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2000

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Articles 331 - 360 of 2647

Full-Text Articles in Physical Sciences and Mathematics

Structural Biology With Carbon Nanotube Afm Probes, Adam T. Woolley, Chin Li Cheung, Jason H. Hafner, Charles M. Lieber Sep 2000

Structural Biology With Carbon Nanotube Afm Probes, Adam T. Woolley, Chin Li Cheung, Jason H. Hafner, Charles M. Lieber

Barry Chin Li Cheung Publications

Carbon nanotubes represent ideal probes for high-resolution structural and chemical imaging of biomolecules with atomic force microscopy. Recent advances in fabrication of carbon nanotube probes with sub-nanometer radii promise to yield unique insights into the structure, dynamics and function of biological macromolecules and complexes.


Ice Nanotube: What Does The Unit Cell Look Like?, Kenichiro Koga, Ruben D. Parra, Hideki Tanaka, Xiao Cheng Zeng Sep 2000

Ice Nanotube: What Does The Unit Cell Look Like?, Kenichiro Koga, Ruben D. Parra, Hideki Tanaka, Xiao Cheng Zeng

Xiao Cheng Zeng Publications

It is discovered that for an n-gonal ice nanotube built from stacking a single type of n-gonal rings of water, the unit cell consists of two stacked n-gonal rings. In one ring the O–H bonds of water molecules line up clockwise whereas in the other ring the O-H bonds line up counterclockwise. Among the n-gonal ice nanotubes examined, the pentagonal or hexagonal ice nanotube appears to be the most stable.


Environmental Finance Charette, Hyannis Park On Lewis Bay: A Case Study, New England Environmental Finance Center, Environmental Finance Center Of University Of Maryland Sep 2000

Environmental Finance Charette, Hyannis Park On Lewis Bay: A Case Study, New England Environmental Finance Center, Environmental Finance Center Of University Of Maryland

Water

The town of Yarmouth currently has a $30 million septic sludge treatment plant and transport lines in place. The vast majority of the dwellings and businesses in the Hyannis Park area are on septic systems that are viable and Title 5 compliant, regardless of age. Conventional, "non-failing" septic systems, however, were never intended to remove form their effluent nutrients such as nitrogen. These have become recognized as an environmental threat only as our understanding of the impacts of excess nutrients on ecosystems has increased in recent decades.


Semantic Web And Information Brokering: Opportunities, Commercialization, And Challenges, Amit P. Sheth Sep 2000

Semantic Web And Information Brokering: Opportunities, Commercialization, And Challenges, Amit P. Sheth

Kno.e.sis Publications

From the chairs' report published in SIGMOD record: The keynote address entitled 'Semantic Web and Information Brokering: Opportunities, Early Commercializations, and Challenges' was delivered by Amit Sheth (University of Georgia and Taalee Corp). Sheth characterized semantics as the next step in the evolution of the WWW and stressed the importance of semantically organized information for supporting ubiquitous, powerful, accurate and efficient access to this information. Sheth also reviewed proposals for semantic interoperability frameworks such as the DAML(DARPA Agent Mark-Up Language), the Oingo family of tools for defining concepts and extracting knowledge from large databases, as well as several scenarios on …


Managing Sprawl In The Land Of Unintended Consequences, Robert S. Bucci Sep 2000

Managing Sprawl In The Land Of Unintended Consequences, Robert S. Bucci

New England Journal of Public Policy

Americans witnessing the bulldozing of their country’s pastures, farmlands, and sensitive habitats to erect suburban housing tracts and commercial centers have come to realize that the remaining open land may be too precious to waste. Residential and commercial development is no longer quickly embraced to stimulate economic progress and prosperity. Municipalities are learning that development often extracts a price — sometimes the loss of community character and local charm, sometimes tax revenues that fall short of increased expenditures, and sometimes just plain ugliness. Responding to the new reality, many community officials have initiated unilateral ordinances regulating the development of open …


Supernumerary Spacing Of Rainbows Produced By An Elliptical-Cross-Section Cylinder. I. Theory, James A. Lock Sep 2000

