Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “voltage and current controllers”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30

Complementary Electrolyte Design for Li Metal Batteries in Electric Vehicle Applications

In this report a complementary electrolyte system with 0.8 M lithium bis(fluorosulfonylimide) (LiFSI) salt and 2 wt % lithium perchlorate (LiCLO4) additive in fluoroethylene carbonate (FEC)/ethyl methyl carbonate (EMC) solution enables not only stable cycling of lithium metal batteries (LMBs) with practical loading (<30 μm lithium anode, cathode loading > 4 mAh/cm 2 ) but also outstanding degradation stability toward the end of cycle life when compared to the conventional electrolyte. Although the use of LiFSI salt can increase the electrolyte conductivity and lengthen the cycle life of LMBs, the aged lithium anode morphology formed by the sacrificial decomposition of LiFSI is highly porous, leading to an abrupt cell capacity drop toward the end of cycling. Moreover, the inability to stop aluminum corrosion by the LiFSI-based electrolyte also causes cracking of the cathode tab during prolonged cycling. It is observed that a highly porous aged lithium consumed electrolyte at a higher rate, leading to the dry-out of electrolyte solvents. On the contrary, dense aged lithium anode morphology increased the localized current applied on the lithium, causing the formation of lithium dendrite. Thus, porosity control is the key to enhance battery performance. In this complementary system, LiClO 4 was introduced as an advanced additive to not only improve the capacity retention rate but also mitigate the abrupt capacity drop toward the end of cycle life because LiClO 4 acted as a pore astringent reducing the porosity of the aged lithium metal anode to the desired level. Moreover, the addition of LiClO 4 can also suppress the AI corrosion, allowing stable high-voltage cycling of LMBs. The synergistic effect of combining LiFSI salt and a LiClO 4 additive leads to an electrolyte system that can facilitate the application of high-energy LMBs with practical electrode loading.

25 ENERGY STORAGE↗

AI for Experimental Controls at Jefferson Lab

We report the AI for Experimental Controls project is developing an AI system to control and calibrate detector systems located at Jefferson Laboratory. Currently, calibrations are performed offline and require significant time and attention from experts. This work would reduce the amount of data and the amount of time spent calibrating in an offline setting. The first use case involves the Central Drift Chamber (CDC) located inside the GlueX spectrometer in Hall D. We use a combination of environmental and experimental data, such as atmospheric pressure, gas temperature, and the flux of incident particles as inputs to a sequential Neural Network (NN) to recommend a high voltage setting and the corresponding calibration constants in order to maintain consistent gain and optimal resolution throughout the experiment. Utilizing AI in this manner represents an initial shift from offline calibration towards near real time calibrations performed at Jefferson Laboratory.

47 OTHER INSTRUMENTATION↗

Mechanically activated and deactivated ion transport across nanopores with heterogeneous surface charge distributions

To mimic the intricate and adaptive functionalities of biological ion channels, electrohydrodynamic ion transport has been studied extensively, albeit mostly, across uniformly charged nanochannels. Here, we analyze the ion transport under coupled electric field and pressure across heterogeneously charged nanopores with oppositely charged sections on their lateral surface. We only consider such pores with symmetric hourglass-like and cylindrical shapes to focus on the effects of the non-uniform surface charge distribution. Finite-element simulations of a continuum model demonstrate that a pressure applied in either direction of the pore-axis equally suppresses or amplifies the ionic conductance, depending on the electric field polarity, by distorting the quasi-static distribution of ions in the pore. The resulting anomalous mechanical deactivation and activation of ionic current under opposite voltage biases exhibit the functional modularity of our setup, while their intensities are highly tunable, substantially greater than those of analogous behaviors in other nanochannels, and fundamentally correlated to ionic current rectification (ICR) in our pores. A detailed study of ICR subsequently reveals its counterintuitive non-monotonous variations, in the pores, with the magnitude of applied voltage and the pore length, that can help optimize their diode-like behavior. We further illustrate that while the hourglass-shaped nanopores yield the more efficient mechanical suppressors of ion transport, their cylindrical analogs are the superior rectifiers and mechanical amplifiers of ion conduction. Therefore, this article provides a blueprint for the strategic design of nanofluidic circuits to attain a robust, modular, and tunable control of ion transport under external electrical and mechanical stimuli.

