide an approach to clock synchronization. Due to the time-varying nature of space networks, absolute consensus is not possible. However, the sheaf Laplacian provides a practical, distributed approach to approximating consensus by allowing data to diffuse through the network. In particular, the sheaf Laplacian is readily computable, lending our approach to implementation. Our approach is well suited to handle the difficulties of space networks. For instance, differences in clock accuracy mean certain nodes are more authoritative than others; we can account for these differences through hierarchies in the network, generalizing the strata in NTP. Furthermore, just as error estimation is an integral part of NTP, we are able to give concrete error bounds for our approach. Indeed, different applications (e.g., communications schedules, pointing, navigation, distributed science) will have different requirements, hence it is necessary to maintain clocks within a given tolerance. We outline some of the necessary steps to turn our approach into a practical network protocol that could be used in DTN, and we conclude the paper with suggestions for future research.

Michael Moy↗

DOE OSTI2020

Hypernetwork science via high-order hypergraph walks

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Organismic materials for beyond von Neumann machines

The elementary basis of intelligence in organisms with a central nervous system includes neurons and synapses and their complex interconnections forming neural circuits. In non-neural organisms such as slime mold with gel-like media, viscosity modulation enables adaptation to changing environments. At a larger scale, collective intelligence emerges via social interactions and feedback in animal colonies. Learning and memory are therefore multi-scale features that evolve as a result of constant interactions with the environment. There is growing interest in emulating such features of intelligence in computing machines and autonomous systems. Materials that can respond to their environment in a manner similar to organisms (referred to as "organismic materials") therefore may be of interest as hardware components in artificial intelligence machines. In this brief review, we present a class of semiconductors called correlated oxides as candidates for learning machines. The term "correlated" refers to the fact that electrons in such lattices strongly interact and the ground state is not what is predicted by classical band theory. Such materials can undergo insulator-metal transitions at near ambient conditions under external stimuli such as thermal or electrical fields, strain, and chemical doping. Depending on the mechanism driving the transition, intermediate states can be metastable with different volatilities, and the time scales of phase change can be controlled over many orders of magnitude. The change in electronic properties can be sharp or gradual, leading to digital or analog behavior. These properties enable the realization of artificial neurons and synapses and emulate the associative and non-associative learning characteristics found in various organisms. We examine microscopic properties concerning electronic and structural transitions leading to collective behavior and theoretical treatments of the ground state and dynamical response, showcasing VO 2 as a model system. Next, we briefly review algorithms designed from the plasticity demonstrated by phase changing systems. Finally, we conclude the brief review with suggestions for future research toward realizing non-von Neumann machines.

42 ENGINEERING↗

NASA NTRS1992

An Engineering Method for Interactive Inviscid-Boundary Layers in Three-Dimensional Hypersonic Flows

An engineering method has been developed that couples an approximate three dimensional inviscid technique with the axisymmetric analog and a set of approximate convective heating equations. The displacement effect on the boundary layer on the outer inviscid flow is calculated and included as a boundary condition in the inviscid technique. This accounts for the viscous interaction present at lower Reynolds numbers. The method is applied to blunted axisymmetric and three dimensional elliptic cones at angle of attack for the laminar hypersonic flow of a perfect gas. The method is applied to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates, pressures, and shock shapes that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes and viscous shock-layer equations. In addition, the inclusion of viscous interaction significantly improves results obtained at lower Reynolds numbers. The new technique represents a major improvement over current engineering aerothermal methods with only a modest increase in computational effort.

Riley, Christopher J.↗

DOE OSTI2023

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

Hardware Interface Description for the Integrated Power, Avionics, and Software (iPAS) Space Telecommunications Radio Ssystem (STRS) Radio

