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At least 883 records · Page 49

A stiff order condition theory for Runge–Kutta methods applied to semilinear ODEs

Classical convergence theory of Runge–Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy, known as order reduction, can arise. Methods with high stage order, e.g., Gauss–Legendre and Radau, are known to avoid order reduction, but they must be fully implicit. For the broad class of semilinear ODEs, which consist of a stiff linear term and non-stiff nonlinear term, we show that weaker conditions suffice. Here, our new semilinear order conditions are formulated in terms of orthogonality relations and can be enumerated by rooted trees. Finally, we prove global error bounds that hold uniformly with respect to stiffness of the linear term.

Mathematics and Computing↗

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

CUPID: The Next-Generation Neutrinoless Double Beta Decay Experiment

We report CUPID is a next-generation tonne-scale bolometric neutrinoless double beta decay experiment that will probe the Majorana nature of neutrinos and discover lepton number violation in case of observation of this singular process. CUPID will be built on experience, expertise and lessons learned in CUORE and will be installed in the current CUORE infra-structure in the Gran Sasso underground laboratory. The CUPID detector technology, successfully tested in the CUPID-Mo experiment, is based on scintillating bolometers of Li 2 MoO 4 enriched in the isotope of interest 100 Mo. In order to achieve its ambitious science goals, the CUPID collaboration aims to reduce the backgrounds in the region of interest by a factor 100 with respect to CUORE. This performance will be achieved by introducing the high efficient α/β discrimination demonstrated by the CUPID-0 and CUPID-Mo experiments, and using a high transition energy double beta decay nucleus such as 100 Mo to minimize the impact of the gamma background. CUPID will consist of about 1500 hybrid heat-light detectors for a total isotope mass of 250 kg. The CUPID scientific reach is supported by a detailed and safe background model based on CUORE, CUPID-Mo and CUPID-0 results. The required performances have already been demonstrated and will be presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Realization of the Werner-Holevo and Landau-Streater Quantum Channels for Qutrits on Quantum Computers.

We realize the Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on IBM quantum computers. These channels correspond to the interaction between a qutrit and its environment that results in the globally unitarily covariant qutrit transformation violating the multiplicativity of the maximal p-norm. Our realization of the LS and WH channels is based on embedding the qutrit states into states of two qubits and using the single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates, hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit computer and a 20-qubit computer, as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by the fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.

completely-positive trace-preserving map↗

Catastrophic Cooling Instability in Optically Thin Plasmas

The solar corona is the prototypical example of a low-density environment heated to high temperatures by external sources. The plasma cools radiatively, and because it is optically thin to this radiation, it becomes possible to model the density, velocity, and temperature structure of the system by modifying the MHD equations to include an energy source term that approximates the local heating and cooling rates. The solutions can be highly inhomogeneous and even multiphase because the well-known linear instability associated with this source term, thermal instability, leads to a catastrophic heating and cooling of the plasma in the nonlinear regime. Here we show that there is a separate, much simpler linear instability accompanying this source term that can rival thermal instability in dynamical importance. The stability criterion is the isochoric one identified by Parker (1953), and we demonstrate that cooling functions derived from collisional ionization equilibrium are highly prone to violating this criterion. If catastrophic cooling instability can act locally in global simulations, then it is an alternative mechanism for forming condensations, and due to its nonequilibrium character, it may be relevant to explaining a host of phenomena associated with the production of cooler gas in hot, low density plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Surface-Topography Challenge: A Multi-Laboratory Benchmark Study to Advance the Characterization of Topography

Surface performance is critically influenced by topography in virtually all real-world applications. The current standard practice is to describe topography using one of a few industry-standard parameters. The most commonly reported number is Ra, the average absolute deviation of the height from the mean line (at some, not necessarily known or specified, lateral length scale). However, other parameters, particularly those that are scale-dependent, influence surface and interfacial properties; for example the local surface slope is critical for visual appearance, friction, and wear. The present Surface-Topography Challenge was launched to raise awareness for the need of a multi-scale description, but also to assess the reliability of different metrology techniques. In the resulting international collaborative effort, 153 scientists and engineers from 64 research groups and companies across 20 countries characterized statistically equivalent samples from two different surfaces: a “rough” and a “smooth” surface. The results of the 2088 measurements constitute the most comprehensive surface description ever compiled. We find wide disagreement across measurements and techniques when the lateral scale of the measurement is ignored. Consensus is established through scale-dependent parameters while removing data that violates an established resolution criterion and deviates from the majority measurements at each length scale. Our findings suggest best practices for characterizing and specifying topography. The public release of the accumulated data and presented analyses enables global reuse for further scientific investigation and benchmarking.

