bluuebunny/crossref_metadata_2025 huggingface dataset:
Predicting the solution morphology of a sulfonated pentablock copolymer in binary solvent mixtures
Authors: Griffin Philip J. , Salmon Grace B. , Ford Jamie , Winey Karen I.
Published: September 2015

The solution morphologies of a midblock‐sulfonated pentablock copolymer in miscible polar/nonpolar solvent blends were characterized as a function of solvent composition and polymer concentration using small angle X‐ray scattering. Three distinct solution morphologies are observed upon changing the composition of the solvent blend. At low weight fractions of polar solvent, spherical, sulfonated‐core micelles are observed, while spherical, sulfonated‐corona (inverted) micelles are observed at high weight fractions of polar solvent. Polymer solution scattering is observed at intermediate concentrations of polar solvent. Additionally, the characteristic dimensions of the sulfonated‐core micelles were found to change strongly upon variation of the solvent blend composition, indicating that these solutions—and correspondingly the morphology and properties of polymer membranes into which they are cast—can be tuned through simple variations in the solvent blend chemistry. We demonstrate that the solution morphologies and the characteristic micelle dimensions of these complex pentablock copolymer/binary solvent blends can be reliably predicted by considering the relative interactions of each polymer block and the solvent blend using the Hansen solubility parameters. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 254–262
Effect of surface tension on the relaxation of a viscoelastic half‐space perturbed by a point load
Authors: Hui Chung‐Yuen , Jagota Anand
Published: September 2015

We study the effect of surface tension on the flattening of a surface perturbed by a point load subsequent to its removal. The surface bounds an infinite isotropic linear viscoelastic incompressible half space. The point load is initially applied for a sufficiently long time so that the half space is fully relaxed before the load removal. An exact solution is obtained assuming small deformation. We then specialize our theory to the case of a standard viscoelastic solid. There is an initial reduction of the surface displacement immediately after load removal that is found to be directly proportional to the ratio of applied load to surface tension. This is followed by a temporal decay of the surface profile that depends only on the relaxation time and the long and short time moduli of the viscoelastic solid. Our work also provides the Green's function for a suddenly applied point load on the surface of a viscoelastic half space. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 274–280
pKa predictions for proteins, RNAs, and DNAs with the Gaussian dielectric function using DelPhi pKa
Authors: Wang Lin , Li Lin , Alexov Emil
Published: September 2015

We developed a Poisson‐Boltzmann based approach to calculate the
values of protein ionizable residues (Glu, Asp, His, Lys and Arg), nucleotides of RNA and single stranded DNA. Two novel features were utilized: the dielectric properties of the macromolecules and water phase were modeled via the smooth Gaussian‐based dielectric function in DelPhi and the corresponding electrostatic energies were calculated without defining the molecular surface. We tested the algorithm by calculating
values for more than 300 residues from 32 proteins from the PPD dataset and achieved an overall RMSD of 0.77. Particularly, the RMSD of 0.55 was achieved for surface residues, while the RMSD of 1.1 for buried residues. The approach was also found capable of capturing the large
shifts of various single point mutations in staphylococcal nuclease (SNase) from
‐cooperative dataset, resulting in an overall RMSD of 1.6 for this set of pKa's. Investigations showed that predictions for most of buried mutant residues of SNase could be improved by using higher dielectric constant values. Furthermore, an option to generate different hydrogen positions also improves
predictions for buried carboxyl residues. Finally, the
calculations on two RNAs demonstrated the capability of this approach for other types of biomolecules. Proteins 2015; 83:2186–2197. © 2015 Wiley Periodicals, Inc.
Amino acid alphabet reduction preserves fold information contained in contact interactions in proteins
Authors: Solis Armando D.
Published: September 2015

To reduce complexity, understand generalized rules of protein folding, and facilitate de novo protein design, the 20‐letter amino acid alphabet is commonly reduced to a smaller alphabet by clustering amino acids based on some measure of similarity. In this work, we seek the optimal alphabet that preserves as much of the structural information found in long‐range (contact) interactions among amino acids in natively‐folded proteins. We employ the Information Maximization Device, based on information theory, to partition the amino acids into well‐defined clusters. Numbering from 2 to 19 groups, these optimal clusters of amino acids, while generated automatically, embody well‐known properties of amino acids such as hydrophobicity/polarity, charge, size, and aromaticity, and are demonstrated to maintain the discriminative power of long‐range interactions with minimal loss of mutual information. Our measurements suggest that reduced alphabets (of less than 10) are able to capture virtually all of the information residing in native contacts and may be sufficient for fold recognition, as demonstrated by extensive threading tests. In an expansive survey of the literature, we observe that alphabets derived from various approaches—including those derived from physicochemical intuition, local structure considerations, and sequence alignments of remote homologs—fare consistently well in preserving contact interaction information, highlighting a convergence in the various factors thought to be relevant to the folding code. Moreover, we find that alphabets commonly used in experimental protein design are nearly optimal and are largely coherent with observations that have arisen in this work. Proteins 2015; 83:2198–2216. © 2015 Wiley Periodicals, Inc.
Enhanced photovoltaic currents in strained Fe‐doped LiNbO3 films
Authors: Inoue Ryotaro , Takahashi Shusuke , Kitanaka Yuuki , Oguchi Takeshi , Noguchi Yuji , Miyayama Masaru
Published: September 2015

