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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2018

An automatic performance model-based scheduling tool for coupled climate system models

The prediction of the climate system is highly depended on the efficient integration of observations and simulations of the Earth. This is regarded as a canonical example of the cyber-physical system. The climate system model, the simulation engine in this cyber-physical system, is one of most challenging applications in scientific computing. It utilizes the multi-physics simulation that couples multiple components, conducts decadal to millennium simulations, and has long been an important application on supercomputers. However, current climate system models suffer from the inefficient task scheduling methods resulting in an intolerable simulation time. Take the Community Earth System Model (CESM), the most widely used climate system model, as an example, one major reason that CESM suffers from bad performances is the huge overhead to rationally distribute processes among the coupled heterogeneous components. According to the report of NCAR, every percent improvement in CESM performance frees up to the equivalent of $250,000 in computing resources in their scientific experiments. To address such challenge, our paper firstly constructs a lightweight and accurate performance model for effectively capturing and predicting the heterogeneous time-to-solution performance of end-to-end CESM components with a given simulation configuration. Then, based on the performance model, we further propose an efficient scheduling strategy based on rectangular packing method to determine the best process layout among different components, and the process numbers assigned to each component. Our evaluations show that we can achieve 58% average run time reductions on CESM comparing to the widely used sequential process layout for a scale of 144 to 480 cores on typical CPU clusters. And we can save 4 million CPU hours when we conduct one standard scientific experiment (a 2870-year simulation), which equals to save $40,089 with a charge of $0.01 per CPU hour. Meanwhile, 26% extra performance improvements could also be gained in our methods comparing to the heuristic branch and bound algorithm with the guidance of the known curve-fitting performance model.

58 GEOSCIENCES↗

DOE OSTI2015

V&V Framework

A Verification and Validation (V&V) framework is presented for the development and execution of coordinated modeling and experimental program s to assess the predictive capability of computational models of complex systems through focused, well structured, and formal processes. The elements of the framework are based on established V&V methodology developed by various organizations including the Department of Energy, National Aeronautics and Space Administration, the American Institute of Aeronautics and Astronautics, and the American Society of Mechanical Engineers. Four main topics are addressed: 1) Program planning based on expert elicitation of the modeling physics requirements, 2) experimental design for model assessment, 3) uncertainty quantification for experimental observations and computational model simulations, and 4) assessment of the model predictive capability. The audience for this document includes program planners, modelers, experimentalist, V &V specialist, and customers of the modeling results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Land-Based Wind Plant Balance-of-System Cost Drivers and Sensitivities (Poster)

With Balance of System (BOS) costs contributing up to 30% of the installed capital cost, it is fundamental to understand the BOS costs for wind projects as well as potential cost trends for larger turbines. NREL developed a BOS model using project cost estimates developed by industry partners. Aspects of BOS covered include engineering and permitting, foundations for various wind turbines, transportation, civil work, and electrical arrays. The data introduce new scaling relationships for each BOS component to estimate cost as a function of turbine parameters and size, project parameters and size, and geographic characteristics. Based on the new BOS model, an analysis to understand the non‐turbine wind plant costs associated with turbine sizes ranging from 1-6 MW and wind plant sizes ranging from 100-1000 MW has been conducted. This analysis establishes a more robust baseline cost estimate, identifies the largest cost components of wind project BOS, and explores the sensitivity of the capital investment cost and the levelized cost of energy to permutations in each BOS cost element. This presentation shows results from the model that illustrate the potential impact of turbine size and project size on the cost of energy from US wind plants.

17 WIND ENERGY↗

DOE OSTI2022

Robust Event Classification Using Imperfect Real-world PMU Data

Here, this paper studies robust event classification using imperfect real-world phasor measurement unit (PMU) data. By analyzing the real-world PMU data, we find it is challenging to directly use this dataset for event classifiers due to the low data quality observed in PMU measurements and event logs. To address these challenges, we develop a novel machine learning framework for training robust event classifiers, which consists of three main steps: data preprocessing, fine-grained event data extraction, and feature engineering. Specifically, the data preprocessing step addresses the data quality issues of PMU measurements (e.g., bad data and missing data); in the fine-grained event data extraction step, a model-free event detection method is developed to accurately localize the events from the inaccurate event timestamps in the event logs; and the feature engineering step constructs the event features based on the patterns of different event types, in order to improve the performance and the interpretability of the event classifiers. Based on the proposed framework, we develop a workflow for event classification using the real-world PMU data streaming into the system in real time. Using the proposed framework, robust event classifiers can be efficiently trained based on many off-the-shelf lightweight machine learning models. Numerical experiments using the real-world dataset from the Western Interconnection of the U.S power transmission grid show that the event classifiers trained under the proposed framework can achieve high classification accuracy while being robust against low-quality data.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

