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DOE OSTI1991

Nuclear Safety [Vol. 32, No. 4, October-December 1991]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 477 Report on the International Symposium on the Use of Probabilistic Safety Assessment for Operational Safety—PSA '91, S. Chakraborty and M. Khatib-Rahbar; 488 Good Relationships Are Pivotal in Nuclear Data Bases, A. S. Heger and B. V. Koen; 494 Technical Note: The Interagency Nuclear Safety Review Panel's Evaluation of the Ulysses Space Mission, J. A. Sholtis, Jr., D. A. Huff, L. B. Gray, N. P. Klug, and R. O. Winchester; ACCIDENT ANALYSIS: 502 The Severe Accident Analysis Program for the Savannah River Nuclear Production Reactors, M. L. Hyder; CONTROL AND INSTRUMENTATION: 511 A Framework for Selecting Suitable Control Technologies for Nuclear Power Plant Systems, R. A. Kisner; DESIGN FEATURES: 521 Containments for Gas-Cooled Power Reactors History and Status, P.W. Williams; ENVIRONMENTAL EFFECTS: 537 Indoor Radon: A Natural Risk, N. H. Harley and J.H. Harley; On the Importance of the Atmospheric Parameters in the Fission Products Distribution of a Severe Reactor Accident, M. C. Barla and A. R. Bayulken; Book Review: Health Effects of Exposure to Low Levels of Ionizing Radiation BEIR V, C. R. Richmond; WASTE AND SPENT FUEL MANAGEMENT: 555 Activities Related to Waste and Spent Fuel Management, M. D. Muhlheim and E. G. Silver OPERATING EXPERIENCES: 567 Effects of Component Aging on the Westhinghouse Control Rod Drive System, K. Sullivan and W. Gunther; 577 Reactor Shutdown Experience, Compiled by J. W. Cletcher, 580 Selected Safety-Related Events, Compiled by G. A. Murphy; 582 Operating U 8 Power Reactors, Compiled by M. D. Muhlheim and E. G. Silver, RECENT DEVELOPMENTS: 596 General Administrative Activities, Compiled by M. D. Muhlheim and E. G. Silver; 610 Reports, Standards, and Safety Guides, D. S. Queener; 614 Proposed Rule Changes as of June 30, 1991; ANNOUNCEMENTS: 520 Workshop on PC PRAISE: A Probabilistic Fracture Mechanics Personal Computer Code for Nuclear Power Plant Piping Reliability Assessment; 536 Fifth Workshop on Nuclear Power Plant Containment Integrity; 624 New OECD "International Information System on Occupational Exposure (ISOE)"; 625 Harvard School of Public Health Announces Short Courses; 625 Eighth Power Plant Dynamics, Control and Testing Symposium; 626 Second Training Course on Off-Site Emergency Planning and Response for Nuclear Accidents; 618 The Authors; 622 Reviewers of Nuclear Safety, Vol 32.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

CoSHA: Code for Stellar Properties Heuristic Assignment—for the MaStar Stellar Library

We introduce CoSHA: a Code for Stellar properties Heuristic Assignment. In order to estimate the stellar properties, CoSHA implements a Gradient Tree Boosting algorithm to label each star across the parameter space (T eff , $\mathrm{log}g$, [Fe/H], and [α/Fe]). We use CoSHA to estimate the stellar atmospheric parameters of 22,000 unique stars in the MaNGA Stellar Library (MaStar). To quantify the reliability of our approach, we run internal tests, using both the Göttingen Stellar Library (a theoretical library) and the first data release of MaStar, and external tests, by comparing the resulting distributions in the parameter space with the APOGEE estimates of the same properties. In summary, our parameter estimates span the ranges T eff = [2900, 12,000] K, $\mathrm{log}g=[-0.5,5.6]$, [Fe/H] = [-3.74, 0.81], and αM = [-0.22, 1.17]. We report internal (external) uncertainties of the properties of ${\sigma }_{{T}_{\mathrm{eff}}}\sim 43(240)$ K, ${\sigma }_{\mathrm{log}g}\sim 0.2(0.4)$, σ [Fe/H] ~ 0.16(0.24), and σ [α/Fe] ~ 0.09(0.08). These uncertainties are comparable to those of other methods with similar objectives. Despite the fact that CoSHA is not aware of the spatial distributions of these physical properties in the Milky Way, we are able to recover the main trends known in the literature. The catalog of physical properties for MaStar can be accessed online.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Industry overview of TRANSCEND - 20271

