Mathematical Modelling of Hydrophilic Ionic Fertiliser Diffusion in Plant Cuticles: Lipophilic Surfactant Effects

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds to reduce their environmental impact and increase financial returns. One way to improve efficacy is by enhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical diffusion within the leaf. It has been noted that a comprehensive set of mechanisms for ionic active ingredient penetration through plant leaves with surfactants is not well defined and oils that enhance penetration have been given little attention. The importance of a mechanistic mathematical model has been noted previously in the literature. Two mechanistic mathematical models have been previously developed by the authors, focusing on plant cuticle penetration of calcium chloride through tomato fruit cuticles. The models included ion binding and evaporation with hygroscopic water absorption, along with the ability to vary the active ingredient concentration and type, relative humidity and plant species. Here we further develop these models to include lipophilic adjuvant effects, as well as the adsorption and desorption of compounds on the cuticle surface with a novel Adaptive Competitive Langmuir model. These modifications to a penetration model provide a novel addition to the literature. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities and relate theoretical predictions to physical mechanisms. The results indicate the addition of the desorption mechanism may be one way to predict increased penetration at late times and the sensitivity of model parameters compares wells to those present in the literature

Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition

At the microscopic level, equilibrium liquid's translational symmetry is spontaneously broken at the so-called dynamic glass transition predicted by the mean-field replica approach. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.Comment: 4 page

Evaluation of ERTS imagery for spectral geological mapping in diverse terranes of New York State

Linear anomalies dominate the new geological information derived from ERTS-1 imagery, total lengths now exceeding 6000 km. Experimentation with a variety of viewing techniques suggests that conventional photogeologic analyses of band 7 results in the location of more than 97 percent of all linears found. The maxima on rose diagrams for ERTS-1 anomalies correspond well with those for mapped faults and topographic lineaments, despite a difference in relative magnitudes of maxima thought due to solar illumination direction. A multiscale analysis of linears showed that single topographic linears at 1:2,500,000 became segmented at 1:1,000,000, aligned zones of shorter parallel, en echelon, or conjugate linears at 1:500,000, and still shorter linears lacking obvious alignment at 1:250,000. Visible glacial features include individual drumlins, best seen in winter imagery, drumlinoids, eskers, ice-marginal drainage channels, glacial lake shorelines and sand plains, and end moraines

Evaluation of ERTS-1 imagery for geological sensing over the diverse geological terrains of New York State

Film positives of ERTS-1 imagery, both as received from NASA and photographically reprocessed, are analyzed by conventional and color additive viewing methods. The imagery reveals bedrock and surficial geological information at various scales. Features which can be identified to varying degrees include boundaries between major tectonic provinces, lithological contacts, foliation trends within massive gneisses, faults, and topographic lineaments. In the present imagery the greatest amount of spectral geology is displayed in the Adirondack region where bedrock geology is strongly linked to topography. Within this basement complex, the most prominantly displayed features are numerous north-northeast trending faults and topographic lineaments, and arcuate east-west valleys developed in some of the weaker metasedimentary rocks. The majority of the faults and lineaments shown on the geologic Map of New York at 1:250,000 appear in the ERTS imagery

Analysis of ERTS-1 linear features in New York State

The author has identified the following significant results. All ERTS-1 linears confirmed to date have topographic expression although they may appear as featureless tonal linears on the imagery. A bias is unavoidably introduced against any linears which may parallel raster lines, lithological trends, or the azimuth of solar illumination. Ground study of ERTS-1 topographic lineaments in the Adirondacks indicates: outcrops along linears are even more rare than expected, fault breccias are found along some NNE lineaments, chloritization and slickensiding without brecciation characterize one EW lineament whereas closely-spaced jointing plus a zone of plastic shear define another. Field work in the Catskills suggests that the prominent new NNE lineaments may be surface manifestations of normal faulting in the basement, and that it may become possible to map major joint sets over extensive plateau regions directly on the imagery. Fall and winter images each display some unique linears, and long linears on the fall image commonly appear as aligned segments on the winter scene. A computer-processed color composite image permitted the extraction or additional information on the shaded side of mountains

Assessment of ERTS-1 imagery as a tool for regional geological analysis in New York State

The author has identified the following significant results. Linear anomalies dominate the new geological information derived from ERTS-1 imagery, total lengths now exceeding 26,500 km. Maxima on rose diagrams for ERTS-1 anomalies correspond well with those for mapped faults and topographic lineaments. Multi-scale analysis of linears shows that single topographic linears at 1:2,500,000 may become dashed linears at 1:1,000,000 aligned zones of shorter parallel, en echelon, or conjugate linears at 1:5000,000, and shorter linears lacking any conspicuous zonal alignment at 1:250,000. Field work in the Catskills suggests that the prominent new NNE lineaments may be surface manifestations of dip slip faulting in the basement, and that it may become possible to map major joint sets over extensive plateau regions directly on the imagery. Most circular features found were explained away by U-2 airfoto analysis but several remain as anomalies. Visible glacial features include individual drumlins, drumlinoids, eskers, ice-marginal drainage channels, glacial lake shorelines, sand plains, and end moraines

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change