Geometry of adiabatic changes. General analysis

The concept of adiabatic change and related notions are discussed. As a representative example, the evolution of a neutron spin in a precessing magnetic field is described briefly. The general setting of the equations for Dirac's evolution coefficients is discussed from the geometric phase point of view. An exactly solvable model of nutation is exhibited and the properties of the solutions are analyzed to reveal the holonomic structure of the problem. The corresponding expression for the geometric phase differs nontrivially from the corresponding expression in the well-known case of the precessing field. In addition, this geometric phase has an imaginary part which completes the picture of spin evolution in a nutation mode. The approach proposed for nutation is used to reexamine the twisted Landau-Zener problem. … Thusγ _n(C) is given by a circuit integral in parametric space and is independent of how the circuit is traversed (provided of course that this is slow enough for the adiabatic approximation to hold).M. V. Berry To the memory of my father.     

Experimental investigation of vibrational excitations in230Th

Nuclear levels in²³⁰Th have been investigated in the decay of²³⁰Pa, the²³⁰Th(d, pn) reaction and the²³²Th(p, t) reaction. TheK =0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands with band heads at 635, 781, and 1010 keV were observed up to the 8⁺, 9⁺, and 7⁺ levels, respectively. A second excited 0⁺ level was identified at 1297 keV which might be interpreted as the usual shape-oscillation. The branching ratios of theE2 transitions from the 0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands are explained in the framework of the rotational model by taking into account the coupling of these bands with the ground-state band, and the coupling between the 0 ₁ ⁺ and 2 ₁ ⁺ band. A strong enhancement ofE2 transitions from the 2 ₁ ⁺ to the 0 ₁ ⁺ band reported earlier is not confirmed. For the octupole vibrations withK =0^–, 1^–, and 2^– theE1 branching ratios are analyzed in terms of the Coriolis coupling of these bands. An almost complete experimental set ofE1 transition moments from these negative-parity bands to the 0 _g ⁺ , 0 ₁ ⁺ , and 2 ₁ ⁺ bands was obtained. It is suggested that octupole correlations might be important in explaining theseE1 moments.We appreciate the help of Mr. Assmus with the proton irradiations and the financial support of the Kernforschungszentrum Karlsruhe GmbH. This work was supported by the Deutsche Forschungsgemeinschaft (grants Bo 1109/1-1, Gr 894/2-1, Gu 179/3-1 and He 1316/2-3) and by the Volkswagen Stiftung.     

Optimal pairs of incomparable clouds in multisets

We consider the partially ordered set ([k] ⁿ, ), which is defined asn-th product of the chain [k] = {0, 1, 2,...,k – 1}, and study pairs (A, B) of incomparable setsA, B [k] ⁿ, that is,a b, a b for alla A, b B or (in short notation) A BWe are concerned with the growth of the functionsf _n: {0, 1,...,k ⁿ} {0, 1,...,k ⁿ},n , defined byf _n() = max {|B|: A, B [k] ⁿ with|A| = and A B} and a characterisation of pairs (A, B), which assume this bound.In the previously studied casek = 2 our results are considerably sharper than earlier results by Seymour, Hilton, Ahlswede and Zhang.     

Approaches to molecular composites from fluorine-containing bis-maleimides: Part II

Continuing our research on molecular composites from fluorine-containing bis-maleimides (reported in this journal as Part I), we have prepared and characterized experimental composite films from a fluorine-free bismaleimide (BMI) with Technora^® fiber and from a fluorine-containing system of BMI and rigid rod by rapid amine-initiated anionic polymerization of the bis-maleimide. We have also explored the effect of increasing amounts of initiator and of system composition on the film structure.     

Some aspects of thermal self-focusing

The factors influencing the intensity at the focal point of a steady thermally self-focused beam are considered in detail and it is shown that in this case the beam will not split into filaments. The self-focusing of short pulses is considered and is shown that the shape of the focus depends on the time constant associated with the change of refractive index.     

M1-transitions and the mutual orientation of the unpaired nucleons in odd-odd nuclei

Experimental lifetimes and branching ratiosB(M1)/B(E2) are used to determine reduced M1-transition probabilities between collective-band levels withI=1 in^{102, 104, 106}Ag and in the odd-odd isotopes of La, Pr, Pm and Tl. The extractedB(M1) values are compared with calculations in the framework of the quasiclassical approximation and the model axial rotor+two quasiparticles. The reduced M1-transition probabilities along with the magnetic moments were found to depend on the mutual orientation of the angular momenta of the unpaired nucleons in the odd-odd nuclei.The authors would like to thank the staffs of Cyclotron Laboratory of P.T.I. in St. Petersburg and the Nuclear Moments Laboratory of I.N.R. in Kiev for assistance in the experiments. One of us (A.I.L.) wishes to thank the Sektion Physik of the Ludwig Maximilians Universität München for its hospitality and financial support.     

