bluuebunny/crossref_metadata_2025 huggingface dataset:
Fractional Calculus Operators Involving the Gauss Function on Spaces Fp,μand F'p,μ
Authors: Saigo Megumi , Glaeske Hans‐Jürgen
Published: November 2010

This paper deals with the study of operators of fractional calculus introduced by Saigo in spaces of generalized functions considered by McBride.
P‐Regular Convergence Spaces
Authors: Kent D. C. , Richardson G. D.
Published: November 2010

A generalized notion of regularity is introduced which enables one to study locally compact spaces, sequential spaces, ω‐regular spaces, and other diverse types of spaces as special wises of p‐regular spaces.
Uniqueness of Solutions to the Systems for Thermoelastic Bodies with Strong Viscosity
Authors: Nečas, J. , Novotný A. , Sčverák V.
Published: November 2010

Under some assumptions on regularity of the initial data the uniqueness theorem to the system for thermoelastic bodies is proved.
Mean Values of Weighted Cells of Stationary Poisson Hyperplane Tessellations of IRd
Authors: Favis Wassilis , Weiß Viola
Published: November 2010

This paper deals with stationary Poisson hyperplane tessellations. Weighted distributions are considered, where the weights are the volume of the cell and the total volume of all faces of the cell. A randomly chosen cell according to such a weighted distribution will be called volume weighted cell and face content weighted cell, respectively. Mean values of cell characteristics for such weighted cells are calculated. These results are connected with second‐order quantities for the typical cell of a stationary Poisson hyperplane tessellation. There are no suppositions to the isotropy of the tessellation, stationarity is sufficient. In case of isotropy already known results for planar tessellations from [AMS], [Mi1] and [Mi2] will be confirmed. A stereological interpretation of weighted cells is given by the aid of suitable intersections.
Tauberian Theorems for Sequences linked by a Convolution
Authors: Warlimont Richard
Published: November 2010

Given sequences g, λ: IN0 → C, g (0) = 1, linked by the convolution λ g = g′1 (g′1(n)= (n + 1) g (n + 1)) we study what can be inferred about λ (n → ∞) from some concrete information about the behaviour of g (n → ∞).
Oscillation of a Class of Higher Order Neutral Differential Equations
Authors: Yang Bo , Zhang B. G.
Published: November 2010

In this paper, we consider the following equationwherep(t)⩾ 0. We give some new oscillation conditions for Eq. (I).
A New Proof of a Theorem of Beorchia on the Genus of Space Curves
Authors: Schlesinger Enrico
Published: November 2010

We give a new proof of a theorem of Beorchia which provides a bound P(d, t) for the maximum genus of a locally Cohen ‐ Macaulay space curve of degree d which does not lie on a surface of degree t ‐ 1.
Asymptotics of Heat Kernels on Projective Spaces of Large Dimensions and on Disk Hypergroups
Authors: Voit Michael
Published: November 2010

In this note we give exact asymptotic rates of convergence of Brownian motions on complex and quaternionic projective spaces to the uniform distribution when the dimension of these spaces tends to infinity. Similar results are also established for the symmetric spaces U(n)/U(n‐1) and disk hypergroups. Proofs will be based on a comparision of heat kernels with Poisson kernels together with a central limit result for Poisson kernels.
On the Eigenvalue Behaviour for a Class of Differential Operators on Semiaxis
Authors: Birman M. Sh. , Laptev A. , Solomyak M.
Published: November 2010

We study the eigenvalue behaviour of a class of ODE acting on the semiaxis. Using interpolation of quasinormed spaces as one of our main tools, we obtain sharp estimates of the counting function of eigenvalues n(λ). In particular, some of our results become reversible if a matrix‐valued “weight” ‐function is nonnegative. The asymptotic behaviour of n(λ) is also discussed.
Absolute Continuity for Curvature Measures of Convex Sets I
Authors: Hug Daniel
Published: November 2010

Let us denote by Cr(K, ·), r ∈ {0,…, d ‐ 1}, the curvature measures of a convex body K in the Euclidean space ℝd with d ≥ 2. According to Lebesgue's decomposition theorem the curvature measure of order r of K, Cr(K, ·), can be written as the sum of an absolutely continuous measure, Car(K, ·), and a singular measure, Csr(K, ·), with respect to (d ‐ 1) ‐ dimensional Hausdorff measure. For example, if K is a polytope, then Car(K, ·) = 0 and if K is sufficiently smooth, then Csr(K, ·) = 0. For a general convex body K, a description of Car(K, ·) in terms of geometric quantities is known. In the present paper, we provide a corresponding explicit representation for the singular part Csr(K, .). Further, denote by Σr (K) the set of r‐singular boundary points of the convex body K· It is known that Σr(K) has σ‐finite, but possibly infinite, r ‐ dimensional Hausdorff measure. Provided that the singular part Csr(K, ·) of the curvature measure of order r vanishes, for a given convex body K, we prove that the r ‐ dimensional Hausdorff measure of Σr (K) also vanishes. Examples show that in a certain sense this result is sharp. Analogous results are established for surface area measures and singular normal vectors.
Hypersurfaces of E4 with Harmonic Mean Curvature Vector
Authors: Leuven Filip Defever Of
Published: November 2010

