bluuebunny/crossref_metadata_2025_split huggingface dataset:
Three‐dimensional stochastic vortex flows
Authors: Esposito R. , Pulvirenti M. , Neunzert H. 
Published: August 2005

AbstractWe discuss the stochastic structure of the Navier–Stokes flow in ℝ3 and prove that it can be approximated by means of a finite‐dimensional stochastic process. Such a process reduces to an algorithm already discussed in Reference 4 for the Euler case, when the viscosity coefficient vanishes.
Stationary solutions of the non‐linear Boltzmann equation in a bounded spatial domain
Authors: van der Mee C. V. M. , Neunzert H. 
Published: August 2005

AbstractA contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non‐linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the piecewise C1 boundary. The boundary data are to be small in a weighted L∞‐norm.
Finite element solution for the transcritical shallow‐water equations
Authors: Goutal Nicole , Nedelec J. C. 
Published: August 2005

AbstractA new solution of the two‐dimensional shallow‐water equations, using a finite element method is described. The formulation is based on the velocity and height variables and follows two steps. In the first step, the convective terms are solved by a characteristic method and in the second step the propagative and diffusion terms are taken into account. The close relation between the latter operator and a Stokes penalized problem is shown; an algorithm of Uzawa type is then used for its solution. Acceleration convergence is obtained by preconditioning, and new methods are presented, the quality of the convergence being shown on application to some sample tests. The overall method has revealed quite efficient and application to industrial cases is already planned.
Bifurcation from the essential spectrum for some non‐compact non‐linearities
Authors: Stuart C. A. , Kirchgässner K. 
Published: August 2005

AbstractConditions ensuring bifurcation from the infimum of the essential spectrum are given. The main result concerns non‐linear eigenvalue problems with variational structure in a Hilbert space. It extends previous results of a similar nature by admitting situations where the non‐linearity is not compact with respect to the graph norm of the linearization. The general result is applied to non‐linear elliptic equations on RN.
Abstract Riccati equations in an L1 space of finite measure and applications to transport theory
Authors: Juang Jonq , Nelson Paul 
Published: August 2005

AbstractWe consider operator‐valued Riccati initial‐value problems of the form R′(t) + TR(t) + R(t)T = TA(t) + TB(t)R(t) + R(t)TC(t) + R(t)TD(t)R(t), R(0) = R0. Here A to D and R0 have values as non‐negative bounded linear operators in L1 (μ), where μ is a finite measure, and T is a closed non‐negative operator in L1 (μ) satisfying additional technical conditions. For such problems the notion of strongly mild solutions is defined, and local existence and uniqueness theorems for such solutions are established. The results of the analysis are applied to the reflection kernels with both isotropically scattering homogeneous and anisotropically scattering inhomogeneous medium.
A hyperbolic singular perturbation of Burgers' equation
Authors: Esham Benjamin F. 
Published: August 2005

AbstractThis paper is concerned with the effect of perturbing Burgers' equation by a small term ϵ2 Utt. It is shown by means of an energy estimate that the solution of Burgers' equation provides a uniform O (ϵ) approximation of the solution of the full hyperbolic problem. Existence and uniqueness of classical solutions for both problems is proved. A related linear problem is first addressed using the Faedo–Galerkin method to obtain key estimates. Important for the hyperbolic problem is the introduction of an ϵ‐dependent energy in order to track the order‐ϵ behaviour of various higher‐order derivatives. Subsequent use of Schauder technique and Banach contraction mapping principle yields solutions of the semilinear problems.
The Sommerfeld half‐plane problem revisited, V: The bifurcated guide with mixed boundary conditions on the septum
Authors: Heins Albert E. 
Published: August 2005

AbstractWe discuss the solution of the boundary value problem in a duct with a centered septum [9]. On the lower wall of the duct a Neumann condition is applied while on the upper wall a Dirichlet condition is applied. On the septum we apply a Dirichlet condition on the lower side and a Neumann condition on the upper one. This problem is formulated as a pair of integral equations of the Wiener–Hopf type for which we supply solutions for two modes of excitation as well as real and complex wave number. A critical examination is made of the construction, which reduces the problem to one in complex analysis. For real wave number, the physical parameters are provided in very simple forms.
On a boundary value problem in the theory of linear water waves
Authors: Weck N. 
Published: August 2005

AbstractA body Ω floating in a fluid is subjected to small periodic displacement. Under idealized conditions the resulting wave pattern can be described by a linear boundary value problem for the Laplacian in an unbounded domain with a non‐coercive boundary condition on part of the boundary. Nevertheless uniqueness can be shown if Ω is confined to certain subsets of the fluid which can be described explicitly. This extends a result of V. G. Maz'ja saying that uniqueness holds provided that the exterior normal for ∂Ω avoids certain directions.
On critical exponents for some quasilinear parabolic equations
Authors: Levine Howard A. , Lieberman Gary M. , Meier Peter 
Published: August 2005

