Results for “Transfer function design” — Page 54

DOE OSTI2022

CO 2 Chemisorption Behavior in Conjugated Carbanion-Derived Ionic Liquids via Carboxylic Acid Formation

Superbase-derived task-specific ionic liquids (STSILs) represent one of the most attractive and extensively studied systems in carbon capture via chemisorption, in which the obtained CO 2 uptake capacity has a strong relationship with the basicity of the anions. High energy input in desorption and side reactions caused by the strong basicity of the anions are still unsolved issues. The development of other customized STSILs leveraging an alternative driving force to achieve efficient CO 2 chemisorption/desorption is highly desirable yet challenging. Here, in this work, carbanion-derived STSILs were developed for efficient CO 2 chemisorption via a carboxylic acid formation pathway. The STSIL with the deprotonated malononitrile molecule ([MN]) as the anion exhibited much higher CO 2 uptake capacity than the one derived from 2-methylmalononitrile ([MMN]). Notably, this trend was opposite to their basicity ([MN] < [MMN]). Detailed characterization of the products, supported by density functional theory simulations of spectra and calculations of the reaction energetics, demonstrated that carboxylic acid was formed upon reacting with CO 2 via proton transfer in [MN]-derived STSILs but not in the case of [MMN] due to lack of an α-H. The preference of the carboxylic acid product over carboxylate formation was driven by the extended conjugation among the central sp 2 carbon, the as-formed carboxylic acid, and the two nitrile groups. The achievements made in this work provide an alternative design principle of STSILs by leveraging the extended conjugation in the CO 2 -integrated product.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Hydrogenation of ethylene over molybdenum–sulfur complexes supported on UiO-66

Development of supported single-site catalysts using small metal sulfide complexes could significantly help in the development of cost-effective catalytic materials to drive selective hydrogenation and hydrogenolysis. The goal of this study is to contribute to the development of metal sulfide catalysts by calculating the thermodynamics of a catalytic cyclic involving a metal organic framework functionalized by insertion of metal sulfide. Anchored metal sulfide complexes can potentially be designed with ligands with distinctly different electronic and catalytic properties for specific catalytic applications. Here we examine the hydrogenation of ethylene as a model. We use density functional theory to investigate molybdenum–sulfur complexes as active catalysts anchored on the metal–organic framework UiO-66 as a stable support. Our calculations show that the anchored complexes with more than two sulfur ligands are unfavorable for ethylene adsorption, so we study complexes with one or two sulfur ligands. Hydrogenation of the unsaturated carbon double bond requires the transfer of two hydrogen atoms, which can occur via heterolytic activation of hydrogen to form a Mo-hydride and a protonated sulfur – either by hydride transfer followed by proton transfer or via proton transfer followed by hydride transfer, and we find that both mechanisms proceed via two-state reactivity involving two spin states along the reaction path. Of the two catalysts studied in gas the phase, the MoS single-sulfur–ligand complex with lower oxidation states produces thermodynamically more favorable intermediates along the pathway for the first hydrogen transfer for both the hydride-first mechanism and the proton-first mechanism. As a result, the quantum mechanical calculations provide experimentally inaccessible partial atomic charges and geometries of the various intermediates encountered along the steps of the reaction mechanisms.

Kermani, Maryam Mansoori [University of Minnesota,↗

DOE OSTI2021

In situ/operando soft x-ray spectroscopy of chemical interfaces in gas and liquid environments

Many energy storage and energy conversion systems are based on the complexity of material architecture, chemistry, and interfacial interactions. To understand and thus ultimately control the energy applications calls for in situ/operando characterization tools. Over the years, in situ/operando soft x-ray spectroscopy has been developed for the studies of gas molecules, molecular liquids, catalytic, and electrochemical reactions. Soft x-ray spectroscopy offers electronic structure characterization of materials in energy conversion, energy storage, and catalysis regarding functionality, complexity of material architecture, and chemical interactions. It has been shown how to use the powerful in situ/operando soft x-ray spectroscopy characterization techniques of interfacial phenomena and how to reveal the mechanism of charge transfer and chemical transformation of solid/gas and solid/liquid interfaces of energy storage and catalytic materials in a realistic environment. It has been demonstrated how to overcome the challenge that soft x-rays cannot easily peek into the high-pressure catalytic or liquid electrochemical reactions. Finally, the unique design of in situ/operando soft x-ray spectroscopy instrumentation and fabrication principle and examples of experiments are presented.

36 MATERIALS SCIENCE↗

NASA NTRS1982

Simultaneous stabilization and simultaneous pole placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed.