A submanifold Mn of a Euclidean space Em is said to have harmonic mean curvature vector field if Δ H, where H denotes the mean curvature vector. B.‐Y. Chen conjectured that the only submanifolds of Euclidean spaces with harmonic mean curvature vector field, are the minimal ones. In this paper, we give a proof of the theorem that every hypersurface of E4 with harmonic mean curvature vector field is minimal. The method gives insight in the role of the principal curvatures.
Translative and Kinematic Formulae for Curvature Measures of Flat Sections
Authors: Rataj Jan
Published: November 2010

Let X be a set of positive reach in the d‐dimensional Euclidean space. We present formulae for the integrals of the curvature measures of flat sections of X with respect to all translations/Euclidean motions of the sectioning flat. We consider the (generalized) curvature measures supported by the corresponding unit normal bundle. As a special case we obtain formulae for the spherical area measures.
Changes of Variable in Besov Spaces
Authors: Bourdaud Gerard , Sickel Winfried
Published: November 2010

We characterize the set of all homeomorphisms π such that the mapping f → f o π is bounded on a homogeneous or inhomogeneous Besov space (0 < s < 1).
Inertia Theorems for Hilbert Space Operators Based on Lyapunov and Stein Equations
Authors: Lerer Leonid , Rodman Leiba
Published: November 2010

Inequalities between the inertias of X and of A, are proved for Hilbert space operators X = X* and A such that AX + XA* is positive semidefinite or such that X ‐ A* XA is positive semidefinite. A weak version of the controllability property is assumed.
Asymptotic Theory for a General Fourth ‐ Order Differential Equation
Authors: Al‐Hammadi A. S. A.
Published: November 2010

An asymptotic theory is developed for a general fourth‐order differential equation. The theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.
On the Relation between Linear Difference and Differential Equations with Polynomial Coefficients
Authors: Immink G. K.
Published: November 2010

This paper represents the third part of a contribution to the “dictionary” of homogeneous linear differential equations with polynomial coefficients on one hand and corresponding difference equations on the other. In the first part (cf. [4]) we studied the case that the differential equation (D) has at most regular singularities at O and at ∞, and arbitrary singularities in the rest of the complex plane. We constructed fundamental systems of solutions of a corresponding difference equation (A), using integral transforms of microsolutions of (D) at its singular points in ℂ. In the second part ([5]) we considered differential equations having at most a regular singularity at O and an irregular one at O. We used integral transforms of asymptotically flat solutions of (D) to define it fundamental system of solutions of (Δ), holomorphic in a right half plane, and integral transforms of sections of the sheaf of solutions of (D) modulo solutions with moderate growth as t → 0 in some sector, to define a fundamental system of (Δ), holomorphic in a left half plane. In this final part we combine the techniques and results of the preceding papers to deal with the general case.
Harmonic Analysis of Fractal Processes viaC* ‐ Algebras
Authors: Jorgensen Palle E. T.
Published: November 2010

We construct a harmonic analysis of iteration systems which include those which arise from wavelet algorithms based on multiresolutions. While traditional discretizations lead to asymptotic formulas, we argue here for a direct Fourier duality; but it is based on a non ‐ commutative harmonic analysis, specifically on representations of the CuntzC* ‐algebras. With this approach the waling from the wavelet takes the form of an endomorphism ofB(H), Ha Hilbert space derived from the lattice of translations. We use this to describe, and to calculate, new invariants for the wavelets. those iteration systems which arise from wavelets and from Julia sets, we show that the associated endomorphisms are in fact Powers shifts.
Pseudodifferential Operators in Function Spaces with Exponential Weights
Authors: Schott Thomas
Published: November 2010

This paper is a continuation of [17]. We study weighted function spaces of type Bapq(u) and Fapq(u) on the Euclidean space ℝn, where u is a weight function of at most exponential growth. In particular, u(x) = exp(±|x|) is an admissible weight. We consider symbols which belong to the Hörmander class Su1,δ, where u ∈ ℝ and 0 ≤ δ ≤ 1. We give sufficient conditions for the boundedness of the corresponding pseudodifferential operators in the above function spaces. As a main tool, we use molecular decompositions of these spaces. Furthermore, we prove that the spaces Bapq (u) and Fapq(u) have the lift property.
On Higher Order Embeddings and n ‐ Connectedness
Authors: Beltrametti M. C. , Di Rocco S. , Lanteri A.
Published: November 2010

Let L be a very ample line bundle on a smooth complex projective surface. The relations between the higher order embedding properties of L, like k ‐ spannedness, k ‐ very ampleness, k ‐ jet ampleness, and the higher numerical connectedness properties of divisors D ε |L| are Investigated. Some applications to adjoint bundles as well as pluricanonical bundles are discussed.
Biliaison Classes of Rank Two Reflexive Sheaves on P3
Authors: Buraggina Antonella
Published: November 2010