Physics↗

High-fidelity modeling of breakdown in helium: initiation processes and secondary electron emission

Understanding the role of physical processes contributing to breakdown is critical for many applications in which breakdown is undesirable, such as capacitors, and applications in which controlled breakdown is intended, such as plasma medicine, lightning protection, and materials processing. The electron emission from the cathode is a critical source of electrons which then undergo impact ionization to produce electrical breakdown. In this study, the role of secondary electron yields due to photons (γ ph ) and ions (γ i ) in direct current breakdown is investigated using a particle-in-cell direct simulation Monte Carlo model. The plasma studied is a one-dimensional discharge in 50 Torr of pure helium with a platinum cathode, gap size of 1.15 cm, and voltages of 1.2–1.8 kV. The current traces are compared with experimental measurements. Larger values of γ ph generally result in a faster breakdown, while larger values of γ i result in a larger maximum current. The 58.4 nm photons emitted from He(2 1 P) are the primary source of electrons at the cathode before the cathode fall is developed. Of the values of γ ph and γ i investigated, those which provide the best agreement with the experimental current measurements are γ ph = 0.005 and γ i = 0.01. In this work, these values are significantly lower than those in the literature for pristine platinum or for a graphitic carbon film which we speculate may cover the platinum. This difference is in part due to the limitations of a one-dimensional model but may also indicate surface conditions and exposure to a plasma can have a significant effect on the secondary electron yields. The effects of applied voltage and the current produced by a UV diode which was used to initiate the discharge, are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toroidal Field Reversing Switch

A motor-driven, high-current switch is being designed by Stäubli Electrical Connectors in collaboration with Princeton Plasma Physics Laboratory to reverse the DIII-D Toroidal field coil current. The existing field reversing procedure requires approximately 4 h of labor performed between run days to reconfigure the bus work, thus requiring a separate run day to complete experimental scans with both field directions. This typically results in different wall conditions which complicate the results or make them invalid. The proposed switch will complete the reversal process in approximately 4-5 min, between shots, so that wall conditions are not a factor, and easily fits within the 10-12 min DIII-D shot cycle. The switch is a compact design fitting into a 157.5 × 41 cm envelope. The switch uses two copper pins that slide between Stäubli MULTILAM contacts. The switch is rated for total current of 180-kA dc for 10 s with a 12-min repetition rate; the maximum operating coil current is 124-kA dc. The switch diagnostics include: voltage drop, current monitor, thermal monitors, position sensors, and motor torque. Here, the switch is rated for 300 cycles per year, and 3000 cycles overall before contact replacement, with contact inspection yearly. The design details and operation of the switch are covered in this article.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Correlating Electronic Structure and Device Physics with Mixing Region Morphology in High-Efficiency Organic Solar Cells

The donor/acceptor interaction in non-fullerene organic photovoltaics leads to the mixing domain that dictates the morphology and electronic structure of the blended thin film. Initiative effort is paid to understand how these domain properties affect the device performances on high-efficiency PM6:Y6 blends. Different fullerenes acceptors are used to manipulate the feature of mixing domain. It is seen that a tight packing in the mixing region is critical, which could effectively enhance the hole transfer and lead to the enlarged and narrow electron density of state (DOS). As a result, short-circuit current (J SC ) and fill factor (FF) are improved. The distribution of DOS and energy levels strongly influences open-circuit voltage (V OC ). The raised filling state of electron Fermi level is seen to be key in determining device V OC . Energy disorder is found to be a key factor to energy loss, which is highly correlated with the intermolecular distance in the mixing region. A 17.53% efficiency is obtained for optimized ternary devices, which is the highest value for similar systems. The current results indicate that a delicate optimization of the mixing domain property is an effective route to improve the V OC , J SC , and FF simultaneously, which provides new guidelines for morphology control toward high-performance organic solar cells.