DOE OSTI2018

Method to estimate uncertainty associated with parcel size in coarse discrete particle simulation

Coarse grained particle methods significantly reduce the computation cost of large‐scale fluidized bed simulation by lumping many real particles into a computation parcel. This research provides a method to estimate the errors associated with parcel size in large‐scale fluidized bed simulations. This uncertainty is first quantified in small scale domains by comparing results of discrete particle method with that employing coarse parcels of different sizes. Then, this uncertainty is correlated with parcel size and simulation domains consisting of a simple homogeneous cooling system and more complex bubbling and circulating fluidized beds. These correlations allow us to accurately estimate the uncertainty in large‐scale fluidized beds based solely on data obtained in smaller systems. The ability to estimate model‐related uncertainty in larger systems makes this method relevant for industrial applications. © 2018 American Institute of Chemical Engineers AIChE J , 64: 2340–2350, 2018

Lu, Liqiang↗

DOE OSTI2018

Modeling the Pseudomonas Sulfur Regulome by Quantifying the Storage and Communication of Information

ABSTRACT Bacteria are not simply passive consumers of nutrients or merely steady-state systems. Rather, bacteria are active participants in their environments, collecting information from their surroundings and processing and using that information to adapt their behavior and optimize survival. The bacterial regulome is the set of physical interactions that link environmental information to the expression of genes by way of networks of sensors, transporters, signal cascades, and transcription factors. As bacteria cannot have one dedicated sensor and regulatory response system for every possible condition that they may encounter, the sensor systems must respond to a variety of overlapping stimuli and collate multiple forms of information to make “decisions” about the most appropriate response to a specific set of environmental conditions. Here, we analyze Pseudomonas fluorescens transcriptional responses to multiple sulfur nutrient sources to generate a predictive, computational model of the sulfur regulome. To model the regulome, we utilize a transmitter-channel-receiver scheme of information transfer and utilize principles from information theory to portray P. fluorescens as an informatics system. This approach enables us to exploit the well-established metrics associated with information theory to model the sulfur regulome. Our computational modeling analysis results in the accurate prediction of gene expression patterns in response to the specific sulfur nutrient environments and provides insights into the molecular mechanisms of Pseudomonas sensory capabilities and gene regulatory networks. In addition, modeling the bacterial regulome using the tools of information theory is a powerful and generalizable approach that will have multiple future applications to other bacterial regulomes. IMPORTANCE Bacteria sense and respond to their environments using a sophisticated array of sensors and regulatory networks to optimize their fitness and survival in a constantly changing environment. Understanding how these regulatory and sensory networks work will provide the capacity to predict bacterial behaviors and, potentially, to manipulate their interactions with an environment or host. Leveraging the information theory provides useful quantitative metrics for modeling the information processing capacity of bacterial regulatory networks. As our model accurately predicted gene expression profiles in a bacterial model system, we posit that the information theory-based approaches will be important to enhance our understanding of a wide variety of bacterial regulomes and our ability to engineer bacterial sensory and regulatory networks.

Larsen, Peter E.↗

DOE OSTI2021

IBM Open Science Price - SWAP Gate Challenge

On November 30, 2020, IBM announced an open science price competition aimed at improving the fidelity of a SWAP gate on their 7 qubit Quantum system named ”Casablanca”. The details of the SWAP gate problem was outlined in a Jupyter notebook, which utilizes the IBM developed open source package Qiskit. The participants were allowed to work in teams with up to five people and restricted to only use open source software in solving the problem. Their results were due on April 16, 2021. Our approach to solving the SWAP gate challenge is based on the quantum optimal control techniques implemented in our open source packages Juqbox.jl and Quandary. The results from the optimal control approach is only as good as the accuracy in the description of the quantum system dynamics, characterized by a Hamiltonian model that was provided by IBM. Based on the calibrated control pulses IBM provide for the standard gate set, we developed a reverse engineering approach to calibrate our computational model. Techniques were developed to translate between Qiskit’s pulse representation and the B-spline formulation used in Juqbox and Quandary. The fidelity of the optimized pulse sequences were estimated using Qiskit’s randomized bench marking techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Examining Food Risk in the Large using a Complex, Networked System-of-sytems Approach