A biliaison theory for rank two reflexive sheaves on projective 3 ‐ space is established, In analogy with the existing theory for curves and, more generally, for 2 ‐ codimensional subschemes of projective n ‐ space. By definition two such sheaves are in the same biliaison class if their first cohomology modules are isomorphic. A parametrization of these classes is given. It is then shown that any class not corresponding to the zero module has a structure described by the Lazarsfeld ‐ Rao property. In particular, it is shown that vector bundles are precisely the minimal elements (in the of the LR ‐ property) in their biliaison classes.
Curves in P3 with Quasi‐‐Linear Resolution
Authors: Franco Davide
Published: November 2010

Our main result is Theorem 1.3 which gives sufficient conditions for the global generation of some classes of vector bundles which arise as kernels of special morphisms between splitting vector bundles of Pn.

Following the paper [3], we apply our result to the construction of space curves admitting quasilinear resolution (see Theorem 1.1).
Operator Interpretation of Resonances Arising in Spectral Problems for 2 × 2 Operator Matrices
Authors: Mennicken Reinhard , Motovilov Alexander K.
Published: November 2010

We consider operator matrices \documentclass{article}\pagestyle{empty}\begin{document}${\rm{H = }}\left( {{_{B_{10} }^{A{_0}}} {_{A_{1} }^{B{_{01}}}} } \right)$\end{document} with self ‐ adjoint entries Ai, i = 0,1, and bounded B10 = B10 acting in the orthogonal sum μ=μ0 ⊕ μ1 of Hilbert spaces μ0 and μ1. We are especially interested in the case where the spectrum of, say, A1 is partly or totally embedded into the continuous spectrum of A0 and the transfer function V1(z) = B10 where (χ ‐ A0)−1 B01, admits analytic continuation (as an operator ‐ valued function) through the cuts along branches of the continuous spectrum of the entry A0 into the unphysical sheet(s) of the spectral parameter plane. The values of χ in the unphysical sheets where M1−1(z) and consequently the resolvent (H ‐ z)−1 have poles are usually called resonances. A main goal of the present work is to find non ‐ selfadjoint operators whose spectra include the resonances as well as to study the completeness and basis properties of the resonance eigenvectors of M1(z) in μ1. To this end we first construct an operator ‐ valued function V1(Y) on the space of operators in μ1 possessing the property: V1(Y)ϕ1 = V1(z)ϕ1 for any eigenvector ϕ1 of Y corresponding to an eigenvalue z and then study the equation H1 = A1 + V1(H1). We prove the solvability of this equation even in the case where the spectra of A0 and A1 overlap. Using the fact that the root vectors of the solutions H1 are at the same time such vectors for M1(z), we prove completeness and even basis properties for the root vectors (including those for the resonances).
Descriptions of Some K Functionals for Three Spaces and Reiteration
Authors: Ericsson Stefan
Published: November 2010

We prove some equivalence formulas for the K functional for three spaces. In particular we calculate K(t, s, f, Lp0, Lp1, Lp2). We also give an integral formula connecting the K functional for triples of the type (A0, A1, A2), where A1 is of class C(θ, A0,A2), with the K functional for the pair (A0, A2). This formula is used to prove a reiteration formula for interpolation of the triple (A0, Al, A2) when Ai is of class C(θi, X, Y)
The Khinchin Inequality for Generalized Rademacher Functions
Authors: Meléndez Yolanda , Tonge Andrew
Published: November 2010

We give a new proof of the Khinchin inequality for the sequence
equation image
of k‐Rademacher functions:
equation image
We obtain constants which are independent of k. Although the constants are not best possible, they improve estimates of Floret and Matos [4] and they do have optimal dependence on p as p → ∞.
Inverse Scattering Transform for the Toda Hierarchy
Authors: Teschl Gerald
Published: November 2010

We provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy. In addition, we revisit the connection between trace formulas and conserved quantities from the viewpoint of Krein's spectral shift theory.
Harmonic Functions in a Cone Which Vanish on the Boundary
Authors: Yoshida Hidenobu , Miyamoto Ikuko
Published: November 2010

A harmonic function defined in a cone and vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth conditions under which it is reduced to a finite sum of them are discussed.
Holomorphic Connections and Extension of Complex Vector Bundles
Authors: Buchdahl N. P. , Harris Adam
Published: November 2010

Let
equation image
be a regular, surjective holomorphic map between complex manifolds such that for all t ∈ Y, π−1(t) is a connected, simply connected Riemann surface. Let K C X be compact, and E ⊂ X \ K a holomorphic vector bundle, equipped with a holomorphic relative connection along the fibres of π. The main result of this note establishes unique existence of a holomorphic vector bundle extension Ê→ X under the added assumptions that π (K) is a proper subset of Y, and π−1 (t) ∪ (X \ K) is always non‐empty and connected. As a corollary of the main theorem, it follows that if X is an arbitrary complex manifold, and A C X is an analytic subset of co dimension at least two, then E → X \ A admits a unique extension if there exists a holomorphic connection ▽:Ox (E) → Ω(E).
Convolutions and the Geometry of Multifractal Measures
Authors: Falconer K. J. , O'Neil T. C.
Published: November 2010

