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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

‪A Novel Methodology for Longitudinal Studies of Home Thermal Comfort Perception and Behavior

Human-building interactions significantly influence building energy consumption and affect peak energy demand. For example, heating and cooling contribute 46% of daily peak residential energy demand. Grid-interactive efficient buildings (GEBs) can potentially increase energy-demand flexibility and accelerate the adoption of renewables. However, traditional demand response (DR) programs focused on shedding peak loads disregard the human-building interactions leading to occupant thermal frustration. Specifically, they do not model occupants’ ability to override thermostat controls, nor how indoor environmental conditions and sociocultural factors affect the timing and magnitude of overrides. Studies have found 20% of occupants override thermostat setpoints during DR events longer than 6 hours yet lack detail about the motivation that might guide more successful efforts. Balancing energy-demand flexibility with occupant thermal comfort requires understanding dynamic occupant behavior, the underlying psychophysiological drivers, in the context of homes. This paper presents methods for scalable longitudinal studies of residential occupant behavior dynamics to inform the development of psychophysiological occupant-centric building models. Smart sensors were installed to measure local environmental conditions in 20 homes in two regions of the United States. Just-in-time ecological momentary assessments (EMAs) provided qualitative data on occupant thermal comfort and local environmental conditions not captured in Internet-of-Things (IoT) based studies or existing datasets. Participant interviews provided insight into environmental attitudes, mental models, and the role of economics in comfort and behavior, which in turn may affect thermostat interactions. Based on these data, interventions in the next phase of the study will collect data and monitor occupant behavior during simulated DR events.

Kane, Michael↗
DOE OSTI2020

Behind the Meter Storage for Electric Vehicle Charging, Electrochemical and Thermal Energy Storage, and Solar Photovoltaic

In response to the potentially large and irregular demand from EVs, along with changing load profiles from buildings with on-site generation, utilities are evaluating multiple options for managing dynamic loads, including time-of-use pricing, demand charges, battery storage, and curtailment of variable generation. Buildings, as well as commercial, public, and workplace EV charging operations, can use a combination of electrochemical battery storage and thermal energy storage coupled with on-site generation to manage energy costs as well as provide resiliency and reliability for EV charging and building energy loads. We are completing a behind the meter storage analysis that focuses on determining the optimal system designs and energy flows for thermal and electrochemical behind the meter storage with on-site solar photovoltaic (PV) generation enabling electric vehicle charging in various climates, building types, and utility rate structures. In completing this analysis, we have developed a tool that combines existing battery models via the System Advisor Model (SAM) and building modeling software via EnergyPlus into a single interface. This tool allows us to simulate a building with a detailed battery model to properly size the battery, thermal energy storage, and solar PV systems to maximize profit for the system owner. This also allows us to assess how the battery degrades under various supervisory control dispatch algorithms to control charging/discharging; we can also see how thermal energy storage is created and used to complement the battery to reduce thermal loads in the building. With this project, we can analyze new batteries that are designed specifically for energy storage, rather than designed to be extremely energy dense for electric vehicle applications, using battery lifetime models from other national labs and the existing SAM battery model, which has detailed lifetime and degradation parameters. We can also assess novel thermal storage technologies by integrating them into the whole building energy simulation program EnergyPlus. Because the model calls both SAM and EnergyPlus, required inputs need to be compatible for both models. These inputs include, on a high-level, the following: weather files, building and electric vehicle load profiles, electricity rate tariff information, and system cost information for the stationary battery, solar PV, and thermal storage system. The various buildings we are studying for this analysis are retail big-box grocery store, commercial office building, fleet vehicle depot and operations facility, multi-family residential, and electric vehicle charging station. For these different applications, the battery and thermal storage will be dispatched differently, and the various technologies are sized differently to optimize cost.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

