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NASA NTRS1997

Ice in Channels and Ice-Rock Mixtures in Valleys on Mars: Did They Slide on Deformable Rubble Like Antarctic Ice Streams?

Recent studies of ice streams in Antarctica reveal a mechanism of basal motion that may apply to channels and valleys on Mars. The mechanism is sliding of the ice on deformable water-saturated till under high pore pressures. It has been suggested by Lucchitta that ice was present in outflow channels on Mars and gave them their distinctive morphology. This ice may have slid like Antarctic ice streams but on rubbly weathering products rather than till. However, to generate water under high pore pressures, elevated heatflow is needed to melt the base of the ice. Either volcanism or higher heatflow more than 2 b.y. ago could have raised the basal temperature. Regarding valley networks, higher heatflow 3 b.y. ago could have allowed sliding of ice-saturated overburden at a few hundred meters depth. If the original, pristine valleys were somewhat deeper than they are now, they could have formed by the same mechanism. Recent sounding of the seafloor in front of the Ross Ice Shelf in Antarctica reveals large persistent patterns of longitudinal megaflutes and drumlinoid forms, which bear remarkable resemblance to longitudinal grooves and highly elongated streamlined islands found on the floors of martian outflow channels. The flutes are interpreted to have formed at the base of ice streams during the last glacial advance. Additional similarities of Antarctic ice streams with martian outflow channels are apparent. Antarctic ice streams are 30 to 80 km wide and hundreds of kilometers long. Martian outflow channels have similar dimensions. Ice stream beds are below sea level. Carr determined that most common floor elevations of martian outflow channels lie below martian datum, which may have been close to or below past martian sea levels. The Antarctic ice stream bed gradient is flat and locally may go uphill, and surface slopes are exceptionally. Martian channels also have floor gradients that are shallow or go uphill locally and have low surface gradients. The depth to the bed in ice streams is 1 to 1.5 km. At bankful stage, the depth of the fluid in outflow channels was 1 to 2 km, according to the height of bordering scarps. The similarity between Antarctic ice streams and martian outflow channels suggests that ice may have flowed through and shaped the outflow channels, and that perhaps the mechanism of motion of Antarctic ice streams also operated in outflow channels. In addition, sliding on deformable rubble may explain the formation of small valley networks. The large Siple Coast Antarctic ice streams are thought to slide over longitudinally grooved, deforming till, where much of the movement is within the till. The till is saturated with water at high pore pressures that nearly supports all of the weight of the ice. The small differential between overburden pressure and pore pressure at the bed is more important than the volume of water, but water needs to be supplied to the till interface. For pore pressures to remain high, the ice streams have to act as a seal that blocks the flow of water through them, and the rock underneath has to be of low permeability to prevent the water from draining away.

Lucchitta, B. K.↗

NASA NTRS2013

Bilayer Protograph Codes for Half-Duplex Relay Channels

Direct to Earth return links are limited by the size and power of lander devices. A standard alternative is provided by a two-hops return link: a proximity link (from lander to orbiter relay) and a deep-space link (from orbiter relay to Earth). Although direct to Earth return links are limited by the size and power of lander devices, using an additional link and a proposed coding for relay channels, one can obtain a more reliable signal. Although significant progress has been made in the relay coding problem, existing codes must be painstakingly optimized to match to a single set of channel conditions, many of them do not offer easy encoding, and most of them do not have structured design. A high-performing LDPC (low-density parity-check) code for the relay channel addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly optimized for a given channel quality, and are not easily adapted without extensive re-optimization for various channel conditions. This code for the relay channel combines structured design and easy encoding with rate compatibility to allow adaptation to the three links involved in the relay channel, and furthermore offers very good performance. The proposed code is constructed by synthesizing a bilayer structure with a pro to graph. In addition to the contribution to relay encoding, an improved family of protograph codes was produced for the point-to-point AWGN (additive white Gaussian noise) channel whose high-rate members enjoy thresholds that are within 0.07 dB of capacity. These LDPC relay codes address three important issues in an integrative manner: low encoding complexity, modular structure allowing for easy design, and rate compatibility so that the code can be easily matched to a variety of channel conditions without extensive re-optimization. The main problem of half-duplex relay coding can be reduced to the simultaneous design of two codes at two rates and two SNRs (signal-to-noise ratios), such that one is a subset of the other. This problem can be addressed by forceful optimization, but a clever method of addressing this problem is via the bilayer lengthened (BL) LDPC structure. This method uses a bilayer Tanner graph to make the two codes while using a concept of "parity forwarding" with subsequent successive decoding that removes the need to directly address the issue of uneven SNRs among the symbols of a given codeword. This method is attractive in that it addresses some of the main issues in the design of relay codes, but it does not by itself give rise to highly structured codes with simple encoding, nor does it give rate-compatible codes. The main contribution of this work is to construct a class of codes that simultaneously possess a bilayer parity- forwarding mechanism, while also benefiting from the properties of protograph codes having an easy encoding, a modular design, and being a rate-compatible code.