Supernumerary Spacing Of Rainbows Produced By An Elliptical-Cross-Section Cylinder. I. Theory, James A. Lock

Physics Faculty Publications

A sequence of rainbows is produced in light scattering by a particle of high symmetry in the short-wavelength Limit, and a supernumerary interference pattern occurs to one side of each rainbow. Using both a ray-tracing procedure and the Debye-series decomposition of first-order perturbation wave theory, I examine the spacing of the supernumerary maxima and minima as a function of the cylinder rotation angle when an elliptical-cross-section cylinder is normally illuminated by a plane wave. I find that the supernumerary spacing depends sensitively on the cylinder-cross-section shape, and the spacing varies sinusoidally as a function of the cylinder rotation angle for …


Stochastic Dynamics Of Infinite-Dimensional Systems (Stochastic And Non-Linear Analysis Seminar, University Of Illinois), Salah-Eldin A. Mohammed Sep 2000

Stochastic Dynamics Of Infinite-Dimensional Systems (Stochastic And Non-Linear Analysis Seminar, University Of Illinois), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

We describe an approach to the dynamics of non-linear stochastic differential systems with finite memory using multiplicative cocycles in Hilbert space. We introduce the notion of hyperbolicity for stationary solutions of stochastic systems with memory. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses ideas from infinite-dimensional multiplicative ergodic theory and interpolation arguments.


Measurements Of Excess O3, Co2, Co, Ch4, C2h4, C2h2, Hcn, No, Nh3, Hcooh, Ch3cooh, Hcho, And Ch3oh In 1997 Alaskan Biomass Burning Plumes By Airborne Fourier Transform Infrared Spectroscopy (Aftir), Jon G. Goode, Robert J. Yokelson, Darold E. Ward, Ronald A. Susott, Ronald E. Babbitt, Mary Ann Davies, Wei Min Hao Sep 2000

Measurements Of Excess O3, Co2, Co, Ch4, C2h4, C2h2, Hcn, No, Nh3, Hcooh, Ch3cooh, Hcho, And Ch3oh In 1997 Alaskan Biomass Burning Plumes By Airborne Fourier Transform Infrared Spectroscopy (Aftir), Jon G. Goode, Robert J. Yokelson, Darold E. Ward, Ronald A. Susott, Ronald E. Babbitt, Mary Ann Davies, Wei Min Hao

Chemistry and Biochemistry Faculty Publications

We used an airborne Fourier transform infrared spectrometer (AFTIR), coupled to a flow-through, air-sampling cell, on a King Air B-90 to make in situ trace gas measurements in isolated smoke plumes from four, large, boreal zone wildfires in interior Alaska during June 1997. AFTIR spectra acquired near the source of the smoke plumes yielded excess mixing ratios for 13 of the most common trace gases: water, carbon dioxide, carbon monoxide, methane, nitric oxide, formaldehyde, acetic acid, formic acid, methanol, ethylene, acetylene, ammonia and hydrogen cyanide. Emission ratios to carbon monoxide for formaldehyde, acetic acid, and methanol were 2.2±0.4%, 1.3±0.4%, and …


Resolving Ambiguities In Gravity Wave Propagation Directions Inherent In Satellite Observations: A Simulation Study, Michael P. Hickey Ph.D., Jason S. Brown Sep 2000

Resolving Ambiguities In Gravity Wave Propagation Directions Inherent In Satellite Observations: A Simulation Study, Michael P. Hickey Ph.D., Jason S. Brown

Publications

We simulate space-based, sub-limb viewing observations of airglow brightness fluctuations caused by atmospheric gravity wave interactions with the O2 atmospheric airglow, and we demonstrate that, due to the geometry associated with such observations, the brightness fluctuations observed for the optically thick 0–0 band emission will always appear stronger for waves traveling towards the observer (satellite). The effect should be most noticeable for waves having relatively small vertical wavelengths (∼10 km) and horizontal wavelengths of 50 km or greater. For waves of short (∼100 km) horizontal wavelength, the brightness fluctuation anisotropy with respect to viewing direction may also be evident in …