36 MATERIALS SCIENCE↗

Breakdown and Discharge Characteristics of High Repetition Frequency Nanosecond Pulsed Air Dielectric Barrier Discharge

This study explores the breakdown characteristics and discharge modes in a parallel plate air dielectric barrier discharge system using repetitive nanosecond pulses, with pulse repetition frequencies (PRFs) from 0.1 to 100 kHz. It examines how pulse parameters—PRF, pulse number and gas pressure—affect the memory effect, leveraging current and voltage measurements, fast imaging and optical emission spectroscopy. The findings show that higher PRFs lead to a reduction in breakdown voltage well below the streamer breakdown threshold. We argue that this effect may be attributed to the cumulative buildup of metastable species and negative ions in the discharge gap which could sustain free electrons in‐between the voltage pulses. Despite observing increased energy deposition with higher PRFs, the impact on filament formation was minimal, highlighting a strong dependence of discharge morphology on the accumulation of plasma‐produced species. This research studies provides valuable insights for controlling discharge regimes in applications such as plasma‐assisted combustion, surface treatment and air treatment by clarifying the interactions between discharge mechanisms at different PRFs and pressures.

42 ENGINEERING↗

Validation of Interconnection and Interoperability of Grid-Forming Inverters Sourced by Hydrogen Technologies in View of 100% Renewable Microgrids

Grid-forming assets are required in microgrids to act as voltage-frequency masters. These grid-forming assets can operate in two modes of operation: grid-following mode and grid-forming mode. In grid-following mode of operation, these assets will follow real power and reactive power setpoints and in grid-forming mode of operation these assets will follow voltage and frequency setpoints. Traditionally, diesel generators or natural gas-based generators are widely used to act as a voltage-frequency master. However, many utilities are aiming to replace generators with grid forming-inverters supplied by solar photovoltaics (PV), batteries or fuel cells. Since grid-forming assets need a long-term reliable energy source, fuel cells are a reasonable and viable choice to supply the grid-forming inverters, but some of the challenges facing the wide deployment of grid-forming fuel cell inverters need to be addressed. Specifically, in our proposed work, we aim to focus on the interconnection and interoperability requirements of grid-forming fuel cell inverters. Currently, state-of-the-art fuel cell inverters follow the general interconnection requirements of distributed energy resources (DERs) and general interoperability requirements of DERs, but these requirements were built with PV and battery systems in mind. Fuel cells have different operational requirements, and therefore these requirements need to be appropriately modified for the grid operators to use. These additional steps add to the investment and operational cost to the grid operators. Through the ARIES platform, this proposed project aims to bridge this gap and use power hardware-in-the-loop (PHIL) and controller hardware-in-the-loop (CHIL) experiments to inform the creation of open-source interconnection and interoperability information that can aid in faster and cheaper installation and operation of grid-forming fuel cell inverters.

grid-forming↗

A dedicated mirror-magnet experiment to study quench characteristics and dependencies in $Nb_{3}Sn$ coils and explore improvements of diagnostics capabilities

A single Nb3Sn short quadrupole coil in a mirror-magnet configuration was employed to investigate a wide range of phenomena and to serve as test-bed for diagnostics developments. A configurable array of spot-heaters was installed on the inner coil surface for control of induced quench conditions. Several different quench antenna arrays were positioned along the coil inner surface, and included significant sensor overlap for assessment of their relative efficiency and operation. Multiple acoustic sensors were placed on the pole and at coil ends. Optical fibers in grid configurations were put in different places on the coil and magnet for strain assessment, along with standard resistive strain gauges. Current spikes in the magnet circuit were monitored. This plethora of instrumentation aimed to support investigations on induced and spontaneous quenches, among other goals, and was supplemented by standard voltage-tap-based measurements. Voltage tap data of induced quenches from various spot-heater configurations was investigated for similarities to voltage development in spontaneous quenches. Quench antennas provided insights about current redistribution in the quenching coil and coil splices. The Quench Current-boosting Device was applied and the effect on coil training examined. This paper describes motivations behind the research, the overall test setup and main results.