This paper relates multifractal features of a measure μ on IRn to those of the projection of the measure onto m‐ dimensional subspaces. We achieve this through the study of appropriately defined convolution kernels. This provides a unified approach to projections of measures and leads to new results on multifractal properties as well as alternative derivations of some existing formulae. These include formulae and estimates for the local dimensions and generalised q‐ dimensions of projected measures as well as more precise information about the limiting behaviour of multifractal expressions. We consider briefly how similar ideas may be applied to sections of a measure by (n ‐ m)‐dimensional planes.
New criterion to aid manual and automatic selection of the arterial input function in dynamic susceptibility contrast MRI
Authors: Bleeker Egbert J. W. , van Osch Matthias J. P. , Connelly Alan , van Buchem Mark A. , Webb Andrew G. , Calamante Fernando
Published: November 2010

Dynamic susceptibility contrast‐MRI requires an arterial input function (AIF) to obtain cerebral blood flow, cerebral blood volume, and mean transit time. The current AIF selection criteria discriminate venous, capillary, and arterial profiles based on shape and timing characteristics of the first passage. Unfortunately, partial volume effects can lead to shape errors in the bolus passage, including a narrower and higher peak, which might be selected as a “correct” AIF. In this study, a new criterion is proposed that detects shape errors based on tracer kinetic principles for computing cerebral blood volume. This criterion uses the ratio of the steady‐state value to the area‐under‐the‐curve of the first passage, which should result in an equal value for tissue and arterial responses. By using a reference value from tissue, partial volume effects–induced shape errors of the AIF measurement can be detected. Different factors affecting the ratio were investigated using simulations. These showed that the new criterion should only be used in studies with T1‐insensitive acquisition. In vivo data were used to evaluate the proposed approach. The data showed that the new criterion enables detection of shape errors, although false positives do occur, which could be easily avoided when combined with current AIF selection criteria. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.
Relaxivity‐iron calibration in hepatic iron overload: Probing underlying biophysical mechanisms using a Monte Carlo model
Authors: Ghugre Nilesh R. , Wood John C.
Published: November 2010

Iron overload is a serious condition for patients with β‐thalassemia, transfusion‐dependent sickle cell anemia, and inherited disorders of iron metabolism. MRI is becoming increasingly important in noninvasive quantification of tissue iron, overcoming the drawbacks of traditional techniques (liver biopsy). Effective transverse relaxation rate (1/effective transverse relaxation time) rises linearly with iron while transverse relaxation rate (1/T2) has a curvilinear relationship in human liver. Although recent work has demonstrated clinically valid estimates of human liver iron, the calibration varies with MRI sequence, field strength, iron chelation therapy, and organ imaged, forcing recalibration in patients. To understand and correct these limitations, a thorough understanding of the underlying biophysics is of critical importance. Toward this end, a Monte Carlo‐based approach, using human liver as a “model” tissue system, was used to determine the contribution of particle size and distribution on MRI signal relaxation. Relaxivities were determined for hepatic iron concentrations ranging from 0.5 to 40 mg iron per gram dry tissue weight. Model predictions captured the linear and curvilinear relationship of effective transverse relaxation rate and transverse relaxation rate with hepatic iron concentrations, respectively, and were within in vivo confidence bounds; contact or chemical exchange mechanisms were not necessary. A validated and optimized model will aid understanding and quantification of iron‐mediated relaxivity in tissues where biopsy is not feasible (heart and spleen). Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.
Rapid MR‐ARFI method for focal spot localization during focused ultrasound therapy
Authors: Kaye Elena A. , Chen Jing , Pauly Kim Butts
Published: November 2010

MR‐guided focused ultrasound (FUS) is a noninvasive therapy for treating various pathologies. MR‐based acoustic radiation force imaging (MR‐ARFI) measures tissue displacement in the focal spot due to acoustic radiation force. MR‐ARFI also provides feedback for adaptive focusing algorithms that could correct for phase aberrations caused by the skull during brain treatments. This work developed a single‐shot echo‐planar imaging–based MR‐ARFI method that reduces scan time and ultrasound energy deposition. The new method was implemented and tested in a phantom and ex vivo brain tissue. The effect of the phase aberrations on the ultrasound focusing was studied using displacement maps obtained with echo‐planar imaging and two‐dimensional spin‐warp MR‐ARFI. The results show that displacement in the focal spot can be rapidly imaged using echo‐planar imaging–based MR‐ARFI with high signal‐to‐noise ratio efficiency and without any measurable tissue heating. Echo‐planar imaging–based displacement images also demonstrate sufficient sensitivity to phase aberrations and can serve as rapid feedback for adaptive focusing in brain treatments and other applications. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.
Retired occupational therapists' experiences in volunteer occupations
Authors: Cole Marilyn B. , Macdonald Karen C.
Published: November 2010