The United Kingdom has a legacy of nuclear facilities to decommission and radioactive waste to manage and dispose of. The TRANSCEND programme is an independent research programme with significant participation from industrial organizations that are involved in that decommissioning programme and radioactive waste management. The participation has led to a programme that is both academically robust enough to attract significant funding from the EPSRC, the universities themselves and relevant enough to be supported financially by the industrial partners who see the needs and drivers. The programme offers benefits in terms of the development of people and in enabling and promoting innovation in both hardware and software tools. Industrial engagement is fundamental to being able to capitalise on that innovation. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI1991

Nuclear Safety [Vol. 32, No. 4, October-December 1991]

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI1995

Nuclear Safety [Vol. 36, No. 2, July-December 1995]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. THE CHORNOBYL ACCIDENT: 195 The Chornobyl Accident Revisited, Part III: Chernobyl Source Term Release Dynamics and Reconstruction of Events During the Active Phase, A. R. Sich; GENERAL SAFETY CONSIDERATIONS: 218 Second ANS Workshop on the Safety of Soviet-Designed Nuclear Power Plants, R. A. Bari; 234 Elements of a Nuclear Criticality Safety Program, C. M. Hopper; 243 Rickover, Excellence, and Criticality Safety Programs, R. E. Wilson; ACCIDENT ANALYSIS: 249 Transient Analysis of the PIUS Advanced Reactor Design with the TRAC-PF1/MOD2 Code, B. E. Boyack, J. L Steiner, S. C. Harmony, H. J. Stumpf, and J. F. Lime; 278 The Hierarchy-By-Interval Approach to Identifying Important Models that Need Improvement in Severe-Accident Simulation Codes, T. J. Heames, M. Khatib-Rahbar, J. E. Kelly, R. P. Jenks-Johnson, and Y.-S. Chen; 290 RELAP5/MOD3 Code Coupling Model, R. P. Martin; 299 Missiles Caused by Severe Pressurized-Water Reactor Accidents, R. Krieg; DESIGN FEATURES: 310 Validation of COMMIX with Westinghouse AP-600 PCCS Test Data, J. G. Sun, T. H. Chien, J. Ding, and W T. Sha; ENVIRONMENTAL EFFECTS: 321 Spent Nuclear Fuel Characterization for a Bounding Reference Assembly for the Receiving Basin for Off-Site Fuel, S. D. Kahook, R. L. Garrett, L. R. Canas, and M J. Beckum; OPERATING EXPERIENCES: 332 Reactor Shutdown Experience, Compiled by J. W. Cletcher; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 335 Reactor Coolant System Blowdown at Wolf Creek on September 17, 1994, J. V. Kauffman and S. L. Israel; RECENT DEVELOPMENTS: 344 Reports, Standards, and Safety Guides, D. S. Oueener; 349 Proposed Rule Changes as of June 30, 1995; ANNOUNCEMENTS: 320 Symposium on Acceptability of Risk From Radiation—Application to Manned Space Flight; 320 24th DOE/NRC Nuclear Air Cleaning and Treatment Conference; 361 Radiation Biology and Radiation Protection— Modern Developments and Tendencies in Radiation Biology; 362 1997 IEEE Sixth Conference on Human Factors and Power Plants; 354 The Authors; 360 Reviewers of Nuclear Safety, Vol. 36.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Efficient approach to kinetic simulation in the inner magnetically insulated transmission line on Z

This project explores the idea of performing kinetic numerical simulations in the Z inner magnetically insulated transmission line (inner MITL) by reduced physics models such as a guiding center drift kinetic approximation for particles and electrostatic and magnetostatic approximation for the fields. The basic problem explored herein is the generation, formation, and evolution of vortices by electron space charge limited (SCL) emission. The results indicate that for relevant to Z values of peak current and pulse length, these approximations are excellent, while also providing tens to hundreds of times reduction in the computational load. The benefits could be enormous: Implementation of these reduced physics models in present particle-in-cell (PIC) codes could enable them to be routinely used for experimental design while still capturing essential non-thermal (kinetic) physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

The inviscid incompressible limit of Kelvin–Helmholtz instability for plasmas

The Kelvin–Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth’s magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo-spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Gamma-ray Spectroscopy in Low-Power Nuclear Research Reactors

Gamma-ray spectroscopy is an effective technique for radioactive material characterization, routine inventory verification, nuclear safeguards, health physics, and source search scenarios. Gamma-ray spectrometers typically cannot be operated in the immediate vicinity of nuclear reactors due to their high flux fields and their resulting inability to resolve individual pulses. Low-power reactor facilities offer the possibility to study reactor gamma-ray fields, a domain of experiments hitherto poorly explored. In this work, we present gamma-ray spectroscopy experiments performed with various detectors in two reactors: The EPFL zero-power research reactor CROCUS, and the neutron beam facility at the Ohio State University Research Reactor (OSURR). We employed inorganic scintillators (CeBr3), organic scintillators (trans-stilbene and organic glass), and high-purity germanium semiconductors (HPGe) to cover a range of typical—and new—instruments used in gamma-ray spectroscopy. The aim of this study is to provide a guideline for reactor users regarding detector performance, observed responses, and therefore available information in the reactor photon fields up to 2 MeV. The results indicate several future prospects, such as the online (at criticality) monitoring of fission products (like Xe, I, and La), dual-particle sensitive experiments, and code validation opportunities.

