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At least 73 records · Page 4

Compositional Reasoning for Hierarchical State Machines

Harel statecharts and its derivatives are popular graphical languages for specifying discrete control systems via hierarchical state machines. Separately, there has been a long line of work on specifying concurrent systems with process calculi which come equipped with an algebraic theory, the ability reason compositionally about various temporal properties, and strong type systems. While these two approaches to modeling systems are tantalizingly similar, the integrated reasoning principles that exist for process calculi have not been demonstrated in hierarchical state machines. A key issue is that operational theories for process calculi do not behave like control systems, and thus, there is virtually no tool support for modeling control systems with such languages. For a control system designer, bringing the integrated, more scalable reasoning from the process calculi to state-machine languages would enable the specification of more complex systems and a more modular systems development process. Our insight is that we can recover many important results from the process calculi in hierarchical state machines with local scope. We employ a structural operational semantics, which is ubiquitous in process and 𝜆-calculi but uncommon in hierarchical statemachine formalizations, to enable inductive reasoning about behavior. Taking inspiration from the structure of process calculi metatheories, we define a calculus of refinement and equivalence that we prove sound with respect to local notion of (bi)simulation. Furthermore, we prove that the calculus preserves the behavioral properties of reactivity, observational determinism, traces, and linear temporal properties. Our results are mechanized in the Rocq proof assistant.

97 MATHEMATICS AND COMPUTING↗

Generalized photoclinometry for Mariner 9

A theory is developed for the photoclinometric determination of topography when the photometric function of a planetary surface is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory are presented together with several approaches to the numerical analysis. Reasons for the differences in numerical techniques are discussed. A preliminary result is considered which has been produced for an early Mariner 9 frame wherein the dust-laden atmosphere seems to exhibit standing-wave patterns. It is shown that if the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometry implies that laminar flow lines in the optically observable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50 meters.

Wildey, R. L.↗

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗

Flat-space quantum gravity in the AdS / CFT correspondence

Motivated by the task of understanding microscopic dynamics of an evolving black hole, we present a scheme describing gauge-fixed continuous time evolution of quantum gravitational processes in asymptotically flat spacetime using the algebra of conformal field theory operators. This allows us to study the microscopic dynamics of the Hawking emission process, although obtaining a full S-matrix may require a modification of the minimal scheme. The role of the operator product expansion is to physically interpret the resulting time evolution by decomposing the Hilbert space of the states for the entire system into those for smaller subsystems. We translate the picture of an evaporating black hole previously proposed by the authors into predictions for nonperturbative properties of the conformal field theories that have weakly coupled dual gravitational descriptions. Finally, we also discuss a possible relationship between the present scheme and a reference frame change in the bulk.

79 ASTRONOMY AND ASTROPHYSICS↗

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗

Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings

Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxiliary equipments. In this model, due to the uncertainties of renewable generations including wind turbines and photovoltaic units, the probabilistic spinning reserves are supplied in the form of chance-constrained; from the perspective of user experience, a heating load model is built with consideration of heat comfort and inertia in buildings. To solve the model, a solution approach based on sequence operation theory (SOT) is developed, where the original CCP-based scheduling model is tackled into a solvable mixed-integer linear programming (MILP) formulation by converting a chance constraint into its deterministic equivalence class, and thereby is solved via the CPLEX solver. We report the simulation results on the modified IEEE 30-bus system demonstrate that the presented method manages to improve operational flexibility of the IES with uncertain renewable generations by comprehensively leveraging thermal inertia of buildings and different kinds of auxiliary equipments, which provides a fundamental way for promoting renewable energy consumption.

30 DIRECT ENERGY CONVERSION↗

Electro-optical measurement of intense electric field on a high energy pulsed power accelerator

We describe a direct electro-optical approach to measuring a strong 118 MV/m narrow pulse width (~ 33 ns) electric field in the magnetically insulated transmission line (MITL) of a pulsed power accelerator. To date, this is the highest direct external electric field measured electro-optically in a pulsed power accelerator, and it is between two to three orders of magnitude higher than values reported in comparable high energy scientific experiments. The MITL electric field is one of the most important operating parameters in an accelerator and is critical to understanding the properties of the radiation output. However, accurately measuring these high fields using conventional pulsed power diagnostics is difficult due to the strength of interfering particles and fields. Our approach uses a free-space laser beam with a dielectric crystal sensor that is highly immune to electromagnetic interference and does not require an external calibration. Here we focus on device theory, operating parameters, laboratory and pulsed power accelerator experiments as well as challenges that were overcome in the measurement environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magneto-optical measurement of magnetic field and electrical current on a short pulse high energy pulsed power accelerator

We describe a direct magneto-optical approach to measuring the magnetic field driven by a narrow pulse width (<10 ns), 20 kA electrical current flow in the transmission line of a high energy pulsed power accelerator. The magnetic field and electrical current are among the most important operating parameters in a pulsed power accelerator and are critical to understanding the properties of the radiation output. However, accurately measuring these fields and electrical currents using conventional pulsed power diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element sensing crystal sensor that is highly resistant to electromagnetic interference and does not require external calibration. Here, we focus on device theory, operating parameters, results from an experiment on a high energy pulsed power accelerator, and comparison to a conventional electrical current shunt sensor.