Dynamic Nanocrystal Superlattices with Thermally Triggerable Lubricating Ligands

The size-dependent and collective physical properties of nanocrystals (NCs) and their self-assembled superlattices (SLs) enable the study of mesoscale phenomena and the design of metamaterials for a broad range of applications. However, the limited mobility of NC building blocks in dried NCSLs often hampers the potential for employing postdeposition methods to produce high-quality NCSLs. In this study, we present tailored promesogenic ligands that exhibit a lubricating property akin to thermotropic liquid crystals. The lubricating ability of ligands is thermally triggerable, allowing the dry solid NC aggregates deposited on the substrates with poor ordering to be transformed into NCSLs with high crystallinity and preferred orientations. The interplay between the dynamic behavior of NCSLs and the molecular structure of the ligands is elucidated through a comprehensive analysis of their lubricating efficacy using both experimental and simulation approaches. Coarse-grained molecular dynamic modeling suggests that a shielding layer from mesogens prevents the interdigitation of ligand tails, facilitating the sliding between outer shells and consequently enhancing the mobility of NC building blocks. Further, the dynamic organization of NCSLs can also be triggered with high spatial resolution by laser illumination. The principles, kinetics, and utility of lubricating ligands could be generalized to unlock stimuli-responsive metamaterials from NCSLs and contribute to the fabrication of NCSLs.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Cloud-based implementation of white-box model predictive control for a GEOTABS office building: A field test demonstration

Model predictive control (MPC) has been proven in simulations and pilot case studies to be a superior control strategy for large buildings. MPC can utilize the weather and occupancy schedule forecasts, together with the system model, to predict the future thermal behavior of the building and minimize the overall energy use and maximize thermal comfort. However, these advantages come with the cost of increased modeling effort, computational demands, communication infrastructure, and commissioning efforts. Thus a typical approach is to, often rapidly, simplify the building modeling and MPC optimization problem while paying a price of not reaching the full performance potential. It has been shown that by employing accurate physics-based models, MPC performance can be notably increased closer to its theoretical performance bound. However, implementation of such high-fidelity MPC in real buildings remains a challenge, resulting in a lack of successful field test studies. This work presents the methodology and field test demonstration of a computationally efficient implementation of the white-box MPC in an office building in Belgium. The detailed model of the building is based on first-principle physical equations. The deployment and supervision of MPC operation in a practical setting are supported by an automated cloud-based communication infrastructure. The motivating factor behind the cloud-based architecture is its compatibility with a commercially appealing control as a service concept. The building is equipped with a ground source heat pump (GSHP) and thermally activated building structures (TABS), where the combination of both is also known as GEOTABS. From a control perspective, GEOTABS buildings are particularly challenging systems due to large scale, complex heating, ventilation and air conditioning (HVAC) system, and slow dynamics with time delays. On the other hand, there is an increased potential for energy savings due to the high thermal mass, which acts as thermal storage. The MPC operation is demonstrated during the challenging transient seasons (switching between heating and cooling), and its performance is compared to a traditional rule-based controller (RBC). We provide a proof of concept of real MPC operation for the most difficult seasons with notable GSHP energy use savings equal to 53.5% and thermal comfort improvement by 36.9%. Other MPC applications found in the literature describe tests for only cooling or only heating, and up to now only for a black-box or a grey-box approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Model predictive control for integrated control of air-conditioning and mechanical ventilation, lighting and shading systems

Modern buildings are increasingly automated and often equipped with multiple building services (e.g., air-conditioning and mechanical ventilation (ACMV), dynamic shading, dimmable lighting). These systems are conventionally controlled individually without considering their interactions, affecting the building’s overall energy inefficiency and occupant comfort. A model predictive control (MPC) system that features a multi-objective MPC scheme to enable coordinated control of multiple building services for overall optimized energy efficiency, indoor thermal and visual comfort, as well as a hybrid model for predicting indoor visual comfort and lighting power is proposed. The MPC system was implemented in a test facility having two identical, side-by-side experimental cells to facilitate comparison with a building management system (BMS) employing conventional reactive feedback control. The MPC system coordinated the control of the ACMV, dynamic façade and automated dimmable lighting systems in one cell while the BMS controlled the building services in the other cell in a conventional manner. The MPC side achieved 15.1–20.7% electricity consumption reduction, as compared to the BMS side. Simultaneously, the MPC system improved indoor thermal comfort by maintaining the room within the comfortable range (-0.5 < predicted mean vote < 0.5) for 98.3% of the time, up from 91.8% of the time on the BMS side. Visual comfort, measured by indoor daylight glare probability (DGP) and horizontal illuminance level at work plane height, was maintained for the entire test period on the MPC side, improving from having visual comfort for 94.5% and 85.7% of the time, respectively, on the BMS side.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

