Dynamic Mode Decomposition for Swirling Jet Flow Undergoing Vortex Breakdown

Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical shear layer and a large recirculation zone around the jet axis. We performed Large-Eddy Simulations (LES) of compressible swirling jet flows at Re=5000, Ma=0.6 in the high swirl number regime (S=1). A nozzle is included in our computational setup to account for more realistic inflow conditions. The obtained velocity fields are analyzed by means of temporal and spatial dynamic mode decomposition (DMD) to get further insight into the characteristic structures dominating the flow. We present eigenvalue spectra for the case under consideration and discuss the stability behaviour in time and space. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecules with multiple switching units on a Au(111) surface: self-organization and single-molecule manipulation

Three different molecules, each containing two azobenzene switching units, were synthesized, successfully deposited onto a Au(111) surface by sublimation and studied by scanning tunneling microscopy at low temperatures. To investigate the influence of electronic coupling between the switching units as well as to the surface, the two azo moieties were connected either via π-conjugated para-phenylene or decoupling meta-phenylene bridges, and the number of tert-butyl groups was varied in the meta-phenylene-linked derivatives. Single molecules were found to be intact after deposition as identified by their characteristic appearance in STM images. Due to their mobility on the Au(111) surface at room temperature, the molecules spontaneously formed self-organized molecular arrangements that reflected their chemical structure. While lateral displacement of the molecules was accomplished by manipulation, trans-cis isomerization processes, typical for azobenzene switches, could not be induced.     

Shear-induced deformations of polyamide microcapsules

The application of microcapsules for technical, cosmetic and pharmaceutical purposes has attracted increased interest in recent years. The design of new capsule types requires a profound knowledge of their mechanical properties. Rheological studies provide interesting information on intrinsic membrane properties and this information can be used to avoid premature release of encapsulated compounds due to the action of external mechanical forces (stirring, swallowing, spreading). In this publication we report a systematic study of polyamide microcapsules. These particles were synthesized by reacting 4-aminomethyl-1,8-diaminooctane and sebacoyl dichloride at the interface between silicone oil and water. Two different experiments were performed to get information on the mechanical properties of the capsule walls. First of all, we used an optical rheometer (rheoscope) to observe the capsule deformation and orientation in shear flow. The polymerization kinetics, relaxation properties, the regime of linear-viscoelastic behavior and the shear modulus of the flat membranes were independently measured in an interfacial rheometer. Both experiments gave complementary results. It turned out that the two-dimensional elongational modulus was about 3–4 times larger than the shear modulus. This result is in fairly good agreement with a theoretical model recently proposed by Barthès-Biesel. Due to the simple synthesis and well-defined structure, polyamide microcapsules can also serve as simple model systems to understand the complicated flow properties of red blood cells. Received: 5 July 1999/Accepted in revised form: 30 August 1999     

Spreading of Linear Disturbances in Boundary Layers at Mach Number Five and the Effect of Wall Cooling

We determine inviscid eigensolutions in zero pressure gradient flat plate boundary layers at Mach number five and evaluate the eigensolutions with the method of steepest descent. The resulting wave packets show that with wall cooling the tail of the packets becomes slower. Although the boundary layers investigated are all convectively unstable we interpret the slow tail of the wave packets as a trend towards an absolute instability. From a comparison of the wave packets with turbulent spot transition, we conclude that for wall cooling the general transition properties are close to those of an absolutely unstable flow. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Decomposable forms and automorphisms