Pakari, Oskari V. (ORCID:0000000337048190)↗

DOE OSTI2022

Quantification of the importance of the modeling fidelity in the Best Estimate Plus Uncertainty analysis

In this work, the multi-physics coupling of CTF-PARCS for both steady-state and transient simulations is evaluated focusing on the quantification of the importance of the modeling fidelity when applied to the Best Estimate Plus Uncertainty safety analysis. For the steady-state, a Picard iteration approach is adopted in the coupled code while for the transient an explicit approach has been developed as a first step. The CTF-PARCS coupling is applied to the REA at HFP BOC scenario proposed in the exercise I-2c of LWR-UAM benchmark Phase III. Two different modeling choices are investigated for the nominal calculations. The first consists of including the 3D burnup information in CTF, and the second of modeling the spacers grids in both PARCS and CTF. It is observed that due to the degradation of the fuel thermal conductivity, the 3D burnup inclusion in CTF leads to significant higher centerline temperatures than the base case, with a difference up to 300 K. The spacer grids modeling shows the expected power and temperature decrease in the axial positions of the spacer grids. For the uncertainty quantification study, the multi-physics modeling including the burnup information in CTF is used. The results show that the inserted reactivity has a relative standard deviation of 13.6% mainly attributed to the nuclear data. The maximum linear power has a relative standard deviation of 16.2% due to the nuclear data as well, while the maximum centerline temperature has a relative standard deviation of 3.5% primarily caused by the fuel thermal conductivity. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

XE-100 modeling and simulation for neutronic analysis in MCNP6.2

XE-100 is a generation IV helium-cooled, graphite-moderated, pebble-bed reactor (HTGR). As part of the pathway toward a conceptually designing and licensing this reactor, an independent Monte Carlo model was created in MCNP6.2, and several distinct neutronic analyses were then performed. The double heterogeneity of TRISO fuel within graphite pebbles introduces unique modeling challenges related to particle and pebble clipping. The results show that for neutron and photon heating of ex-core components such as the reflector, RCSS, core barrel (CB), the model that contains clipping produces higher heating values. It is therefore concluded that removing clipping via compression of the particles and pebbles within the model distributes the neutrons and gammas preferentially toward the core center, and reduces the heating that is experienced toward the reactor periphery. Thus, the most conservative model for ex-core heating contains particle and pebble clipping. Also presented are results on the impact of chamfers that exist on the corners of graphite reflector blocks. As these chamfers could potentially create streaming paths, the neutron and gamma flux from the core to the CB were analyzed. It was determined that the chamfers do not significantly impact the neutron or gamma signatures on the CB, in that the shape of the neutron and photon flux on a detector imposed on the CB shows no preferential streaming path. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Nonlocal, diamagnetic electromagnetic effects in magnetically insulated transmission lines

We identify the time-dependent physics responsible for the critical reduction of current losses in magnetically insulated transmission lines (MITLs) due to uninsulated space charge-limited currents of electrons emitted by field stress. A drive current of sufficiently short pulse length introduces a strong enough time dependence that steady-state results alone become inadequate for the complete understanding of current losses. The time-dependent physics can be described as a nonlocal, diamagnetic electromagnetic response of space charge limited currents. As the pulse length is increased or equivalently, the MITL length reduced, these time-dependent effects diminish and current losses converge to those predicted by the well-known Child–Langmuir law in the external (vacuum) fields. We present a simple one-dimensional (1D) model that encapsulates the essence of this physics. We find excellent agreement with 2D particle-in-cell simulations for two MITL geometries, Cartesian parallel plate and azimuthally symmetric straight coaxial. Based on the 1D model, we explore various scaling dependencies of MITL losses with relevant parameters, e.g., peak current, pulse length, geometrical dimensions, etc. We propose an improved physics model of magnetic insulation in the form of a Hull curve, which could also help improve predictions of current losses by common circuit element codes, such as BERTHA. Finally, we describe how to calculate the temperature rise due to electron impact within the 1D model.