Ghosh, B. K.↗

NASA NTRS1983

Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed. Previously announced in STAR as N82-31031

Ghosh, B. K.↗

NASA NTRS1987

Frequency-response identification of XV-15 tilt-rotor aircraft dynamics

The timely design and development of the next generation of tilt-rotor aircraft (JVX) depend heavily on the in-depth understanding of existing XV-15 dynamics and the availability of fully validated simulation models. Previous studies have considered aircraft and simulation trim characteristics, but analyses of basic flight vehicle dynamics were limited to qualitative pilot evaluation. The present study has the following objectives: documentation and evaluation of XV-15 bare-airframe dynamics; comparison of aircraft and simulation responses; and development of a validated transfer-function description of the XV-15 needed for future studies. A nonparametric frequency-response approach is used which does not depend on assumed model order or structure. Transfer-function representations are subsequently derived which fit the frequency responses in the bandwidth of greatest concern for piloted handling-qualities and control-system applications.

Tischler, Mark B.↗

NASA NTRS1990

A bit-serial VLSI array processing chip for image processing

An array processing chip integrating 128 bit-serial processing elements (PEs) on a single die is discussed. Each PE has a 16-function logic unit, a single-bit adder, a 32-b variable-length shift register, and 1 kb of local RAM. Logic in each PE provides the capability to mask PEs individually. A modified grid interconnection scheme allows each PE to communicate with each of its eight nearest neighbors. A 32-b bus is used to transfer data to and from the array in a single cycle. Instruction execution is pipelined, enabling all instructions to be executed in a single cycle. The 1-micron CMOS design contains over 1.1 x 10 to the 6th transistors on an 11.0 x 11.7-mm die.

Heaton, Robert↗

NASA NTRS2002

Life Cycle Systems Engineering Approach to NASA's 2nd Generation Reusable Launch Vehicle

The overall goal of the 2nd Generation RLV Program is to substantially reduce technical and business risks associated with developing a new class of reusable launch vehicles. NASA's specific goals are to improve the safety of a 2nd- generation system by 2 orders of magnitude - equivalent to a crew risk of 1 -in- 10,000 missions - and decrease the cost tenfold, to approximately $1,000 per pound of payload launched. Architecture definition is being conducted in parallel with the maturating of key technologies specifically identified to improve safety and reliability, while reducing operational costs. An architecture broadly includes an Earth-to-orbit reusable launch vehicle, on-orbit transfer vehicles and upper stages, mission planning, ground and flight operations, and support infrastructure, both on the ground and in orbit. The systems engineering approach ensures that the technologies developed - such as lightweight structures, long-life rocket engines, reliable crew escape, and robust thermal protection systems - will synergistically integrate into the optimum vehicle. Given a candidate architecture that possesses credible physical processes and realistic technology assumptions, the next set of analyses address the system's functionality across the spread of operational scenarios characterized by the design reference missions. The safety/reliability and cost/economics associated with operating the system will also be modeled and analyzed to answer the questions "How safe is it?" and "How much will it cost to acquire and operate?" The systems engineering review process factors in comprehensive budget estimates, detailed project schedules, and business and performance plans, against the goals of safety, reliability, and cost, in addition to overall technical feasibility. This approach forms the basis for investment decisions in the 2nd Generation RLV Program's risk-reduction activities. Through this process, NASA will continually refine its specialized needs and identify where Defense and commercial requirements overlap those of civil missions.

Thomas, Dale↗

DOE OSTI2020

Quantal diffusion approach for multinucleon transfer processes in the 58,64 Ni + 208 Pb reactions: Toward the production of unknown neutron-rich nuclei

In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power. Purpose: This article aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni + 208 Pb at E c.m. = 268 MeV and 58 Ni + 208 Pb at E c.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++. Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Engineering the electronic and strained interface for high activity of PdM core @Pt monolayer electrocatalysts for oxygen reduction reaction

Alloyed nanoparticles with core-shell structures provide a favorable model to modulate interfacial interaction and surface structures at the atomic level, which is important for designing electrocatalysts with high activity and durability. Herein, core-shell structured Pd 3 M@Pt/C nanoparticles with binary PdM alloy cores (M = Fe, Ni, and Co) and a monolayer Pt shell were successfully synthesized with diverse interfaces. Among these, Pd 3 Fe@Pt/C exhibited the best oxygen reduction reaction catalytic performance, roughly 5.4 times more than that of the commercial Pt/C catalyst used as reference. The significantly enhanced activity is attributed to the combined effects of strain engineering, interfacial electron transfer, and improved Pt utilization. Density functional theory simulations and extended X-ray absorption fine structure analysis revealed that engineering the alloy core with moderate lattice mismatch and alloy composition (Pd 3 Fe) optimizes the surface oxygen adsorption energy, thereby rendering excellent electrocatalytic activity. Finally, future researches may use this study as a guide on the construction of highly effective core-shell electrocatalysts for various energy conversions and other applications.

