asymptotic Analysis

The Sweet-Parker layer in a system that exceeds a critical value of the Lundquist number ͑S͒ is unstable to the plasmoid instability. In this paper, a numerical scaling study has been done with an island coalescing system driven by a low level of random noise. In the early stage, a primary Sweet-Parker layer forms between the two coalescing islands. The primary Sweet-Parker layer breaks into multiple plasmoids and even thinner current sheets through multiple levels of cascading if the Lundquist number is greater than a critical value S c Ӎ 4 ϫ 10 4 . As a result of the plasmoid instability, the system realizes a fast nonlinear reconnection rate that is nearly independent of S, and is only weakly dependent on the level of noise. The number of plasmoids in the linear regime is found to scales as S 3/8 , as predicted by an earlier asymptotic analysis ͓N. F. Loureiro et al., Phys. Plasmas 14, 100703 ͑2007͔͒. In the nonlinear regime, the number of plasmoids follows a steeper scaling, and is proportional to S. The thickness and length of current sheets are found to scale as S −1 , and the local current densities of current sheets scale as S −1 . Heuristic arguments are given in support of theses scaling relations.

We investigate the critical speeding up of heat equilibration by the piston effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a homogeneous porous medium. We perform an asymptotic analysis of the averaged linearized mass, momentum and energy equations to describe the response of the medium to a boundary heat flux. While nearing the critical point (CP), we find two universal crossovers depending on porosity, intrinsic permeability and viscosity. Closer to the CP than the first crossover, a pressure gradient appears in the bulk due to viscous effects, the PE characteristic time scale stops decreasing and tends to a constant. In infinitly long samples the temperature penetration depth is larger than the diffusion one indicating that the PE in porous media is not a finite size effect as it is in pure fluids. Closer to the CP, a second cross over appears which is characterized by a pressure gradient in the thermal boundary layer (BL). Beyond this second crossover, the PE time remains constant, the expansion of the fluid in the BL drops down and the PE ultimately fades away.

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( ${\mathop a\limits^ \cdot }$ ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar ${\mathop a\limits^ \cdot }$ -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

The asymptotic structure of laminar, moderately rich, premixed methane flames is analyzed using a reduced chemical-kinetic mechanism comprising four global reactions. This reduced mechanism is different from those employed in previous asymptotic analyses of stoichiometric and lean flames, because a steady-state approximation is not introduced for CH 3 . The aim of the present analysis is to develop an asymptotic model for rich flames, which can predict the rapid decrease of the burning velocity with increasing equivalence ratio . In the analysis, the flame structure is presumed to consist of three zones: a preheat zone with a normalized thickness of the order of unity, a thin reaction zone, and a postflame zone. The preheat zone is presumed to be chemically inert, and in the postflame zone the products are in chemical equilibrium and the temperature is equal to the adiabatic flame temperature T b . In the reaction zone the chemical reactions are presumed to take place in two layers: the inner layer and the oxidation layer. The rate constants of these reactions are evaluated at T 0 , which is the characteristic temperature at the inner layer. In the inner layer the dominant reactions taking place are those between the fuel and radicals, and between CH 3 and the radicals. An important difference between the structure of the inner layer of rich flames and that of lean flames analyzed previously is the enhanced influence of the chain-breaking reaction CH 3 ϩ H ϩ (M) 3 CH 4 ϩ (M) in rich flames. Here M represents any third body. This reaction decreases the concentration of H radicals, which in turn decreases the values of the burning velocity. In the oxidation layer of rich flames, the reactive-diffusive balance of O 2 is considered. This differs from the structure of the oxidation layer of lean flames where the reactive-diffusive balance of H 2 and CO was of primary interest. The burning velocities calculated using the results of the asymptotic analysis agree reasonably well with the burning velocities calculated numerically using chemical-kinetic mechanisms made up of elementary reactions. The values of the characteristic temperature at the inner layer T 0 are found to increase with increasing values of the equivalence ratio and to approach T b at ϭ 1.36. When T 0 is very close to T b , the asymptotic analysis developed here is no longer valid and an alternative asymptotic analysis must be developed for even larger equivalence ratios.

We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the history of the interaction and developed within the confines of the problem of double contingency. We examine interaction strategies in the light of the message-exchange description using analytical and computational methods.

