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At least 847 records · Page 47

Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model

The phase-space structure of zero-temperature quarkyonic matter is a Fermi sphere of quark matter surrounded by a shell of nucleonic matter. Here, we construct a quasiparticle model of quarkyonic matter based on the constituent quark model, where the quark and nucleon masses are related by $m_Q = m_N/N_c$, and $N_c$ is the number of quark colors. The region of occupied states is for quarks $k_Q < k_F/N_c$ and for nucleons $k_F < k_N < k_F + Δ$. We first consider the general problem of quarkyonic matter with hard-core nucleon interactions. We then specialize to a quasiparticle model where the hard-core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard-core size and for large densities becomes a thin shell. We explore the basic features of such a model and argue this model has the semiquantitative behavior needed to describe neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Realizability-preserving discontinuous Galerkin method for spectral two-moment radiation transport in special relativity

Here we present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.

79 ASTRONOMY AND ASTROPHYSICS↗

DC-Link Current Minimization Control for Current Source Converter-Based Solid-State Transformer

This article proposes a fast predictive control method and a small DC-link inductor to minimize the DC-link current in current-source converter (CSC)-based solid-state transformer. The DC-link current minimization can significantly reduce power loss and improve efficiency. The challenge of this problem is on improving both steady-state and dynamic performance. PI control methods and large DC-link inductors are conventionally used in the CSC but have limited dynamic performance. A model predictive control (MPC) method is proposed to achieve switching-cycle-level settling time, and the DC-link inductor is sized for 40% ripple to enable fast current change. Importantly, this article also proposes to minimize the DC-link current by varying the current even within a line cycle under single-phase load to improve the steady-state performance, in contrast with the reduction to a constant value in the literature. The proposed MPC features a constant switching frequency without weighting factors. The MPC does not have a high computational burden and is implemented in a regular digital controller for a prototype of soft-switching solid-state transformer (S4T) with reduced conduction loss. The effectiveness of the proposed method has been experimentally verified on the SiC S4T prototype during steady-state and dynamics under different multiport power flow conditions up to 2 kV peak. Here, the DC-link current in the experiments is close to the minimum current with a short zero-vector duration, which further verifies the performance of the proposed method.

14 SOLAR ENERGY↗

Investigation and Diagnosis of Faulty Data Channels in CMS Outer Tracker Module Testing

The High-Luminosity Large Hadron Collider (HL-LHC) is currently undergoing upgrades to improve its luminosity. In parallel, this requires an upgrade to the Compact Muon Solenoid (CMS)’s Outer Tracker, consisting of Pixel-Strip (PS) and Strip-Strip (2S) modules that can accurately track the path of charged particles originating from the collisions. It follows that such complex modules call for extensive testing, requiring a sophisticated Data Acquisition (DAQ) system that can perform specific tests to assess their performance. In addition, errors caused by the hardware of a given testing station, and its associated data channel, need to be accurately identified to guarantee proper testing of modules. We have developed a software extension to the Phase-II Outer Tracker Analyzer of Test Outputs (POTATO), which is a specialized software designed to analyze and grade all of the module tests through a centralized database. This extension categorizes and analyzes module test results by its station and data channel. Its analysis can be used to identify trends in grading that indicate issues in these channels’ grading process rather than in the individual modules. This poster shows our methodology and results for identifying faulty data channels. Using this extension, we can quickly diagnose and address problems in our DAQ system, ensuring proper evaluation corrections for each module.

Chen, Angus [Fermilab]↗

Investigation and Diagnosis of Faulty Data Channels in CMS Outer Tracker Module Testing

The High-Luminosity Large Hadron Collider (HL-LHC) is currently undergoing upgrades to improve its luminosity. In parallel, this requires an upgrade to the Compact Muon Solenoid (CMS)’s Outer Tracker, consisting of Pixel-Strip (PS) and Strip-Strip (2S) modules that can accurately track the path of charged particles originating from the collisions. It follows that such complex modules call for extensive testing, requiring a sophisticated Data Acquisition (DAQ) system that can perform specific tests to assess their performance. In addition, errors caused by the hardware of a given testing station, and its associated data channel, need to be accurately identified to guarantee proper testing of modules. We have developed a software extension to the Phase-II Outer Tracker Analyzer of Test Outputs (POTATO), which is a specialized software designed to analyze and grade all of the module tests through a centralized database. This extension categorizes and analyzes module test results by its station and data channel. Its analysis can be used to identify trends in grading that indicate issues in these channels’ grading process rather than in the individual modules. This poster shows our methodology and results for identifying faulty data channels. Using this extension, we can quickly diagnose and address problems in our DAQ system, ensuring proper evaluation corrections for each module.