Divsalar, Dariush↗

NASA NTRS2014

An RF Sensor for Gauging Screen-Channel Liquid Acquisition Devices for Cryogenic Propellants

A key requirement of a low-gravity screen-channel liquid acquisition device (LAD) is the need to retain 100% liquid in the channel in response to propellant outflow and spacecraft maneuvers. The point at which a screen-channel LAD ingests vapor is known as breakdown, and can be measured several different ways such as: visual observation of bubbles in the LAD channel outflow; a sudden change in pressure drop between the propellant tank and LAD sump outlet; or, an indication by wet-dry sensors placed in the LAD channel or outflow stream. Here we describe a new type of sensor for gauging a screen-channel LAD, the Radio Frequency Mass Gauge (RFMG). The RFMG measures the natural electromagnetic modes of the screen-channel LAD, which is very similar to an RF waveguide, to determine the amount of propellant in the channel. By monitoring several of the RF modes, we show that the RFMG acts as a global sensor of the LAD channel propellant fill level, and enables detection of LAD breakdown even in the absence of outflow. This paper presents the theory behind the RFMG-LAD sensor, measurements and simulations of the RF modes of a LAD channel, and RFMG detection of LAD breakdown in a channel using a simulant fluid during inverted outflow and long-term stability tests.

microwave sensor↗

DOE OSTI2021

High-sensitivity multi-channel atomic magnetometer

High-sensitivity multi-channel atomic magnetometers are described. Methods for operating multi-channel atomic magnetometers are also described. Moreover, devices incorporating a plurality of multi-channel atomic magnetometers are described. A multi-channel atomic magnetometer may use the spin-exchange relaxation-free (SERF) technique. A multi-channel atomic magnetometer may achieve multi-channel operation in a single module, reducing the cost of sensors. A multi-channel atomic magnetometer may be a 16-channel atomic magnetometer. A multi-channel atomic magnetometer may include a single large vapor cell including alkali-metal atoms and at least one buffer gas that restricts motion of atomic spins of the alkali-metal atoms, thereby making relatively small internal cell volumes act as a multiple independent local sensing channels. A multi-channel atomic magnetometer may include a broad pump beam that simultaneously polarizes all (or substantially all) of the alkali-metal atoms in each internal sensing volume of the vapor cell, and a broad probe beam that simultaneously measures magnetic fields at multiple sensing volumes with a photodiode array.

Kim, Young Jin↗

DOE OSTI2025

Impact of Ligands on the Ion–Ion Selectivity of Ligand-Appended-Pillar[ n ]arene Channels