DEVAP-EDDR-TES (Simulation framework for a desiccant assisted air conditioning system with heat pump regeneration and energy storage) [SWR-24-66]

This software is a simulation framework that models a load flexible air conditioner system. The system consists of an evaporatively cooled liquid desiccant air conditioner (eLD-AC) subsystem, an electrically driven desiccant regenerator (EDDR) subsystem, and a stratified liquid desiccant storage (SLDS) subsystem. The software can be used to 1) predict the steady-state performance of the system given user-specified convergence criteria; 2) predict the dynamic performance of the entire system over a typical drive cycle operation subjected to user-specified building thermal loads and desired electrical load profile; 3) evaluate the synergy of all three subsystems operating altogether and improve the energy storage control strategy.

Huang, Ransisi↗
DOE OSTI2022

Electro-Thermal Characterization of Dynamical VO 2 Memristors via Local Activity Modeling

We report translating the surging interest in neuromorphic electronic components, such as those based on nonlinearities near Mott transitions, into large-scale commercial deployment faces steep challenges in the current lack of means to identify and design key material parameters. These issues are exemplified by the difficulties in connecting measurable material properties to device behavior via circuit element models. Here, the principle of local activity is used to build a model of VO 2 /SiN Mott threshold switches by sequentially accounting for constraints from a minimal set of quasistatic and dynamic electrical and high-spatial-resolution thermal data obtained via in situ thermoreflectance mapping. By combining independent data sets for devices with varying dimensions, the model is distilled to measurable material properties, and device scaling laws are established. The model can accurately predict electrical and thermal conductivities and capacitances and locally active dynamics (especially persistent spiking self-oscillations). The systematic procedure by which this model is developed has been a missing link in predictively connecting neuromorphic device behavior with their underlying material properties, and should enable rapid screening of material candidates before employing expensive manufacturing processes and testing procedures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Thermally induced structural evolution and nanoscale interfacial dynamics in Bi-Sb-Te layered nanostructures

Layered chalcogenides, including Bi-Sb-Te ternary alloys and heterostructures, are renowned as thermoelectric and topological insulators and have recently been highlighted as plasmonic building blocks beyond noble metals. Here, we conduct joint in situ transmission electron microscopy and density functional theory calculations to investigate the temperature-dependent nanoscale dynamics and interfacial properties, identifying the role of native defects and edge configurations in the anisotropic sublimation of Bi 2 Te 3 -Sb 2 Te 3 heterostructures and Sb 2-x Bi x Te 3 alloys. We report structural dynamics, including edge evolution, layer-by-layer sublimation, and the formation and coalescence of thermally induced polygonal nanopores. These nanopores are initiated by preferential dissociation of tellurium, reducing thermal stability in heterostructures. Triangular and quasi-hexagonal configurations dominate nanopore structures in heterostructures. Our calculations reveal antisite defects (Te Sb and Te Bi ) as key players in defect-assisted sublimation. These findings enhance our understanding of nanoscale dynamics and assist in designing tunable low-dimensional chalcogenides.

Bi2Te3-Sb2Te3 heterostructure↗
NASA NTRS1997

Proceedings of the Eighth Annual Thermal and Fluids Analysis Workshop: Spacecraft Analysis and Design

This document contains papers presented at the Eighth Annual Thermal and Fluids Analysis Workshop (TFAWS) on Spacecraft Analysis and Design hosted by the NASA/Johnson Space Center (JSC) on September 8-11, 1997, and held at the University of Houston - Clear Lake (UHCL) in the Bayou Building. The Workshop was sponsored by NASA/JSC. Seminars were hosted and technical papers were provided in fluid and thermal dynamics. Seminars were given in GASP, SINDA, SINAPS Plus, TSS, and PHOENICS. Seventeen papers were presented.