As shown by Dufour, Khalaf, Brenard and Genest, exact tests for heteroskedasticity can be obtained, by using Monte Carlo (MC) techniques, if it is assumed that the true form of the error distribution under the null hypothesis is known. The corresponding nonparametric bootstrap tests are only asymptotically valid, but do not require speci…cation of the error law. Since information about the precise form of the error distribution is not often available to applied workers, two questions merit attention. First, how robust are MC tests to incorrect assumptions about the error distribution? Second, are nonparametric bootstrap tests markedly inferior to MC tests when the latter use the correct error distribution? Results relevant to these two questions are derived using asymptotic analysis and simulation experiments. The evidence suggests that the combination of an asymptotically pivotal test statistic with a nonparametric bootstrap gives a robust and well-behaved procedure.

In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two elastic structures. The glue is supposed to be elastic and to have its stiffness of the same order than those of the elastic structures. An original numerical method is developed to solve the mechanical problem of stiff interface at order 1, based on the Nitsche's method. Several numerical examples are provided to show the efficiency of both the analytical approximation and the numerical method.

A field method is proposed for determining the three-dimensional hydraulic conductivity tensor and specific storage of an anisotropic porous or fractured medium. The method, known as cross-hole testing (to distinguish it from conventional single-hole packer tests), consists of injecting fluid into (or withdrawing fluid from) packed-off intervals in a number of boreholes and monitoring the transient head response in similar intervals in neighboring boreholes. The directions of the principal hydraulic conductivities need not be known prior to the test, and the boreholes may have arbitrary orientations (e.g., they can all be vertical). An important aspect of the proposed method is that it provides direct field information on whether it is proper to regard the medium as being uniform and anisotropic on the scale of the test. The first paper presents theoretical expressions describing transient and steady state head response in monitonng intervals of arbitrary lengths and orientations, to constant-rate injection into (or withdrawal from) intervals having similar or different lengths and orientations. The conditions under which these intervals can be treated mathematically as points are • investigated by an asymptotic analysis. The effect of planar no-flow and constant-head boundaries on the response is analyzed by the theory of images. The second paper describes the field methodology and shows how the proposed approach works in the case of fractured granitic rocks.

The steady-state simplified P N approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified P N (SP N ) equations (up to N = 3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SP N equations. Second, we use an approach similar to the original derivation of the steady-state SP N equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium

A call center is a service operation that caters to customer needs via the telephone. Call centers typically consist of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents.

We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function approach for a bivariate model, that

This paper addresses the problem of signal parameter estimation of narrow-band emitter signals impinging on an array of sensors. A multidimensional estimation procedure is proposed, which applies to arbitrary array structures and signal correlation. The method is based on the recently introduced weighted subspace fitting (WSF) criterion, and includes schemes for both detecting the number of sources and estimating the signal parameters. A Gauss-Newton type algorithm is suggested for minimizing the WSF criterion. A new detection scheme is also formulated based on the asymptotic distribution of the WSF cost function. Strong consistency of the detection algorithm is proved for arbitrary signal correlation, including coherence. The WSF detection method is compared to a recently proposed information theoretic approach, and found to provide a significant improvement for high signal correlation scenarios. Simulations are carried out comparing the proposed WSF technique to the deterministic maximum likelihood (ML) method. The WSF scheme is found to be limited only by the estimation accuracy and not by the initialization or detection. This does not appear to be true for the ML method.

The purpose of this paper is to derive and study a new asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. In the asymptotic process, the thickness of the piezoelectric plate is driven to zero and the convergence of the unknowns is studied. This leads to two-dimensional Kirchhoff-Love plate equations, in which mechanical displacement and electric potential are partly decoupled. Based on this model numerical examples are presented that illustrate the mutual interaction between the mechanical displacement and the electric potential. We observe that, compared to purely elastic materials, piezoelectric bodies yield a significantly different contact behavior.

The ''double cleavage drilled compression" specimen is used for the determination of crack growth rates under mode-I and general mixed-mode loading conditions. In this paper, a fracture mechanics analysis is presented for the DCDC specimen, using a finite-element analysis to determine stresses, strains and surface displacements. Weight functions are derived, and the consequence of load misalignment is demonstrated. Finally, side-surface displacements at the crack terminating region are studied using a 3-dimensional, finiteelement computation in combination with results from the literature that are based on an ''asymptotic analysis". Calculated side-surface displacements in the vicinity of the crack tip are found to agree with published values obtained by others via measurements using the atomic force microscope.

A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures.

Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any fixed t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive limiting distributions for T_{N(t)} by assuming some convergence properties for the counting process. This is even achieved when both the numerator and the denominator defining T_{N(t)} exhibit an erratic behavior (\mathbb{E}X_1=\infty) or when only the numerator has an erratic behavior (\mathbb{E}X_1<\infty and \mathbb{E}X_1^2=\infty). Thanks to these results, we obtain asymptotic properties pertaining to both the sample coefficient of variation and the sample dispersion.

s Abstract Filament-stretching rheometers are devices for measuring the extensional viscosity of moderately viscous non-Newtonian fluids such as polymer solutions. In these devices, a cylindrical liquid bridge is initially formed between two circular end-plates. The plates are then moved apart in a prescribed manner such that the fluid sample is subjected to a strong extensional deformation. Asymptotic analysis and numerical computation show that the resulting kinematics closely approximate those of an ideal homogeneous uniaxial elongation. The evolution in the tensile stress (measured mechanically) and the molecular conformation (measured optically) can be followed as functions of the rate of stretching and the total strain imposed. The resulting rheological measurements are a sensitive discriminant of molecularly based constitutive equations proposed for complex fluids. The dynamical response of the elongating filament is also coupled to the extensional rheology of the polymeric test fluid, and this can lead to complex viscoelastic-flow instabilities such as filament necking and rupture or elastic peeling from the rigid end-plates.

In this book, the author has documented his lecture notes on computational fluid dynamics ͑CFD͒ which he has developed over the past 20 years to form this textbook. This textbook is intended for senior undergraduate and first-year graduate students who will be developing or using codes in the numerical simulation of fluid flows or other physical phenomena governed by partial differential equations. The book is organized into 11 chapters. The fundamental numerical methods discussed in this book are based on the finite difference method as a method of discretization on Cartesian mesh systems, in the physical domain, or in the computational domain after coordinate transformation. The author has discussed the finite volume method for discretization for arbitrary mesh systems including unstructured meshes. The fundamental theory and techniques are presented in Chapter 2, which include the Taylor expansion and the complex mode analysis. Further, the accuracy and stability analyses for these methods are also discussed. The ordinary differential equations ͑ODEs͒ and their integration are given in Chapter 3. The general discussions of PDEs are given in Chapter 4, which include the discussions on the type and classifications of PDEs and the concepts of characteristic surfaces, computational relations, and the jump conditions associated with conservation laws. The connection between the physical phenomena of wave propagation,

This paper presents an overview of the cohesive crack model, one of the basic models used so far to describe the fracture of concrete and other quasibrittle materials. Recent developments and needs for further research are discussed. The displayed evidence and the discussion are based on considering the cohesive crack model as a constitutive assumption rather than an ad hoc model for the behaviour ahead of a preexisting crack. Topics addressed are fracture of unnotched specimens, mixed mode fracture, diffuse cracking, anomalous stress-strain curves, size effect and asymptotic analysis, and strength of structural elements with notches.

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter ε > 0 while the distance of the body to the water surface is also of order ε. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely, it is proved that, for any given d > 0 and integer N > 0, there exists ε(d, N ) > 0 such that the problem has at least N eigenvalues in the interval (0, d) of the continuous spectrum in the case ε ∈ (0, ε(d, N )). The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes.

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with timeperiodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.  2004 Elsevier Inc. All rights reserved.

In this paper we perform asymptotic analysis of the compressible viscous isothermal flow in a periodic domain. We start our analysis by studying the compressible Stokes system in a thin domain of thickness ε 1. As ε tends to zero we obtain the effective behavior of the flow, i.e. the Reynolds model, known from engineering literature, that describes the flow of a gas lubricant. Uniqueness of the solution to Reynolds equations is discussed as well.

In this paper, we present asymptotic theory as a viable alternative solution method for infectious disease models. We consider a particular model of a pathogen attacking a host whose immune system responds defensively, that has been studied previously [Mohtashemi and Levins in J. Math. Biol. 43: 446-470 (2001)]. On rendering this model dimensionless, we can reduce the number of parameters to two and note that one of them has a large value that suggests an asymptotic analysis. On doing this analysis, we obtain a satisfying qualitative description of the dynamic evolution of each population, together with simple analytic expressions for their main features, from which we can compute accurate quantitative values.

In a recent article (Larsen, Morel, and Miller, J .Comput. Phys. 69, 283 (1987)), a theoretical method is described for assessing the accuracy of transport differencing schemes in highly scattering media with optically thick spatial meshes. In the present article, this method is extended to enable one to determine the accuracy of such schemes in the presence of numerically unresolved boundary layers. Numerical results are presented that demonstrate the validity and accuracy of our analysis.