Stoynev, Stoyan [Fermilab]↗

MULTI-FIDELITY MODELING AND UNCERTAINTY QUANTIFICATION OF INVERTER BASED RESOURCES IN INTEGRATED T&D SYSTEMS

Uncertainty quantification plays a pivotal role in improving the accuracy and reliability of inverter operation within modern power systems that are increasingly dominated by inverter-based resources (IBRs). IBRs, especially those operating under grid forming (GFM) control, rely heavily on a complex set of control parameters and system measurements to maintain voltage, frequency, and power balance. Traditional deterministic modeling approaches often fail to capture these parameter deviations, potentially resulting in suboptimal control actions, reduced system stability, or even instability under high penetration of IBRs. In this paper, we demonstrate the application of model calibration and uncertainty quantification (UQ) principles to an integrated transmission and distribution (T&D) model involving a GFM converter and provide a framework for prioritizing control improvements, guiding robust design, and informing adaptive strategies that can accommodate real-time variability in system conditions. The proposed approach could be valuable in enhancing the robustness of current and future power systems under increased IBR penetrations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Additive manufacturing for electrocaloric terpolymer thin films

Current heating, venting, and air conditioning (HVAC) systems have drawbacks of high energy consumption, large CO 2 emissions, and low efficiency. Electrocaloric (EC) cycles present an eco-friendly alternative by converting thermal energy to electrical energy. Defect-free thin films with uniform thickness are required to achieve optimal EC performance. A scalable thin film fabrication process is essential for integrating EC cycles into HVAC systems. This study introduces EC thin films prepared by electrospray (ES) processing, a manufacturing method that deposits EC polymer layer by layer using high voltage. The resulting films show superior thickness control, smoother surfaces, and improved thermal and electrical properties compared with solution casting. In addition, post-annealing at 120°C enhances the thermal and EC performance, with films achieving a temperature change (ΔT) of 3.6°C at 100 MV/m when tested near room temperature. With the potential for future scalability, the ES method offers a promising approach for fabricating EC thin films.

36 MATERIALS SCIENCE↗

A New Configuration of Paralleled Modular ANPC Multilevel Converter Controlled by an Improved Modulation Method for 1 MHz, 1 MW EV Charger

In this work, a new configuration of the modular multilevel converter (MLC) based on the parallel connection of three-level active-neutral-point-clamped (3L-ANPC) cells as well as its improved modulation method is proposed for 1 MHz, 1 MW electric vehicle (EV) megacharger. In the proposed paralleled modular ANPC-MLC, only six high-frequency silicon carbide (SiC) power switches operating at 333 kHz are required to generate 1 MHz switching frequency spectrum. Moreover, the operating voltage of all power devices is halved, the magnitude of the first switching frequency harmonic cluster is decreased by the factor of five, and the load current is equally distributed between the 3L-ANPC legs by employing the proposed improved modulation method. Hence, the modularity, efficiency, and power density of the proposed converter are notably increased, whereas the value of passive components and the overall switching loss are remarkably decreased. In addition, an optimized design of the one 3L-ANPC cell of the proposed paralleled modular ANPC-MLC for 1 MHz, 1MW EV megacharger using Ansys SIwave, Icepak, and Q3D finite element method platforms is presented and analyzed in detail. The provided experimental results of the down-scaled setup verify the feasibility and viability of the proposed configuration as well as its improved switching pattern.

42 ENGINEERING↗

Oak Ridge National Laboratory Pilot Demonstration of an Attestation and Anomaly Detection Framework using Distributed Ledger Technology for Power Grid Infrastructure

