Transonic wind tunnel test sections

Zusammenfassung Um von Windkanalversuchen auf die Verhältnisse beim freien Flug schliessen zu können, müssen die Einflüsse der Kanalwände auf die Geschwindigkeitsverteilung am Modell berücksichtigt werden. Bei schallnaher Strömung sind diese Einflüsse an Modellen üblicher Grösse so stark, dass sie die Messungen vollständig verfälschen.Die hier beschriebenen Methoden beruhen auf der Berechnung von 4 Arten von Interferenzen in einem Punkt des Modells. Von diesen werden auf einfache Art die Interferenzgeschwindigkeiten in den anderen Punkten des Modells abgeleitet.Ausgehend von einer gemittelten Grenzbedingung werden die Interferenzgeschwindigkeiten für teilweise offene Kanalwände berechnet. Durch die Wahl verschiedener Wandkonstruktionen können einzelne Interferenzen eliminiert werden. Die Tabellen 1 und 2 zeigen eine Zusammenstellung der Möglichkeiten für verschiedene Arten von teilweise offenen Kanalwänden.

---

---

This work was sponsored by the Office of Scientific Research of the Air Research and Development Command of the United States Air Force.     

Theoretical aspects of information security

In this work, the authors obtain a topological classification of the simplest diffeomorphisms of the sphere S ² having exactly one orbit of one-sided heteroclinic tangency. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 54, Suzdal Conference–2006, Part 2, 2008.     

Theoretical aspects of ill-posed problems in statistics

Ill-posed problems arise in a wide variety of practical statistical situations, ranging from biased sampling and Wicksell's problem in stereology to regression, errors-in-variables and empirical Bayes models. The common mathematics behind many of these problems is operator inversion. When this inverse is not continuous a regularization of the inverse is needed to construct approximate solutions. In the statistical literature, however, ill-posed problems are rather often solved in an ad hoc manner which obccures these common features. It is our purpose to place the concept of regularization within a general and unifying framework and to illustrate its power in a number of interesting statistical examples. We will focus on regularization in Hilbert spaces, using spectral theory and reduction to multiplication operators. A partial extension to a Banach function space is briefly considered.Research supported by the Air Force Office of Scientific Research.     

Theoretical aspects of synchronization in transverse galloping aeroelastic instability

We investigate, for the first time to the best of our knowledge, theoretical aspects of synchronization in transverse galloping aeroelastic instability. The current study is a generalization of previous studies that considered the dynamics of a single-cylinder, and therefore, precluded the option to study synchronization. Here, we consider both the deterministic and stochastic dynamics of a system comprising two weakly coupled cylinders, which are attached to the ground with linear springs and dashpots, and are immersed in a high velocity airstream. We derive the conditions for the instability threshold. We give a detailed and simplified procedure to compute the amplitudes, phase differences, and frequencies of the synchronized solutions. We calculate quantitative measures of the amplitude and phase noises, including an explicit calculation of the phase noise reduction due to synchronization, which can enhance the performance of transverse galloping-based energy harvesters. Furthermore, we provide simple mappings for the amplitudes and phase difference dynamics, which we show to be highly useful for understanding both the deterministic and the stochastic dynamics of the amplitudes and the phase difference dynamics from geometric point of view.     

Shunting yard operations: Theoretical aspects and applications

Almost ever since freight has been transported via rail, shunting yards (also called classification or marshaling yards) are operated in order to separate freight trains and reassemble new trains. The efficient use of shunting yards has a deep impact on the efficiency and reliability of rail freight services. Thus, much research on shunting yards has been published, starting from the 1950s. Lately, several publications mostly focusing on the sorting procedures have livened up research on shunting yards. This paper reviews the literature on the operational processes at shunting yards over the last 40 years and discusses the operational challenges of freight transshipment. The approaches are classified according to different sorting strategies which allows an easy access to the models for both, researchers and practitioners. The paper concludes with an overview on future research challenges.     

Theoretical and numerical aspects of contact problems for shells

The paper deals with the contact problem of a shell with rigid housing enclosing it or with a set of punches. Using Timoshenko's shell theory, a basic regularized functional of total energy without any distributions (Dirac's delta functions) has been considered. Properties of this functional as well as the question of the existence of a solution have been formulated as theorems. Applying the method of variational inequalities, a numerical method has also been developed. Applications of these theorems on the contact of an axially symmetrical cylinder with a rigid housing have been presented.

---

Résumé Dans cet article on considère le probleme du contact d'une coque avec le logement rigide ou avec un groupe de poinçons. En profitant des équations du type de Timoshenko pour les coques, on forme la fonctionelle d'énergie totale dans laquelle on élimine les distributions du type de delta de Dirac que l'on trouve dans les formes classiques. Les propriétés de cette fonctionelle ainsi que la question de l'existence d'une solution ont été formulées comme ensemble de théorèmes. L'analyse numérique du problème est effectuée en appliquant la méthode des inéquations variationelles. Ces théorèmes sont appliqués à l'exemple du contact d'un cylindre axisymétrique avec le logement rigide.