The Space Telecommunications Radio System (STRS) provides a common, consistent framework for software defined radios (SDRs) to abstract the application software from the radio platform hardware. The STRS standard aims to reduce the cost and risk of using complex, configurable and reprogrammable radio systems across NASA missions. To promote the use of the STRS architecture for future NASA advanced exploration missions, NASA Glenn Research Center (GRC) developed an STRS-compliant SDR on a radio platform used by the Advance Exploration System program at the Johnson Space Center (JSC) in their Integrated Power, Avionics, and Software (iPAS) laboratory. The iPAS STRS Radio was implemented on the Reconfigurable, Intelligently-Adaptive Communication System (RIACS) platform, currently being used for radio development at JSC. The platform consists of a Xilinx ML605 Virtex-6 FPGA board, an Analog Devices FMCOMMS1-EBZ RF transceiver board, and an Embedded PC (Axiomtek eBox 620-110-FL) running the Ubuntu 12.4 operating system. Figure 1 shows the RIACS platform hardware. The result of this development is a very low cost STRS compliant platform that can be used for waveform developments for multiple applications.The purpose of this document is to describe how to develop a new waveform using the RIACS platform and the Very High Speed Integrated Circuits (VHSIC) Hardware Description Language (VHDL) FPGA wrapper code and the STRS implementation on the Axiomtek processor.

Flight Computer↗

NASA NTRS2006

Prototype Software for Future Spaceflight Tested at Mars Desert Research Station

NASA scientists in MDRS Crew 49 (April 23-May 7, 2006) field tested and significantly extended a prototype monitoring and advising system that integrates power system telemetry with a voice commanding interface. A distributed, wireless network of functionally specialized agents interacted with the crew to provide alerts (e.g., impending shut-down of inverter due to low battery voltage), access md interpret historical data, and display troubleshooting procedures. In practical application during two weeks, the system generated speech over loudspeakers and headsets lo alert the crew about the need to investigate power system problems. The prototype system adapts the Brahms/Mobile Agents toolkit to receive data from the OneMeter (Brand Electronics) electric metering system deployed by Crew 47. A computer on the upper deck was connected to loudspeakers, four others were paired with wireless (Bluetooth) headsets that enabled crew members to interact with their personal agents from anywhere in the hab. Voice commands and inquiries included: 1. What is the {battery | generator} {volts | amps | volts and amps}? 2. What is the status of the {generator | inverter | battery | solar panel}? 3. What is the hab{itat} {power usage | volts | voltage | amps | volts and amps}? 4. What was the average hab{itat} {amps | volts | voltage} since <#> {AM | PM)? 5. When did the {generator | batteries} change status? 6. Tell {me I | everyone} when{ ever} the generator goes offline. 7. Tell {me | | everyone} when the hab{itat} {amps | volts | voltage} {exceeds | drops brelow} <#>. 8. {Send | Take | Record} {a} voice note {(for | to} } {at }. This research demonstrates the principles of design in the context of use, investigating requirements through experimental use of prototype systems in an analog setting, and use of MDRS as a research facility for designing and implementing new systems.

Clancey, William J.↗

DOE OSTI2020

Primal interface debonding formulation for finite strain isotropic plasticity

In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.

42 ENGINEERING↗

DOE OSTI2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Proof that Combining the Forced-collision and DXTRAN Monte Carlo Variance-reduction Techniques is Fair

This report provides mathematical proof that the MCNP DXTRAN (also known in other codes as forced-flight) and forced-collision variance-reduction techniques do not bias the expected value of Monte Carlo simulation estimates when combined. Proof is also provided that the techniques are unbiased when used independently. To prove that the techniques are unbiased, this report derives the first History Score Moment Equation (HSME) for non-multiplying media employing only forced collisions, only DXTRAN, and then both the variance-reduction techniques combined, as defined next. The HSMEs are found by forming the History Score Probability Density Functions (HSPDFs) and then taking the first score moment. Following its derivation, each HSME with a variance-reduction technique employed is reduced to the HSME for an analog simulation. Because the HSME represents the expected contribution to estimators in the simulation, reducing the HSME with variance reduction to the analog HSME shows that the simulation is unbiased despite the variance-reduction technique considered in the HSME. Analysis regarding higher-score moments of each technique is the subject of prior work and is not addressed herein. Throughout this work, the phase space p is defined to be the particle position x, direction-of-flight unit vector $\hat{Ω}$, energy E, and statistical weight w, $$p ≡ (x; \hat{Ω}; E; w).$$ A reduced phase-space excluding the statistical weight of the particle, $$r ≡ (x; \hat{Ω}; E),$$ is also used.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