We investigate the impact of strain on photovoltaic current (Jz) characteristics for iron‐doped LiNbO3 (Fe‐LN) under visible light illumination by thin‐film experiments. The Jz values are demonstrated to be dramatically enhanced for the film with a tensile strain along the Ps direction, which is over 500 times as large as that of the bulk (strain‐free) Fe‐LN crystals. Density functional theory (DFT) calculations show that the tensile strain increases an off‐center displacement of Fe2+ that is opposite to the Ps direction. Our experimental and DFT study demonstrates that the control of the lattice strain is effective in enhancing the photovoltaic effect in the Fe‐LN system.
Optical properties and lattice dynamics of CuZnGeSe quaternary semiconductor: A density‐functional study
Authors: Litvinchuk Alexander P.
Published: September 2015

Density‐functional calculations of the electronic band structure, optical properties, and lattice dynamics of kesterite CuZnGeSe semiconductor (space group ) are reported. Theoretical optical properties of the material are shown to agree quantitatively with available spectroscopic ellipsometry experimental data that allow detailed interpretation of the main spectral features around the fundamental absorption edge. A good agreement between theoretical and experimental vibrational mode frequencies is also established and the assignment of observed phonon modes to specific lattice eigenmodes is performed.
Identification of bacteria by fatty acid profiling with direct analysis in real time mass spectrometry
Authors: Cody Robert B. , McAlpin Casey R. , Cox Christopher R. , Jensen Kirk R. , Voorhees Kent J.
Published: September 2015

Rationale

Bacterial fatty acid profiling is a well‐established technique for bacterial identification. Current methods involving esterification and gas chromatography/mass spectrometry (GC/MS) or matrix‐assisted laser desorption/ionization (MALDI) analysis are effective, but there are potential benefits to be gained by investigating ambient ionization methods that can provide rapid analysis without derivatization or additional sample handling.

Methods

Lipid extracts from colonies of five Gram‐positive and five Gram‐negative pathogenic bacteria were analyzed by Direct Analysis in Real Time (DART) ionization coupled with a time‐of‐flight mass spectrometer. Fatty acid profiles were obtained from the negative‐ion DART mass spectra without additional derivatization or sample preparation.

Results

Fatty acid profiles obtained from the deprotonated molecules [M – H]− were found to be highly species‐specific and reproducible. Leave‐one‐out cross validation (LOOCV) for principal component analysis (PCA) showed 100% correct classification accuracy.

Conclusions

The results of this preliminary feasibility study show good precision and accuracy, and the fatty acid patterns are clearly distinctive for each of the ten species examined. The speed and ease of analysis and the high classification accuracy for this initial study indicate that DART is an effective method for bacterial fatty acid profiling. Copyright © 2015 John Wiley & Sons, Ltd.
Unsolvability in 3 × 3 Matrices
Authors: Paterson Michael S.
Published: September 2015

A set of 3 × 3 matrices over the integers will be said to be mortal if the zero matrix can be expressed as a finite product of members of the set. It is shown in this paper that the problem of deciding whether a given finite set is mortal is recursively unsolvable.
Some Inviscid “Cat's Eye” Flows
Authors: Bergeron R. F.
Published: September 2015

Some inviscid flows with the combined shear and periodic disturbance characteristic of the Kelvin “eat's eye” pattern are presented. The solutions have constant vorticity in each region of closed streamlines, with discontinuities in vorticity (but not velocity) allowed across boundaries.
On the Boundary Condition at the Surface of a Porous Medium
Authors: Saffman P. G.
Published: September 2015

A theoretical justification is given for an empirical boundary condition proposed by Beavers and Joseph [1]. The method consists of first using a statistical approach to extend Darcy's law to non homogeneous porous medium. The limiting case of a step function distribution of permeability and porosity is then examined by boundary layer techniques, and shown to give the required boundary condition. In an Appendix, the statistical approach is checked by using it to derive Einstein's law for the viscosity of dilute suspensions.
Comparison of Pseudospectral and Spectral Approximation
Authors: Orszag Steven A.
Published: September 2015

The accuracy of pseudospectral (collocation) approximation is compared to spectral (Galerkin) approximation in some simple model problems. It is found that both approximations give similar errors, despite the inclusion of aliasing terms in pseudospectral approximation.
The Van Der Waals Interaction Across Non‐Uniform Electrolyte
Authors: Barouch E. , Perram J. W. , Smith E. R.
Published: September 2015

The interaction of like colloidal particles separated by electrolyte is the resultant of the attractive Vander Waals force and the repulsive electrostatic forces, screened by the non‐uniform electrolyte. Hitherto, these contributions have been estimated separately. In this paper, the coupling of the low frequency electromagnetic fluctuations to the static charge distribution between two planes is examined. This coupling is expressed by a pair of second order coupled differential equations, which are solved exactly. The resulting eigenvalue equation is derived and the zero frequency contribution to the Vander Waals free energy calculated.
Wave Propagation m Continuous Random Media
Authors: Lange Charles G.
Published: September 2015