Peters, Todd↗
DOE OSTI2025

Data-driven modeling of dynamic occupant thermostat override behavior for demand response applications

Buildings consume nearly 40% of global energy and produce similar emissions. Whiletechnological advances address efficiency, occupant behavior causes energy use variations up to 300% between identical buildings. This gap between predicted and actual building performance impacts building design, operations, and grid demand management programs. Through analyses of smart thermostat data from 1,400 single-occupant homes, the researchdemonstrates that occupants respond to 8°F thermostat setpoint changes within a median of 15 minutes, while 2°F changes trigger responses within a median of 30 minutes. This highlights an understudied temporal relationship between thermostat setbacks and response time of occupant behaviors. Models of such behavior dynamics are required to incorporate occupant impacts into building performance simulation. A key contribution of this dissertation is the Thermal Frustration Theory (TFT), which positsthat thermal discomfort driven behaviors are caused by the time-accumulation of discomfort, not simply a temperature deviation threshold or a delay from an initiating event. Using a dataset of 634 thermostats, each with 25+ manual setpoint changes, a comparative analysis of TFT and comfort zone and a delayed response theories demonstrated that personalized TFT models better predict when manual setpoint change occur. This was measured by the area under the curve statistical measure (AUC); all three models perform similarly by a Matthews Correlation Coefficient measure. Higher AUC performance is especially important for modeling occupant behavior in demand response programs where false negatives of rare occupant interactions could adversely affect grid stability. EnergyPlus based simulations were conducted with TFT-derived occupant models, demonstrating the ability to identify parameters of known TFT models from only data observable with smart thermostats, even under the presence of noise from routine overrides. Overall, the dissertation highlights that thermostat interactions are neither static,instantaneous, nor driven solely by the environment. Instead, temporal accumulation of discomfort and routine-based behavior play important roles. The methodology and results offer a pathway towards more accurate modeling of human-building interactions for policy assessment, building design, and demand response programs.

Sharma, Kunind [Northeastern University] (ORCID:00↗
DOE OSTI2021

Dynamic tunability of phase-change material transition temperatures using ions for thermal energy storage

Thermal energy storage (TES) based on phase-change materials (PCMs) has many current and potential applications, such as climate control in buildings, thermal management for batteries and electronics, thermal textiles, and transportation of pharmaceuticals. Despite its promise, the adoption of TES has been limited, in part due to limited tunability of the transition temperature, which hinders TES performance for varying use temperatures. Transition temperature tuning of a material using an external stimulus, such as pressure or an electric field, typically requires very large stimuli. To circumvent this problem, here, we report on the dynamic transition temperature tunability of a PCM using ions. We achieve a transition temperature tunability up to 6°C in polyethylene glycol (PEG) by using the salt lithium oxalatodifluoroborate at a low voltage of 2.5 V, which may enable simpler and safer devices/system designs. We also explain the thermal properties of the salt/PCM solution using the Flory-Huggins theory.

25 ENERGY STORAGE↗
DOE OSTI2022

Resilient cooling through geothermal district energy system

Decarbonization and resilience to heat waves have recently become high priorities for building and district energy systems. Geothermal coupled district heating and cooling systems that operate a water loop near ground temperature gain increasing adoption to support decarbonization. In these systems, vapor-compression machines, distributed in the energy transfer stations, lift the temperature up or down to the needs of the particular building. In principle, these systems can provide low-power, free cooling from the geothermal bore field during heat waves when electricity is often scarce. However, the performance of such a resilience operation mode and its implication on the energy system configuration and the sizing of the bore field and HVAC equipment is not yet understood. Consequently, we are assessing their resilience, power use and design implications under a scenario of a heat wave on five working days during which chillers are switched off to reduce electrical consumption. Our analysis is based on high-fidelity, coupled dynamic models of district energy, building-side HVAC and actual control logic, with whole building energy simulation used to assess thermal conditions in a 2004 vintage multi-zone office building in Chicago, IL. The results show that relying only on waterside economizer cooling, the indoor thermal conditions can be maintained in a tolerable range for the majority of the building zones with half the electrical energy compared to standard chiller operation. Thermal comfort in the hottest zones can be further improved by oversizing the cooling coil. However, the waterside economizer has significant implications on the system configuration and sizing: The geothermal bore field needs to be sized about 30% larger than the upper limit of the range observed for conventional geothermal systems. Nevertheless, if a central chiller plant is added, the bore field can be downsized to the typical design range. The latter configuration still allows compressor-less cooling during the heat wave with peak power reduced by 60% compared to the standard design and chiller operation.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Performance evaluation of underground thermal storage integrated dual-source heat pump systems