42 ENGINEERING↗

Predicting Critical Transitions in Multiscale Data

Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.

97 MATHEMATICS AND COMPUTING↗

Absolute magneto-optical measurement of magnetic field on a long pulse high electrical current driven solenoid

We describe a direct absolute magneto-optical approach to measuring the magnetic field driven by long pulse width (>5 ms) and high electrical current (∼kA) in a solenoidal coil. The magnetic field and electrical current are among the most important operating parameters in lightning research and electrical power distribution and are essential to understanding the properties of the radiation output in pulsed energy accelerators as well as other research platforms. However, accurately measuring these magnetic fields and electrical currents using conventional electrical diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element material sensing crystal that is highly resistant to electromagnetic interference, allows for absolute measurement, and does not require an external calibration. Here, we focus on device theory, operating parameters, magneto-optical results from an experiment on a high current solenoid, and comparison with a calculation of the magnetic field and reference electrical current flowing downstream of the solenoid.

Owens, Israel [Sandia National Laboratories (SNL-N↗

Deep transfer operator learning for partial differential equations under conditional shift

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. Here, we propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains.

42 ENGINEERING↗

Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model

In this work, we propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Three paths toward the quantum angle operator

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Renormalization of beta decay at three loops and beyond

The anomalous dimension for heavy-heavy-light effective theory operators describing nuclear beta decay is computed through three-loop order in the static limit. The result at order Z 2 α 3 corrects a previous result in the literature. An all-orders symmetry is shown to relate the anomalous dimensions at leading and subleading powers of Z at a given order of α . The first unknown coefficient for the anomalous dimension now appears at O ( Z 2 α 4 ) . Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

e + e – → ZH process in the SMEFT beyond leading order

We systematically study potential effects of Beyond the Standard Model physics in the e + e – → ZH process. To this end, we include all relevant dimension-6 Standard Model Effective Field Theory operators and work to next-to-leading order (NLO) accuracy in the electroweak coupling. We consider both polarized and unpolarized electron and positron beams and present results for $\sqrt {s}$ = 240, 365 and 500 GeV, emphasizing contributions where the NLO predictions differ significantly from the leading order results. At NLO, a sensitivity arises to operators that do not contribute at tree level, such as the Higgs tri-linear coupling, CP-violating operators, and dimension-6 operators involving the top quark, among many others. We compare the prospects of future e + e – colliders to explore these new physics effects with existing measurements from the LHC, electron EDMs (for CP violating operators), and Z pole measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Vector boson scattering and anomalous quartic couplings in final states with ℓνqq or ℓℓqq plus jets using proton-proton collisions at $\sqrt{s}=13$ TeV

A measurement is presented of the electroweak vector boson scattering production of ZV (V = W, Z) boson pairs associated with two jets in proton-proton collisions at a center-of-mass energy of 13 TeV. The data, corresponding to an integrated luminosity of 138 fb −1 , were collected at the CERN LHC with the CMS detector during the 2016–2018 data-taking period. The analysis targets final states with a pair of isolated electrons or muons from Z boson decays and three or four jets, depending on the momentum of the vector boson that decays into quarks. Signal strength is measured for events characterized by a large invariant mass of two forward jets with a wide pseudorapidity gap between them. The electroweak production of ZV in association with two jets is measured with an observed (expected) significance of 1.3 (1.8) standard deviations. A combination of the analyses of ZV channel and the previously published WV channel in the lepton plus jets final state places constraints on effective field theory parameters that describe anomalous electroweak production of WW, WZ, and ZZ boson pairs in association with two jets. Several world best limits are set on anomalous quartic gauge couplings in terms of dimension-8 standard model effective field theory operators.

Hadron-Hadron Scattering↗

Measurements of electroweak production of a photon in association with two jets in proton-proton collisions at $\sqrt{s}=13$ TeV

The first observation of electroweak production of a photon in association with two forward jets in proton-proton collisions is presented. The measurement uses data recorded by the CMS experiment at the LHC during 2016–2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb −1 . The analysis is performed in a region enriched in photon production via vector boson fusion, with a requirement on the transverse momentum of the photon to exceed 200 GeV. The cross section is measured to be ${202}_{-32}^{+36}$ fb, at a significance with respect to the null hypothesis that exceeds five standard deviations. This is in agreement with the standard model prediction of ${177}_{-12}^{+13}$ fb. Differential cross sections are measured as a function of various observables. Limits are set on dimension-6 effective field theory operators that contribute to the WW γ interaction. The observed 95% confidence intervals for the corresponding Warsaw basis Wilson coefficients c W and c HWB are [−0.11, 0.16] and [−1.6, 1.5], respectively.

electroweak interaction↗