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At least 145 records · Page 8

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Recursive encoding and decoding of the noiseless subsystem and decoherence-free subspace

When an environmental disturbance to a quantum system has a wavelength much larger than the system size, all qubits in the system are under the action of the same error operator. The noiseless subsystem and decoherence-free subspace are immune to such collective noise. We construct simple quantum circuits that implement these error-avoiding codes for a small number n of physical qubits. A single logical qubit is encoded with n=3 and 4, while two and three logical qubits are encoded with n=5 and 7, respectively. Recursive relations among subspaces employed in these codes play essential roles in our implementation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Target tracking via recursive Bayesian state estimation in radar networks

Modern cognitive radar networks incorporating intelligent and cognitive support-modules can actively adjust the radar-target geometry and optimally select a subset of radars to track the target of interest. Based on the theories of dynamic graphical models (DGM) and recursive Bayesian state estimation (RBSE), we propose a framework for single target tracking in mobile and cooperative radar networks, jointly considering path planning and radar selection. We formulate the tracking procedure as two iterative steps: (i) solving a combinatorial problem based on the expected cross-entropy measure to select the optimal subset of radars and their locations, and (ii) tracking the target using RBSE technique. We simulate the proposed framework using an illustrative example in 2-D space and demonstrate the tracking performance.

Xiang, Yijian↗

Evaluating Recursive Blind Forecast Against API and Baseline: A Puerto Rican Case Study on Solar Irradiance for Normal and Extreme Weather

This paper leverages ongoing work in a community microgrid in Adjuntas, Puerto Rico to forecast global horizontal irradiance (GHI) and compare performance in normal and extreme weather. Given a positive correlation of 0.98 between GHI and PV power, forecasting GHI can be an effective, indirect forecast of photovoltaic (PV) power, especially in microgrids where the end-users, owners, operators, or other stakeholders are reluctant to share data for training or validation due to privacy and security concerns. A recursive one-shot (termed as "blind") forecast is, hence, formulated, wherein a gradient-boosted regression tree (GBR) is built to forecast GHI for a 7-day horizon in normal weather, and a 2-day horizon in extreme weather. To demonstrate its resilience, the architecture is trained on normal and hurricane weather GHI from 2002-2022. It is generalized on February 9-16, 2023, and on the landfall of Hurricane Nicole (Nov 4-5, 2022), respectively. Forecasts from GBR are compared against that from a satellite-based API resource and three baselines: persistence, averaging, and exponential smoothing. Results show GBR and persistence outperform sophisticated API in both types of weather for this case study.

Sundararajan, Aditya↗

Management of Large-Scale Wireless Sensor Networks Utilizing Multi-Parent Recursive Area Hierarchies

Autonomously configuring and self-healing a largescale wireless sensor network requires a light-weight maintenance protocol that is scalable. Further, in a battery powered wireless sensor network duty-cycling a node’s radio can reduce the power consumption of a device and extend the lifetime of a network. With duty-cycled nodes the power consumption of a node’s radio depends on the amount of communication is must perform and by reducing the communication the power consumption can also be reduced. Multi-parent hierarchies can be used to reduce the communication cost when constructing a recursive area clustering hierarchy when compared to singleparent solutions that utilize inefficient communication methods such as flooding and information propagation via single-hop broadcasts. The multi-parent hierarchies remain scalable and provides a level of redundancy for the hierarchy.

Environmental Molecular Sciences Laboratory↗

Recursive Blind Forecasting of Photovoltaic Generation and Consumer Load for Microgrids

Existing forecasting frameworks that predict time-series photovoltaic (PV) generation and consumer load for micro-grids' operation and control assume near-continuous availability of real-time predictors from the field. The incoming data are used to periodically re-train the models and update forecast snapshots over a moving horizon window. However, such frameworks are not resilient to disruptions in data availability caused by losses in communications between the field sensors and data loggers. This paper bridges the shortcoming by leveraging a previously proposed forecasting framework that is resilient to abrupt changes in data quality caused by communication losses. Assuming no availability of real-time field system data, which is typical in extreme weather events such as hurricanes, the framework uses lightweight recursive time-series models to independently forecast solar irradiance, ambient temperature, PV power, and consumer load for three horizon windows: 24 hours, 12 hours, and 1 hour. Four types of ensemble-based regression trees-simple gradient boosted trees (GBR), GBR with an adaptive component (A-GBR), random forests (RF), and extra trees (ExTR)-are leveraged and their performances are compared against a simple historical weekly mean. Numerical results show that A-GBR performs better on average by 32% for 24-hour horizon and 39% for 12-hour horizon, whereas ExTR outdoes the other models on average by 10% for 1-hour horizon.

Sundararajan, Aditya↗

Emergent Recursive Multiscale Interaction in Complex Systems

This project studied the potential for multiscale group dynamics in complex social systems, including emergent recursive interaction. Current social theory on group formation and interaction focuses on a single scale (individuals forming groups) and is largely qualitative in its explanation of mechanisms. We combined theory, modeling, and data analysis to find evidence that these multiscale phenomena exist, and to investigate their potential consequences and develop predictive capabilities. In this report, we discuss the results of data analysis showing that some group dynamics theory holds at multiple scales. We introduce a new theory on communicative vibration that uses social network dynamics to predict group life cycle events. We discuss a model of behavioral responses to the COVID-19 pandemic that incorporates influence and social pressures. Finally, we discuss a set of modeling techniques that can be used to simulate multiscale group phenomena.

42 ENGINEERING↗