Intramolecular transport of charge carriers in trimeric aniline upon a three-step acid doping process

The "acid doping" of a methyl-capped aniline trimer, N-[4-(dimethylamino)phenyl]-N-(4-{[4-(dimethylamino)phenyl]imino}-2,5- cyclohexadien-1-ylidene)-amine (TANI), was performed stoichiometrically to study the nature of charge carriers induced by the acid protonation process. The redox centers in TANI were found to undergo a reversible three-step protonation with 1 equiv, 2 equiv and a large molar excess of dodecylbenzenesulfonic acid (DBSA) in chloroform, as evidenced by three different chromophores (doping levels I, II and III) observed using UV-vis-NIR. Acidity of the dopants and solvent polarity were controlling factors. As revealed by electron paramagnetic resonance spectroscopy (EPR), the doping levels I, II, and III achieved by doping 0.1 mM TANI/chloroform solutions with different amounts of DBSA exhibited relative spin densities of 1:1.2:2.2. Since the expected maximum spin population of TANI through acid doping is two spins per molecule, the reduced paramagnetism given by the doubly protonated TANI (doping level II) indicated partially coupled unpaired spins. The third protonation step (doping level III) produced almost double the unpaired spin concentration compared to the lower doping levels and a multiline EPR spectrum likely comprising two overlapping signals of similar overall line width. The hyperfine couplings contributing to the splittings in this signal were estimated by simulation incorporating 6-H and 1-N nuclei most likely from one highly localized unpaired spin on a terminal dimethylamino group, with an underlying apparent singlet arising from a delocalized unpaired spin; the diradical proposed as the species exhibiting the multiplet EPR signal is isolated by the bridging ammonium cation created by the third doping step. The phenomena suggested the stepwise evolution of partly formed diamagnetic bipolarons from polaron interactions at doping level II and the transformation to the more isolated unsymmetrical system we label "two polarons on a chain" in a triplet state at doping level III. The results provide the characterization of novel doping behaviors for a trimeric aniline molecule in organic solution.     

Impedance study of thiolated polyaniline

Covalent attachment of thiolated probes to conducting polymers such as polyaniline (PANI) is a promising approach towards the development of electrochemical sensors and biosensors. However, thiolation alters the conjugated polymer backbone and influences the electrochemical behavior of the conducting polymer. PANI studied in this work was electropolymerized on glassy carbon (GC) electrodes from a solution of 0.1 M aniline in 0.5 or 1.0 M H₂SO₄. The GC/PANI electrodes were then functionalized by covalent attachment of 2-mercaptoethanol to the PANI backbone. The progress of thiolation was studied by cyclic voltammetry and electrochemical impedance spectroscopy (EIS). Thiolation of PANI was found to cause an initial decrease in electroactivity at 0–0.25 V and an increase in electroactivity at 0.25–0.6 V. However, prolonged thiolation caused a loss of electroactivity of PANI, which could be seen from EIS measurements as a dramatic decrease in the bulk redox capacitance of PANI.     

Effect of polyaniline particle size on the properties of a polyaniline-nylon 6 composite

A method is proposed for the preparation of a conducting polyaniline-nylon 6 composite with controlled morphology of its surface. The method consists of the ammonium persulfate-induced oxidation polymerization of aniline in the presence of nylon 6. As has been established with the use of atomic force microscopy, spherical polyaniline particles are formed on the surface of nylon 6 and their sizes decrease with an increase in the duration of nylon 6 hydrothermal modification at 100° C. It is shown that a decline in polyaniline particle size in the polyaniline-nylon 6 composite enhances its reactivity with respect to KI.     

Intersection theorems under dimension constraints

In Ahlswede et al. [Discrete Math. 273(1-3) (2003) 9-21] we posed a series of extremal (set system) problems under dimension constraints. In the present paper, we study one of them: the intersection problem. The geometrical formulation of our problem is as follows. Given integers 0?t, k?n determine or estimate the maximum number of (0,1)-vectors in a k-dimensional subspace of the Euclidean n-space Rⁿ, such that the inner product (“intersection”) of any two is at least t. Also we are interested in the restricted (or the uniform) case of the problem; namely, the problem considered for the (0,1)-vectors of the same weight ω.The paper consists of two parts, which concern similar questions but are essentially independent with respect to the methods used.In Part I, we consider the unrestricted case of the problem. Surprisingly, in this case the problem can be reduced to a weighted version of the intersection problem for systems of finite sets. A general conjecture for this problem is proved for the cases mentioned in Ahlswede et al. [Discrete Math. 273(1-3) (2003) 9-21]. We also consider a diametric problem under dimension constraint.In Part II, we study the restricted case and solve the problem for t=1 and k<2ω, and also for any fixed 1?t?ω and k large.