Chen, Angus [Fermilab]↗

Massively parallel phase-field simulations targeting exascale

The interface thickness in the phase-field (PF) method limits its simulation scales. Consequently, large-scale PF simulations become prohibitively expensive for resolving the extremely fine microstructures that typically form during rapid solidification processing. This challenge is significant in predicting microstructure evolution in metal additive manufacturing and has been identified by the United States Department of Energy’s Exascale Computing Project. Here, to address this, we develop a multi-GPU and MPI-based massively parallel simulation code, utilizing state-of-the-art algorithms, software, and libraries, for large-scale three-dimensional (3D) PF simulations. We report the first GPU-parallel PF simulations on Frontier (currently the second TOP500 exascale cluster) and Summit machines, taking dendritic growth as an example problem. We evaluate the parallel performance of our implementation using scaling studies with more than 24 000 GPUs (among the largest known computations to date) and the acceleration performance using large-scale simulations of dendritic growth in 3D. Finally, massively parallel GPUs in these supercomputers enabled the first coupled multiscale simulations of laser melting and subsequent dendritic solidification on the scale of a full melt-pool, demonstrating the feasibility of performing PF simulations with a point total over 2 billion grid points within an acceptable time.

Exascale↗

Deep convolutional autoencoders as generic feature extractors in seismological applications

The idea of using a deep autoencoder to encode seismic waveform features and then use them in different seismological applications is appealing. In this paper, we designed tests to evaluate this idea of using autoencoders as feature extractors for different seismological applications, such as event discrimination (i.e., earthquake vs. noise waveforms, earthquake vs. explosion waveforms), and phase picking. These tests involve training an autoencoder, either undercomplete or overcomplete, on a large amount of earthquake waveforms, and then using the trained encoder as a feature extractor with subsequent application layers (either a fully connected layer, or a convolutional layer plus a fully connected layer) to make the decision. By comparing the performance of these newly designed models against the baseline models trained from scratch, we conclude that the autoencoder feature extractor approach may only outperform the baseline under certain conditions, such as when the target problems require features that are similar to the autoencoder encoded features, when a relatively small amount of training data is available, and when certain model structures and training strategies are utilized. The model structure that works best in all these tests is an overcomplete autoencoder with a convolutional layer and a fully connected layer to make the estimation.

58 GEOSCIENCES↗

An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.

42 ENGINEERING↗

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs–Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design

SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.

58 GEOSCIENCES↗

Melting of spatially modulated phases at domain wall/surface junctions in antiferrodistortive multiferroics

A physical understanding of the nature of spatially modulated phases (SMPs) in rare-earth-doped antiferrodistortive (AFD) multiferroics and how they behave close to surfaces and interfaces is lacking. Here the emergence of the antiferroelectric (AFE), ferroelectric (FE), or ferrielectric (AFE-FE) spatial modulation in the vicinity of the morphotropic phase transition in La x Bi 1 – x Fe O 3 ( x ~ 0.2 ) is explored on the atomic level using high-resolution scanning transmission electron microscopy (HRSTEM). The suppression, or “melting,” of the AFE-type SMP in the vicinity of the AFD twin wall/surface junction is revealed by HRSTEM in La 0.22 Bi 0.78 Fe O 3 films and explained by the hybrid approach combining Landau-Ginzburg-Devonshire (LGD) phenomenology and the semimicroscopic four-sublattice model (FSM). The LGD-FSM approach reduces the problem of AFE (or AFE-FE) SMP emergence and stability to the thermodynamic analysis of the free-energy functional with AFE, FE, and AFD long-range order parameters and two master parameters: the FE-AFE coupling strength between four neighboring A sites and the nonstoichiometry factor, which are proportional to the variations of La concentration in La x Bi 1 – x Fe O 3 films. Finally, we establish that the surface-induced melting of SMPs and the associated broadening of AFE AFD domain walls minimize the film free energy under certain conditions imposed on the master parameters and gradient energy below the critical value. The observed behavior provides insight into the origin of SMPs in AFD multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterizing Impacts of Dry Coal Feeding in High Pressure Oxy-Coal Combustion Systems

