A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

Dependence of the Phase Transition Temperature on the Domain Size

Dependence of the phase transition temperature on the domain size is investigated for a double-well quadratic potential. It is shown that for a domain whose boundary is subjected to a hydrostatical pressure, the temperature of phase transitions is independent of the domain and the surface tension coefficient and depends exclusively on the properties of the elastic media. If the displacement field vanishes on the boundary, then for sufficiently small domains, the temperature also does not depend on the surface tension and domain size and is determined by properties of the elastic media only. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 98–113.     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Energy losses of dipoles traveling relative to a moving medium

We consider the radiation from nonoscillating dipoles traveling with constant velocity directed parallel or antiparallel to the velocity of a homogeneous transparent moving medium. It is assumed that the medium in its rest frame is isotropic and has no spatial dispersion. We obtain expressions for the radiative energy losses and estimate the polarization energy losses of electric and magnetic dipoles of different orientations. In particular, it is shown that the energy loss of a source is negative if it moves in the direction of the medium motion and the source velocity is less than the medium velocity. Estimates for the energy losses of dipoles in the cases of an electron beam and a flow of a weakly dispersive medium are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 502–512, June 2006.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.     

Velocity measurements in liquid sodium by means of ultrasound Doppler velocimetry

A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field. Received: 12 June 2001/Accepted: 27 October 2001     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002