42 ENGINEERING↗

Formal verification and validation of run-to-completion style state charts using Event-B

State chart notations with ‘run to completion’ semantics are popular with engineers for designing controllers that react to environment events with a sequence of state transitions but lack formal refinement and rigorous verification methods. State chart models are typically used to design complex control systems that respond to environmental triggers with a sequential process. The model is usually constructed at a concrete level and verified and validated using animation techniques relying on human judgement. Event-B, on the other hand, is based on refinement from an initial abstraction and is designed to make formal verification by automatic theorem provers feasible. Abstraction and formal verification provide greater assurance that critical (e.g. safety or security) properties are not violated by the control system. In this paper, we introduce a notion of refinement into a ‘run to completion’ state chart modelling notation and leverage Event-B’s tool support for theorem proving. We describe the difficulties in translating ‘run to completion’ semantics into Event-B refinements and suggest a solution. We illustrate our approach and show how models can be validated at different refinement levels using our scenario checker animation tools. We show how critical invariant properties can be verified by proof despite the reactive nature of the system and how behavioural aspects of the system can be verified by testing the expected reactions using a temporal logic, model checking approach. To verify liveness, we outline a proof that the run to completion is deadlock-free and converges to complete the run.

97 MATHEMATICS AND COMPUTING↗

Dihadron azimuthal asymmetry and light-quark dipole moments at the Electron-Ion Collider

Here, we propose a novel method to probe light-quark dipole moments by examining the azimuthal asymmetries between a collinear pair of hadrons in semi-inclusive deep inelastic lepton scattering off an unpolarized proton target at the Electron-Ion Collider. These asymmetries provide a means to observe transversely polarized quarks, which arise exclusively from the interference between the dipole and the Standard Model interactions, thereby depending linearly on the dipole couplings. We demonstrate that this novel approach can enhance current constraints on light-quark dipole operators by an order of magnitude, free from contamination of other new physics effects. Furthermore, it allows for a simultaneous determination of both the real and imaginary parts of the dipole couplings, offering a new avenue for investigating potential CP-violating effects at high energies.

dihadron fragmentation↗

Triaxial Constraint and Tensile Strength Enhancement in Brazed Joints

A brazed joint consists of a low-melting point and thin interlayer sandwiched between the high-melting-point base materials, in which the interlayer strength is typically lower than that of the base material. When this butt-joined composite is loaded uniaxially in the direction perpendicular to the plane of the brazing layer, the tensile strength is found to be much higher than that of the braze. This seems to violate the iso-stress condition in such a butt-joint serial configuration. Furthermore, the stress triaxiality has been usually ascribed, but without a quantitative rationalization, as being responsible for this tensile strength enhancement. Here a complete finite element simulation has been conducted to study the dependence of triaxiality and strength enhancement on geometric and material parameters. Two asymptotic limit solutions (based on Bridgman and Xia–Shih solutions, respectively) have been identified to understand the simulation results. The critical role of void evolution has been revealed when making a quantitative comparison to available experiments. In addition, ductility of the brazed joint, which has not been fully addressed in literature, is investigated by the Gurson–Tvergaard–Needleman model.