A study is made of the way in which small random inhomogeneities in a transmission medium affect the statistical properties of a system of waves. It is shown that provided the spectral cumulants are sufficiently smooth at some initial time, a sequence of closures for the zeroth order spectral functions can be deduced which describe asymptotically the transfer of energy between wave numbers. Of particular importance is the fact that the closure equations are derived without the need to resort to ad hoc statistical assumptions. The general theory is applied to the problem of the propagation of water waves over an irregular bottom topography.
Interaction and Dispersion of Long Waves
Authors: Benney D. J.
Published: September 2015

The mathematical nature of nonlinear long wave interactions and the dispersive characteristics of a single nonlinear mode are investigated.
On the Formation of Vortex Rings
Authors: Saffman P. G.
Published: September 2015

The production of a vortex ring formed by using a piston to drive fluid through an orifice is considered. A cylindrical vortex sheet is supposed to be formed initially which rolls up into a vortex ring. Energy and momentum are conserved during rollup and determine the speed and size of the ring. It is shown that these quantities are independent of the vorticity distribution in the core of the ring. Reasonable agreement with experimental observations is found. A speculation is made about the criterion for the rings to be laminar or turbulent.
Annihilators in Nonrepetitive Semigroups
Authors: Li Shuo‐Yen R.
Published: September 2015

It is well known that one can construct an infinite sequence on three or more symbols such that no two consecutive blocks are identical. In this paper we give a combinatorial characterization for those finite sequences which are maximal in the sense that appending to them even one more symbol yields two consecutive identical blocks.
On The Navier‐Stokes Equations with Constant Total Temperature
Authors: Gottlieb David , Gustafsson Berti
Published: September 2015

For various applications in fluid dynamics, one can assume that the total temperature is constant. Therefore, the energy equations can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed in this paper. It is shown that the system is strictly hyperbolic and well posed for the initial‐value problem. Boundary conditions are described such that the linearized system is well posed. The hopscotch method is investigated and numerical results are presented.
On the Deformation of a Viscous Droplet Caused by Variable Surface Tension
Authors: Greenspan H. P.
Published: September 2015

The surface tension of a small viscous droplet is made variable by the deposition of a surface active material. The resultant shear forces produce a deformation of and a fluid motion within the droplet. The process, including the nonlinear convection or spread of surfactant, is examined theoretically. Some experimental results are reported, and application to cell division is discussed.
The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance
Authors: Rubenfeld L. A.
Published: September 2015

An asymptotic procedure for deriving equations governing the passage of a weakly coupled nonlinear system of oscillators is discussed. The procedure avoids an inner‐outer‐matching technique and is valid when the small coupling and detuning parameters are arbitrary. Resonance is permitted to occur at one or several instances of time or to last for a finite length of time. Numerical results are discussed.
The Existence of Steady Wave Solutions to a Non‐Local Version of the K.P.P. Equation
Authors: Atkinson C.
Published: September 2015

For the equationurn:x-wiley:00222526:media:sapm197859295:sapm197859295-math-0002with, wave solutions of the formc(x1+at)(c(+ ∞) = 1,c(− ∞) = 0) are shown to exist for a range of values ofa. For velocities outside this range non‐existence theorems are proved.
The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation
Authors: Ma Yan‐Chow
Published: September 2015

A detailed analysis is given to the solution of the cubic Schrödinger equation iqt + qxx + 2|q|2q = 0 under the boundary conditions as |x|→∞. The inverse‐scattering technique is used, and the asymptotic state is a series of solitons. However, there is no soliton whose amplitude is stationary in time. Each soliton has a definite velocity and “pulsates” in time with a definite period. The interaction of two solitons is considered, and a possible extension to the perturbed periodic wave [q(x + T,t) = q(x,t) as |x|→∞] is discussed.
Density Wave Theory of Spiral Structure of Galaxies
Authors: Lin C. C. , Lau Y. Y.
Published: September 2015

The density wave theory of spiral structure in galaxies is studied as a dynamical problem: the gravitational instability of a galactic disk with respect to spiral modes. The asymptotic theory for tightly wound spirals is presented in detail, although the problem has been formulated in a more general form to open the way to future research work in other directions. Some preliminary results based on the general formulation are included; they confirm those based on the asymptotic theory in cases where the latter should be applicable. The fluid dynamical model is adopted; reference to the stellar dynamical model is made when necessary. Besides providing a coherent account of the present status of the theory, it is hoped that this article will further stimulate workers in continuum mechanics to play their important role in future research work in the astrophysics of galaxies.
Admissible Domains for Higher Order Differential Equations
Authors: Kelly Brian J.
Published: September 2015