The increasing demand for electricity stresses the existing electric grids. Buildings consume 73% of all U.S. electricity and are responsible for 30% of U.S. greenhouse gas emissions. Integrating thermal energy storage (TES) in building heating/cooling systems, which consume considerable electricity, can mitigate the challenges to electric grids. Here, this study reports on a novel thermal energy storage device integrated heat pump system to reshape the building electricity demand profile while maintaining thermal comfort. The annual performance of the proposed system has been evaluated through a dynamic system simulation with high fidelity in the Modelica platform. The dynamic model of the novel hybrid component named ‘dual purpose underground thermal battery’ was developed and validated. It was then incorporated into the system model. Given a time-of-use tariff, a rule-based control strategy was designed to shift the electric demand and switch the heat pump source for a typical single-family house in different climate zones of the United States. The system performance of the new TES-integrated dual-source heat pump was compared with that of a conventional air-source heat pump system. The results indicate that the proposed system can reduce the annual HVAC electricity cost by up to 52% while saving 45.2% on electricity consumption. In the Northern areas, the annual peak load of the HVAC system can be reduced by 64.9%. However, this reduction is less in the Southern areas as the system’s higher efficiency in winter dominates the overall energy-saving potential.

25 ENERGY STORAGE↗
NASA NTRS1992

Control-structure-thermal interactions in analysis of lunar telescopes

The lunar telescope project was an excellent model for the CSTI study because a telescope is a very sensitive instrument, and thermal expansion or mechanical vibration of the mirror assemblies will rapidly degrade the resolution of the device. Consequently, the interactions are strongly coupled. The lunar surface experiences very large temperature variations that range from approximately -180 C to over 100 C. Although the optical assemblies of the telescopes will be well insulated, the temperature of the mirrors will inevitably fluctuate in a similar cycle, but of much smaller magnitude. In order to obtain images of high quality and clarity, allowable thermal deformations of any point on a mirror must be less than 1 micron. Initial estimates indicate that this corresponds to a temperature variation of much less than 1 deg through the thickness of the mirror. Therefore, a lunar telescope design will most probably include active thermal control, a means of controlling the shape of the mirrors, or a combination of both systems. Historically, the design of a complex vehicle was primarily a sequential process in which the basic structure was defined without concurrent detailed analyses or other subsystems. The basic configuration was then passed to the different teams responsible for each subsystem, and their task was to produce a workable solution without requiring major alterations to any principal components or subsystems. Consequently, the final design of the vehicle was not always the most efficient, owing to the fact that each subsystem design was partially constrained by the previous work. This procedure was necessary at the time because the analysis process was extremely time-consuming and had to be started over with each significant alteration of the vehicle. With recent advances in the power and capacity of small computers, and the parallel development of powerful software in structural, thermal, and control system analysis, it is now possible to produce very detailed analyses of intermediate designs in a much shorter period of time. The subsystems can thus be designed concurrently, and alterations in the overall design can be quickly adopted into each analysis; the design becomes an iterative process in which it is much easier to experiment with new ideas, configurations, and components. Concurrent engineering has the potential to produce efficient, highly capable designs because the effect of one subystem on another can be assessed in much more detail at a very early point in the program. The research program consisted of several tasks: scale a prototype telescope assembly to a 1 m aperture, develop a model of the telescope assembly by using finite element (FEM) codes that are available on site, determine structural deflections of the mirror surfaces due to the temperature variations, develop a prototype control system to maintain the proper shape of the optical elements, and most important of all, demonstrate the concurrent engineering approach with this example. In addition, the software used for the finite element models and thermal analysis was relatively new within the Program Development Office and had yet to be applied to systems this large or complex; understanding the software and modifying it for use with this project was also required. The I-DEAS software by Structural Dynamics Research Corporation (SDRC) was used to build the finite element models, and TMG developed by Maya Heat Transfer Technologies, Ltd. (which runs as an I-DEAS module) was used for the thermal model calculations. All control system development was accomplished with MATRIX(sub X) by Integrated Systems, Inc.