Inexpensive Implementation of Many Strain Gauges

It has been proposed to develop arrays of strain gauges as arrays of ordinary metal film resistors and associated electronic readout circuitry on printed circuit boards or other suitable substrates. This proposal is a by-product of a development of instrumentation utilizing metal film resistors on printed-circuit boards to measure temperatures at multiple locations. In the course of that development, it was observed that in addition to being sensitive to temperature, the metal film resistors were also sensitive to strains in the printed-circuit boards to which they were attached. Because of the low cost of ordinary metal film resistors (typically <$0.01 apiece at 2007 prices), the proposal could enable inexpensive implementation of arrays of many (e.g., 100 or more) strain gauges, possibly concentrated in small areas. For example, such an array could be designed for use as a computer keyboard with no moving parts, as a device for sensing the shape of an object resting on a surface, or as a device for measuring strains at many points on a mirror, a fuel tank, an airplane wing, or other large object. Ordinarily, the effect of strain on resistance would be regarded as a nuisance in a temperature-measuring application, and the effect of temperature on resistance would be regarded as a nuisance in a strain-measuring application. The strain-induced changes in resistance of the metal film resistors in question are less than those of films in traditional strain gauges. The main novel aspect of present proposal lies in the use of circuitry affording sufficient sensitivity to measure strain plus means for compensating for the effect of temperature. For an array of metal film resistors used as proposed, the readout circuits would include a high-accuracy analog-to-digital converter fed by a low noise current source, amplifier chain, and an analog multiplexer chain. Corrections would be provided by use of high-accuracy calibration resistors and a temperature sensor. By use of such readout circuitry, it would be possible to read the resistances of as many as 100 fixed resistors in a time interval of 1 second at a resolution much greater than 16 bits. The readout data would be processed, along with temperature calibration data, to deduce the strain on the printed-circuit board or other substrate in the areas around the resistors. It should also be possible to also deduce the temperature from the readings.

Berkun, Andrew C.↗

NASA NTRS2016

Self-Guided Multimedia Stress Management and Resilience Training for Flight Controllers

Stress and anxiety-related problems are among the most common and costly behavioral health problems in society, and for those working in operational environments (i.e. astronauts, flight controllers, military) this can seriously impact crew performance, safety, and wellbeing. Technology-based interventions are effective for treating behavioral health problems, and can significantly improve the delivery of evidence-based health care. This study is evaluating the effectiveness, usefulness, and usability of a self-guided multimedia stress management and resilience training program in a randomized controlled trial (RCT) with a sample of flight controllers at Johnson Space Center. The intervention, SMART-OP (Stress Management and Resilience Training for Optimal Performance), is a six-session, cognitive behavioral-based computer program that uses self-guided, interactive activities to teach skills that can help individuals build resilience and manage stress. In a prior RCT with a sample of stressed but otherwise healthy individuals, SMART-OP reduced perceived stress and increased perceived control over stress in comparison to an Attention Control (AC) group. SMART-OP was rated as "highly useful" and "excellent" in usability and acceptability. Based on α-amylase data, individuals in SMART-OP recovered quicker and more completely from a social stress test as compared to the AC group [1]. In the current study, flight controllers are randomized either to receive SMART-OP training, or to a 6-week waitlist control period (WLC) before beginning SMART-OP. Eligible participants include JSC flight controllers and instructors without any medical or psychiatric disorder, but who are stressed based on self-report. Flight controllers provide a valid analog sample to astronauts in that they work in an operational setting, use similar terminology to astronauts, are mission-focused, and work under the same broader work culture. The study began in December 2014, and to date 79 flight controllers and instructors have expressed interest in the study, 49 of those were cleared for participation, we have screened 44 for eligibility, and 23 have met inclusion criteria. Recruitment is ongoing and the study will continue until December 2016. Outcome measures include perceived stress, perceived control over stress, resilience, mood, personality, emotion regulation, sleep, health behaviors, and psychophysiological data such as 24-hour heart rate, alpha amylase, and urinary and salivary cortisol. We are also collecting user feedback such as usability, working alliance, usefulness, and treatment credibility.

Rose, R. D.↗

DOE OSTI2020

Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

In this note we compute the 1-loop partition function of spin- s s fields on Euclidean de Sitter space S^{2n+1} S 2 n + 1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription L_{\text{AdS}}\to iL_{\text{dS}} L AdS → i L dS , appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1} AdS 2 n + 1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal \text{AdS}_{2n+1} AdS 2 n + 1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p} S 2 n + 1 / ℤ p . We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