This paper analyzes the geometric structure of certain domains in the complex plane which arise in the asymptotic theory of linear ordinary differential equations containing a parameter. These domains, called admissible, are domains in which an asymptotic representation of the solution of the differential equation may be found and across whose boundaries these representations may undergo a rapid change of asymptotic behavior (the Stokes phenomenon). A knowledge of the disposition of those domains associated with a particular differential equation is necessary for a satisfactory asymptotic theory of the equation. The main analysis gives necessary and sufficient conditions for identifying admissible domains and gives a procedure for obtaining particular admissible subdomains of a given domain. Sufficient conditions are established to determine the maximality of admissible domains. A section of examples is included to highlight the salient features of this theory. In all of the results, criteria involving only purely local properties of the boundary are needed to determine the global properties of admissibility and maximal admissibility .
Bifurcation and Stability Theory of Periodic Solutions For Integrodifferential Equations
Authors: Landman Kerry A.
Published: September 2015

This paper is concerned with a nonlinear integrodifferential equation (the delay logistic equation) governing the growth dynamics of a single species N(t) for time t > 0. This equation contains a positive parameter λ. Suppose that there exists a positive equilibrium solution N = c which is stable for all small values of λ. Assume also that this solution loses stability as λ is increased past a critical value λ*. This will correspond to a simple pure imaginary conjugate pair of roots of a characteristic equation associated with the linearized stability of N = c at λ = λ*. Then we will construct a unique bifurcating time periodic solution of the equation as a Taylor series in a parameter ε. Furthermore this solution exists either for supercritical values of the parameter (λ > λ*) or for subcritical values (λ < λ*). The stability behavior of this small periodic solution can be characterized according to whether the bifurcation is supercritical or subcritical‐supercritical solutions are stable, but subcritical solutions are unstable. Therefore these results are analogous to Hoprs bifurcation theorem for autonomous systems of differential equations.
Similarity Solutions of Some Two‐Space‐Dimensional Nonlinear Wave Evolution Equations
Authors: Redekopp Larry G.
Published: September 2015

Similarity reductions of the two‐space‐dimensional versions of the Korteweg‐deVries, modified Korteweg‐deVries, Benjamin‐Davis‐Ono, and nonlinear Schrödinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two‐dimensional Korteweg‐deVries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painlevé transcendent.
A Singular Perturbation Analysis for a Reaction‐Diffusion System Describing Pattern Formation
Authors: Mottoni P. , Rothe F.
Published: September 2015

A reaction‐diffusion system describing a simple activator‐inhibitor reaction is investigated in the limiting case of “very large” diffusion rate of the inhibitor. Using singular perturbation techniques, an inner and an outer expansion are derived. The latter, describing the large‐time behavior of the system, is governed by equations that, in the first orders of approximation, possess asymptotically stable space‐inhomogeneous equilibria (patterns), and whose set of equilibria is globally attractive.
Perturbations of Solitons and Solitary Waves
Authors: Kodama Yuji , Ablowitz Mark J.
Published: September 2015

A direct perturbation method is developed to investigate the evolution of solitary waves in the presence of small perturbations. A uniformly valid first order solution is constructed. The method is applied to several nonlinear evolution equations which support solitons or solitary waves. Finally, the method is compared with other approaches in the literature.
An Explicit Example of a Local and a Nonlocal Potential Whose Hamiltonians Are Unitarily Equivalent and Whose Scattering Operators Are Identical
Authors: Abraham P. B. , DeFacio B. , Mose H. E.
Published: September 2015

An explicit example is given for the one‐dimensional Schrodinger equation in which two unitarily equivalent Hamiltonians, one with a local scattering potential and the other with a nonlocal scattering potential, have the same scattering operator and bound‐state measure. The result has obvious implications for the inverse scattering problem. The unitary operator which maps one Hamiltonian to the other is of interest because it is expressed as the product of two operators, neither of which has an inverse.
On the Bifurcation of a Random Spectrum of Weakly Nonlinear Deep‐Water Gravity Waves
Authors: Ma Yan‐Chow
Published: September 2015

The bifurcation of a narrow‐band homogeneous random spectrum of deep‐water gravity waves into an inhomogeneous random spectrum is studied under the assumption of weak nonlinearity. The modulational wavenumber for the bifurcation depends on the characteristic bandwidth of the spectrum as well as on the energy of the spectrum. The stability of the bifurcated spectrum is examined.
A Suggested Mechanism for Nonlinear Wall Roughness Effects on High Reynolds Number Flow Stability
Authors: Hall P. , Smith F. T.
Published: September 2015

The interactions between an uneven wall and free stream unsteadiness and their resultant nonlinear influence on flow stability are considered by means of a related model problem concerning the nonlinear stability of streaming flow past a moving wavy wall. The particular streaming flows studied are plane Poiseuille flow and attached boundary‐layer flow, and the theory is presented for the high Reynolds number regime in each case. That regime can permit inter alia much more analytical and physical understanding to be obtained than the finite Reynolds number regime; this may be at the expense of some loss of real application, but not necessarily so, as the present study shows. The fundamental differences found between the forced nonlinear stability properties of the two cases are influenced to a large extent by the surprising contrasts existing even in the unforced situations. For the high Reynolds number effects of nonlinearity alone are destabilizing for plane Poiseuille flow, in contrast with both the initial suggestion of earlier numerical work (our prediction is shown to be consistent with these results nevertheless) and the corresponding high Reynolds number effects in boundary‐layer stability. A small amplitude of unevenness at the wall can still have a significant impact on the bifurcation of disturbances to finite‐amplitude periodic solutions, however, producing a destabilizing influence on plane Poiseuille flow but a stabilizing influence on boundary‐layer flow.
Long Eddies in Sheared Flows
Authors: Varley E. , Blythe P. A.
Published: September 2015