As the baby boomer generation, born 1945–1963, begins its transition to retirement, what might be the position of volunteering within their new life structure? Using retired occupational therapists as a purposive sample (n = 50), this survey provides a description of the volunteer experience in three distinct phases: 1) Pre‐retirement contemplation and preparation; 2) Actions, thoughts and feelings during the volunteer experience; and 3) Thoughts and feelings related to ending their volunteer roles. Results reveal that while retirees are highly motivated by altruism and the wish to stay engaged and connected with others through volunteering, they often find the existing structure of the organizations unable and unwilling to provide the kinds of volunteer roles that meet their needs and goals. These findings closely align with evidence from multidisciplinary and public health literature on civic engagement in the Third Age, retired but not disabled. In conclusion, results imply three new roles for occupational therapy practitioners with volunteering: 1) Promoting volunteer exploration and participation for older adult clients with disabilities; 2) Providing group interventions for Third Agers transitioning to retirement; and 3) Consulting with the organizations that depend on volunteers to guide them in revising the way they define and organize volunteer roles. Study is limited to one specific population but paves the way for replication with a broader range of participants. Copyright © 2010 John Wiley & Sons, Ltd.
Modelling of Wave Propagation using Spectral Finite Elements
Authors: Hennings Bianca , Lammering Rolf
Published: November 2010

For the analysis of wave propagation at high frequencies, the spectral finite element method (SFEM) is under investigation. In contrast to the conventional finite element method high‐order shape functions are used. They are composed of Lagrange polynomials with nodes at the Gauß‐Lobatto‐Legendre points. The Gauß‐Lobatto‐Legendre integration scheme is applied in order to obtain a diagonal mass matrix. So, the resulting system equations can be solved efficiently. In the numerical examples, spectral finite elements with shape functions of different order are applied to a plane strain problem. The numerical examples cover structures without and with stiffness discontinuities. It is shown that the results agree well with analytical solutions. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling Techniques for Coupled, Rotating Beams
Authors: Gattringer Hubert , Hubinger Stefan , Mayrhofer Karl , Höbarth Wolfgang , Bremer Hartmut
Published: November 2010

Beams are parts of many industrial applications, like robot links, rolls in paper industry and turbo charger. In this work, a rotordynamical problem, the powertrain for a mill stand, is under consideration. Torsional and bending vibrations are used to describe the dynamical behavior. There are several methods for deriving the dynamical equations of motion. In this paper, the Projection Equation, a synthetical method, is used, leading to partial differential equations for the distributed parameter system. A simplification can be done by using the Ritz approximation method. This method requires the fulfillment of the geometric boundary conditions. For our example, a combination of rigid body modes and elastic modes is chosen. Also models for the gear box system and bearings are included. The solutions for the overall example are nonlinear ordinary differential equations which can be integrated numerically. The system is excited by constant torques and forces. Simulation results for this elastic multibody system are presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Control Strategies for a Hybrid Articulated Robot
Authors: Höbarth Wolfgang , Gattringer Hubert , Staufer Peter , Bremer Hartmut
Published: November 2010

Due to higher requirements in productivity and cost efficiency of production lines, robots and other manipulators have to move faster. One possibility to fulfill the mentioned goals is to build lightweight constructions having elastic deformations in joints and links. The elastic components tend to vibrations and static deflections. Methods that compensate or minimize these drawbacks are the focus of this paper.

An articulated robot with 6 joints and flexibility in joints and links is under consideration. The joints are actuated by DC motors combined with Harmonic Drive gears which offer high gear ratios but undergo elastic deformations. The links are flexible in two bending directions and in torsional sense. To achieve ordinary differential equations, a Ritz approach together with the projection equation is used. The obtained model is used for feedforward and feedback control design.

Based on reference trajectories and on a rigid body model, estimations for the elastic deflections are calculated. These deflections are used to alter the reference trajectory in order to minimize the error of the tool center point. For basic active damping, non‐local curvature feedback is used. Together with PD joint control and the feedforward control, satisfying results are obtained. Additionally, a sliding control approach is presented. The stiffness of the tool center point is enhanced with the drawback of less active damping.

Simulation results and measured data are presented and compared. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Energy momentum consistent force formulation for the optimal control of multibody systems
Authors: Koch Michael W. , Leyendecker Sigrid
Published: November 2010

This work considers the optimal control of multibody systems being actuated with control forces which impact the system's motion directly. The goal is to find a dynamically feasible trajectory of states and control leading from an initial to a desired final state, while minimising an objective function. The optimal control problem is solved using a direct transcription method, i.e. boundary conditions and a discrete version of the equations of motion serve as constraints for the minimisation of a cost function with respect to the discrete state and control trajectory. Here, a particular time stepping scheme, an energy momentum integrator based on discrete derivatives is used. Corresponding to a constrained formulation of multibody systems, we develop an energy momentum consistent discrete force formulation that fits into the energy momentum integrator. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A novel algorithm for the inverse problem in elasticity imaging by means of variational r‐adaption
Authors: Arnold Alexander , Bruhns Otto T. , Mosler Jörn
Published: November 2010

