6,473 research outputs found
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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 Laplaceâs 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, Laplaceâ
Review of modern concepts in the engineering interpretation of earthquake response spectra
The design response spectrum is typically the starting point of most codified seismic design and assessment procedures and is used predominantly to prescribe the applied inertia forces induced by earthquake ground motions. This paper introduces and reviews modern concepts related to the effective development and application of earthquake design response spectra, including the conventional acceleration response spectrum, the velocity spectrum, and the displacement spectrum. It further briefly reviews the concepts of the inelastic response spectrum and the capacity spectrum. A number of the ideas presented are targeted particularly at assisting practising engineers working in low- and moderate-seismicity environments. The principal purpose is to enlighten engineers to modern concepts in response spectra development, in order to subsequently facilitate the effective use of the information contained in an earthquake response spectrum for both analysis and design applications.published_or_final_versio
The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water
We use numerical simulation to examine the possibility of a reversible
liquid-liquid transition in supercooled water and related systems. In
particular, for two atomistic models of water, we have computed free energies
as functions of multiple order parameters, where one is density and another
distinguishes crystal from liquid. For a range of temperatures and pressures,
separate free energy basins for liquid and crystal are found, conditions of
phase coexistence between these phases are demonstrated, and time scales for
equilibration are determined. We find that at no range of temperatures and
pressures is there more than a single liquid basin, even at conditions where
amorphous behavior is unstable with respect to the crystal. We find a similar
result for a related model of silicon. This result excludes the possibility of
the proposed liquid-liquid critical point for the models we have studied.
Further, we argue that behaviors others have attributed to a liquid-liquid
transition in water and related systems are in fact reflections of transitions
between liquid and crystal
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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
Negative mass corrections in a dissipative stochastic environment
We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly, gives an additional negative mass correction. The effect of the negative mass correction is illustrated by studying a harmonic oscillator interacting with a dissipative stochastic environment. While it is well known that the friction coefficient causes a reduction of the oscillation frequency, we show that the negative mass correction can lead to its enhancement. By studying an exactly solvable model of a magnet coupled to a spin environment evolving under standard non-conserving dynamics we show that the effect is present even beyond the validity of the adiabatic perturbation theory.We are grateful to M Kolodrubetz for the careful reading of the manuscript and helpful comments. This work was partially supported by BSF 2010318 (YK and AP), NSF DMR-1506340 (LD and AP), AFOSR FA9550-10-1-0110 (LD and AP), ARO W911NF1410540 (LD and AP) and ISF grant (YK). LD acknowledges the office of Naval Research. YK is grateful to the BU visitors program. (2010318 - BSF; DMR-1506340 - NSF; FA9550-10-1-0110 - AFOSR; W911NF1410540 - ARO; ISF grant)Accepted manuscrip
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
Disaggregation of spatial rainfall fields for hydrological modelling
International audienceMeteorological models generate fields of precipitation and other climatological variables as spatial averages at the scale of the grid used for numerical solution. The grid-scale can be large, particularly for GCMs, and disaggregation is required, for example to generate appropriate spatial-temporal properties of rainfall for coupling with surface-boundary conditions or more general hydrological applications. A method is presented here which considers the generation of the wet areas and the simulation of rainfall intensities separately. For the first task, a nearest-neighbour Markov scheme, based upon a Bayesian technique used in image processing, is implemented so as to preserve the structural features of the observed rainfall. Essentially, the large-scale field and the previously disaggregated field are used as evidence in an iterative procedure which aims at selecting a realisation according to the joint posterior probability distribution. In the second task the morphological characteristics of the field of rainfall intensities are reproduced through a random sampling of intensities according to a beta distribution and their allocation to pixels chosen so that the higher intensities are more likely to be further from the dry areas. The components of the scheme are assessed for Arkansas-Red River basin radar rainfall (hourly averages) by disaggregating from 40 km x 40 km to 8 km x 8 km. The wet/dry scheme provides a good reproduction both of the number of correctly classified pixels and the coverage, while the intensitiy scheme generates fields with an adequate variance within the grid-squares, so that this scheme provides the hydrologist with a useful tool for the downscaling of meteorological model outputs. Keywords: Rainfall, disaggregation, General Circulation Model, Bayesian analysi
Rare switching events in non-stationary systems
Physical systems with many degrees of freedom can often be understood in
terms of transitions between a small number of metastable states. For
time-homogeneous systems with short-term memory these transitions are fully
characterized by a set of rate constants. We consider the question how to
extend such a coarse-grained description to non-stationary systems and to
systems with finite memory. We identify the physical regimes in which
time-dependent rates are meaningful, and state microscopic expressions that can
be used to measure both externally time-dependent and history-dependent rates
in microscopic simulations.Comment: 14 pages, 8 figure
Investigating situated cultural practices through cross-sectoral digital collaborations: policies, processes, insights
The (Belfast) Good Friday Agreement represents a major milestone in Northern Ireland's recent political history, with complex conditions allowing for formation of a âcross-communityâ system of government enabling power sharing between parties representing Protestant/loyalist and Catholic/nationalist constituencies. This article examines the apparent flourishing of community-focused digital practices over the subsequent âpost-conflictâ decade, galvanised by Northern Irish and EU policy initiatives armed with consolidating the peace process. Numerous digital heritage and storytelling projects have been catalysed within programmes aiming to foster social processes, community cohesion and cross-community exchange. The article outlines two projectsââdigital memory boxesâ and âinteractive galleonââdeveloped during 2007â2008 within practice-led PhD enquiry conducted in collaboration with the Nerve Centre, a third-sector media education organisation. The article goes on to critically examine the processes involved in practically realising, and creatively and theoretically reconciling, community-engaged digital production in a particular socio-political context of academic-community collaboration
Fluctuations of water near extended hydrophobic and hydrophilic surfaces
We use molecular dynamics simulations of the SPC-E model of liquid water to
derive probability distributions for water density fluctuations in probe
volumes of different shapes and sizes, both in the bulk as well as near
hydrophobic and hydrophilic surfaces. To obtain our results, we introduce a
biased sampling of coarse-grained densities, which in turn biases the actual
solvent density. The technique is easily combined with molecular dynamics
integration algorithms. Our principal result is that the probability for
density fluctuations of water near a hydrophobic surface, with or without
surface-water attractions, is akin to density fluctuations at the water-vapor
interface. Specifically, the probability of density depletion near the surface
is significantly larger than that in bulk. In contrast, we find that the
statistics of water density fluctuations near a model hydrophilic surface are
similar to that in the bulk
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