36 MATERIALS SCIENCE↗

An innovative heterogeneous transfer learning framework to enhance the scalability of deep reinforcement learning controllers in buildings with integrated energy systems

Deep Reinforcement Learning (DRL)-based control shows enhanced performance in the management of integrated energy systems when compared with Rule-Based Controllers (RBCs), but it still lacks scalability and generalisation due to the necessity of using tailored models for the training process. Transfer Learning (TL) is a potential solution to address this limitation. However, existing TL applications in building control have been mostly tested among buildings with similar features, not addressing the need to scale up advanced control in real-world scenarios with diverse energy systems. This paper assesses the performance of an online heterogeneous TL strategy, comparing it with RBC and offline and online DRL controllers in a simulation setup using EnergyPlus and Python. The study tests the transfer in both transductive and inductive settings of a DRL policy designed to manage a chiller coupled with a Thermal Energy Storage (TES). The control policy is pre-trained on a source building and transferred to various target buildings characterised by an integrated energy system including photovoltaic and battery energy storage systems, different building envelope features, occupancy schedule and boundary conditions (e.g., weather and price signal). The TL approach incorporates model slicing, imitation learning and fine-tuning to handle diverse state spaces and reward functions between source and target buildings. Results show that the proposed methodology leads to a reduction of 10% in electricity cost and between 10% and 40% in the mean value of the daily average temperature violation rate compared to RBC and online DRL controllers. Moreover, online TL maximises self-sufficiency and self-consumption by 9% and 11% with respect to RBC. Conversely, online TL achieves worse performance compared to offline DRL in either transductive or inductive settings. However, offline Deep Reinforcement Learning (DRL) agents should be trained at least for 15 episodes to reach the same level of performance as the online TL. Therefore, the proposed online TL methodology is effective, completely model-free and it can be directly implemented in real buildings with satisfying performance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A multi-stage stochastic programming model for adaptive biomass processing operation under uncertainty

Variations of physical and chemical characteristics of biomass reduce equipment utilization and increase operational costs of biomass processing. Biomass processing facilities use sensors to monitor the changes in biomass characteristics. Integrating sensory data into the operational decisions in biomass processing will increase its flexibility to the changing biomass conditions. In this paper, we propose a multi-stage stochastic programming model that minimizes the expected operational costs by identifying the initial inventory level and creating an operational decision policy for equipment speed settings. These policies take the sensory information data and the current biomass inventory level as inputs to dynamically adjust inventory levels and equipment settings according to the changes in the biomass' characteristics. We ensure that a prescribed target reactor utilization is consistently achieved by penalizing the violation of the target reactor feeding rate. A case study is developed using real-world data collected at Idaho National Laboratory's biomass processing facility. We show the value of multi-stage stochastic programming from an extensive computational experiment. Our sensitivity analysis indicates that updating the infeed rate of the system, the processing speed of equipment, and bale sequencing based on the moisture level of biomass improves the processing rate of the reactor and reduces operating costs.

09 BIOMASS FUELS↗

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Methodology to determine printability criteria of highly concentrated pastes through rheological characterization

Material extrusion is an additive manufacturing technique that enables the creation of reproducible and complex hardware by depositing a viscous, shear-thinning ink onto a substrate in a custom-pattern via extrusion through a syringe. Here, the ability of an ink to be extruded onto a substrate in many layers, and maintain the desired shape is what defines the printability. Printability is often investigated by formulating, printing, and postmortem analysis of final parts in an iterative manner. Investigations of printability through rheological characterization have often been concerned with inks that straddle the line between printable and too thin, leaving out an entire class of inks that are highly-filled pastes, where extrudability is the limiting factor. Highly-filled pastes continue to pose issues for researchers as the effect of filler morphology, size, loading, and packing fraction on the ink rheology and corresponding printability is not understood. While traditional rheological characterizations may be useful for some inks, we show that protocols utilizing steady-shear, or large-amplitude oscillatory shear are difficult and unreliable for highly-filled pastes. Through transient rheology paired with real-time images we show that each traditional protocol produces inhomogeneous deformations that violate the assumptions that underly common rheological definitions. Instead, we demonstrate metrics measured with small-amplitude oscillatory shear that are correlated to the printability of various ink formulations ranging in loading. The rheological measures that accurately predict the printability of the inks are the axial stress measured at small amplitudes, and the critical stress amplitude above which rheological characterizations become impossible. In addition, we estimate the maximum packing fraction for each filler, based on the exponent common to hard sphere models, and show that the printability of each ink can be predicted by the ratio of the packing fraction to the theoretical maximum. We show how small-amplitude oscillatory shear allows users to develop printability criteria for any ink to enhance the workflow in the development of new inks, increase the performance of material extrusion printing, and improve the stability of printed parts, with less wasted time and materials.