AbstractWe study the Cauchy problem for the quasilinear parabolic equation
magnified image
where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with − ⩽ sψ′(s)/ψ(s) ⩽ θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.
On the vanishing viscosity limit for two‐dimensional Navier–Stokes equations with singlular initial data
Authors: Marchioro Carlo 
Published: August 2005

AbstractWe study the solutions of the Navier–Stokes equations when the initial vorticity is concentrated in small disjoint regions of diameter ϵ. We prove that they converge, uniformily in ϵ. for vanishing viscosity to the corresponding solutions of the Euler equations and they are connected to the vortex model.
The scattering of electromagnetic waves by a perfectly conducting infinite cylinder
Authors: Colton David , Monk Peter 
Published: August 2005

AbstractWe consider the scattering of a plane time‐harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k, where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let FD(θ, α)k be the far‐field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let FN(θ; α)k be the far‐field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {αn}n=1∞ be a distinct set of angles in [ − π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 − μ)FD(θ;αn) + μFN(θ;αn)}n = 1∞ to be complete in L2[ − π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far‐field data.
The use of polarization effects in electromagnetic inverse scattering problems
Authors: Colton David , Kirsch Andreas 
Published: August 2005

AbstractWe consider the scattering of plane, time‐harmonic electromagnetic waves by a perfect conductor D. We first show that the set ℱλ consisting of the span of a fixed linear combination of the electric and magnetic far‐field patterns is dense in the space of square‐integrable tangential vector fields defined on the unit sphere for all values of the wave number k ≠ 0 provided that Im k ≥0. We next consider the affine hull 𝒜λ of ℱλ and characterize the set ℱ in terms of electric Herglotz fields. This result is then used to derive an optimization scheme for solving the inverse scattering problem of determining D from a knowledge of ℱλ and it is shown that this (unconstrained) optimization scheme has zero as its greatest lower bound.
The double‐layer potential operator over polyhedral domains II: Spline Galerkin methods
Authors: Elschner Johannes 
Published: August 2005

AbstractWe examine the numerical approximation of the integral equation (λ − K)u =f, where K is the double layer (harmonic) potential operator on a closed polyhedral surface in ℝ3 and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method in L2. Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a smooth surface.
A stream‐function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
Authors: Girault V. , Giroire J. , Sequeira A. 
Published: August 2005

AbstractIn this paper we derive a mixed variational formulation for the exterior Stokes problem in terms of the vorticity and stream function, or the vector potential in three dimensions. The main steps are the construction of the stream function (or vector potential) and the proof of the Babuška–Brezzi ‘inf‐sup’ condition. The two‐ and three‐dimensional cases are treated separately because the structure of the stream function differs substantially according to the number of dimensions considered. The conclusion of this work is that if the problem is set in the weighted Sobolev spaces of Hanouzet and Giroire, the analysis of the exterior Stokes problem is quite the same as if the domain were bounded.
Existence of stationary, collisionless plasmas in bounded domains
Authors: Rein Gerhard 
Published: August 2005

AbstractWe consider a collisionless plasma, which consists of electrons and positively charged ions and is confined to a bounded domain in ℝ3. The distribution functions of the particles are assumed to satisfy specular reflections on the boundary of the domain and the boundary is assumed to be perfectly conducting. We establish the existence of stationary plasmas in the non‐relativistic, electrostatic case described by the Vlasov–Poisson system as well as in the relativistic, electrodynamic case described by the relativistic Vlasov–Maxwell system.
Radially symmetric global classical solutions of non‐linear wave equations
Authors: Pecher Hartmut 
Published: August 2005

AbstractThe Cauchy problem for semilinear wave equations utt − Δu + h(|x|)up = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non‐negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.
The effects of chemically induced polarisation in the out‐of‐cage products of methyl and other alkyl radicals during the decomposition of di‐t‐butylperoxalate
Authors: Kessenikh A. V. , Ignatenko A. V. , Rykov S. V. 
Published: August 2005

AbstractThe out‐of‐cage CIDNP effects, and kinetics of the out‐of‐cage reactions between the methyl radicals and the other radicals produced from the donor admixtures have been studied during the thermal decomposition of di‐t‐butylperoxalate (DTBPO). The DTBPO decomposition proves to be a good source of methyl radicals.The CIDNP effects on the methyl protons and on the nuclei of the other alkyl radicals are determined both by the out‐of‐cage radical collisions and the kinetics of out‐of‐cage recombination.
Microscopic magnetic resonance elastography (μMRE)
Authors: Othman Shadi F. , Xu Huihui , Royston Thomas J. , Magin Richard L. 
Published: August 2005