Elasticity imaging or elastography is a powerful technique in medicinal imaging for visualizing the stiffness distribution in soft tissue in vivo. It is motivated by the observation that the stiffness in soft tissue is affected by pathologies in many cases. More precisely, diseased tissue tends to be stiffer than the healthy surrounding tissue. The two steps involved in elasticity imaging are: first deforming the tissue and measuring the displacement field in the region of interest using ultrasound or MRI signals; second calculating the underlying stiffness distribution using an inverse analysis. While in common approaches this inverse analysis is based on minimizing the distance between the measured and the computed deformation field depending only on the unknown stiffness distribution, an additional variation of the underlying finite element discretization is the focus of the present work. In doing so, the triangulation is optimized improving the accuracy of the results and increasing the efficiency of the computational framework. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical investigations on physiological contact in the human hip joint
Authors: Fietz K. , Nackenhorst U.
Published: November 2010

In this contribution, an efficient computational approach for modeling the physiological contact conditions in synovial joints is presented. A detailed three‐dimensional finite element model of the hip joint is generated based on CT‐data. The synovial gap between the porous cartilage layers is discretized with shell‐like liquid interface elements. In these elements, the Stokes flow equations are solved and the contact conditions are treated in a staggered fluid structure interaction scheme. The development of the synovial contact elements is described and boundary conditions which represent the joint capsule are introduced. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structure Preserving Simulation of Optimal Index Finger Trajectories during Grasping
Authors: Maas Ramona , Leyendecker Sigrid
Published: November 2010

Trajectory planning of human motion is done unconsciously by the central nervous system (CNS). To get a better understanding about how the human CNS controls movements in a particular example, we investigate the trajectory of the index finger during grasping. Varying forefinger movements are formulated as optimal control problems for constrained motion. For the solution of the optimal control problem, DMOCC (Discrete Mechanics and Optimal Control for Constrained Systems, introduced in [4]) is used. The structure preserving formulation distinguishes DMOCC from other direct transcription methods. It guarantees that certain characteristic properties of the real motion are inherited by the approximate trajectory. This is crucial, since numerical dissipation would lead to over‐ or underestimation of the joint torques. As in [2], the motion corresponding to different objective functions like total control effort, torque change, kinetic energy and jerk in the fingertip is compared. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stress‐triaxiality‐dependent modeling of ductile damage and fracture behavior
Authors: Brünig Michael , Gerke Steffen , Albrecht Daniel
Published: November 2010

The paper deals with the effect of stress triaxiality on the inelastic behavior of aluminum alloys. The proposed continuum model takes into account stress‐triaxiality‐dependence of the yield condition as well as of the damage criterion and the fracture condition with different branches corresponding to different micro‐mechanisms. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An enhanced model for probabilistic cleavage fracture assessment considering local constraint effects
Authors: Hardenacke Volker , Hohe Jörg , Luckow Sabrina , Siegele Dieter
Published: November 2010

The present study is concerned with the development of an enhanced probabilistic model for cleavage assessment of ferritic steels. An enhanced model for the probabilistic cleavage fracture assessment has to consider the conditions for both, nucleation and propagation of micro defects. Hence, a propagation based model is enhanced by a combination of the local plastic strain and the local stress triaxiality to account for the nucleation of potentially critical micro defects. The formulation of the new model is based on the local mechanical field quantities determined numerically at the cleavage origins for a variety of standard deep and shallow crack specimens as well as for small scale cruciform bending specimens. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fracture and Fragmentation of Silicon Dies
Authors: Laun Christoph , Pandolfi Anna , Ghisi Aldo , Weinberg Kerstin
Published: November 2010

Different failure modes of silicon are observed. Experimental results are not able to explain these variations clearly and therefore numerical simulations have been performed. In order to reduce high computational costs a simplified method to introduce weakened areas on silicon chips is presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Residual capacities of uniaxially compressed, delaminated composite panels
Authors: Völlmecke Christina
Published: November 2010

The mechanical buckling and postbuckling behaviour of a delaminated panel under uniaxial compression is investigated using a semi‐analytical geometrically nonlinear panel model. A Rayleigh‐Ritz procedure based on trigonometric displacement functions is used in conjunction with minimum energy principles to ascertain the mechanical response of the panels. The model includes the effect of delamination propagation resulting from the buckling of the laminates utilizing a discrete cohesive zone model. With the model developed, a detailed assessment of the residual capacity of the panel is provided due to its capability of tracing the equilibrium paths far into the postbuckling range. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled transport and damage model for concrete at high temperatures
Authors: Cramer Friedhelm , Ostermann Lars , Dinkler Dieter
Published: November 2010

A model for the numerical analysis of hygro‐thermal behavior of concrete at high temperatures which includes transport and reaction processes is presented. For the description of transport the model comprises the balance equation for mass and enthalpy and the constitutive equations for concrete at high temperatures. The degradation of the cement minerals C‐S‐H and portlandite is described by two chemical reactions. Finally, the finite element formulation for solving the coupled balance equations regarding the primary variables temperature and relative humidity is presented and the results of a 3‐D example are discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Postbuckling of Composite Airframe Structures: Closed‐Form Approximate Solutions
Authors: Mittelstedt Christian , Schröder Kai‐Uwe
Published: November 2010