Computer simulation↗

DOE OSTI2025

pvcracks: trained VAE model

The resulting model weights for the variational autoencoder for solar cell crack parametrization to be loaded into the python code for other to use

14 SOLAR ENERGY↗

DOE OSTI2022

Genetic algorithm-based optimisation of the few-group structure for lead fast reactors analysis

The optimal choice of the few-group structure for full-core transient analyses is still an open issue in reactor physics, especially for fast system like the lead fast reactor. One possible approach to select the group boundaries is represented by heuristic search algorithms, such as evolutionary ones. In this paper, a genetic algorithm coupled with the SIMMER code is employed to determine optimized six-group boundaries for the analysis of the ALFRED reactor. The Serpent Monte Carlo code is adopted to produce both the fine-group cross section library and the fine-group flux, used as a figure of merit to drive the genetic optimisation. The results show that the algorithm is indeed able to find satisfactory solutions that comply with the set objectives and can be reasonably interpreted in light of the underlying physics of the considered core. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

On the theory of multi-target coded sources for high-energy, high-resolution, and high-brightness x-ray radiography

Explore the source record for details and available documents.

Physics↗

DOE OSTI2023

Multiphysics modelling in PyLith: poroelasticity

SUMMARY PyLith, a community, open-source code for modelling quasi-static and dynamic crustal deformation with an emphasis on earthquake faulting, has recently been updated with a flexible multiphysics implementation. We demonstrate the versatility of the multiphysics implementation by extending the code to model fully coupled continuum poromechanics. We verify the newly incorporated physics using standard benchmarks for a porous medium saturated with a slightly compressible fluid. The benchmarks include the 1-D consolidation problem as outlined by Terzaghi, Mandel’s problem for the 2-D case, and Cryer’s problem for the 3-D case. All three benchmarks have been added to the PyLith continuous integration test suite. We compare the closed form analytical solution for each benchmark against solutions generated by our updated code, and lastly, demonstrate that the poroelastic material formulation may be used alongside the existing fault implementation in PyLith.

Geochemistry & Geophysics↗

DOE OSTI2024

Solid-to-plasma transition of polystyrene induced by a nanosecond laser pulse within the context of inertial confinement fusion

Laser Direct Drive (LDD) Inertial Confinement Fusion (ICF) involves irradiating a spherical target of thermonuclear fuel coated with an ablator, usually made of polystyrene. Laser energy absorption near the target surface leads to matter ablation, hydrodynamic shocks, and ultimately capsule implosion. The conservation of spherical symmetry is crucial for implosion efficiency, yet spatial modulations in laser intensity can induce nonuniformities, causing the laser imprint phenomenon. Understanding laser imprint, especially considering the initial solid state, is essential for advancing LDD ICF. A first microscopic model of solid-to-plasma transition was built in 2019, accounting for laser absorption in the solid state with a band structure based ionization model. This model has been improved to include chemical fragmentation and a more accurate description of electron collision frequency in various matter states. The latest development involves assessing the model reliability by comparing theoretical predictions with experimental observations. Despite the success of this approach, questions remain, leading to further investigations and observations under different irradiation conditions. This work presents an experiment with a nanosecond pulse, taking into account hydrodynamic effects, and measures transmission dynamics over the entire laser beam area to observe two-dimensional effects. As a result, the objective is to adapt the theoretical model, couple it with a hydrodynamic code, and observe additional effects related to the initial solid state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

A coarse-grain force field based on quantum mechanics (CGq FF) for molecular dynamics simulation of poly(ethylene glycol)- block -poly(ε-caprolactone) (PEG- b -PCL) micelles

In order to provide the means to predict from molecular dynamics (MD) simulations the structures of copolymer-based micelles in solution, we developed coarse grain force field (CGq FF) parameters for poly(ethylene glycol) (PEG) and for poly(ε-caprolactone) (PCL). A key advance here is the use of quantum mechanics to train the parameters describing the non-bonded (NB) interactions between the CG beads. The functional forms are the same as the MARTINI CG FF so standard MD codes can be used. Our CGq FF describes well the experimentally observed properties for the polymer–air and polymer–water interfaces, indicating the accuracy of the NB interactions. Additionally, the structural properties (density, radius of gyration ( R g ), and end-to-end distance ( h )) match both experiment and all atom (AA) simulations. We illustrate the application of this CGq FF by following the formation of a spherical micelle from 250 chains of PEG 23 - b -PCL 9 diblock copolymer, each block with molecular weight of 1000 Daltons (10 500 beads, corresponding to 123 250 atoms), in a water box with 119 139 water beads (426 553 water molecules).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