To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations. Its main idea is to model solid obstacles as porous media with porosity, /, and viscous permeability approaching zero. It has the pronounced advantages of mathematical proof of error bound, strong convergence, and ease of numerical implementation with the volume penalization technique. In this paper, it is extended to compressible flows. The straightforward extension of penalizing momentum and energy equations using Brinkman penalization with respective normalized viscous, g, and thermal, g T , permeabilities produces unsatisfactory results, mostly due to nonphysical wave transmissions into obstacles, resulting in considerable energy and mass losses in reflected waves. The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media. In addition to penalizing momentum and energy equations, the continuity equation for porous media is considered inside obstacles. In this model, the penalized porous region acts as a high impedance medium, resulting in negligible wave transmissions. The asymptotic analysis reveals that the proposed Brinkman penalization technique results in the amplitude and phase errors of order O((g/) 1/2 ) and O((g/g T ) 1/4 / 3/4 ), when the boundary layer within the porous media is respectively resolved or unresolved. The proposed method is tested using 1-and 2-D benchmark problems. The results of direct numerical simulation are in excellent agreement with the analytical solutions. The numerical simulations verify the accuracy and convergence rates.

We consider the eigenvalue problem associated to the vibrations of a string with rapidly oscillating periodic density. In a previous paper we stated asymptotic formulas for the eigenvalues and eigenfunctions when the size of the microstructure is shorter than the wavelength of the eigenfunctions 1/ √ λ . On the other hand, it has been observed that when the size of the microstructure is of the order of the wavelength of the eigenfunctions ( ∼ 1/ √ λ ) singular phenomena may occur. In this paper we study the behavior of the eigenvalues and eigenfunctions when 1/ √ λ is larger than the critical size . We use the WKB approximation which allows us to find an explicit formula for eigenvalues and eigenfunctions with respect to . Our analysis provides all order correction formulas for the limit eigenvalues and eigenfunctions above the critical size.

We consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations. A solution over a length of time that is inversely proportional to δ > 0 (where δ > 0 is a small disturbance of the pre-ignition state) is sought. This problem has a transient at the midpoint of the integration interval. The solution changes from being non-stiff to stiff, and afterwards becomes non-stiff again. We provide its asymptotic and numerical solution obtained via a variety of methods. Comparisons are made for the numerical results which we obtain with the MATLAB ode solvers (ode45, ode15s and ode23s) and some nonstandard finite difference methods. Results corresponding to standard finite difference method are also presented. Furthermore, the discussion on these approaches along with the others, provides several open problems for new and young researchers.

The Neumann problem for the Poisson equation is considered in a domain Ω ε ⊂ R n with boundary components posed at a small distance ε > 0 so that in the limit, as ε → 0 + , the components touch each other at the point O with the tangency exponent 2m ≥ 2. Asymptotics of the solution u ε and the Dirichlet integral x u ε ; L 2 (Ω ε) 2 are evaluated and it is shown that main asymptotic term of uε and the existence of the finite limit of the integral depend on the relation between the spatial dimension n and the exponent 2m. For example, in the case n < 2m − 1 the main asymptotic term becomes of the boundary layer type and the Dirichlet integral has no finite limit. Some generalization are discussed and certain unsolved problems are formulated, in particular, non-integer exponents 2m and tangency of the boundary components along smooth curves. AMS subject classification: primary 35J25, secondary 46E35,35J20.

A new approach is presented for modeling steady combustion of energetic solids, in particular HMX. A simplified, global, gas phase chain reaction kinetic mechanism is employed. Specifically, a zero-order, high activation energy thermal decomposition initiation reaction in the condensed phase followed by a second-order, low activation energy chain reaction in the gas phase is assumed. A closed-form solution is obtained, which is based on the activation energy asymptotics analysis of Lengelle in the condensed phase and the assumption of zero activation energy in the gas phase. Comparisons between the model and a variety of experimental observations over a wide range of pressures and initial temperatures are presented and demonstrate the validity of the approach. The model provides excellent agreement with burning rate data (including sensitivity to pressure and initial temperature) and temperature profile data (in particular the gas phase). This suggests that in the realm of simplified, approximate kinetics modeling of energetic solids, the low gas phase activation energy limit is a more appropriate model than the classical high activation energy limit or heuristic flame sheet models. The model also indicates that the condensed phase reaction zone plays an important role in determining the deflagration rate of HMX, underscoring the need for better understanding of the chemistry in this zone.

In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as highorder terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution.

Conventionally, in each low-density parity-check (LDPC) decoding iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (flooding schedule). An alternative, more efficient, approach is to update the nodes' messages serially (serial schedule). A theoretical analysis of serial message passing decoding schedules is presented. In particular, the evolution of the computation tree under serial scheduling is analyzed. It shows that the tree grows twice as fast in comparison to the flooding schedule's one, indicating that the serial schedule propagates information twice as fast in the code's underlying graph. Furthermore, an asymptotic analysis of the serial schedule's convergence rate is done using the density evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that for long codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule, when working near the ensemble's threshold. This observation is generally proved for the binary erasure channel (BEC) under some natural assumptions. Finally, an accompanying concentration theorem is proved.

