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.     

The effect of dipole-dipole interaction on zero-THz frequency polarisation

The effect of intramolecular dipole-dipole interaction on polarisation at frequencies from 0 – 10¹² Hz in dipolar media is investigated using a numerical solution of the Sturm-Liouville eigenvalue problem to which the governing Smoluchowski equation reduces. The results of Budó for the long-wavelength limit are extended to all frequencies up to the far infrared, where the predominant inertial effects are treated using a preliminary first-order correction. The numerical method of Pryce may be used to investigate much more realistic interaction potentials than the simple harmonic and cosine form considered by Budó. These simple forms are, however, sufficient to indicate that the integrated absorption intensity per molecule in the far infrared is very sensitive to dipole-dipole interaction and relative hydrodynamic drag on both interacting groups. Applications of the theory to the disordered solid and nematic phases are considered.     

Rapid computer simulation of ESR spectra. Conventional ESR of axially symmetric 14N-nitroxide spin labels

A computer algorithm is presented for the simulation of the effect of molecular tumbling on ESR spectra, and is applied to simulation of the conventional ESR signal (the absorption signal detected at the first harmonic of the modulation frequency and in-phase with the modulation frequency, in the limit of low microwave and modulation power) of axially symmetric ¹⁴N-nitroxide spin labels. The algorithm is extremely fast and is economical in terms of computer memory requirements.