The characteristic feature of the wide variety of hydraulic shear flows analyzed in this study is that they all contain a critical level where some of the fluid is turned relative to the ambient flow. One example is the flow produced in a thin layer of fluid, contained between lateral boundaries, during the passage of a long eddy. The boundaries of the layer may be rigid, or flexible, or free; the fluid may be either compressible or incompressible. A further example is the flow produced when a shear layer separates from a rigid boundary producing a region of recirculating flow. The equations used in this study are those governing inviscid hydraulic shear flows. They are similar in form to the classical boundary layer equations with the viscous term omitted. The main result of the study is to show that when the hydraulic flow is steady and contained between lateral boundaries, the variation of vorticity ω(ψ) cannot be prescribed at any streamline which crosses the critical level. This variation is, in fact, determined by (1) the vorticity distribution at all streamlines which do not cross the critical level, by (2) the auxiliary conditions which must be satisfied at the boundaries of the fluid layer, and by (3) the dimensions of the region containing the turned flow. If at some instant the vorticity distribution is specified arbitrarily at all streamlines, generally the subsequent flow will be unsteady. In order to emphasize this point, a class of exact solutions describing unsteady hydraulic flows are derived. These are used to describe the flow produced by the passage of a long eddy which distorts as it is convected with the ambient flow. They are also used to describe the unsteady flow that is produced when a shear layer separates from a boundary. Examples are given both of flows in which the shear layer reattaches after separation and of flows in which the shear layer does not reattach. When the shear layer vorticity distribution has the form ωαyn, where y is a distance measure across the layer, the steady flows are of Falkner‐Skan type inside, and adjacent to, the separation region. The unsteady flows described in this paper are natural generalizations of these Falkner‐Skan flows. One important result of the analysis is to show that if the unsteady flow inside the separation region is strongly sheared, then the boundary of the separation region moves upstream towards the point of separation, forming large transverse currents. Generally, the assumption of hydraulic flow becomes invalid in a finite time. On the other hand, if the flow inside the separation region is weakly sheared, this region is swept downstream and the flow becomes self‐similar.
The Evolution of Finite Amplitude Solitary Rossby Waves on a Weak Shear
Authors: Warn T.
Published: September 2015

The evolution equation urn:x-wiley:00222526:media:sapm1983692127:sapm1983692127-math-0001 is derived for finite amplitude, long Rossby waves on a weak shear generalizing an earlier version given by Benney [1].
On the Inverse Scattering of the Time‐Dependent Schrödinger Equation and the Associated Kadomtsev‐Petviashvili (I) Equation
Authors: Fokas A. S. , Ablowitz M. J.
Published: September 2015

The Kadomtsev‐Petviashvili equation, a two‐spatial‐dimensional analogue of the Korteweg‐deVries equation, arises in physical situations in two different forms depending on a certain sign appearing in the evolution equation. Here we investigate one of the two cases. The initial‐value problem, associated with initial data decaying sufficiently rapidly at infinity, is linearized by a suitable extension of the inverse scattering transform. Essential is the formulation of a nonlocal Riemann‐Hilbert problem in terms of scattering data expressible in closed form in terms of given initial data. The lump solutions, algebraically decaying solitons, are given a definite spectral characterization. Pure lump solutions are obtained by solving a linear algebraic system whose coefficients depend linearly on x, y, t. Many of the above results are also relevant to the problem of inverse scattering for the so‐called time‐dependent Schrödinger equation.
Modulational Stability of Two‐Phase Sine‐Gordon Wavetrains
Authors: Ercolani Nicholas , Forest M. Gregory , McLaughlin David W.
Published: September 2015

A modulational stability analysis is presented for real, two‐phase sine‐Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine‐Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh‐Gordon modulations. The twophase results are as follows: kink‐kink trains are stable, while the breather trains and kink‐radiation trains are unstable, to modulations.
Superantichains in the Lattice of Partitions of a Set
Authors: Jichang Sha , Kleitman D. J.
Published: September 2015

A construction of superantichains in the lattice of partitions of finite sets is presented that works for set sizes above 107. The construction refines Canfield's, which worked only for set sizes above 1020, and provides a classification of the properties of partitions which allow such antichains to exist.
Nonlinear Cusped Caustics for Dispersive Waves
Authors: Haberman Richard , Sun Ren‐ji
Published: September 2015