     

Theoretical and numerical aspects in the multiphasic modelling of human brain tissue

A surgical intervention is often required if the functionality of the sensitive human brain tissue is seriously compromised, e. g., due to the occurrence of malignant brain tumours. A promising method for an effective tumour-treatment procedure is given by the so-called convection-enhanced drug delivery (CED), cf. [1]. In this regard, the aim of this contribution is to simulate the expected effects as well as coupled impacts of a (scheduled) CED-procedure with the help of numerical computations, which base on a sophisticated multiphasic and multi-physical modelling strategy applied to human brain tissue. In particular, a quaternary porous-media model, cf. [3–5], is used for the discussion of selected numerical examples and demonstrates the applicability of the model. In detail, the optimal catheter placement and the application of multiple infusion catheters are studied in terms of the occurring anisotropic therapeutic spreading of the infused drug. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ to waves requires polynomial type bounds for operators related to the operator Δ − s ² in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and -hard obstacles, by homogeneous and non-homogeneous obstacles.     

Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects

This paper gives basic definitions and properties related to what we call the non-homogeneous semi-Markov processes with a finite number of states using the formalism of counting processes, i.e. with intensity functions. We show how it is possible to get generalized Polya processes as a very particular case. We also treat the computational aspect by discretisation and as an application, we develop a social security problem.     

Algorithms for nonlinear piecewise polynomial approximation: Theoretical aspects

In this article algorithms are developed for nonlinear -term Courant element approximation of functions in ( ) on bounded polygonal domains in . Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rate of the best approximation and provide the basis for numerical implementation. Simple thresholding criteria enable approximation of a target function to optimally high asymptotic rates which are determined and automatically achieved by the inherent smoothness of . The algorithms provide direct approximation estimates and permit utilization of the general Jackson-Bernstein machinery to characterize -term Courant element approximation in terms of a scale of smoothness spaces (-spaces) which govern the approximation rates.

     

Continua with affine microstructure: Theoretical aspects and applications

In the present contribution we discuss an axiomatic stucture of extended continua with affine microstructure in the sense of Eringen [2]. Postulating and evaluating the observer-invariance of the balance of energy we obtain the governing balance equations of generalized continua which are closed by a specific set of kinematical assumptions and constitutive equations. Furthermore, we discuss two specific models characterized by an additional scalar (volumetrical) order parameter. Interestingly, the resulting effects lead to completely different interpretations of the results with respect to the coupling effects. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks on the solvability of transonic flow problems

The paper is devoted to the study of the viscosity method and upwinding in the transonic flow problems. We weaken the conditions from [6,7] under which we can obtain a nonviscous compressible transonic flow as a limit of viscous solutions, if the viscosity and heat conductivity tend to zero. Further, we give the justification of the density upwinding applied often in the calculation of transonic potential flows.     

Theoretical and experimental researches of size effect in micro-indentation test

Micro-indentation tests at scales on the order of sub-micron have shown that the measured hardness increases strongly with the indent depth or indent size decreasing, which is frequently referred to as the size effect. However, the trend is at odds with the size-independence implied by conventional elastic-plastic theory. In this paper, strain gradient plasticity theory is used to model the size effect for materials undergoing the micro-indenting. Meanwhile, the micro-indentation experiments for single crystal copper and single crystal aluminum are carried out. By the comparison of the theoretical predictions with experimental measurements, the micro-scale parameter of strain gradient plasticity theory is predicted, which is fallen into the region of 0.8–1.5 micron for the conventional metals such as copper (Cu), aluminum (Al) and silver (Ag). Moreover, the phenomena of the pile-up and sink-in near micro-indent boundary are investigated and analyzed in detail.     

The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects

In this paper we consider the singular value decomposition (SVD) of a fundamental matrix solution in order to approximate the Lyapunov and exponential dichotomy spectra of a given system. One of our main results is to prove that SVD techniques are sound approaches for systems with stable and distinct Lyapunov exponents. We also show how the information which emerges with the SVD techniques can be used to obtain information on the growth directions associated to given spectral intervals.     

On behavior of the small perturbations of one-dimensional steady transonic flows

Behavior of unsteady perturbations of steady solutions of quasilinear hyperbolic or parabolic degenerate systems of differential equations in partial derivatives is considered in the critical point neighborhood. The sought functions of analyzed equations are assumed dependent on two arguments, viz. coordinate x and time t., with an arbitrary number of sought functions. The point at which one of the system characteristic velocities vanishes, is called critical.     

The solution of transonic flow problems by the method of stabilization

The paper deals with the study of the perturbated Full Potential Equation. The proofs of existence, unicity and regularity of the solution are given. The main result consists in the fact that the resulting strong solution is the generic solution for the Transonic Flow Problem