Ligand-appended pillar[5]arene (LAP) channels are emerging as a promising platform for ion-selective membranes. In this study, we investigated the ion selectivities of three LAP channels functionalized with distinct ligands: diglycolamine, carbamoylmethyl phosphine oxide, and propionamide phosphonic acid. These ligands were chosen based on their demonstrated affinities for lanthanides in solvent extraction studies. We examined the selectivity of each channel toward a series of monovalent, divalent, and trivalent ions: Li + , Na + , K + , Mg 2+ , Ca 2+ , La 3+ , Eu 3+ , and Yb 3+ . To quantify ion-channel interactions and the energetics of translocation, we computed the potential of mean force (PMF) profiles for each ion. These PMFs were subsequently recast into permeability coefficients, enabling a direct evaluation of ion permselectivity. Our results reveal distinct selectivity patterns governed by the chemical nature of the appended ligands. The diglycolamine-functionalized channel exhibits strong interactions with monovalent ions, leading to replication of the Li + bulk hydration shell within the channel. This promotes preferential transport Li + ions while effectively excluding divalent and trivalent species. In contrast, the carbamoylmethyl phosphine oxide-functionalized channel displays a reduced selectivity between monovalent ions while similarly exhibiting an effective rejection of divalent and trivalent ions. This arises from steric hindrance around channel-lining oxygens imposed by the ligand's bulky phenyl groups which limits heavy ion coordination and promotes retention of hydration shells effectively increasing effective ion size. The propionamide phosphonic acid-functionalized channel exhibits a different trend, favoring ions with lower hydration free energies, with K + ions showing enhanced permeation. These findings highlight the critical role of ligand-ion interactions in modulating ion selectivity within LAP channels. In particular, the strong coordination exhibited by diglycolamine and propionamide phosphonic acid ligands significantly influences the ion transport energetics and selectivity profiles.

hydration↗

DOE OSTI2024

Direct Numerical Simulation of Involute Channel Turbulence

A direct numerical simulation (DNS) study was performed on turbulent flow in the high flux isotope reactor involute channel geometry to develop a numerical database and determine the differences compared with a flat parallel channel. The varying channel curvature along the walls was studied for differences in mean profiles. Parameters of interest include streamwise velocity, turbulent kinetic energy (TKE), and turbulence dissipation rate, as well as Reynolds stresses and turbulence transport terms. Profile sampling was carried out at 10 locations along the span of the involute. Additional DNS studies were performed on smaller domains of comparable curvature to the involute domain: a high curvature channel (high circular), a low curvature channel (low circular), and a flat channel (flat). Here, each of these four cases was compared against each other and to other DNS studies performed on parallel flows. The results indicate that the bulk involute channel flow does not differ significantly from a flat parallel channel flow and that the curvature of the walls does not significantly alter the mean flow parameters. However, the regions of the involute channel near the side walls exhibit relatively low magnitude twin recirculation structures driven toward the side walls from the centerline of the channel, which warrants further study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Experimental Study of Microgel Conformance-Control Treatment for a Polymer-Flooding Reservoir Containing Superpermeable Channels

Summary Polymer flooding has been widely used to improve oil recovery. However, its effectiveness would be diminished when channels (e.g., fractures, fracture-like channels, void-space conduits) are present in a reservoir. In this study, we designed a series of particular sandwich-like channel models and tested the effectiveness and applicable conditions of micrometer-sized preformed particle gels (PPGs, or microgels) in improving the polymer-flooding efficiency. We studied the selective penetration and placement of the microgel particles, and their abilities for fluid diversion and oil-recovery improvement. The results suggest that polymer flooding alone would be inefficient to achieve a satisfactory oil recovery as the heterogeneity of the reservoir becomes more serious (e.g., permeability contrast kc/km > 50). The polymer solution would vainly flow through the channels and leave the majority of oil in the matrices behind. Additional conformance-treatment efforts are required. We tried to inject microgels in an attempt to shut off the channels. After the microgel treatment, impressive improvement of the polymer-flooding performance was observed in some of our experiments. The water cut could be reduced significantly by as high as nearly 40%, and the sweep efficiency and overall oil recovery of the polymer flood were improved. The conditions under which the microgel-treatment strategy was effective were further explored. We observed that the microgels form an external impermeable cake at the very beginning of microgel injection and prevent the gel particles from entering the matrices. Instead, the microgel particles could selectively penetrate and shut off the superpermeable channels under proper conditions. Our results suggest that the 260-µm microgel particles tested in this study are effective to attack the excessive-water-production problem and improve the oil recovery when the channel has a high permeability (>50 darcies). The gels are unlikely to be effective for channels that are less than 30 darcies because of the penetration/transport difficulties. After the gels effectively penetrate and shut off the superpermeable channel, the subsequent polymer solution is diverted to the matrices (i.e., the unswept oil zones) to displace the bypassed oil. Overall, this study provides important insights to help achieve successful polymer-flooding applications in reservoirs with superpermeable channels.