A multiple‐scale perturbation analysis for slowly varying weakly nonlinear dispersive waves predicts that the wave number breaks or folds and becomes triple‐valued. This theory has some difficulties, since the wave amplitude becomes infinite. Energy first focuses along a cusped caustic (an envelope of the rays or characteristics). The method of matched asymptotic expansions shows that a thin focusing region with relatively large wave amplitudes, valid near the cusped caustic, is described by the nonlinear Schrödinger equation (NSE). Solutions of the NSE are obtained from an asymptotic expansion of an equivalent linear singular integral equation related to a Riemann‐Hilbert problem. In this way connection formulas before and after focusing are derived. We show that a slowly varying nearly monochromatic wave train evolves into a triple‐phased slowly varying similarity solution of the NSE. Three weakly nonlinear waves are simultaneously superimposed after focusing, giving meaning to a triple‐valued wave number. Nonlinear phase shifts are obtained which reduce to the linear phase shifts previously described by the asymptotic expansion of a Pearcey integral.
Exact Solutions for Large Amplitude Waves in Dispersive and Dissipative Systems
Authors: Varley Eric , Seymour Brian
Published: September 2015

This paper describes some applications of a transformation which takes a system of two, first order, quasilinear, partial differential equations in two dependent and two independent variables into a similar system. Typically, the equations govern wave propagation in dispersive and dissipative systems. It is shown that certain nonlinear equations which are of current practical interest can be transformed into linear equations.
A Proposal for Toeplitz Matrix Calculations
Authors: Strang Gilbert
Published: September 2015

In contrast to the usual (and successful) direct methods for Toeplitz systems Ax = b, we propose an algorithm based on the conjugate gradient method. The preconditioner is a circulant, so that all matrices have constant diagonals and all matrix‐vector multiplications use the Fast Fourier Transform. We also suggest a technique for the eigenvalue problem, where current methods are less satisfactory. If the first indications are supported by further experiment, this new approach may have useful applications—including nearly Toeplitz systems, and parallel computations.
Solitary‐Wave Interactions in Elastic Rods
Authors: Clarkson Peter A. , LeVeque Randall J. , Saxton Ralph
Published: September 2015

The propagation of longitudinal deformation waves in an elastic rod is modelled by the nonlinear partial differential equation
urn:x-wiley:00222526:media:sapm198675295:sapm198675295-math-0001
with p = 3 or 5. This equation is first derived under a range of possible constraints. We then show that this equation and even certain generalizations do not pass the Painlevé test, and hence are probably not completely integrable. Finally, we study the head‐on collision of two equal solitary waves numerically and also asymptotically for small and large amplitude.
The Feynman‐Kac Formula with a Lebesgue‐Stieltjes Measure and Feynman's Operational Calculus
Authors: Lapidus Michel L.
Published: September 2015

We investigate what happens if in the Feynman‐Kac functional, we perform the time integration with respect to a Borel measureηrather than ordinary Lebesgue measurel. Letu(t) be the operator associated with this functional through path integration. We show thatu(t), considered as a function of timet, satisfies a certain Volterra‐Stieltjes integral equation. This result establishes a “FeynmanKac formula with Lebesgue‐Stieltjes measureη.” One recovers the classical Feynman‐Kac formula by lettingη=l. We deduce from the integral equation thatu(t) satisfies a differential equation associated with the continuous partμofηwhenη=μ=l, this differential equation reduces to the heat or the Schrödinger equation in the probabilistic or quantum‐mechanical case, respectively. Moreover, we observe a new phenomenon, due to the discrete partvofη: the functionu(t) undergoes a discontinuity at every point in the support ofv, assumed here to be finite. Further, one obtains an explicit expression foru(t) in terms of operators alternatively associated withμandv. Our results are new even in the probabilistic or “imaginary time” case and allow us to unify various concepts. The derivation of our integral equation has an interesting combinatorial structure and makes essential use of the “generalized Dyson series”— recently introduced by G. W. Johnson and the author—that “disentangle” the operatoru(t). We provide natural physical interpretations of our results in both the diffusion and quantum‐mechanical cases. We also suggest further connections with FeynmanȈs operational calculus for noncommuting operators.
Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
Authors: Benzaid Z. , Lutz D. A.
Published: September 2015

Our purpose is to asymptotically represent solutions of linear difference equations x(k + 1) = [A0 + A(k)]x(k) when k → + ∞ and A(k) is “small” by transforming them into so‐called L‐diagonal form. Two properties are then responsible for the asymptotic equivalence of an L‐diagonal form to a diagonal one: a dichotomy condition on the diagonal part, and a growth condition on the perturbation term. In this manner, we derive some known asymptotic results from a central point of view and also several new extensions and generalizations of them. Some examples are constructed which demonstrate the need for a dichotomy‐type condition, which shows incidentally that results of M. A. Evgrafov are incorrect, since they omit such a condition.
Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations
Authors: Beals Richard , Tenenblat Keti
Published: September 2015

The generalized wave equations and generalized sine‐Gordon equations are known to be associated to linear spectral problems. In this paper we show that the geometric Backlund transformation for the nonlinear equations corresponds to changing the discrete part of the scattering data for the linear problems.
On a Class of P5‐Free Graphs
Authors: Jamison B. , Olariu S.
Published: September 2015

A graph G is perfect in the sense of Berge if for every induced subgraph G′ of G, the chromatic number χ(G′) equals the largest number ω(G′) of pairwise adjacent vertices in G′. The Strong Perfect Graph Conjecture asserts that a graph G is perfect if, and only if, neither G nor its complement Ḡ contains an odd chordless cycle of length at least five. We prove that the conjecture is true for a class of P5‐free graphs.
Interaction of Simple Particles in Soliton Cellular Automata
Authors: Fokas A. S. , Papadopoulou E. P. , Saridakis Y. G. , Ablowitz M. J.
Published: September 2015