In the late 19th century Jordan initiated the study of forms of higher degree and derived (see Memoire sur l'equivalence des formes, Oeuvres III, Gauthier Villars, Paris, 1962) the finiteness of the automorphism group Aut(f) of complex forms of degree ?3 and non-zero discriminant. This result has been extended to forms over arbitrary fields by Schneider (J. Algebra 27 (1973) 112), see also Curtis and Reiner (Representation Theory of Finite Groups and Associative Algebras, Wiley, New York, 1962) for related topics. Orlik and Solomon gave some bounds for the cardinality of Aut(f) using cohomological arguments in Orlik and Solomon (Math. Ann. 231 (1978) 229); besides this, little seems to be known about this group in general.In connection with his study (Monatsh. Math., submitted for publication) of representations of forms by linear forms, the author was led to an investigation of the group of automorphisms of decomposable forms f through the permutations of the linear factors these automorphisms induce. The main result (Theorem 4.2 in Chapter 4) states that almost all forms in k?2 variables of degree d?max{5,k+2} have only the trivial automorphisms that consist in multiplying each variable by the same dth root of unity. The case k=2,d=4 has already been studied (see Survey in Algebraic Geometry, Part 2, Invariant theory, Encyclopaedia of Mathematical Sciences, Vol. 55, Springer, Berlin, 1994); however, it is treated in full detail to illustrate the elaborated techniques.The first chapters are devoted to the proof of some general results concerning the structure of the permutation group associated to a form f which also help to understand the case of forms with non-trivial automorphisms. In a few special cases, this allows to determine this group explicitly; in general we give a bound for the cardinality of Aut(f) depending only on the degree of f which is relevant for some diophantine problems (see e.g. Ann. Math. 155 (2002) 553).The author is indebted to G. Wuestholz for his substantial help and encouragement during the redaction of the paper, he also wishes to thank V. Popov for several helpful remarks.     

Examples on projective spectra of (LB)-spaces

Summary In this note we present examples of projective spectraɛ=(E _n ) _n ∈ℕ of (LB)-spaces satisfying proj¹ ε≠0 such that the inductive spectrum (E _n ′) _n ∈ℕ of the duals is strict. Moreover, we characterize proj¹ε=0 for projective spectra of Moscatelli type. This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag     

Reaction of the i-C4H5 (CH2CCHCH2) radical with O2

The resonantly stabilized radical i-C(4)H(5) (CH(2)CCHCH(2)) is an important intermediate in the combustion of unsaturated hydrocarbons and is thought to be involved in the formation of polycyclic aromatic hydrocarbons through its reaction with acetylene (C(2)H(2)) to form benzene + H. This study uses quantum chemistry and statistical reaction rate theory to investigate the mechanism and kinetics of the i-C(4)H(5) + O(2) reaction as a function of temperature and pressure, and unlike most resonantly stabilized radicals we show that i-C(4)H(5) is consumed relatively rapidly by its reaction with molecular oxygen. O(2) addition occurs at the vinylic and allenic radical sites in i-C(4)H(5), with respective barriers of 0.9 and 4.9 kcal mol(-1). Addition to the allenic radical form produces an allenemethylperoxy radical adduct with only around 20 kcal mol(-1) excess vibrational energy. This adduct can isomerize to the ca. 14 kcal mol(-1) more stable 1,3-divinyl-2-peroxy radical via concerted and stepwise processes, both steps with barriers around 10 kcal mol(-1) below the entrance channel energy. Addition of O(2) to the vinylic radical site in i-C(4)H(5) directly forms the 1,3-divinyl-2-peroxy radical with a small barrier and around 36.8 kcal mol(-1) of excess energy. The 1,3-divinyl-2-peroxy radical isomerizes via ipso addition of the O(2) moiety followed by O atom insertion into the adjacent C-C bond. This process forms an unstable intermediate that ultimately dissociates to give the vinyl radical, formaldehyde, and CO. At higher temperatures formation of vinylacetylene + HO(2), the vinoxyl radical + ketene, and the 1,3-divinyl-2-oxyl radical + O paths have some importance. Because of the adiabatic transition states for O(2) addition, and significant reverse dissociation channels in the peroxy radical adducts, the i-C(4)H(5) + O(2) reaction proceeds to new products with rate constant of around 10(11) cm(3) mol(-1) s(-1) at typical combustion temperatures (1000-2000 K). For fuel-rich flames we show that the reaction of i-C(4)H(5) with O(2) is likely to be faster than that with C(2)H(2), bringing into question the importance of the i-C(4)H(5) + C(2)H(2) reaction in initiating ring formation in sooting flames.