Engineering↗

NASA NTRS1980

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that Pierce's pulse position modulation scheme with 2 to the L pulse positions used on a self-noise-limited direct detection optical communication channel results in a 2 to the L-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint-length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

NASA NTRS1981

Capacity, cutoff rate, and coding for a direct-detection optical channel

It is shown that when Pierce's pulse-position modulation scheme with 2 to the L power positions (where L is some positive integer) is used on a self-noise-limited direct-detection optical communication channel, there results a (2 to the L power)-ary erasure channel that is equivalent to the parallel combination of L completely correlated binary erasure channels. The capacity of the full channel is the sum of the capacities of the component channels, but the cutoff rate of the full channel is shown to be much smaller than the sum of the cutoff rates. An interpretation of the cutoff rate is given that suggests a complexity advantage in coding separately on the component channels. It is shown that if short-constraint length convolutional codes with Viterbi decoders are used on the component channels, then the performance and complexity compare favorably with the Reed-Solomon coding system proposed by McEliece (1979) for the full channel. The reasons for this unexpectedly fine performance by the convolutional code system are explored in detail, as are various facets of the channel structure.

Massey, J. L.↗

NASA NTRS1992

Channels and valleys on Venus - Preliminary analysis of Magellan data

A preliminary survey of Magellan imagery reveals more than 200 newly discovered relic channel and valley landform complexes. For purposes of discussion the channels can be classed as simple, complex, and compound. Integrated valleys also occur. Simple channels include: (1) sinuous rilles that closely resemble their lunar counterparts and (2) a newly recognized long sinuous form of high width-to-depth ratio and remarkably constant width. Herein designated canali, the most spectacular of these channels is 6800 km long. One of the compound channels, an outflow complex in Lada Terra, extends over 1200 km and is up to 30 km wide. Streamlined hills and spill relationships at a cross-axial ridge are similar to features in flood channels. Venusian channels have a global distribution with most of the large canali-type channels developed on volcanic plains. Alternative hypotheses for the channel-forming processes include genesis by the following erosive fluids: ultramafic silicate melts, sulfur, and carbonate lavas. Each of these causative agents has profound implications for Venusian planetology. The remote possibility of an aqueous origin, indicated by apparent regime behavior of the active channeling process, cannot be excluded with absolute certainty.

Baker, V. R.↗

NASA NTRS1997

West-Antarctic Ice Streams: Analog to Ice Flow in Channels on Mars

Sounding of the sea floor in front of the Ross Ice Shelf in Antarctica recently revealed large persistent patterns of longitudinal megaflutes and drumlinoid forms, which are interpreted to have formed at the base of ice streams during the list glacial advance. The flutes bear remarkable resemblance to longitudinal grooves and highly elongated streamlined islands found on the floors of some large martian channels, called outflow channels. ln addition, other similarities exist between Antarctic ice streams and outflow channels. Ice streams are 30 to 80 km wide and hundreds of kilometers long, as are the martian channels. Ice stream beds are below sea level. Floors of many martian outflow channels lie below martian datum, which may have been close to or below past martian sea levels. The Antarctic ice stream bed gradient is flat and locally may go uphill, and surface slopes are exceptionally low. So are gradients of martian channels. The depth to the bed in ice streams is 1 to 1.5 km. At bankful stage, the depth of the fluid in outflow channels would have been 1 to 2 km. These similarities suggest that the martian outflow channels, whose origin is commonly attributed to gigantic catastrophic floods, were locally filled by ice that left a conspicuous morphologic imprint. Unlike the West-Antarctic-ice streams, which discharge ice from an ice sheet, ice in the martian channels came from water erupting from the ground. In the cold martian environment, this water, if of moderate volume, would eventually freeze. Thus it may have formed icings on springs, ice dams and jams on constrictions in the channel path, or frozen pools. Given sufficient thickness and downhill surface gradient, these ice masses would have moved; and given the right conditions, they could have moved like Antarctic ice streams.

