A new UTD for the electromagnetic plane wave scattering by a canonical circular cylinder with an impedance boundary condition

A UTD solution is developed for describing the scattering by a circular cylinder with an impedance boundary condition (IBC), when it is illuminated by an obliquely incident electromagnetic (EM) plane wave. The solution to this canonical problem will be crucial for the construction of a more general UTD solution valid for an arbitrary smooth convex surface with an IBC, when it is illuminated by an arbitrary EM ray optical field. The canonical solution is uniformly valid across the surface shadow boundary that is tangent to the surface at grazing incidence. This canonical solution contains cross polarized terms in the scattered fields, which arise from a coupling of the TEz and TMz waves at the impedance boundary on the cylinder. Here, z is the cylinder axis. Numerical results show very good accuracy for the simpler and efficient UTD solution, when compared to exact but very slowly convergent eigenfunction solution.

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Mode matches and their locations in the hydrophobic free energy sequences of peptide ligands and their receptor eigenfunctions

Patterns in sequences of amino acid hydrophobic free energies predict secondary structures in proteins. In protein folding, matches in hydrophobic free energy statistical wavelengths appear to contribute to selective aggregation of secondary structures in “hydrophobic zippers.” In a similar setting, the use of Fourier analysis to characterize the dominant statistical wavelengths of peptide ligands’ and receptor proteins’ hydrophobic modes to predict such matches has been limited by the aliasing and end effects of short peptide lengths, as well as the broad-band, mode multiplicity of many of their frequency (power) spectra. In addition, the sequence locations of the matching modes are lost in this transformation. We make new use of three techniques to address these difficulties: (i) eigenfunction construction from the linear decomposition of the lagged covariance matrices of the ligands and receptors as hydrophobic free energy sequences; (ii) maximum entropy, complex poles power spectra, which select the dominant modes of the hydrophobic free energy sequences or their eigenfunctions; and (iii) discrete, best bases, trigonometric wavelet transformations, which confirm the dominant spectral frequencies of the eigenfunctions and locate them as (absolute valued) moduli in the peptide or receptor sequence. The leading eigenfunction of the covariance matrix of a transmembrane receptor sequence locates the same transmembrane segments seen in n-block-averaged hydropathy plots while leaving the remaining hydrophobic modes unsmoothed and available for further analyses as secondary eigenfunctions. In these receptor eigenfunctions, we find a set of statistical wavelength matches between peptide ligands and their G-protein and tyrosine kinase coupled receptors, ranging across examples from 13.10 amino acids in acid fibroblast growth factor to 2.18 residues in corticotropin releasing factor. We find that the wavelet-located receptor modes in the extracellular loops are compatible with studies of receptor chimeric exchanges and point mutations. A nonbinding corticotropin-releasing factor receptor mutant is shown to have lost the signatory mode common to the normal receptor and its ligand. Hydrophobic free energy eigenfunctions and their transformations offer new quantitative physical homologies in database searches for peptide-receptor matches.

Beach changes at Long Beach Island, New Jersey, 1962-73 /

Beach profile line data collected from 32 profile sites along Long Beach Island, New Jersey. A total of 2,158 profile line surveys were examined, using empirical eigenfunction analysis and other measures of beach variability. Most profile lines have shown an accretionary trend since 1962 with rates between 2.3 and 0.24 meter per year in spite of erosion estimates due to sea level rise on the order of 0.68 meter per year. A great deal of variability in profile line change takes place along the beach, increasing from north to south, due to the location of profile lines relative to structures and offshore linear shoals. Detailed closely spaced profile lines taken over a year in a groin field near the north end of the island indicate littoral transport directions shift from north to south. Evidence of a littoral transport node near the north end of the groin field has been found. Net transport of the node is toward the south, but the rate could not be established due to lack of adequate wave data. Profile line variability within groin cells shows that single profile lines are not sufficient to determine the net change within a cell. The design of future beach monitoring studies should consider coastal structures, offshore bathymetry, the method of analysis, and the scales of processes under study. A coastal storm in November 1968 moved the MSL back as much as 22 meters; however, the beach recovered without artificial measures. The offshore bathymetry shows a series of shoreface-connected linear shoals at several locations along the island. Limited data show that these have remained stable and that most beach variability takes place in water shallower than 3 meters.

Numerical Results for the Generalized Mittag-Leffler Function

Mathematics Subject Classification: 33E12, 33FXX PACS (Physics Abstracts Classification Scheme): 02.30.Gp, 02.60.Gf

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30

Problems for P-Monge-Ampere Equations

2010 Mathematics Subject Classification: 35A23, 35B51, 35J96, 35P30, 47J20, 52A40.

Metacommunity Structure Along Resource and Disturbance Gradients in Everglades Wetlands

We evaluated metacommunity hypotheses of landscape arrangement (indicative of dispersal limitation) and environmental gradients (hydroperiod and nutrients) in structuring macroinvertebrate and fish communities in the southern Everglades. We used samples collected at sites from the eastern boundary of the southern Everglades and from Shark River Slough, to evaluate the role of these factors in metacommunity structure. We used eigenfunction spatial analysis to model community structure among sites and distance-based redundancy analysis to partition the variability in communities between spatial and environmental filters. For most animal communities, hydrological parameters had a greater influence on structure than nutrient enrichment, however both had large effects. The influence of spatial effects indicative of dispersal limitation was weak and only periphyton infauna appeared to be limited by regional dispersal. At the landscape scale, communities were well-mixed, but strongly influenced by hydrology. Local-scale species dominance was influenced by water-permanence and nutrient enrichment. Nutrient enrichment is limited to water inflow points associated with canals, which may explain its impact in this data set. Hydroperiod and nutrient enrichment are controlled by water managers; our analysis indicates that the decisions they make have strong effects on the communities at the base of the Everglades food web.

Sloshing and slamming oscillations in collapsible channel flow

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to an external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes contribute increasingly to the global instability and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.