AbstractMagnetic resonance elastography (MRE) was extended to the microscopic scale to image low‐frequency acoustic shear waves (typically less than 1 kHz) in soft gels and soft biological tissues with high spatial resolution (34 μm × 34 μm × 500 μm). Microscopic MRE (μMRE) was applied to agarose gel phantoms, frog oocytes, and tissue‐engineered adipogenic and osteogenic constructs. Analysis of the low‐amplitude shear wave pattern in the samples allowed the material stiffness and viscous loss properties (complex shear stiffness) to be identified with high spatial resolution. μMRE experiments were conducted at 11.74 T in a 56‐mm vertical bore magnet with a 10 mm diameter × 75 mm length cylindrical space available for the elastography imaging system. The acoustic signals were generated at 550–585 Hz using a piezoelectric transducer and high capacitive loading amplifier. Shear wave motion was applied in synchrony with the MR pulse sequence. The field of view (FOV) ranged from 4 to 14 mm for a typical slice thickness of 0.5 mm. Increasing the agarose gel concentration resulted in an increase in shear elasticity and shear viscosity. Shear wave motion propagated through the frog oocyte nucleus, enabling the measurement of its shear stiffness, and in vitro shear wave images displayed contrast between adipogenic and osteogenic tissue‐engineered constructs. Further development of μMRE should enable its use in characterizing stiffer materials (e.g., polymers, composites, articular cartilage) and assessing with high resolution the mechanical properties of developing tissues. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Quantifying dynamic contrast‐enhanced MRI of the knee in children with juvenile rheumatoid arthritis using an arterial input function (AIF) extracted from popliteal artery enhancement, and the effect of the choice of the AIF on the kinetic parameters
Authors: Workie Dagnachew W. , Dardzinski Bernard J. 
Published: August 2005

AbstractQuantification of dynamic contrast‐enhanced (DCE) MRI based on pharmacokinetic modeling requires specification of the arterial input function (AIF). A full representation of the plasma concentration data, including the initial rise and decay parts, considering the delay and dispersion of the bolus contrast is important. This work deals with modeling of DCE‐MRI data from the knees of children with a history of juvenile rheumatoid arthritis (JRA) by using an AIF extracted from the signal enhancement data from the nearby popliteal artery. Three models for the AIFs were considered: a triexponential (AIF1), a gamma‐variate plus a biexponential (AIF2), and a biexponential (AIF3). The pharmacokinetic parameters obtained from the model were Ktrans′, kep, and V. The results from AIF1 and AIF2 showed no statistically significant difference. However, some statistically significant differences were seen with AIF3, particularly for parameters Ktrans′ and V in the synovium (SNVM). These results suggest the importance of obtaining an appropriate AIF representation in pharmacokinetic modeling of JRA. Specifically, the initial rising part of the AIF should be incorporated for optimal pharmacokinetic modeling results. The pharmacokinetic parameters (mean ± SD) derived from AIF1, using the average plasma concentration data, were as follows: SNVM Ktrans′(min−1) = 0.52 ± 0.34, kep(min−1) = 0.71 ± 0.39, and V = 0.33 ± 0.16, and for the distal femoral physis (DFP) Ktrans′(min−1) = 1.83 ± 1.78, kep(min−1) = 2.65 ± 1.80, and V = 0.46 ± 0.31. The pharmacokinetic parameters in the SNVM may be useful for investigating activity and therapeutic efficacy in studies of JRA. Longitudinal studies are necessary to find or demonstrate the parameter that is more sensitive to disease activity. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Improved data reconstruction method for GRAPPA
Authors: Wang Ze , Wang Jiongjiong , Detre John A. 
Published: August 2005

AbstractThis paper presents an improved data reconstruction method for generalized autocalibrating partially parallel acquisitions (GRAPPA) using multicolumn multiline interpolation (MCMLI). Both nearest acquired line (ky) neighboring points and column (kx) neighboring points from all components of an array coil were used to reconstruct each missing datum through interpolation. A new fitting scheme was designed to estimate the interpolation weights. Both simulations and in vivo experiments demonstrated that the proposed method yields higher‐quality data reconstruction than the original GRAPPA method, especially with high acceleration factors. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Practical approaches to the evaluation of signal‐to‐noise ratio performance with parallel imaging: Application with cardiac imaging and a 32‐channel cardiac coil
Authors: Reeder Scott B. , Wintersperger Bernd J. , Dietrich Olaf , Lanz Titus , Greiser Andreas , Reiser Maximilian F. , Glazer Gary M. , Schoenberg Stefan O. 
Published: August 2005