Reaction Engineering International (REI) has managed a team of experts from the University of Utah, Southeast University (SEU) in Nanjing, China, Electric Power Research Institute (EPRI), Corrosion Management Ltd. (C-M), Praxair, and Brigham Young University (BYU) to investigate dry pulverized coal feeding for pressurized oxy-coal combustion. Dry feed firing systems for entrained flow, pressurized, oxy-coal combustors have not been well developed, although related technologies have been used in the Shell Gasification Process and for pressurized fluid bed combustion. DOE-funded research recently completed at REI and the University of Utah focused on characterizing impacts of high temperatures and pressures in oxy-coal combustion systems. For high pressure combustion, that research used a coal slurry feed into a 17 bar pressurized combustor. As a consequence of that research, it was identified that fuel feeding and firing system flexibility are challenges that require attention. Based on that experience, the approach of using a coal slurry feed system leads to challenges in producing consistent atomization of the slurry, which causes burnout problems, especially at high pressures. In addition, slurry atomization processes may be difficult to scale to sizes appropriate for practical commercial use. Dry pressurized coal burner systems, on the other hand, have the potential to yield efficiency gains, improve flexibility and facilitate applications at larger scales. Experimental work was conducted at the University of Utah Industrial Combustion and Gasification Research Facility as well as the 100 kW pressurized oxy-coal combustor (POC) facility at Brigham Young University. Mechanism development and CFD-based combustion and dense-phase flow modeling were performed at REI. Successful completion of the project objectives has resulted in the following key deliverables: 1) Design and prototype of a pressurized pulverized coal feeding and oxy-firing system 2) Data from a 100kW, pressurized (15 bar) entrained flow reactor with a dry feeding delivery and burner system that describes flame characteristics, radiative heat flux profiles, carbon burnout, along with characteristics of ash aerosols, fouling, and slagging. 3) Validated and transportable models that describe the relevant conditions in pressurized oxy-combustion systems and that can be used for scale-up and optimization. 4) Principles to guide design of high pressure, pilot-scale and full-scale coal oxy-firing systems. 5) Assessment of pressurized oxy-combustion impacts on key parameters relevant to oxy-coal fired utility boilers such as coal devolatilization, char oxidation, mineral matter transformation, deposition, and corrosion. The experimental data, pressurized oxy-firing system principles, and process mechanisms provided by this work can be used by electric utilities, boiler OEMs, equipment suppliers, design firms, software vendors, consultants and government agencies to assess the use of high temperature and high pressure oxy-combustion in current research and to guide development of new oxy-coal boiler designs.

01 COAL, LIGNITE, AND PEAT↗

Characterizing Impacts of Dry Coal Feeding in High Pressure Oxy-Coal Combustion Systems