We consider a certain cellular automaton recently introduced by Park, Steiglitz, and Thurston. By introducing appropriate mathematical notation, the interaction of simple particles evolving according to this automaton rule is completely characterized analytically. It is found that: (1) If two particles have different speed and they interact, then they interact solitonically and, although they may interact a number of times, they finally separate with the faster particle moving in front of the slower one. (2) If two particles have the same speed and are close enough so that they interact, there exist two cases: either they will interact only once and then they will separate, travelling independently of each other, or they will form a new periodic configuration by interacting forever.
On Equations Which Describe Pseudospherical Surfaces
Authors: Rabelo Mauro L.
Published: September 2015

Using the notion of a differential equation which describes an η‐pseudospherical surface (η‐p.s.s.), we give a characterization of the equations of type uxt = F(u, ux,…, ∂ku / ∂xk), k ≥ 2, with this property. We obtain a systematic procedure to determine a linear problem for which a given equation is the integrability condition. The equations of type uxt = F(u, ux) were characterized by Rabelo and Tenenblat in another paper. The theory is applied to several equations, some of which were not known to describe η‐p.s.s.
A Note on Spin up Effects in a Rotating Mixture
Authors: Greenspan H. P.
Published: September 2015

The centrifugal batch separation of an initially homogeneous mixture of particles and fluid is considered in containers of finite length for which end‐wall effects can be important. The “full” nonlinear theory can be reduced to the determination of an appropriate analytic function. Vortex‐line stretching due to suction into the Ekman layers counteracts the baroclinic generation of vorticity caused by the pressure and density fields.
Hyper‐rook Domain Inequalities
Authors: Carnielli Walter A.
Published: September 2015

A hyper‐rook domain of an element x in the space
(words of length n over alphabets with k elements) is a sphere with center x and fixed radius j in Hamming distance. The number j determines the dimension of the hyper‐rook domain. The classical (and far from solved) problem of covering by rook domains (here considered as the 1‐dimensional case) is the problem of finding minimal coverings of
by such spheres. Very few results are known in the literature for dimensions ≥ 2. We prove in this paper certain classes of inequalities based on coverings using matrices, which give upper and lower bounds for several cases of the problem for higher dimensions.
Semi infinite Orthotropic Cantilevered Strips and the Foundations of Plate Theories
Authors: Lin Yihan , Wan Frederic Y. M.
Published: September 2015

Elastostatic problems of semiinfinite orthotropic cantilevered strips with traction‐free edges and loading at infinity are reduced to the solution of a single scalar Fredholm integral equation of the first kind with a generalized Cauchy kernel. The known complex variable method for equations with a Cauchy type kernel is extended to handle the singularities in the solution for the generalized Cauchy kernel. The reduced problem lends itself to a more efficient numerical solution scheme than all existing methods. Moments of stresses at the root of the cantilever are accurately evaluated and used for the correct formulation of displacement boundary conditions for a plate theory solution (or the actual interior solution) of the elastostatics of thin flat bodies.
The Distributional Hankel Transform of δ(k)(m2×P
Authors: Aguirre Manuel A. , Trione Susana Elena
Published: September 2015

In this note we give a sense to certain kinds of n‐dimensional distributional Hankel transforms of the Dirac measure δ(k)(m2 + P). The most important result is the interchange formula between the product and the convolution of the Hankel transform of δ(k)(m2 + P).
Resonant Flow of a Rotating Fluid Past an Obstacle: The General Case
Authors: Grimshaw R.
Published: September 2015

We consider the flow of a rotating fluid past an antisymmetric obstacle placed on the axis of a cylindrical tube, for the case when the upstream flow is nearly resonant, or critical, so that the speed of a free linear long wave is nearly zero in the frame of reference of the obstacle. The perturbed flow is dominated by the resonant mode, whose amplitude satisfies a forced Korteweg—de Vries equation in this general case when the upstream flow contains radial shear andjor radially dependent angular velocity.
Stirling Number Asymptotics from Recursion Equations Using the Ray Method
Authors: Knessl Charles , Keller Joseph B.
Published: September 2015

A technique for computing asymptotic expansions of combinatorial quantities from their recursion relations is presented. It is applied to the Stirling numbers of the first and second kinds, s(n, k) and S(n, k), for n ≫ 1 and three ranges of k: (i) k = O(1), (ii) n − k = O(1), (iii) k ≫ 1, 0 < k / n < 1, The technique uses asymptotic methods of applied mathematics such as the ray method and the method of matched asymptotic expansions.
Singular Perturbations of Limit Points with Application to Tubular Chemical Reactors
Authors: Lange Charles G. , Weinitschke Hubertus J.
Published: September 2015

