An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’

Perturbation theory of the mass enhancement for a polaron coupled to acoustic phonons

We use both a perturbative Green's function analysis and standard perturbative quantum mechanics to calculate the decrease in energy and the effective mass for an electron interacting with acoustic phonons. The interaction is between the difference in lattice displacements for neighbouring ions, and the hopping amplitude for an electron between those two sites. The calculations are performed in one, two, and three dimensions, and comparisons are made with results from other electron-phonon models. We also compute the spectral function and quasiparticle residue, as a function of characteristic phonon frequency. There are strong indications that this model is always polaronic on one dimension, where an unusual relation between the effective mass and the quasiparticle residue is also found.Comment: 9 pages, 5 figures, submitted to PR

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Density of States for a Specified Correlation Function and the Energy Landscape

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter

Institutional market reforms in Russia and China through the lenses of Polanyi’s double movement

Objective: To compare the specifics of the “public protection responses” to the deepening of marketisation in Russia andChina and to the strengthening of “market fundamentalism” in Western countries.Methods: The methodology is based on the concept of “double movement”, developed in the works of Karl Polanyi, and on the categorical apparatus of the author’s theory of institutional X - and Y -matrices.Results: It is shown that since the 1980s, in most countries of the world, a process of liberalisation of national economies has been taking place, including the active introduction of market institutions in various spheres of social life. In Russia and China, this process is known as post-socialist “market reforms”. However, after the global financial and economic crisis of 2007-2008, which showed once again the instability of the market economy and the continuous growth of social inequality, there have been widespread and continuing attempts to strengthen public control over spontaneous market forces. A similar process took place in the 1930s in Europe and the United States after the Great Depression, and Karl Polanyi then called it a “double movement” or “countermovement”. He described it as a public response to the expansion of the market, “aimed at protecting human life and nature”. The “double movement” has both its positive perspectives and risks. The main risks as Polanyi noticed were the spread of populist ideologies in societies, including fascism, and the associated threat of social instability. The consideration of the Polanyian approach with the categorical apparatus of the theory of institutional X - Y -matrices revealed the specificity of the “double movement” in Russia and China compared to the capitalist countries of the West. It is shown that in Russia and China, the scale of state participation in the economy and social control over the market, compared with Western countries, is significantly higher, which makes the economic development of these two countries more stable and predictable in the context of the continuing “era of uncertainty.” The specific risks of “double movement” for these countries were also identified associated with excessive strengthening of the unitary principle in the political system and an “overdose” of collectivist ideas to the detriment of personal aspirations and values.Scientific novelty: Identification of the specific features of the “public response” to excessive marketisation in countries where either X - or Y -institutional matrices dominate.Practical significance: The results obtained can be used as theoretical and illustrative material in courses on institutional economics and economic sociology, as well as for examining the implications of various and differing institutional designs of national economic policies

Inter-molecular structure factors of macromolecules in solution: integral equation results

The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of random phase (RPA) like structure are derived for the inter-molecular structure factor on large distances when inter-molecular excluded volume is incorporated at the microscopic level. This leads to a non-linear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents, $\nu$, above a spatial-dimension dependent value, $\nu_c=2/d$, mean field like density scaling is recovered, but for $\nu<\nu_c$ the density scaling becomes non-trivial in agreement with field theoretic results and justifying phenomenological extensions of RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large scale Monte Carlo simulations are added. Finally a new possibility to determine the correction to scaling exponent $\omega_{12}$ is suggested.Comment: 11 pages, 5 figures; to be published in Phys. Rev. E (1999

The Aggregation Kinetics of a Simulated Telechelic Polymer

We investigate the aggregation kinetics of a simulated telechelic polymer gel. In the hybrid Molecular Dynamics (MD) / Monte Carlo (MC) algorithm, aggregates of associating end groups form and break according to MC rules, while the position of the polymers in space is dictated by MD. As a result, the aggregate sizes change every time step. In order to describe this aggregation process, we employ master equations. They define changes in the number of aggregates of a certain size in terms of reaction rates. These reaction rates indicate the likelihood that two aggregates combine to form a large one, or that a large aggregate splits into two smaller parts. The reaction rates are obtained from the simulations for a range of temperatures. Our results indicate that the rates are not only temperature dependent, but also a function of the sizes of the aggregates involved in the reaction. Using the measured rates, solutions to the master equations are shown to be stable and in agreement with the aggregate size distribution, as obtained directly from simulation data. Furthermore, we show how temperature induced variations in these rates give rise to the observed changes in the aggregate distribution that characterizes the sol-gel transition.Comment: 9 pages, 10 figure

Inference of Soil Hydrologic Parameters from Electronic Soil Moisture Records

Soil moisture is an important control on hydrologic function, as it governs vertical fluxes from and to the atmosphere, groundwater recharge, and lateral fluxes through the soil. Historically, the traditional model parameters of saturation, field capacity, and permanent wilting point have been determined by laboratory methods. This approach is challenged by issues of scale, boundary conditions, and soil disturbance. We develop and compare four methods to determine values of field saturation, field capacity, plant extraction limit (PEL), and initiation of plant water stress from long term in-situ monitoring records of TDR-measured volumetric water content (Θ). The monitoring sites represent a range of soil textures, soil depths, effective precipitation and plant cover types in a semi-arid climate. The Θ records exhibit attractors (high frequency values) that correspond to field capacity and the PEL at both annual and longer time scales, but the field saturation values vary by year depending on seasonal wetness in the semi-arid setting. The analysis for five sites in two watersheds is supported by comparison to values determined by a common pedotransfer function and measured soil characteristic curves. Frozen soil is identified as a complicating factor for the analysis and users are cautioned to filter data by temperature, especially for near surface soils

Structure of Colloid-Polymer Suspensions

We discuss structural correlations in mixtures of free polymer and colloidal particles based on a microscopic, 2-component liquid state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the relevant polymer degree of freedom is the center of mass, for polymers larger than the (nano-) particles conformational rearrangements need to be considered. They have the important consequence that the polymer depletion layer exhibits two widely different length scales, one of the order of the particle radius, the other of the order of the polymer radius or the polymer density screening length in dilute or semidilute concentrations, respectively. Their consequences on phase stability and structural correlations are discussed extensively.Comment: 37 pages, 17 figures; topical feature articl