Reaction Engineering International (REI) has managed a team of experts from the University of Utah, Southeast University (SEU) in Nanjing, China, Electric Power Research Institute (EPRI), Corrosion Management Ltd. (C-M), Praxair, and Brigham Young University (BYU) to investigate dry pulverized coal feeding for pressurized oxy-coal combustion. Dry feed firing systems for entrained flow, pressurized, oxy-coal combustors have not been well developed, although related technologies have been used in the Shell Gasification Process and for pressurized fluid bed combustion. DOE-funded research recently completed at REI and the University of Utah focused on characterizing impacts of high temperatures and pressures in oxy-coal combustion systems. For high pressure combustion, that research used a coal slurry feed into a 17 bar pressurized combustor. As a consequence of that research, it was identified that fuel feeding and firing system flexibility are challenges that require attention. Based on that experience, the approach of using a coal slurry feed system leads to challenges in producing consistent atomization of the slurry, which causes burnout problems, especially at high pressures. In addition, slurry atomization processes may be difficult to scale to sizes appropriate for practical commercial use. Dry pressurized coal burner systems, on the other hand, have the potential to yield efficiency gains, improve flexibility and facilitate applications at larger scales. Experimental work was conducted at the University of Utah Industrial Combustion and Gasification Research Facility as well as the 100 kW pressurized oxy-coal combustor (POC) facility at Brigham Young University. Mechanism development and CFD-based combustion and dense-phase flow modeling were performed at REI. Successful completion of the project objectives has resulted in the following key deliverables: 1) Design and prototype of a pressurized pulverized coal feeding and oxy-firing system 2) Data from a 100kW, pressurized (15 bar) entrained flow reactor with a dry feeding delivery and burner system that describes flame characteristics, radiative heat flux profiles, carbon burnout, along with characteristics of ash aerosols, fouling, and slagging. 3) Validated and transportable models that describe the relevant conditions in pressurized oxy-combustion systems and that can be used for scale-up and optimization. 4) Principles to guide design of high pressure, pilot-scale and full-scale coal oxy-firing systems. 5) Assessment of pressurized oxy-combustion impacts on key parameters relevant to oxy-coal fired utility boilers such as coal devolatilization, char oxidation, mineral matter transformation, deposition, and corrosion. The experimental data, pressurized oxy-firing system principles, and process mechanisms provided by this work can be used by electric utilities, boiler OEMs, equipment suppliers, design firms, software vendors, consultants and government agencies to assess the use of high temperature and high pressure oxy-combustion in current research and to guide development of new oxy-coal boiler designs.

pressurized oxy-coal combustion, sub-micron ash ae↗

Characterizing Impacts of Dry Coal Feeding in High Pressure Oxy-Coal Combustion Systems

Reaction Engineering International (REI) has managed a team of experts from the University of Utah, Southeast University (SEU) in Nanjing, China, Electric Power Research Institute (EPRI), Corrosion Management Ltd. (C-M), Praxair, and Brigham Young University (BYU) to investigate dry pulverized coal feeding for pressurized oxy-coal combustion. Dry feed firing systems for entrained flow, pressurized, oxy-coal combustors have not been well developed, although related technologies have been used in the Shell Gasification Process and for pressurized fluid bed combustion. DOE-funded research recently completed at REI and the University of Utah focused on characterizing impacts of high temperatures and pressures in oxy-coal combustion systems. For high pressure combustion, that research used a coal slurry feed into a 17 bar pressurized combustor. As a consequence of that research, it was identified that fuel feeding and firing system flexibility are challenges that require attention. Based on that experience, the approach of using a coal slurry feed system leads to challenges in producing consistent atomization of the slurry, which causes burnout problems, especially at high pressures. In addition, slurry atomization processes may be difficult to scale to sizes appropriate for practical commercial use. Dry pressurized coal burner systems, on the other hand, have the potential to yield efficiency gains, improve flexibility and facilitate applications at larger scales. Experimental work was conducted at the University of Utah Industrial Combustion and Gasification Research Facility as well as the 100 kW pressurized oxy-coal combustor (POC) facility at Brigham Young University. Mechanism development and CFD-based combustion and dense-phase flow modeling were performed at REI. Successful completion of the project objectives has resulted in the following key deliverables: 1) Design and prototype of a pressurized pulverized coal feeding and oxy-firing system 2) Data from a 100kW, pressurized (15 bar) entrained flow reactor with a dry feeding delivery and burner system that describes flame characteristics, radiative heat flux profiles, carbon burnout, along with characteristics of ash aerosols, fouling, and slagging. 3) Validated and transportable models that describe the relevant conditions in pressurized oxy-combustion systems and that can be used for scale-up and optimization. 4) Principles to guide design of high pressure, pilot-scale and full-scale coal oxy-firing systems. 5) Assessment of pressurized oxy-combustion impacts on key parameters relevant to oxy-coal fired utility boilers such as coal devolatilization, char oxidation, mineral matter transformation, deposition, and corrosion. The experimental data, pressurized oxy-firing system principles, and process mechanisms provided by this work can be used by electric utilities, boiler OEMs, equipment suppliers, design firms, software vendors, consultants and government agencies to assess the use of high temperature and high pressure oxy-combustion in current research and to guide development of new oxy-coal boiler designs.