Analysis Of The Nico2O4 Spinel Surface With Auger And X-Ray Photoelectron Spectroscopy, J.-G. Kim, D. L. Pugmire, D. Battaglia, Marjorie Langell Sep 2000

Analysis Of The Nico2O4 Spinel Surface With Auger And X-Ray Photoelectron Spectroscopy, J.-G. Kim, D. L. Pugmire, D. Battaglia, Marjorie Langell

Marjorie A. Langell Publications

Nickel cobaltite, NiCo2O4, has been synthesized by sol–gel and thermal decomposition techniques and the surface composition studied with Auger (AES) and X-ray photoelectron spectroscopies (XPS). The asintroduced samples are near-stoichiometric, although samples fabricated by thermal decomposition tend to be oxygen-defi cient by approximately 25% of the predicted spinel concentration. Nickel 2p XPS indicates the predominant form of the metal to be Ni2+, with the cations located in octahedral sites. The cobalt cations are equally divided between tetrahedral and octahedral sites as Co3+. The oxygen XP 1s spectrum is composed of two peaks, …


Rapid Identification Of The Bacterial Pathogens Responsible For Urinary Tract Infections Using Direct Injection Ce, Daniel W. Armstrong, Jeffrey M. Schneiderheinze Sep 2000

Rapid Identification Of The Bacterial Pathogens Responsible For Urinary Tract Infections Using Direct Injection Ce, Daniel W. Armstrong, Jeffrey M. Schneiderheinze

Chemistry Faculty Research & Creative Works

The use of high-performance capillary electrokinetic techniques for the separation, identification, and quantitation of intact microbes represents a new frontier for separation science. In this work, it is demonstrated that pathogens most responsible for urinary tract infections can be distinguished from one another after direct injection of untreated urine. High efficiencies (often exceeding 1 000 000 plates/m) and short analysis times (< 10 min) are characteristics of this approach. The concentration of the urine matrix appears to be able to cause a small, but definite, change in the electroosmotic flow velocity. This high-efficiency separation-based approach could prove to be invaluable for the diagnosis and tracking of certain diseases. It also could form the basis for a variety of rapid microbial assays.


Evaluation Of A Vancomycin Chiral Stationary Phase In Capillary Electrochromatography Using Polar Organic And Reversed-Phase Modes, Charlotte Karlsson, Lars Karlsson, Daniel W. Armstrong, Paul K. Owens Sep 2000

Evaluation Of A Vancomycin Chiral Stationary Phase In Capillary Electrochromatography Using Polar Organic And Reversed-Phase Modes, Charlotte Karlsson, Lars Karlsson, Daniel W. Armstrong, Paul K. Owens

Chemistry Faculty Research & Creative Works

A vancomycin chiral stationary phase (CSP) was fully evaluated in capillary electrochromatography (CEC) in reversed phase and polar organic modes for a number of racemic pharmaceutical compounds. High efficiency and resolution values were obtained for a number of compound classes including thalidomide in both the polar organic mode (190 000 plates meter-1 and Rs = 13.8) and reversed-phase mode (125 000 plates meter-1 and Rs = 13.0). Experimental parameters, including organic modifier, organic solvent ratio, ionic strength, pH, temperature, and voltage, were examined in both the aqueous and nonaqueous modes to deduce their effect on the resultant EOF, retention times, …


Field Trip Guide (For The Nebraska Well Drillers Association) Eastern Nebraska Geology, Scott Summerside, Duane Eversoll, Mark Kuzila, Matt Joeckel Sep 2000

Field Trip Guide (For The Nebraska Well Drillers Association) Eastern Nebraska Geology, Scott Summerside, Duane Eversoll, Mark Kuzila, Matt Joeckel

Conservation and Survey Division: Faculty and Staff Publications

No abstract provided.


Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter Sep 2000

Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter

Mathematical Sciences Technical Reports (MSTR)

The problem of kaleidoscopically tiling a surface by congruent triangles is equivalent to finding groups generated in certain ways. In order to admit a tiling, a group must have a specific set of generators as well as an involutary automorphism, T, that acts to reverse the orientation of the tiles. The purpose of this paper is to explore group theoretic and computational methods for determining the existence of symmetry groups and tiling groups, as well as to classify the symmetry and tiling groups on hyperbolic Riemann surfaces of genus 6 and 7.


Boomerang Data Suggest A Purely Baryonic Universe, Stacy S. Mcgaugh Sep 2000

Boomerang Data Suggest A Purely Baryonic Universe, Stacy S. Mcgaugh

Faculty Scholarship

The amplitudes of peaks in the angular power spectrum of anisotropies in the microwave background radiation depend on the mass content of the universe. The second peak should be prominent when cold dark matter is dominant but is depressed when baryons dominate. Recent microwave background data are consistent with a purely baryonic universe with Ωm = Ωb and ΩA ∼ 1.


Electroweak Quantum Chemistry For Possible Precursor Molecules In The Evolution Of Biomolecular Homochirality, Robert Berger, Martin Quack, Gregory S. Tschumper Sep 2000

Electroweak Quantum Chemistry For Possible Precursor Molecules In The Evolution Of Biomolecular Homochirality, Robert Berger, Martin Quack, Gregory S. Tschumper

Chemistry Faculty Research & Creative Works

The unified 'electroweak' theory of the electromagnetic and weak nuclear interactions in physics predicts a small energy difference (ΔE(pv)) between the left- and right-handed enantiomers of chiral molecules. Thus, electroweak theory provides one of several possible explanations for the origin of biomolecular homochirality (nature's preference for L-amino acids and D-monosaccharides). Recent systematic electroweak quantum-chemical studies find ΔE(pv) to be an order of magnitude larger than previously anticipated, which has sparked renewed interest in the subject. The present paper addresses, for the first time, the question of the relative stability of certain possible prebiotic precursor molecules suggested in the work of …


The Effects Of Sulfuric Acid On The Mechanical Properties Of Ice Single Crystals, Y. L. Trickett, I. Baker, P. M.S Pradhan Sep 2000

The Effects Of Sulfuric Acid On The Mechanical Properties Of Ice Single Crystals, Y. L. Trickett, I. Baker, P. M.S Pradhan

Dartmouth Scholarship

Ice single crystals of various orientations containing various concentrations of H2SO4 up to 11.5 ppm were cut from large pucks of laboratory-grown ice. Constant-strain-rate compression tests were performed on the doped ice crystals both at −20°C at an axial strain rate of 1 × 10−5 s−1 and at −10°C at 1 × 106 s−1. The stress–strain curves showed a linearly rising stress with increasing strain, followed by a sharply declining stress after reaching a peak. With further strain, the sharp decline in stress slowed. The tests clearly showed, for the first time, that this naturally occurring impurity dramatically decreases both …


Dynamical Properties Of Forced Shear Layers In An Annular Geometry, Evangelos A. Coutsias, Keith Bergeron, J.P. Lynov, A.H. Nielsen Sep 2000

Dynamical Properties Of Forced Shear Layers In An Annular Geometry, Evangelos A. Coutsias, Keith Bergeron, J.P. Lynov, A.H. Nielsen

Branch Mathematics and Statistics Faculty and Staff Publications

Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr-Sommerfeld operator for plane, circular Couette …


A Theory For Stretchiness, Brandon R. Brown Sep 2000

A Theory For Stretchiness, Brandon R. Brown

Physics and Astronomy

No abstract available.