In this contribution, the postbuckling behaviour of imperfect rectangular composite plates under compression is treated in a closed‐form analytical manner. Based on rather simple shape functions for the postbuckling deflections and the plate imperfections, the requirement for compatibility of the membrane strains leads to an explicit solution for Airy's stress function. The equilibrium condition in the out‐of‐plane direction is not fulfilled explicitly, but rather in an integral sense using a Galerkin‐type formulation, leading to an approximate closed‐form solution for the postbuckling deflections. Eventually, rather simple closed‐form approximate solutions for all postbuckling state‐variables can be derived that can be used conveniently in engineering practice. The quality of the closed‐form solution is established by comparison with the results of other authors. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Strain‐gradient viscoplasticity in one‐dimensional structural dynamics
Authors: Nguyen A.D. , Stoffel M. , Weichert D.
Published: November 2010

Based on the static theory of strain‐gradient viscoplasticity proposed by [1], a one‐dimensional dynamic analysis is derived for finite element computation of isotropic hardening materials. The kinetic energy is assumed to be composed of the conventional and internal kinetic energy. The internal energy is described phenomenologically in terms of the equivalent plastic strain in order to capture the heterogeneity of plastic flow. Herein, the microscopic density is assumed to be related to the macroscopic one through a microscopic‐inertia parameter. The macroscopic‐ and microscopic‐force balances including inertia effects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a one‐dimensional dynamic problem. A parameter study to find the microscopic‐inertia parameter is carried out. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Assessment of structural sensitivity on the basis of artificial neural networks
Authors: Pannier Stephan , Graf Wolfgang
Published: November 2010

In engineering practice, the assessment of sensitivity is utilized to detect influential parameters in order to facilitate subsequent numerical simulation techniques. As sensitivity analyses are preprocessing methods for sophisticated numerical simulation techniques, e.g. reliability based optimization procedures, their application is always linked to an increase of the computational expense. In result, it is reasonable to couple sensitivity analysis and artificial neural networks (ANN). Therefore, multi‐faceted global sensitivity measures (GSM) may be formulated, taking advantage of different characteristics of the ANNs. Additionally, to take into account nonlinearities of the response surface, a new approach of sectional global n sensitivity measures is introduced. Generally, the sensitivity can be determined with $S_{i}=\hat{S}_{i}/\sum\limits_{j=1}^{n}\hat{S}_{j}$. Thereby, $S_{i}$ denotes the sensitivity of interest and $\hat{S}_{i}$ a characteristic of the function $f:\mathcal{R}^n\rightarrow\mathcal{R}$ under investigation. This can be either the response $f$ itself or the first partial derivative thereof $\partial_{i}f$. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
About the stress‐strain state of growing viscoelastic systems
Authors: Pulyaevskiy Denis V. , Potapov Vadim D.
Published: November 2010

A problem of calculation of the stress‐strain state of viscoelastic heterogeneously ageing growing systems at the various moments of time is considered. The efficient numerical technique based on the Finite Element Method (FEM) is suggested. The constitutive equation between stresses and strains in the viscoelastic growing solid is corresponded with the Maslov‐Arutyunyan theory. The general system of equations of the FEM‐based technique is being formed for nodal displacement increments on the basis of variation of the total energy functional by components of the vector of nodal displacement increments. The numerical technique allows to take into account linear and nonlinear creep of the material, shrinkage (if it is necessary) and the instantly‐elastic modulus time‐dependence. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stabilized Mixed Tetrahedrals with Volume and Area Bubble Functions at Large Deformations
Authors: Widany Kai‐Uwe , Caylak Ismail , Mahnken Rolf
Published: November 2010

In this contribution, stabilized mixed finite tetrahedral elements are presented in order to avoid volume locking and stress oscillations. Geometrically non‐linear elastic problems are addressed. The mixed method of incompatible modes is considered. As a key idea, volume and area bubble functions are used for the method of incompatible modes [1], thus giving it the interpretation of a mixed finite element method with stabilization terms. Concerning non‐linear problems these are non‐linearly dependent on the current deformation state, however, linearly dependent stabilization terms are used. The approach becomes most attractive for the numerical implementation, since the use of quantities related to the previous Newton iteration step is completely avoided. The variational formulation for the standard two‐field method, the method of incompatible modes in finite deformation problems is derived for a hyper elastic Neo‐Hookean material. In the representative examples Cook's membrane problem and a block under central pressure illustrate the good performance of the presented approaches compared to existing finite element formulations. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comments on Membrane Locking
Authors: Winkler Robert
Published: November 2010

Membrane locking is a severe issue frequently neglected in the context of low‐order (four node isoparametric) shell elements. From a theoretical point of view, the present contribution illustrates the underlying mechanism by means of shallow shell theory. From a numerical point of view, different element formulations based on standard enhanced assumed membrane strains and reduced integration methods have been compared to each other applying standard as well as modified benchmark examples. A modified integration scheme is proposed. According to preliminary results it behaves virtually optimal within the limits of finite element perfectibility. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Validierung eines Simulationsmodells für Wälzlager durch Abgleich von Simulations‐ mit Messdaten
Authors: Fritz Felix , Bücheler David , Seemann Wolfgang
Published: November 2010

Wälzlager besitzen abhängig von Drehwinkel und Belastung unterschiedliche Steifigkeit sowie Dämpfungs‐ und Reibverluste. Um das dynamische Verhalten und die Lebensdauer einer Maschine durch Simulationen zu beurteilen, werden daher die nichtlinearen Reaktionskräfte des Lagers als generisches Maschinenelement implementiert.