The food production infrastructure is a highly complex system of systems. Characterizing the risks of intentional contamination in multi-ingredient manufactured foods is extremely challenging because the risks depend on the vulnerabilities of food processing facilities and on the intricacies of the supply-distribution networks that link them. A pure engineering approach to modeling the system is impractical because of the overall system complexity and paucity of data. A methodology is needed to assess food contamination risk 'in the large', based on current, high-level information about manufacturing facilities, corrunodities and markets, that will indicate which food categories are most at risk of intentional contamination and warrant deeper analysis. The approach begins by decomposing the system for producing a multi-ingredient food into instances of two subsystem archetypes: (1) the relevant manufacturing and processing facilities, and (2) the networked corrunodity flows that link them to each other and consumers. Ingredient manufacturing subsystems are modeled as generic systems dynamics models with distributions of key parameters that span the configurations of real facilities. Networks representing the distribution systems are synthesized from general information about food corrunodities. This is done in a series of steps. First, probability networks representing the aggregated flows of food from manufacturers to wholesalers, retailers, other manufacturers, and direct consumers are inferred from high-level approximate information. This is followed by disaggregation of the general flows into flows connecting 'large' and 'small' categories of manufacturers, wholesalers, retailers, and consumers. Optimization methods are then used to determine the most likely network flows consistent with given data. Vulnerability can be assessed for a potential contamination point using a modified CARVER + Shock model. Once the facility and corrunodity flow models are instantiated, a risk consequence analysis can be performed by injecting contaminant at chosen points in the system and propagating the event through the overarching system to arrive at morbidity and mortality figures. A generic chocolate snack cake model, consisting of fluid milk, liquid eggs, and cocoa, is described as an intended proof of concept for multi-ingredient food systems. We aim for an eventual tool that can be used directly by policy makers and planners.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2013

Understanding Building Infrastructure and Building Operation through DOE Asset Score Model: Lessons Learned from a Pilot Project

The U.S. Department of Energy (DOE) is developing a national voluntary energy asset score system to help building owners to evaluate the as-built physical characteristics (including building envelope, the mechanical and electrical systems) and overall building energy efficiency, independent of occupancy and operational choices. The energy asset score breaks down building energy use information by simulating building performance under typical operating and occupancy conditions for a given use type. A web-based modeling tool, the energy asset score tool facilitates the implementation of the asset score system. The tool consists of a simplified user interface built on a centralized simulation engine (EnergyPlus). It is intended to reduce both the implementation cost for the users and increase modeling standardization compared with an approach that requires users to build their own energy models. A pilot project with forty-two buildings (consisting mostly offices and schools) was conducted in 2012. This paper reports the findings. Participants were asked to collect a minimum set of building data and enter it into the asset score tool. Participants also provided their utility bills, existing ENERGY STAR scores, and previous energy audit/modeling results if available. The results from the asset score tool were compared with the building energy use data provided by the pilot participants. Three comparisons were performed. First, the actual building energy use, either from the utility bills or via ENERGY STAR Portfolio Manager, was compared with the modeled energy use. It was intended to examine how well the energy asset score represents a building’s system efficiencies, and how well it is correlated to a building’s actual energy consumption. Second, calibrated building energy models (where they exist) were used to examine any discrepancies between the asset score model and the pilot participant buildings’ [known] energy use pattern. This comparison examined the end use breakdowns and more detailed time series data. Third, ASHRAE 90.1 prototype buildings were also used as an industry standard modeling approach to test the accuracy level of the asset score tool. Our analysis showed that the asset score tool, which uses simplified building simulation, could provide results comparable to a more detailed energy model. The buildings’ as-built efficiency can be reflected in the energy asset score. An analysis between the modeled energy use through the asset score tool and the actual energy use from the utility bills can further inform building owners about the effectiveness of their building’s operation and maintenance.