Conductivity Of Irradiated Pure Water, Jerry Goodisman, Rick Blades Sep 2000

Conductivity Of Irradiated Pure Water, Jerry Goodisman, Rick Blades

Chemistry - All Scholarship

The conductivity of water having parts per billion concentrations of oxygen, hydrogen, and bicarbonate was measured while the water was irradiated by a low-pressure mercury vapor lamp, which was turned on and off periodically. A cell normally used for measurement of dissolved oxidizable carbon was modified for use in these measurements. When the lamp is turned on, the conductivity increases (sometimes decreases) with a time constant of about 50 ms; when the lamp is turned off, the conductivity changes in the opposite direction with a time constant of about 275 ms, but does not return to its value before the …


Optically Simulating A Quantum Associative Memory, Dan A. Ventura, John C. Howell, John A. Yeazell Sep 2000

Optically Simulating A Quantum Associative Memory, Dan A. Ventura, John C. Howell, John A. Yeazell

Faculty Publications

This paper discusses the realization of a quantum associative memory using linear integrated optics. An associative memory produces a full pattern of bits when presented with only a partial pattern. Quantum computers have the potential to store large numbers of patterns and hence have the ability to far surpass any classical neural network realization of an associative memory. In this work two 3-qubit associative memories will be discussed using linear integrated optics. In addition, corrupted, invented and degenerate memories are discussed.


Optically Simulating A Quantum Associative Memory, John C. Howell, John A. Yeazell, Dan Ventura Sep 2000

Optically Simulating A Quantum Associative Memory, John C. Howell, John A. Yeazell, Dan Ventura

Mathematics, Physics, and Computer Science Faculty Articles and Research

This paper discusses the realization of a quantum associative memory using linear integrated optics. An associative memory produces a full pattern of bits when presented with only a partial pattern. Quantum computers have the potential to store large numbers of patterns and hence have the ability to far surpass any classical neural-network realization of an associative memory. In this work two three-qubit associative memories will be discussed using linear integrated optics. In addition, corrupted, invented and degenerate memories are discussed.


Western Rangeland Noxious Weeds: Collecting, Sharing And Using Information, U.S. Department Of Interior, U.S. Department Of Agriculture, Riley Memorial Foundation Sep 2000

Western Rangeland Noxious Weeds: Collecting, Sharing And Using Information, U.S. Department Of Interior, U.S. Department Of Agriculture, Riley Memorial Foundation

All U.S. Government Documents (Utah Regional Depository)

Western rangeland weeds such as yellow starthistle, leafy spurge, Canada thistle and Russian knapweed are causing tremendous losses to agricultural industries, including both crop and livestock production, and to environmental resources on private lands. Concurrently, many public lands managed by federal agencies are being steadily invaded. As a result, these lands held in the public trust are experiencing reductions in commodity yields, recreational opportunities, biodiversity and ecosystem function.


Effect Of Collagen Turnover On The Accumulation Of Advanced Glycation End Products, Nicole Verzijl, Jeroen Degroot, Suzanne R. Thorpe, Ruud A. Bank, J. Nikki Shaw, Timothy J. Lyons, Johannes Wj Bijlsma, Floris Pjg Lafeber, John W. Baynes, Johan M. Tekoppele Sep 2000

Effect Of Collagen Turnover On The Accumulation Of Advanced Glycation End Products, Nicole Verzijl, Jeroen Degroot, Suzanne R. Thorpe, Ruud A. Bank, J. Nikki Shaw, Timothy J. Lyons, Johannes Wj Bijlsma, Floris Pjg Lafeber, John W. Baynes, Johan M. Tekoppele

Faculty Publications

Collagen molecules in articular cartilage have an exceptionally long lifetime, which makes them susceptible to the accumulation of advanced glycation end products (AGEs). In fact, in comparison to other collagen-rich tissues, articular cartilage contains relatively high amounts of the AGE pentosidine. To test the hypothesis that this higher AGE accumulation is primarily the result of the slow turnover of cartilage collagen, AGE levels in cartilage and skin collagen were compared with the degree of racemization of aspartic acid (% D-Asp, a measure of the residence time of a protein). AGE (Ne- (carboxymethyl)lysine, Ne-(carboxyethyl)lysine, and pentosidine) and % D-Asp concentrations increased …