Um die Güte dieses Elements zu validieren werden verschiedene Messungen an einem Wälzlagerprüfstand durchgeführt. Anschließend wird ein Modell dieses Prüfstandes in MSC/ADAMS aufgebaut und zum Abgleich die Experimente als Simulationen nachgebildet. Die untersuchten Größen sind die Lagersteifigkeit sowie das Reibmoment im Wälzlager. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear Vibrations with Friction: A Multiharmonic Approach
Authors: Herzog Anna , Panning Lars
Published: November 2010

Turbine blades are subjected to vibrations caused by static and dynamic loads. To avoid damage, the arising dynamic stresses can be reduced by generating friction contacts between the blades leading to additional damping. The resulting nonlinear equations of motion of the blade dynamics can be solved by the Multiharmonic Balance Method (MHBM), which is described in this paper. With the MHBM, it is possible to consider a multiharmonic excitation as well as a response consisting of several harmonics. In this paper, the MHBM is applied to both a simple 1 DOF nonlinear oscillator and a cyclic model of a blade integrated disk (blisk). (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Dynamic Aspects and Pattern Generation in Vehicle‐Road Interaction
Authors: Vogt Heike , Seemann Wolfgang
Published: November 2010

Increasing transport capacity leads to new vehicle designs and increasing axle loads. Still it has to be better understood until which extend especially heavy vehicles cause corrugation of roads. Therefore, basic investigations concerning vehicle‐road interaction are helpful to augment the understanding of the basic mechanisms. Firstly, in order to investigate the oscillatory behavior of a vehicle a MDoF oscillator moving with constant velocity on a rippled road is considered. From this, general results about wear pattern generation of the road are derived from analytical considerations concerning the dynamic contact force between vehicle and road. Secondly, a simple vehicle road interaction model is presented which consists of a vehicle model and a road exhibiting viscoelastic plastic characteristics. Results of numerical simulations are compared with the findings deduced from the analytical MDoF model. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Microstructure evolution during rolling and annealing of mild steels
Authors: Bienger Pierre , Butz Alexander , Helm Dirk
Published: November 2010

The process chain for components made of sheet metals consists of different forming techniques like hot rolling, cold rolling, and deep drawing as well as heat treatment operations like annealing. For the design and optimization of the whole manufacturing process and the final component behavior, a correct representation of the material behavior and the application of appropriate numerical simulation techniques are required. For our first investigations, a ferritic mild steel DC04, which is a typical steel grade for automotive applications, is analyzed. Therefore, specimens are taken out of a real manufacturing process after hot and cold rolling and after annealing. These specimens are intensively investigated in order to study the texture evolution and the development of other material properties, like yield function during the process chain. In this paper different homogenization methods are used to simulate the texture evolution during cold rolling. The results are compared concerning accuracy and efficiency of the considered models. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Microstructural changes of filled rubber‐like materials under cyclic loading
Authors: Dargazany Roozbeh , Itskov Mikhail , Liu Junwei
Published: November 2010

The concept of network decomposition has vastly been used in many micro‐mechanical models describing stress‐softening of rubber‐like materials in the first loading cycle as for example the Mullins‐effect. Nevertheless, this concept highly simplifies the rubber matrix by decomposing it into two parallel networks that have no interactions with each other.

In order to take into account the interactions between these networks some further extensions to the network decomposition concept seem necessary. To this end, a third network is introduced and the concept of rubber cell is proposed and developed. Using this concept, the influence of the filler network on elasticity of the two networks can be predicted by considering the cell as a RVE. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On a model of viscoelasticity with internal state variables
Authors: Peters Johanna , von Estorff Otto , Achenbach Manfred , Lion Alexander
Published: November 2010

In classical theories of viscoelasticity, time‐dependent effects are accounted for only with respect to the mechanical properties. However, glass‐forming materials such as polymers, for example, also show viscoelastic effects in their thermal properties as can be seen from measurements of the coefficient of thermal expansion or the heat capacity. In this contribution, a model is presented that is able to describe effects associated with the glass transition in the mechanical as well as the thermal properties in one consistent approach. To this end, the state space known from equilibrium thermodynamics is enlarged by internal state variables. These variables are to describe the deviation from equilibrium, hence allowing for a description of viscoelastic effects. Closed form expressions for the complex modulus as well as the compliance, the complex heat capacity at constant stress as well as at constant strain, and the complex coefficient of thermal expansion as well as the thermal modulus are derived and discussed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)