Wang, Na↗

DOE OSTI2016

Systems Biology for Organotypic Cell Cultures

Translating in vitro biological data into actionable information related to human health holds the potential to improve disease treatment and risk assessment of chemical exposures. While genomics has identified regulatory pathways at the cellular level, translation to the organism level requires a multiscale approach accounting for intra-cellular regulation, inter-cellular interaction, and tissue/organ-level effects. Tissue-level effects can now be probed in vitro thanks to recently developed systems of three-dimensional (3D), multicellular, “organotypic” cell cultures, which mimic functional responses of living tissue. However, there remains a knowledge gap regarding interactions across different biological scales, complicating accurate prediction of health outcomes from molecular/genomic data and tissue responses. Systems biology aims at mathematical modeling of complex, non-linear biological systems. We propose to apply a systems biology approach to achieve a computational representation of tissue-level physiological responses by integrating empirical data derived from organotypic culture systems with computational models of intracellular pathways to better predict human responses. Successful implementation of this integrated approach will provide a powerful tool for faster, more accurate and cost-effective screening of potential toxicants and therapeutics. On September 11, 2015, an interdisciplinary group of scientists, engineers, and clinicians gathered for a workshop in Research Triangle Park, North Carolina, to discuss this ambitious goal. Participants represented laboratory-based and computational modeling approaches to pharmacology and toxicology, as well as the pharmaceutical industry, government, non-profits, and academia. Discussions focused on identifying critical system perturbations to model, the computational tools required, and the experimental approaches best suited to generating key data. This consensus report summarizes the discussions held.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2011

PowerGrid - A Computation Engine for Large-Scale Electric Networks

This Final Report discusses work on an approach for analog emulation of large scale power systems using Analog Behavioral Models (ABMs) and analog devices in PSpice design environment. ABMs are models based on sets of mathematical equations or transfer functions describing the behavior of a circuit element or an analog building block. The ABM concept provides an efficient strategy for feasibility analysis, quick insight of developing top-down design methodology of large systems and model verification prior to full structural design and implementation. Analog emulation in this report uses an electric circuit equivalent of mathematical equations and scaled relationships that describe the states and behavior of a real power system to create its solution trajectory. The speed of analog solutions is as quick as the responses of the circuit itself. Emulation therefore is the representation of desired physical characteristics of a real life object using an electric circuit equivalent. The circuit equivalent has within it, the model of a real system as well as the method of solution. This report presents a methodology of the core computation through development of ABMs for generators, transmission lines and loads. Results of ABMs used for the case of 3, 6, and 14 bus power systems are presented and compared with industrial grade numerical simulators for validation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2019

Two-tier model reduction of viscoelastically damped finite element models

Transient simulations of linear viscoelastically damped structures necessitate critical computational resources to directly integrate the full-order finite element model with time-stepping algorithms. Traditional modal reduction techniques are not directly applicable to these systems since viscoelastic materials depend on time and frequency. A more appropriate reduction basis is obtained from the nonlinear, complex eigenvalue problem, whose eigenvectors capture the appropriate kinematics and enable frequency-based mode selection; unfortunately, the computational cost is prohibitive for computing these modes from large-scale engineering models. To address this shortcoming, this work proposes a novel two-tier reduction procedure to reduce the upfront cost of solving the complex, nonlinear eigenvalue problem. The first reduction step reduces the full-order model with real mode shapes linearized about various centering frequencies to capture the kinematics over a full range of viscoelastic material behavior (glassy, rubbery, and glass-transition zones). This tier-one reduction preserves time-temperature superposition and allows the equations to depend parametrically on operating temperature. The second-level reduction then solves the complex, nonlinear eigenmode solutions in the tier-one reduced space about a fixed temperature to further reduce the equations-of-motion. The method is demonstrated on a cantilevered sandwich plate to display its accuracy and efficiency in comparison to full-order model predictions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Development of a rate-based ENRTL-RK process model for a water-lean solvent

Advanced water-lean solvents (WLS) for post-combustion CO2 capture offer several advantages over the aqueous amine solvents . WLS have lower parasitic energy penalty, lower corrosion, lower temperature and high-pressure CO2 regeneration leading to lower cost of CO2 capture. RTI International, with funding from the US Department of Energy, has been developing its novel water-lean solvent, that has shown specific reboiler duty of 2.3 GJ/t-CO2 at the 60-kWe pilot testing unit (Tiller Plant, SINTEF, Norway) and 2.6 GJ/t-CO2 at the engineering scale testing system (12 MWe) at the Technology Centre Mongstad (TCM) in Norway. All heat duties, including the one from TCM testing, were consistent with Aspen Plus modeling of the specific configuration of each test plant. This work focuses on the development of a detailed process model using in-house laboratory measurements and process data at pilot scale. The eNTRL-RK model used in this work is based on an unsymmetric activity coefficient model with the reference states chosen to be pure liquids for solvents and ideal dilute solution at unit solute molality (resulting in activity coefficient of unity at infinite dilution) for electrolytes. It uses the Redlich-Kwong equation of state for vapor phase properties and Henry’s law for solubility of supercritical gases. The model was validated using process data from the pilot-scale campaign at the Tiller plant, and the engineering scale test campaign at TCM. Data on CO2 capture rate, absorber, and regenerator temperature profiles and specific reboiler duties from two different test campaigns at Tiller and TCM, were used to further refine and validate the model and the model compares favorably to experimental data. The validation results against TCM campaign will be presented in this work.