Lucchitta, B. K.↗

NASA NTRS2006

Channel-wing System for Thrust Deflection and Force/Moment Generation

An aircraft comprising a Channel Wing having blown c h - ne1 circulation control wings (CCW) for various functions. The blown channel CCW includes a channel that has a rounded or near-round trailing edge. The channel further has a trailing-edge slot that is adjacent to the rounded trailing edge of the channel. The trailing-edge slot has an inlet connected to a source of pressurized air and is capable of tangentially discharging pressurized air over the rounded trailing edge. The aircraft further has a propeller that is located in the channel and ahead of the rounded trailing edge of the channel. The propeller provides a propeller thrust exhaust stream across the channel wing to propel the aircraft through the air and to provide high lift. The pressurized air being discharged over the rounded trailing edge provides a high lift that is obtained independent of an aircraft angle of attack, thus preventing the asymmetry. separated flow, and stall experienced by the CC wing at the high angle of attack it required for high lift generation. The aircraft can further include blown outboard circulation control wings (CCW) that are synergistically connected to the blown channel CCWs. The blown outboard CCWs provide additional high lift, control thrust/drag interchange, and can provide all three aerodynamic moments when differential blowing is applied front-to-rear or left-to-right. Both the blown channel CCW and the outboard CCW also have leading-edge blowing slots to prevent flow separation or to provide aerodynamic moments for control.

Englar, Robert J.↗

NASA NTRS2020

Ion Channels – From Structure to Electrophysiology and Back

A reliable way to establish whether our understanding of a channel is satisfactory is to reproduce its measured ionic conductance over a broad range of applied voltages in computer simulations. In molecular dynamics (MD), this can be done by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. Since this approach is computationally very expensive, we have developed a markedly more efficient alternative in which MD is combined with the electrodiffusion (ED) equation. In this approach, the assumptions of the ED equation can be rigorously tested, and the precision and consistency of the calculated conductance can be determined. We have demonstrated that the full current/voltage dependence and the underlying free energy profile for a simple channel can be reliably calculated from equilibrium or non-equilibrium MD simulations at a single voltage. Free energy profiles can be obtained from non-equilibrium simulations without a loss of accuracy even without the knowledge of diffusion coefficient. To carry out MD simulations, a structural model of a channel has to be assumed, which is an important constraint, considering that high-resolution structures are available for only very few simple channels. If the comparison of calculated ionic conductance with electrophysiological data is satisfactory, it greatly increases our confidence that the structure and the function are described sufficiently accurately. We examined the validity of the ED for several channels embedded in phospholipid membranes - four naturally occurring channels: trichotoxin, alamethicin, p7 from hepatitis C virus (HCV) and Vpu from the HIV-1 virus, a synthetic, hexameric channel, formed by a 21-residue peptide that contains only leucine and serine and a bacterial pentameric ligand-gated ion channel, GLIC. All these channels mediate transport of potassium and chloride ions. It was found that the ED equation is satisfactory for these systems. In some of them, experimental and calculated electrophysiological properties are in good agreement, whereas in others there are strong indications that the structural models are incorrect.

Pohorille, Andrew↗

DOE OSTI2022

Method of manufacturing a waveguide comprising stacking dielectric layers having aligned metallized channels formed therein to form the waveguide

Waveguides and methods for manufacturing a waveguide that include forming a first channel in a first layer of dielectric material, the first channel comprising one or more walls; forming a second channel in a second layer of dielectric material, the second channel comprising one or more walls; depositing electrically conductive material on the one or more walls of the first channel; depositing electrically conductive material on the one or more walls of the second channel; arranging the first layer adjacent to the second layer to form a stack with the first channel axially aligned with and facing the second channel; and heating the stack so that the conductive material on the one or more walls of the first channel and the conductive material on the one or more walls of the second channel connect to form the waveguide.