Rejex-It® Bird Repellents - Mode Of Action, Peter F. Vogt Sep 2000

Rejex-It® Bird Repellents - Mode Of Action, Peter F. Vogt

Wildlife Damage Management Conference Proceedings

Rejex-it® bird repellents are used to repel birds and reduce bird predation. Rejex-it® represents a long-needed, logical alternative to inhumane bird control methods such as poisoning and shooting. Its effectiveness as a nuisance bird repellant is based on a common, naturally-occurring, com lly recognized as safe" food and ponent of food that has been designated by the FDA as a "generafragrance additive. Methyl Anthranilate (MA), the active ingredient in Rejex-it® Bird Repellents, acts as a sensory repellent by irri tating the bird's taste buds, skin, and trigeminal chemoreceptors in the beaks, gizzards, eyes, and mucous membranes. Irritation occurs as a …


Sm–Co–Cu–Ti High-Temperature Permanent Magnets, Jian Zhou, Ralph Skomski, C. Chen, George C. Hadjipanayis, David J. Sellmyer Sep 2000

Sm–Co–Cu–Ti High-Temperature Permanent Magnets, Jian Zhou, Ralph Skomski, C. Chen, George C. Hadjipanayis, David J. Sellmyer

David Sellmyer Publications

A class of promising permanent-magnet materials with an appreciable high-temperature coercivity of 8.6 kOe at 500 °C is reported. The Sm–Co–Cu–Ti magnets are prepared by arc melting and require a suitable heat treatment. Magnetization measurements as a function of temperature and x-ray diffraction patterns indicate that the samples are two-phase mixtures of 2:17 and 1:5 structures. Depending on heat treatment and composition, some of the magnets exhibit a positive temperature coefficient of coercivity. The promising high-temperature behavior of the coercivity is ascribed to the temperature dependence of the domain-wall energy, which affects the curvature of the walls and the pinning …


Search For Second And Third Generation Leptoquarks Including Production Via Technicolor Interactions In Pp̅ Collisions At √S = 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration Sep 2000

Search For Second And Third Generation Leptoquarks Including Production Via Technicolor Interactions In Pp̅ Collisions At √S = 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration

Kenneth Bloom Publications

We report the results of a search for second and third generation leptoquarks using 88 pb-1 of data recorded by the Collider Detector at Fermilab. Color triplet technipions, which play the role of scalar leptoquarks, are investigated due to their potential production in decays of strongly coupled color octet technirhos. Events with a signature of two heavy flavor jets and missing energy may indicate the decay of a second (third) generation leptoquark to a charm (bottom) quark and a neutrino. As the data are found to be consistent with standard model expectations, mass limits are determined.


Search For New Particles Decaying To Tt̅ In Pp̅ Collisions At √S = 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration Sep 2000

Search For New Particles Decaying To Tt̅ In Pp̅ Collisions At √S = 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration

Kenneth Bloom Publications

We use 106 pb-1 of data collected with the Collider Detector at Fermilab to search for narrow-width, vector particles decaying to a top and an antitop quark. Model independent upper limits on the cross section for narrow, vector resonances decaying to tt̅ are presented. At the 95% confidence level, we exclude the existence of a leptophobic Z′ boson in a model of top-color-assisted technicolor with mass MZ′ < 480 GeV/c2 for natural width Γ = 0.012MZ0 , and MZ′ < 780 GeV/c2 for Γ = MZ′ .


Pushpush And Push-1 Are Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke Sep 2000

Pushpush And Push-1 Are Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push-1. Both puzzles consist of unit square blocks on an integer lattice; all blocks are movable. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover when a …


The Effect Of Stochastic Cloud Structure On The Icing Process, A. R. Jameson, Alexander Kostinski Sep 2000

The Effect Of Stochastic Cloud Structure On The Icing Process, A. R. Jameson, Alexander Kostinski

Department of Physics Publications

Current understanding of the icing process through collisions between a surface and supercooled cloud droplets is based upon two factors. First, for a given temperature, when the cloud liquid water content, W, exceeds a critical value, wc (the Schumann–Ludlam limit), the ice that collects, whether on the surface of a hailstone or on the wing of an aircraft, changes from lower densities to values close to that of water. Second, it is assumed that cloud droplets are dispersed in space as uniformly as randomness allows (“Poissonian” clouds).

It is now becoming well established, however, that clouds are not Poissonian. …