Thompson, Roger C.↗
NASA NTRS1979

Cryogenic thermal diode heat pipes

The development of spiral artery cryogenic thermal diode heat pipes was continued. Ethane was the working fluid and stainless steel the heat pipe material in all cases. The major tasks included: (1) building a liquid blockage (blocking orifice) thermal diode suitable for the HEPP space flight experiment; (2) building a liquid trap thermal diode engineering model; (3) retesting the original liquid blockage engineering model, and (4) investigating the startup dynamics of artery cryogenic thermal diodes. An experimental investigation was also conducted into the wetting characteristics of ethane/stainless steel systems using a specially constructed chamber that permitted in situ observations.

Alario, J.↗
DOE OSTI2023

An evaluation of the demand response potential of integrated dynamic window and HVAC systems

Demand response (DR) increases the flexibility and reliability of the electricity grid as use of intermittent renewable energy sources increases. HVAC and envelope DR measures present the largest aggregate energy and peak demand savings potential of all commercial building end uses because their net demand savings occur during critical peak demand periods. Controllable envelope measures include switchable electrochromic windows, operable window attachments such as outdoor louvers, roller shades, and awnings, as well as other innovative facade technologies that can modulate both solar heat gain and daylight admission over a broad solar-optical range. This study evaluated the technical potential of DR-enabled dynamic windows to reduce critical peak demand for a prototypical medium office building situated in all 16 U.S. climates. Model predictive control (MPC) algorithms were designed to minimize electricity cost in daylit perimeter office zones through control of an electrochromic window with and without HVAC thermostat setpoint control. Conventional and time-of-use rates were used to shape the degree of DR. Median annual peak demand savings with window and thermostat control across all climate zones were 24.3 kW (4.4 W/m 2 ) per building or 15.9 W/m 2 for non-north perimeter zones. Resource adequacy at the whole building level was estimated to be 13.1 to 43.4 $/kW per year over the 30-year life of the installation. Co-benefits were increased energy efficiency, and reduced electricity cost and emissions. Visual and thermal comfort requirements were met at all times. Dynamic facades controlled by MPC have substantial technical potential for DR across all U.S. climates and warrant serious consideration for inclusion in DR portfolios.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Advancing Mass Timber Buildings: Novel Methods Improve Thermal Assessment and Material Use

For nearly a century, thermal demand calculations for buildings have relied on simplified models developed to match the technical constraints of their era. The first standards, introduced in Germany and Austria in 1929, established climate zones and material conductivity coefficients that, with only incremental updates, still underpin many current assessments. Yet, methods such as Hot box testing, originally designed for lightweight insulation, continue to be applied for mass timber buildings, overlooking thermodynamic characteristics confer real-world advantages. Recent research at Oak Ridge National Laboratory incorporates updated methodologies, aligned with ASHRAE Standard 55 (ASHRAE, 2023) accounting for factors such as thermal inertia, inner surface temperatures, emissivity, solar gains, and dynamic outdoor conditions. These factors better reflect observed heating and cooling loads and highlight opportunities for efficient use of materials in mass timber construction. This work provides a framework for designing comfortable, resilient, and resource-efficient buildings while aligning with performance expectations in energy codes.

Pickett, Robert [International Mass Timber Allianc↗
DOE OSTI2022

Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics

This review focuses on a recent class of path-integral-based methods for the simulation of nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. As a result, the remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