25 ENERGY STORAGE↗

DOE OSTI2024

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1976

Experiments on the properties of superfluid helium in zero gravity

The paper describes a research program designed to study the behavior of superfluid liquid helium in low and zero gravity in order to determine the properties which are critically important to its use as a stored cryogen for cooling scientific instruments aboard spacecraft for periods up to several months. The experiment program consists of a series of flights of an experiment package on a free-fall trajectory both on an aircraft and on a rocket. The objectives are to study thickness of thin films of helium as a function of acceleration, heat transfer in thin films, heat transfer across copper-liquid helium interfaces, fluid dynamics of bulk helium in high and low accelerations and under various conditions of rotations, alternate methods of separation of liquid and vapor phases and of efficient venting of the vapor, and undesirable thermomechanical oscillations in the vent pipes. Preliminary results from aircraft tests are discussed.

Mason, P.↗

NASA NTRS1986

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Mingori, D. L.↗

NASA NTRS1990

Factors shaping the evolution of electronic documentation systems

The main goal is to prepare the space station technical and managerial structure for likely changes in the creation, capture, transfer, and utilization of knowledge. By anticipating advances, the design of Space Station Project (SSP) information systems can be tailored to facilitate a progression of increasingly sophisticated strategies as the space station evolves. Future generations of advanced information systems will use increases in power to deliver environmentally meaningful, contextually targeted, interconnected data (knowledge). The concept of a Knowledge Base Management System is emerging when the problem is focused on how information systems can perform such a conversion of raw data. Such a system would include traditional management functions for large space databases. Added artificial intelligence features might encompass co-existing knowledge representation schemes; effective control structures for deductive, plausible, and inductive reasoning; means for knowledge acquisition, refinement, and validation; explanation facilities; and dynamic human intervention. The major areas covered include: alternative knowledge representation approaches; advanced user interface capabilities; computer-supported cooperative work; the evolution of information system hardware; standardization, compatibility, and connectivity; and organizational impacts of information intensive environments.

Dede, Christopher J.↗

NASA NTRS1993

TOAD Editor

Transferable Output ASCII Data (TOAD) computer program (LAR-13755), implements format designed to facilitate transfer of data across communication networks and dissimilar host computer systems. Any data file conforming to TOAD format standard called TOAD file. TOAD Editor is interactive software tool for manipulating contents of TOAD files. Commonly used to extract filtered subsets of data for visualization of results of computation. Also offers such user-oriented features as on-line help, clear English error messages, startup file, macroinstructions defined by user, command history, user variables, UNDO features, and full complement of mathematical statistical, and conversion functions. Companion program, TOAD Gateway (LAR-14484), converts data files from variety of other file formats to that of TOAD. TOAD Editor written in FORTRAN 77.

Bingle, Bradford D.↗

NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗

NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗

DOE OSTI2021

A hybrid CoOOH-rGO/Fe 2 O 3 photoanode with spatial charge separation and charge transfer for efficient photoelectrochemical water oxidation

As a promising photoanode for photoelectrochemical (PEC) water oxidation, hematite (Fe 2 O 3 ) still suffers from poor charge mobility and serious charges recombination and sluggish surface oxygen evolution kinetics. Herein, a hybrid photoanode of cobalt (oxy)hydroxide coupled with reduced graphene oxide modified Fe 2 O 3 (CoOOH-rGO/Fe 2 O 3 ) is well crafted by a facile hydrothermal synthesis with a chelation-mediated in-situ growth method. Morphology characterizations indicate rGO forms the internal network among isolated Fe 2 O 3 and CoOOH nanosheets distribute on the terminal of Fe 2 O 3 , forming a spatial separated nanostructure. The resultant CoOOH-rGO/Fe 2 O 3 exhibits an obviously reduced onset potential of ca. 150 mV and a significantly enhanced photocurrent density of 2.56 mA cm -2 at 1.23 V, which is ca. 3.3 times higher than that of bare Fe 2 O 3 . Especially, the functions of rGO and CoOOH are studied by using electrochemical impedance spectroscopy, open circuit potentials and intensity modulated photocurrent spectroscopy. It is found rGO act as conductive network which facilitates the electron transfer from Fe 2 O 3 to the substrate, while CoOOH evidently passivate the surface states of Fe 2 O 3 , improve charge separation and provide catalytic active sites for water oxidation. Additionally, the spatial charge separation and charge transfer caused by CoOOH and rGO are responsible for the enhanced PEC performance of water oxidation. The rational design and the facile fabrication strategy exhibit great potential to be used for other PEC system with great efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