This report summarizes the design and pilot demonstration of a framework called Grid Guard that was created to provide increased data and device trustworthiness to electric grid devices by leveraging distributed ledger technology (DLT), specifically blockchain. Grid Guard contains a combination of core cryptographic methods such as the secure hash algorithm (SHA), and asymmetric cryptography, private permissioned blockchain, baselining configuration data, consensus algorithm (Raft) and the Hyperledger Fabric (HLF) framework. The system implements a low energy, fast, and robust enhancement to system trustworthiness within and across electric grid systems such as substations, control centers and metering infrastructures. Blockchain is a distributed database structured that provides a practically unalterable (immutable) timeline of stored transactions. By relying on hashing and the Raft consensus algorithm, if an entity tries to illegitimately alter a record at one instance of the database the other ledger nodes are not altered. They work to cross-reference each other and easily locate any incorrectly added data and remove it. The bulk raw data is stored in an off-chain storage (outside of the blockchain ledger) and a hash of this baseline data is stored in the Blockchain ledger via hashing windows of time-series and configuration data, after aggregation and filtering. The bulk off-chain data repository is then considered to be trust-anchored using the hashes stored in the blockchain. To secure the electric grid testbed devices and data, device configuration baselines were compared to those baselines that had been previously stored in the ledger. Statistical baselines for device configurations, network communication patterns, and high-speed sensor data are calculated and then stored off-chain and hashes stored in the ledger. Measurements such as three-phase voltage and current, frequency, breaker status, protection scheme settings, network configuration settings (and other device configuration artifacts) and network traffic features (packet interarrival times) are compared every minute or other selected time windows. During phase 1 of the Grid Guard DLT project different DLT technologies were studies, and an assessment was performed on DLT technology vulnerabilities, uses, and key characteristics. DLT consensus protocols were studies (e.g., RAFT, named after Reliable, Replicated, Redundant, And Fault-Tolerant). Also, cryptography, public, private and permissioned or permissionless systems were assessed. Grid Guard implements a permissioned private DLT. Consensus algorithm selection and choice of DLT implementation depended heavily on the use-case. For this use-case, parameters were selected to measure performance and existing tools for assessment. Benchmarking was performed theoretically and practically. During phase 2 hashed transactions/blocks were inserted into the ledger every second. During phase 2 of the Grid Guard DLT project, a prototype framework was developed and demonstrated for attestation of critical substation devices and data using precision timing systems that use PTP and IRIG-B protocols) on a testbed of operational devices that emulated a distribution substation, control center, and power metering infrastructure using real Operational Technology (OT). The testbed includes OT devices such as protective relays, human machine interfaces (HMI), and power meters. To determine when to collect and compare system and network baselines, an initial examination of an anomaly detection capability to identify malicious manipulation of data streams was conducted. The resulting anomaly detection was demonstrated in a set of experiments and leveraged to trigger device artifact attestation checks. Attestation checks occur against device configuration baselines when compared with the immutable blockchain-stored baselines, which provided a cryptographically supported means by which to store baselines. The electrical substation-grid testbed was created to test the Grid Guard framework. The testbed emulates the operations of a portion of a power grid and SCADA systems as closely as possible. The testbed integrates real protocols, mainly IEC 61850 standard protocols, such as the Sampled Value (SV) and the GOOSE protocols. The testbed also supports DNP3 and other layer 2 and layer 3 protocols such as Telnet, SSH, SFTP/FTP and other proprietary protocols needed to connect to industrial control system equipment. The testbed emulates real power conditions using the OpalRT hardware-in-the-loop (HIL) device which can create fault situations that cannot be easily tested on real systems. The electrical substation-grid testbed was created using real measurement, communication, and protection devices that electrical utilities commonly use.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Electrostatic Gating of Ionic Conductance through Heterogeneous van der Waals Nanopores

Nanofluidic ionic transistors typically require gate voltages above 1 V and operate only at submillimolar ionic strengths, limiting their biocompatible applications. We demonstrate ionic transistors consisting of single sub-10 nm nanopores drilled in van der Waals (vdW) heterostructures with internal gate electrodes made of few-layer graphene. These devices deliver up to 10-fold current modulation at gate voltages as low as 0.3 V in 10 mM KCl, and ∼2-fold modulation at near-physiological 100 mM KCl. Baseline conductance with no gate shows surface-charge-dominated transport below 100 mM KCl, consistent with negatively charged hBN walls and ∼5 nm opening of the pores. The surface charge and the electrochemical asymmetry introduced by the three-electrode configuration govern the device’s behavior: negative gate voltage (V G ) enriches ionic concentrations and enhances current, whereas positive V G induces a local depletion zone that suppresses transport. The current modulation by V G is dependent on the polarity of the transmembrane potential and leads to ion current rectification. Molecular dynamics simulations of a nanopore in a hBN–graphene–hBN stack reveal confinement and surface charge-dependent suppression of the relative permittivity of interfacial water. Continuum modeling with radially varying interfacial water permittivity reproduces the asymmetric I–V characteristics and explains how the embedded gate sculpts local potential and ion concentrations. By enabling sub-0.5 V control of ionic transport at up to 100 mM salt concentrations, these devices address a key need in nanofluidics to create low-power ionic circuits and biosensing.

