Action functionals for strings in four dimensions

All possible action functionals on the space of surfaces in ${\bf R}^4$ that depend only on first and second derivatives of the functions, entering the equation of the surface, and satisfy the condition of invariance with respect to rigid motions are described.Comment: 9 pages, LaTeX, 7 figure

Complex Susceptibility of Liquid Water as a Two-Potential System of Reorienting Polar Molecules

The theory elaborated in ref. 1 and 2 is applied to the calculation of the liquid water wide-band (0 < ν/cm^(-1) < 1000) dielectric spectra. These comprise the Debye relaxation region at the centimetre/millimetre wavelengths and the two-humped absorption coefficient frequency dependence in the far infrared (FIR) region. It is supposed that a major part of H2O molecules, called [L]-particles or [L]-molecules, are bonded by relatively strong H-bonds; [L]-molecules perform librations of relatively small amplitude β (β is about 20°). The remaining molecules called R-molecules have more rotational / translational mobility. A new microscopic molecular confined rotator / doble well potential (CR DWP) model of liquid water is developed. The contributions of [L]-and [R]-molecules to the complex permittivity ε are found on the basis of the confined rotator (CR) and the double well potential (DWP) models, with rectangular and cos^2(θ) intermolecular potential profiles, respectively. It is shown that the CR/DWP model gives a good description of the Debye relaxation and a qualitative description of FIR the dielectric spectra of water

Low-temperature acoustic characteristics of the amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5

The temperature dependences of the sound velocity v and attenuation alpha of high-frequency (50–160 MHz) sound in the bulk amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5 are studied at helium temperatures in the normal and superconducting states. The alloy is characterized by a relatively small constant C determining the intensity of interaction between an elastic wave and two-level systems. The density of states of the latter systems is estimated. The peculiarities in the variation of v during the superconducting transition point to the possibility of a gapless superconductivity in a narrow temperature interval near Tc

Dielectric Response and a Phenomenon of a Narrow Band Absorption for a Classical Rotor in a Double Well Potential

The theory of dielectric relaxation in a planar ensemble of polar molecules is presented for a model where dipoles rotate in an intermolecular conservative double well potential, having a profile U = U_0*sin^2(θ). The evolution of the wide band dielectric spectra is demonstrated when the potential depth U_0 is varied; an isotropic and anisotropic medium being taken as examples. The spectra comprise the Debye relaxation and the quasi-resonant Poley absorption region. The rigorous theory is compared with a simplified one which was called the hybrid quasi-elastic bond / extended diffusion model. This approximation is valid for a qualitative description and also for the quantitative one at the large field parameter p = (U_0/((k_B)T))^(1/2). For P >> 1 the spectrum comprises one narrow absorption band and one Debye relaxation region considerably shifted to low frequencies. It is show that in the long lifetime limit τ there exists a minimum absorption band Δν_0(p). The quantity Δν_0 becomes small if the parameter p >> 1.The dielectric relaxation in ice 1 is discussed with regards to this phenomenon

Generic canonical form of pairs of matrices with zeros

We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all of these pairs reduce to the same pair (C, D) from this family, except for pairs whose arbitrary entries are zeros of a certain polynomial. The polynomial and the pair (C D) are constructed by a combinatorial method based on properties of a certain graph.Comment: 13 page