36 MATERIALS SCIENCE↗

The response field and the saddle points of quantum mechanical path integrals

Highlights: • Moyal quantum mechanics and Marinov’s path integral. • Classical and semiclassical limits of Marinov’s path integral. • Oscillating functional integrals. • Instantons of the Marinov’s path integral. In quantum statistical mechanics, Moyal’s equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal’s equation is given by Marinov’s path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov’s integral, plays for pure states even. The discussion focuses on how the integral’s semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov’s integral based upon the concept of “Airy averaging”, a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued (“Wick rotated”) response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Casimir effect in Very Special Relativity at finite temperature

Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy–momentum tensor for the electromagnetic field is calculated. From this, the Stefan–Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. A comparative analysis with the Casimir effect for the standard electromagnetic case is developed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geometry and entanglement in the scattering matrix

A formulation of nucleon–nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix –that appears at leading-order in the EFT description– possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Load altering attack-tolerant defense strategy for load frequency control system

Cyber attacks are emerging threats to every information-oriented energy management system. By violating the cyber systems, the hacker can disrupt the security and stability due to the strong coupling between the cyber and physical facilities. In this paper, one type of cyber attacks designated as the load altering attack is studied for the power system frequency control, and corresponding defense strategies are proposed to improve the frequency control performance. Considering the difficulty of the application of model-based controller into large-scale power systems, a novel model-free defense framework is for the first time presented. Under this framework, both active defense and passive defense strategies are designed. The former assumes that the defender has the initiative to learn different attack scenarios. Adaptive defense strategies are implemented using the online attack identification information and off-line trained strategy pool. The latter assumes that the defender passively tolerates various attack scenarios via the pre-trained off-line strategy. Both approaches prove to be effective through validation based on the IEEE benchmark systems. The proposed defense framework and defense strategies can be extended to other energy control systems to enhance their attack tolerance capability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Online transfer learning strategy for enhancing the scalability and deployment of deep reinforcement learning control in smart buildings

In recent years, advanced control strategies based on Deep Reinforcement Learning (DRL) proved to be effective in optimizing the management of integrated energy systems in buildings, reducing energy costs and improving indoor comfort conditions when compared to traditional reactive controllers. However, the scalability and implementation of DRL controllers are still limited since they require a considerable amount of time before converging to a near-optimal solution. This issue is currently addressed in literature through the offline pre-training of the DRL agent. However this solution results in two main critical issues: (1) the need to develop a building surrogate model to perform the training task, and (2) the need to perform a fine-tuning process over several training episodes to obtain a near-optimal control policy. In this context, this paper introduces an Online Transfer Learning (OTL) strategy that exploits two knowledge-sharing techniques, weight-initialization and imitation learning, to transfer a DRL control policy from a source office building to various target buildings in a simulation environment coupling EnergyPlus and Python. A DRL controller based on discrete Soft Actor–Critic (SAC) is trained on the source building to manage the operation of a cooling system consisting of a chiller and a thermal storage. Several target buildings are defined to benchmark the performance of the OTL strategy with that of a Rule-Based Controller (RBC) and two DRL-based control strategies, deployed in offline and online fashion. The strategy adopted for OTL emulates the real world implementation with a simulation process by implementing the transferred DRL agent for a single episode in the target buildings. Target buildings have the same geometrical features and are served by the same energy system as the source building, but differ in terms of weather conditions, electricity price schedules, occupancy patterns, and building envelope efficiency levels. The results show that the OTL strategy can reduce the cumulated sum of temperature violations on average by 50% and 80% respectively when compared to RBC and online DRL while enhancing the energy system operation with electricity cost savings ranging between 20% and 40%. Furthermore, the OTL agent performs slightly worse than the offline DRL controller but it does not require any modeling effort and can be implemented directly on target buildings emulating a real-world implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