Adiabatic approximation in nonperturbative time-dependent density-functional theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.     

Conductivity in an activity gradient

A procedure to evaluate conductivity measurements on a sample exposed to an activity gradient is presented The method allows the measured mean conductivity to be subsequently associated with a denned activity It offers not only an experimentally simple alternative to the Wagner-Hebb experiment, but also enables detailed information to be obtained about the activity dependence of the conductivity in polarization measurements with two blocking electrodes as well as in concentration cell experiments, no matter whether a two- or four-point arrangement is used It is further shown how the steady-state activities, which are necessary to compute the desired mean value, can be obtained from the initial and boundary conditions     

The radiation of rotating magnetic dipoles in vacuo in general relativity

An approximate solution of Maxwell's equations for the rotating oblique magnetic dipole is given on the geometrical background of the Schwarzschild metric. The energy radiation is calculated for both the case of the Schwarzschild geometry and the linearized Kerr metric on the basis of the Newman-Penrose formalism. It is shown that general relativistic effects are not sufficient to explain by themselves the experimentally measured slowdown laws of realistic pulsars.     

The impact parameter dependence of the Pb + Pb K − MO spectrum

Molecular orbital X-rays are emitted during ion-atom collisions. The theoretical treatment, numerical results for the Pb + Pb system and a comparison with background radiation like NNB, SEB and γ-decay of Coulomb excited nuclei are presented.     

Calculation of wavefunctions and frequencies for noninfinitesimal vibrations: Comparison of various methods using ab initio CI potential curves

Three computational methods employing different means of representing molecular potentials are used to obtain wavefunctions and energy levels for noninfinitesimal vibrations. An interpolation scheme based on a cubic spline fitting procedure is introduced to supplement the CI energy results obtained explicitly in actual calculations. As long as a representative set of potential points is available it is found that the results of all three methods (two of variational and one of numerical integration type) are quite consistent, for both bending and stretching vibrations of ground and electronically excited states (examples for HCN and O₂ are considered). In addition a comparison of one- and two-dimensional bending vibrational treatments is made.     

Phase transitions in experimental systems

Scaling functions of the support and of the measure have been used to characterize the scaling behavior of a dynamical system. While scaling functions for the scaling of the measure, ƒ(), have been calculated for a number of experimental systems, examples of scaling functions φ(λ) for the scaling of the support are difficult to obtain. In this contribution, we report on a phase-transition-like effect of an experimental p-doped germanium semiconductor sample. It is found that the results obtained from the dynamical scaling function agree with those obtained by Horita et al. from model maps, indicating that scaling functions for the scaling of the support are a powerful method of characterizing experimental dynamical systems.     

A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n ² ) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.     

The contributions of amplitude-and phase-sensitive detection to the synchronous demodulation in a RF SQUID magnetometer

It is known that the tank-circuit voltage of the rf SQUID carries information about the magnetic flux to be detected in amplitude and phase. The coherent demodulationtechnique utilizes mixing circuits to shift the rf tank voltage spectrum to dc without loss of any signal-information both in amplitude and phase (AM & Pm-detection). Vice versa such a combined detection can be devided into two several detection channels, amplitude sensitive detection (AM) and phase sensitive detection (PM). The contribution of each single mode to the combined detection AM & PM is analysed theoretically in the limit of small magnetic signals and measured in special rf circuits of the magnetometer, which apply PLL-techniques. The influence of feedback is also calculated. For refined studies of the interesting parameters the reference signal of the rf mixer allows to be phase-shifted by an arbitrary amount. All three modes of detections are sketched in diagrams as magnetometeroutput versus phase-shift of that reference signal. In addition, noise analysis is included and measured for vanishing signal. Basic formulas are derived for signal-to-noise ratios. A correlation coefficient is defined for recording correlated noise sources between AM and PM, whereby the possibility of S/N-improvement is pointed out. By computer support the graphs of equations are fitted to measured data with least mean-square deviation. More logical than functional circuit diagrams complete the insight into the treated basic ideas.     

Compactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments

When a cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L ²=L ²(R) with dilation integer factor M2, the standard matrix extension approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notion of vanishing moment recovery (VMR) was introduced in our earlier work (and independently by Daubechies et al.) for dilation M=2 to increase the order of vanishing moments. This present paper extends the tight frame results in the above mentioned papers from dilation M=2 to arbitrary integer M2 for any compactly supported M-dilation scaling functions. It is shown, in particular, that M compactly supported tight frame generators suffice, but not M–1 in general. A complete characterization of the M-dilation polynomial symbol is derived for the existence of M–1 such frame generators. Linear spline examples are given for M=3,4 to demonstrate our constructive approach.