AbstractIn this work, two practical methods for the measurement of signal‐to‐noise‐ratio (SNR) performance in parallel imaging are described. Phantoms and human studies were performed with a 32‐channel cardiac coil in the context of ultrafast cardiac CINE imaging at 1.5 T using steady‐state free precession (SSFP) and TSENSE. SNR and g‐factor phantom measurements using a “multiple acquisition” method were compared to measurements from a “difference method”. Excellent agreement was seen between the two methods, and the g‐factor shows qualitative agreement with theoretical predictions from the literature. Examples of high temporal (42.6 ms) and spatial (2.1 × 2.1 × 8 mm3) resolution cardiac CINE SSFP images acquired from human volunteers using TSENSE are shown for acceleration factors up to 7. Image quality agrees qualitatively with phantom SNR measurements, suggesting an optimum acceleration of 4. With this acceleration, a cardiac function study consisting of 6 image planes (3 short‐axis views, 3 long‐axis views) was obtained in an 18‐heartbeat breath‐hold. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Transmitting boundaries: A comparison
Authors: Roesset José M. , Ettouney Mohammed M. 
Published: August 2005

AbstractThe use of discrete models for the dynamic analysis of a contiuum requires the existence of a finite domain with well defined boundaries. When these boundaries do not exist naturally but have to be artificially imposed it may be necessary to apply appropriate conditions on forces or displacements at the boundary nodes to reproduce the physical behaviour of the actual problem. In the solution of soil structure interaction problems these conditions are simulated through the use of transmitting boundaries. In this paper several of these boundaries are evaluated comparing the results they produce in the amplification of seismic motions, the determination of foundation stiffnesses and the structural response. The distance of the boundaries to the zone of interest, the level of excitation (influencing the amount of internal soil damping), the geometry of the problem (finite soil layer versus a half‐space) and the relative frequency of the structure with respect to the soil and the specified motion are all parameters which must be taken into account for this evaluation.
Seepage flow problems by variational inequalities: Theory and approximation
Authors: Kikuchi Noboru 
Published: August 2005

AbstractThe theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h1.25‐δ), 0 < δ < 0.25, respectively, if the permeability is constant.
Finite element simulation of freezing processes in soils
Authors: Del Giudice S. , Comini G. , Lewis R. W. 
Published: August 2005

AbstractThe finite element method, formulated for non‐linear heat conduction, allows the solution of practically any ground freezing problem. Stabilization of wet soils by artificial freezing and freezing under roads induced by cold winter conditions are considered in this paper.Special features of the program used include parabolic isoparametric elements, a new time stepping scheme and an improved procedure for the estimation of thermal properties.
Strain‐softening of brittle geologic materials
Authors: Sture Stein , Ko Hon‐Yim 
Published: August 2005

AbstractStability equations for a strain‐softening system are derived from expressions describing the energy variation in a variable stiffness stiff testing machine and a brittle rock specimen. A normal strain‐softening expression and a shear strain‐softening expression are derived to predict the stability of laboratory tests on brittle rocks, which through machine stiffness adjustment, exhibited critical stability in the strain‐softening range. From these comparisons it was found that the shear strain‐softening model gave consistently good results. The analytical and laboratory modelling indicates that strain‐softening in brittle geologic media is closely connected with joints, faults, and interfaces where shear distortions take place.
Dynamic response of elastic plates on the surface of the half‐space
Authors: Savidis S. A. , Richter T. 
Published: August 2005

AbstractA ‘mixed method’ for the dynamic calculation of foundations on soil is presented. The half‐space is computed analytically, the foundation with finite elements. The method is very well suited for the solution of three‐dimensional problems including interaction. Numerical results for a simple case involving a dynamically loaded elastic plate are presented and the influence of plate stiffness is studied.
Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity
Authors: Carter J. P. , Randolph M. F. , Wroth C. P. 
Published: August 2005

AbstractThe disturbance of a clay mass, due to either the installation of a driven pile or the expansion of a pressuremeter membrane, is often modelled as a cylindrical cavity expansion. In addition, it is usual (and convenient) to assume that the expansion occurs under conditions of plane strain. For this problem a method of analysis is presented which considers the soil to be a saturated two‐phase material with a pore fluid which flows according to Darcy's Law. Non‐linearity in material behaviour is permitted as long as the effective stress–strain law can be written in an incremental or rate form. The use of a consolidation analysis allows the changes in effective stress and pore pressure to be determined at any stage during both the cavity expansion and the subsequent period of reconsolidation. Expansions may occur at any prescribed rate, including the very fast (undrained) and the very slow (fully drained) case. The technique is illustrated by considering the expansion of a cavity in two different types of elastoplastic soil. It is shown how these solutions may be used to model the disturbance of the soil due to pile driving.