Materials science↗

Electrically controlled emission from singlet and triplet exciton species in atomically thin light-emitting diodes

We report electrically tunable spin singlet and triplet exciton emission from atomically aligned transition metal dichalcogenide (TMD) heterostructures. Furthermore, the observation of these states in both 0° and 60° heterostructures provides the stacking orientation degree of freedom for polarization switching in interlayer excitons. We confirm the spin configurations of the light-emitting excitons employing magnetic fields to measure effective exciton g factors. The interlayer tunneling current across the TMD heterostructure enables the electrical generation of singlet and triplet exciton emission in this atomically thin p-n junction. We demonstrate tunability between the singlet and triplet exciton photoluminescence via electrostatic gates and excitation power. By tuning the gates and interlayer bias voltage, the electroluminescence of the singlet and triplet can be switched with ratios of 10:1. Atomically thin TMD heterostructure light-emitting diodes thus enable a route for optoelectronic devices that can configure spin and valley quantum states independently.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Online Optimization for Networked Distributed Energy Resources With Time-Coupling Constraints

This paper proposes a Lyapunov optimization-based online distributed (LOOD) algorithmic framework for active distribution networks (ADNs) with numerous photovoltaic inverters and inverter air conditionings (IACs). In the proposed scheme, ADNs can track an active power setpoint reference at the substation in response to transmission-level requests while concurrently minimizing the social utility loss and ensuring the security of voltages. Conventional distributed optimization methods are rarely feasible to track the optimal solutions in fast variable environments using a fine-grained sampling interval where the underlying optimization problem evolves with the iterations of the algorithms. In contrast, based on the framework of online convex optimization (OCO), the developed approach uses a distributed algebraic update to compute the next round decisions relying on the current feedback of measurements. Notably, the time-coupling constraints of IACs are decoupled for online implementation with Lyapunov optimization technique. An incentive scheme is tailored to coordinate the customer-owned assets in lieu of the direct control from network operators. Optimality and convergency are characterized analytically. Finally, we corroborate the proposed method on a modified version of 33-node test feeder. Benchmark tests show that the proposed method is computationally and economically efficient, and outperforming existing algorithms.

active distribution networks↗

High‐Efficiency Solar Cells Grown on Spalled Germanium for Substrate Reuse without Polishing

Abstract Radical reduction of III–V device costs requires a multifaceted approach attacking both growth and substrate costs. Implementing device removal and substrate reuse provides an opportunity for substrate cost reduction. Controlled spalling allows removal of thin devices from the expensive substrate; however, the fracture‐based process currently generates surfaces with significant morphological changes compared to polished wafers. 49 single junction devices are fabricated across the spalled surface of full 50 mm germanium wafers without chemo‐mechanical polishing before epitaxial growth. Device defects are identified and related to morphological spalling defects—arrest lines, gull wings, and river lines—and their impact on cell performance using physical and functional characterization techniques. River line defects have the most consistent and detrimental effect on cell performance. Devices achieve a single junction efficiency above 23% and open‐circuit voltage of 1.01 V, demonstrating that spalled germanium does not need to be returned to a pristine, polished state to achieve high‐quality device performance.

14 SOLAR ENERGY↗

Mesoscale Confinement Effects and Emergent Quantum Interference in Titania Antidot Thin Films

The effect of confinement on electron and ion transport in oxide films is of interest both fundamentally and technologically for the design of next-generation electronic devices. In metal oxides with mobile ions and vacancies, it is the interplay of the different modes of charge transport and the corresponding current–voltage signatures that is of interest. We developed a patterned structure in titania films, with feature sizes of 11–20 nm, that allow us to explore confined transport. In this study, we describe how confinement changes the competing charge transport mechanisms, the patterned antidot array leads to displacement fields and confines the charge density that results in modified and emergent electron transport with an increase in conductivity. This emergent behavior can be described by considering electron interference effects. Characterization of the charge transport with electron holography and impedance spectroscopy, and through comparison with modeling, show that nanoscale confinement is a way to control quantum interference.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