01 COAL, LIGNITE, AND PEAT↗

Emergent moments in a Hund's impurity

Here, motivated by the relevance of Hund's coupling in the context of multiorbital superconductors, we revisit the problem of a multiorbital Kondo impurity with Hund's interaction. Using dynamical large-N techniques, we propose an efficient approach that retains the essential physics at play, while providing a pathway to scalable quantum impurity solvers. We are able to follow the ground state, dynamic, and thermodynamic properties of this system over many decades of temperature. Our approach captures the emergence of large moments and follows the stretched evolution of the physics down to their exponentially suppressed Kondo temperature. We focus our analysis on the intermediate finite temperature phase which presents an alternate paramagnetic state due to the emergent moment and discuss the relevance of this regime to Hund's metals.

36 MATERIALS SCIENCE↗

Deep Reinforcement Learning Based Volt-VAR Optimization in Smart Distribution Systems

This paper develops a model-free volt-VAR optimization (VVO) algorithm via multi-agent deep reinforcement learning (DRL) in unbalanced distribution systems. This method is novel since we cast the VVO problem in distribution networks to an intelligent deep Q-network (DQN) framework, which avoids solving a specific optimization model directly when facing time-varying operating conditions in the systems. We consider statuses/ratios of switchable capacitors, voltage regulators, and smart inverters installed at distributed generators as the action variables of the agents. A delicately designed reward function guides these agents to interact with the distribution system, in the direction of reinforcing voltage regulation and power loss reduction simultaneously. The forward-backward sweep method for radial three-phase distribution systems provides accurate power flow results within a few iterations to the DRL environment. The proposed method realizes the dual goals for VVO. We test this algorithm on the unbalanced IEEE 13-bus and 123-bus systems. Numerical simulations validate the excellent performance of this method in voltage regulation and power loss reduction.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Semi-Analytical Leakage Solutions for Aquifers (SALSA) v1

SALSA is a semi-analytical modeling tool that can provide assessments of pressure perturbations and brine leakage because of fluid injection and extraction activities in sedimentary basins. Sedimentary basins typically contain vertical sequences of near-horizontal aquifers separated by less-permeable aquitards. In the context of geologic carbon sequestration (GCS), while aquitards are relied upon to contain injected buoyant free-phase CO2 and limit inter-aquifer brine flow, the large number of leaky wells (e.g., unused/unsuccessful exploration wells, or improperly plugged water or oil/gas wells) that are present in sedimentary basins creates concerns for potential leakage and groundwater contamination. The mathematical theory and solution method included in SALSA is presented in our recent manuscript under review. SALSA is the first to account for the coupled leakage through aquitards and leaky wells, with geologic pressurization sources. SALSA based on semi-analytical solutions can be computationally very efficient for problems containing many injection and leaky wells in multilayered sedimentary systems, compared to any numerical simulation software requiring local mesh refinement around each well to obtain accurate results. Therefore, stakeholders (e.g., regulators, operators) for site screening, injection and post-injection pressure behavior and assessing leakage risks can use SALSA as a fast-predictive tool in GCS applications in multilayered aquifer systems.

Cihan, Abdullah↗

Minimum stabilizing energy release for mixing processes

Diffusive operations, which mix the populations of different elements of phase space, can irreversibly transform a given initial state into any of a spectrum of different states from which no further energy can be extracted through diffusive operations. We call these ground states. Here, the lower bound of accessible ground-state energies represents the maximal possible release of energy. This lower bound, sometimes called the diffusively accessible free energy, is of interest in theories of instabilities and wave-particle interactions. On the other hand, the upper bound of accessible ground-state energies has escaped identification as a problem of interest. Yet, as demonstrated here, in the case of a continuous system, it is precisely this upper bound that corresponds to the paradigmatic “quasilinear plateau” ground state of the bump-on-tail distribution. Although for general discrete systems the complexity of calculating the upper bound grows rapidly with the number of states, using techniques adapted from treatments of the lower bound, the upper bound can in fact be computed directly for the three-state discrete system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