CO2 capture↗

DOE OSTI2022

Development of Integrated Thermal Fluids Modeling Capability for MSRs

The DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad class of light-water and advanced reactor concepts. The research and development approach under thermal fluids technical area synergistically combines three length and time scales in a hierarchal multi-scale approach. To demonstrate the feasibility and capabilities of a multi-scale thermal fluids capability using these codes, a key joint effort has been pursued to develop an integrated system-and engineering-scale thermal fluids analysis capability with the MOOSE-based codes, through integration of SAM and Pronghorn, both based on the MOOSE framework. This report summarizes the progress in developing an integrated system- and engineering-scale thermal fluids analysis capability based on SAM and Pronghorn for molten salt reactors (MSRs), which gained significant interest in recently years. Two coupling approaches were studied, i.e. separate domain or domain-segregated coupling approach and the domain-overlapping approach. A series of coupled multi-physics models have been developed for a common reference molten salt fast reactor (MSFR) concept, ranging from standalone SAM system model to integrated SAM-Pronghorn-Griffin models. Both the steady state and the transient simulations are performed to the state-of-the-art simulation capabilities of NEAMS software suite in MSFR system applications. This report also covers further development and testing of the gas transport model in SAM for MSR modeling support. The presence of noncondensable gas in MSR systems would have strong impacts on fission gas removal and transport of noble metals throughout the system. Fission products removed through the off-gas system can also impact reactivity and can act as an additional point of heat removal. To ensure that the gas transport model is adequately tested, the supported modeling capabilities and features of SAM were identified, and a suite of tests were developed to test the model for each identified feature. Validation and UQ testing were also performed for the model and demonstrated that the buoyancy term, which was originally developed using non-salt/helium gas experimental data, can capture the experimental gas bubble velocity and diameter to within experimental and code uncertainty. An existing MSRE model was also modified in this work to include the gas transport model and to demonstrate the gas model behavior for realistic conditions of interest.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Reinforcement learning for adaptive maintenance policy optimization under imperfect knowledge of the system degradation model and partial observability of system states

Maintenance policy optimization usually is faced with challenges that arise from an imperfect knowledge of system degradation models and from the partial observability of system degradation states. Here, this paper proposes a reinforcement learning method to address these two challenges for a class of maintenance problems with Markov degradation processes. The reinforcement learning approach consists of a learning component and a planning component. Using sequentially collected observations, at each step of decision-making the learning component improves the knowledge of system degradation in terms of the probability distributions of the transition rates based on sequential Bayesian inference. Using the updated transition rates, at each step of decision-making the maintenance policy optimization problem is then formulated as a partially observable Markov decision problem, and the planning component computes the optimal maintenance policy that maximizes the expected cumulative reward. The proposed method is illustrated using a numerical example with repair and inspection maintenance actions. The result shows that as more observations are collected, the learning component progressively learns the true system degradation process, and the planning component adjusts the optimal maintenance policy accordingly as well, which leads to increased reward.

42 ENGINEERING↗

DOE OSTI2026

Finite-element-based simulations of electrodes for CO 2 cascade reduction reactions

The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Asymptotic analysis of the fluid flow with a pressure-dependent viscosity in a system of thin pipes

We consider the incompressible fluid with a pressure-dependent viscosity flowing through a multiple pipe system. The viscosity–pressure relation is given by the Barus law commonly used in the engineering applications. Assuming that the ratio between pipes thickness and its length is small, we propose a rigorous asymptotic approach based on the concept of the transformed pressure. As a result, we obtain new macroscopic model describing the effective behavior of the fluid in the system. In particular, the generalized version of the Kirchhoff’s law is derived giving the explicit formula for the junction pressure. The error estimate for the asymptotic approximation is also provided. Mathematical analysis presented here can be applied to a general viscosity–pressure relation satisfied by other empiric laws.

97 MATHEMATICS AND COMPUTING↗