Krueger, Daniel Scott↗

DOE OSTI2023

Embedded waveguide including a substrate with a channel formed therein which includes conductive walls formed thereon and with solid via connections

Krueger, Daniel Scott↗

DOE OSTI2024

Waveguide including a conductive channel embedded in a substrate and with vias connected to an antenna and a circuit component

Krueger, Daniel Scott↗

NASA NTRS2020

Technology Advancements for Channel Wall Nozzle Manufacturing In Liquid Rocket Engines

A regeneratively-cooled or dump-cooled nozzle is a critical component for expansion of hot gases to enable high temperature and performance in liquid rocket engines systems. Regeneratively-cooled channel wall nozzles are a design solution used across the propulsion industry as a simplified method to fabricate the nozzle structure with internal coolant passages. The scale and complexity of the channel wall nozzle (CWN) design can be challenging to fabricate which results in extended lead times and higher costs. Some of these challenges include: 1) Unique and high temperature materials, 2) Tight tolerances on large parts during manufacturing and assembly to contain high pressure propellants, 3) Thin-walled features to maintain adequate wall temperatures, and 4) Unique manufacturing process operations and complex tooling. The United States (U.S.) National Aeronautics and Space Administration (NASA) and U.S. specialty manufacturing vendors are maturing modern fabrication techniques to reduce complexity and decrease costs associated with channel wall nozzle manufacturing technology. Additive Manufacturing (AM) is one of the key technology advancements under evaluation for channel wall nozzles. Much of additive manufacturing for propulsion components has focused on laser powder bed fusion (L-PBF), but the scale is not yet feasible for application to large scale nozzles. NASA is evolving directed energy deposition (DED) techniques for nozzles including arc-based deposition, blown powder deposition, and Laser Wire Direct Closeout (LWDC). There are different approaches being considered for fabrication of the nozzle, and each of these DED processes offer unique process steps for rapid fabrication. The arc-based and blown powder deposition techniques are used for the forming of the CWN liner. A variety of materials are being demonstrated including Inconel 625, Haynes 230, JBK-75, and NASA HR-1. The blown powder DED process is also being demonstrated for forming an integral channel nozzle in a single operation in similar materials. The LWDC process is a method for closing out the channels within the liner and forming the structural jacket using a localized laser wire deposition technique. Identical materials mentioned above have been used for this process in addition to bimetallic closeout (C-18150–SS347, and C-18150–Inconel 625). NASA has completed process development, material characterization, and hot-fire testing on a variety of these channel wall nozzle fabrication technique. This publication presents an overview of the various channel wall nozzle manufacturing processes and materials under evaluation including results from the hot-fire testing. Future development and technology focus areas is also discussed relative to channel wall nozzle manufacturing.

Additive manufacturing↗

DOE OSTI2020

Distinguishing Potassium Channel Resting State Conformations in Live Cells with Environment-Sensitive Fluorescence

Ion channels are polymorphic membrane proteins whose high-resolution structures offer images of individual conformations, giving us starting points for identifying the complex and transient allosteric changes that give rise to channel physiology. Here, we report live-cell imaging of voltage-dependent structural changes of voltage-gated Kv2.1 channels using peptidyl tarantula toxins labeled with an environment-sensitive fluorophore, whose spectral shifts enable identification of voltage-dependent conformation changes in the resting voltage sensing domain (VSD) of the channel. We synthesize a new environment-sensitive, far-red fluorophore, julolidine phenoxazone (JP) azide, and conjugate it to tarantula toxin GxTX to characterize Kv2.1 VSD allostery during membrane depolarization. JP has an inherent response to the polarity of its immediate surroundings, offering site-specific structural insight into each channel conformation. Using voltage-clamp spectroscopy to collect emission spectra as a function of membrane potential, we find that they vary with toxin labeling site, the presence of Kv2 channels, and changes in membrane potential. With a high-affinity conjugate in which the fluorophore itself interacts closely with the channel, the emission shift midpoint is 50 mV more negative than the Kv2.1 gating current midpoint. This suggests that substantial conformational changes at the toxin-channel interface are associated with early gating charge transitions and these are not concerted with VSD motions at more depolarized potentials. These fluorescent probes enable study of conformational changes that can be correlated with electrophysiology, putting channel structures and models into a context of live-cell membranes and physiological states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