This paper performs an asymptotic analysis of penalized spline estimators. We compare P -splines and splines with a penalty of the type used with smoothing splines. The asymptotic rates of the supremum norm of the difference between these two estimators over compact subsets of the interior and over the entire interval are established. It is shown that a Pspline and a smoothing spline are asymptotically equivalent provided that the number of knots of the P-spline is large enough, and the two estimators have the same equivalent kernels for both interior points and boundary points.

Abstract. We consider multiprocessing systems where processes make independent, Poisson distributed resource requests with mean arrival time 1. We assume that resources are not released. It is shown that the expected deadlock time is never less than 1, no matter how many processes and resources are in the system. Also, the expected number of processes blocked by deadlock time is one-half more than half the number of initially active processes. We obtain expressions for system statistics such as expected deadlock time, expected total processing time, and system efficiency, m terms of Abel sums. We derive asymptotic expressions for these statistics in the case of systems with many processes and the case of systems with a fixed number of processes. In the latter, generahzations of the Ramanujan Q-function arise. We use singularity analysis to obtain asymptotlcs ot coefficients of generalized Q-functions.

We consider a magnetic Schrödinger operator H h = (−ih∇ − A) 2 with the Dirichlet boundary conditions in an open set Ω ⊂ R 3 , where h > 0 is a small parameter. We suppose that the minimal value b 0 of the module | B| of the vector magnetic field B is strictly positive, and there exists a unique minimum point of | B|, which is non-degenerate. The main result of the paper is upper estimates for the low-lying eigenvalues of the operator H h in the semiclassical limit. We also prove the existence of an arbitrary large number of spectral gaps in the semiclassical limit in the corresponding periodic setting.

The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g. in microfluidic pumps and electrochemical sensors. Since the 1950s, several modifications of the PB equation have been proposed to account for the finite size of ions in equilibrium, but in this two-part series, we consider steric effects on diffuse charge dynamics (in the absence of electro-osmotic flow). In this first part, we review the literature and analyze two simple models for the charging of a thin double layer, which must form a condensed layer of close-packed ions near the surface at high voltage. A surprising prediction is that the differential capacitance typically varies non-monotonically with the applied voltage, and thus so does the response time of an electrolytic system. In PB theory, the capacitance blows up exponentially with voltage, but steric effects actually cause it to decrease above a threshold voltage where ions become crowded near the surface. Other nonlinear effects in PB theory are also strongly suppressed by steric effects: The net salt adsorption by the double layers in response to the applied voltage is greatly reduced, and so is the tangential "surface conduction" in the diffuse layer, to the point that it can often be neglected compared to bulk conduction (small Dukhin number).

The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied over erasure channels and the binary symmetric channel. The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic softdecision decoding over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional Berlekamp-Massey decoding. As an application, a bit-level generalized minimum distance decoding algorithm is proposed. The proposed decoding compares favorably with many other Reed-Solomon soft-decision decoding algorithms over various channels. Moreover, owing to the simplicity of the proposed bit-level generalized minimum distance decoding, its performance can be tightly bounded using order statistics.

When the coating film around a vertical fibre exceeds a critical thickness hc, the interfacial disturbances triggered by Rayleigh instability can undergo accelerated growth such that localized drops much larger in dimension than the film thickness appear. We associate the initial period of this strongly nonlinear drop formation phenomenon with a self-similar intermediate asymptotic blow-up solution to the long-wave evolution equation which describes how static capillary forces drain fluid into the drop. Below hc, we show that strongly nonlinear coupling between the mean flow and axial curvature produces a finite-amplitude solitary wave solution which prevents local finite-time blow up and hence disallows further growth into drops. We thus estimate hc by determining the existence of solitary wave solutions. This is accomplished by a matched asymptotic analysis which joins the capillary outer region of a large solitary wave to the thin-film inner region. Our estimate of hc = 1.68R3H–2...

In this thesis, the coupled flow of a Newtonian fluid both above and through a porous medium is considered. This work was motivated from a pulp and paper application, namely twin-wire forming. In the fluid-only region, the two-dimensional flow field is governed by the Navier-Stokes equation. In the porous region, the flow field is governed by the Brinkman-extended Darcy law relationship. Inertial terms are retained in both regions and the interface conditions between the two domains are those as outlined by Ochoa