Singular perturbation techniques are used to study solutions of certain nonlinear boundary‐value problems defined on domains with a circular hole of radius ε, in the limit ε → 0. Asymptotic expansions are constructed to describe the behavior of solutions at and near simple and double limit points (cusps). In particular, the behavior of axisymmetric solutions in an annular domain at limit points is investigated. The results are applied to two model problems arising in chemical‐reactor theory. The asymptotic analysis predicts a surprisingly large sensitivity of limit points to the ε‐domain perturbation considered here.
Greedy Families for Linear Objective Functions
Authors: Brylawski Thomas
Published: September 2015

The following structures are characterized: for which families of feasible subsets of a finite set does the greedy algorithm return the optimum subset independent of the weighting of a linear objective function on the set? Characteristically, the family must then have as bases the bases of a matroid (even when the feasible family is not a system of independent sets), and for every accessible feasible set X, the subset of elements by which X can be augmented is the complement of a proper closed set of the matroid. Another characterization is given for a family in which the greedy algorithm gives the optimum subset at every stage: the family is that of the bases of a sequence of matroid strong maps resulting in a natural duality theory. Theoretical underpinnings are given for several classical instances such as the algorithms of Kruskal, Prim, and Dijkstra.
Singular Perturbation Analysis of Boundary Value Problems for Differential‐Difference Equations. IV. A Nonlinear Example with Layer Behavior
Authors: Lange Charles G. , Miura Robert M.
Published: September 2015

A study is made of boundary value problems for a class of singularly perturbed nonlinear, second‐order, differential‐difference equations, i.e., where the highest‐order derivative is multiplied by a small parameter. Depending on the region of parameter space, solutions of the nonlinear problem may not be unique, can exhibit extreme sensitivity to the values of the parameters, or may not exist. Typically, solutions exhibit layer behavior and/or exponentially large amplitudes. Approximate solutions of these boundary value problems are obtained by using singular perturbation methods and numerical computations and are then compared. Numerical computations of representative solutions illustrate the wide variety of possible behaviors.
Asymptotics beyond All Orders in a Model of Crystal Growth
Authors: Kruskal Martin D. , Segur Harvey
Published: September 2015

In its simplest form, the geometric model of crystal growth is a third‐order, nonlinear, ordinary differential equation for θ(s, ε):
urn:x-wiley:-wiley:00222526:media:sapm1991852129-math-0001
A needle crystal is a solution that satisfies boundary conditions
urn:x-wiley:-wiley:00222526:media:sapm1991852129-math-0002
The geometric model admits a needle‐crystal solution for ε = 0; for small ε, it admits an asymptotic expansion that is valid to all orders for such a solution. Even so, we prove that the geometric model in this form admits no needle crystal for any small, nonzero ε, a fact that lies beyond all orders of the asymptotic expansion. A more complicated version of the geometric model is
urn:x-wiley:-wiley:00222526:media:sapm1991852129-math-0003
where α represents crystalline anisitropy. We show that for 0 < α < 1, the geometric model admits needle crystals for a discrete set of values of α. The number of such values of α increases like ε−1 as ε → 0.
Internal Solitary Waves
Authors: Weidman P. D. , Velarde M. G.
Published: September 2015

The expansion procedure introduced by Benney (1966) for weakly nonlinear, planar shallow‐water waves is used to provide an alternative derivation of the more general results of Benjamin (1966) for shallow fluid layers possessing arbitrary vertical stratification and horizontal shear. New solutions that include the effects of both shear and stratification are presented. The evolution equation for slowly varying cylindrical solitary waves traveling in a density‐stratified fluid is found using two‐timing techniques. Not surprisingly, one obtains the same coefficients for the nonlinear and dispersive terms as in the planar case. In the limit for uniform density it is shown that the free‐surface evolution equation of Miles (1978) for axisymmetric Boussinesq waves is recovered.
Asymptotic Behavior of Solutions to Nonlinear Equations with Dissipation for Large x and t
Authors: Naumkin P. I.
Published: September 2015

In this paper we continue to study large time asymptotic behavior of solutions to the Cauchy problem for a class of nonlinear nonlocal equations with dissipation. When t → ∞ and x → ∞ simultaneously, the asymptotics of solutions for a generalization of the Kolmogorov‐Petrovsky‐Piscounov equation, a model equation studied by Whitham, and an equation introduced by Ott, Sudan, and Ostrovsky is found. The character of asymptotics obtained is quasilinear.
Low‐Frequency Multidimensional Instabilities for Reacting Shock Waves
Authors: Majda A. , Roytburd V.
Published: September 2015

This paper presents a weakly nonlinear analysis for one scenario for the development of transversal instabilities in detonation waves in two space dimensions. The theory proposed and developed here is most appropriate for understanding the behavior of regular and chaotically irregular pulsation instabilities that occur in detonation fronts in condensed phases and occasionally in gases. The theory involves low‐frequency instabilities and through suitable asymptotics yields a complex Ginzburg‐Landau equation that describes simultaneously the evolution of the detonation front and the nonlinear interactions behind this front. The asymptotic theory mimics the familiar theory of nonlinear hydrodynamic instability in outline; however, there are several novel technical aspects in the derivation because the phenomena studied here involve a complex free boundary problem for a system of nonlinear hyperbolic equations with source terms.