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We investigate vibrational excitation broadening in one dimensional Fibonacci model of quasicrystals (QCs). The chain is constructed from particles with two masses following the Fibonacci inflation rule. The eigenmode spectrum depends crucially on the mass ratio. We calculate the eigenstates and eigenfunctions. All calculations performed self-consistently within the regular expansion over the three wave coupling constant. The approach can be extended to three dimensional systems. We find that in the intermediate range of mode coupling constants, three-wave broadening for the both types of systems (1D Fibonacci and 3D QCs) depends universally on frequency. Our general qualitative conclusion is that for a system with a non-simple elementary cell phonon spectrum broadening is always larger than for a system with a primitive cell (provided all other characteristics are the same).

An exact expression of the bridge-mediated donor-acceptor effective coupling, Hda, is derived. For systems represented by a tight-binding Hamiltonian with nearest-neighbor interactions, we show that |Hda|2 is equal to the product over all squares of nearest-neighbor couplings divided by an appropriate product of level spacing of eigen energies of the Hamiltonian. These results are subsequently compared with those obtained using perturbation approaches.

The anomalous fluctuation contribution to viscosity coefficients ηfl of dilute lyotropic systems induced by fluctuations of membranes constituting the system is investigated. This contribution is determined by non-linear interaction of hydrodynamic modes with the bending mode, describing the relaxation of the shape of membranes. The explicit expressions for the ηfl can be obtained in the framework of Wyld diagram technique by summation of a principal series of diagrams. There are two regions of frequencies ω where ηfl behaves as |ω|-5/3 and as |ω|-1/3 and is proportional to the concentration of surfactant molecules. In the low-frequency limit ηfl depends neither on ω nor on and exceeds the viscosity of the pure solvent.

The low-frequency dynamics of smectics C is studied. A system of non-linear equations is given, on the basis of which a spectrum of eigenmodes of smectic C is obtained. An estimate is made of the coefficients entering the dispersion laws and a description of their critical behaviour near A-C transition is given. The analysis shows that orientation and undulation modes always couple strongly, which results in an essential difference of the undulation dispersion law in smectic C compared to smectic A or B. Owing to this the coefficients at omega -1 in anomalous fluctuational contributions to the viscosities of smectics A and C differ. The results of this paper make it possible to give a complete interpretation of the experimental data on sound attenuation in smectics.

Physical and biological observation methods provide a variety of bilayer membranes' shapes and their transformations. Besides, the topological and geometrical methods allow us to deduce a classification of all possible membrane surfaces. This double-sided approach leads to a deeper insight into membranes properties. Our goal is to apply an appropriate mathematical technique for classifying vesicles (closed surfaces in mathematical terminology) and for their transformation ways. The problem turned out to be an intricate one, and to our knowledge no mathematical techniques have been applied to its solution. We find that all vesicles can be decomposed in a small number of universality classes generated by a few 'bricks': a torus, a screwed torus, and the real projective plane. We consider several ways of transforming membrane surfaces, bearing in mind that they possess an additional extremal property. Our method exploits different constructions of minimal surfaces in S3. We estimate energetic barrier for transformation of minimal membrane surfaces using the so-called doubling procedure. This problem is far from being a pure theoretical exercise. For instance, almost all cells' biological functions, or tumor progression, are accompanied by apparently singular cell membrane transformations.

In this communication we present a theoretical analysis of sound modes in non-magnetic solids or fluids in static and uniform magnetic field. The physics behind is based on the so-called gyromagnetic phenomena i.e., the appearance of a magnetic moment due to the intrinsic orbital moment of vibrational modes. The gyromagnetic contributions into the Lagrangian describing vibrations, conceptually dramatically modify the correlation (and linear response) functions of the displacements. Namely, in the response function one gets singular branching points (instead of simple poles which determine sound mode dispersion laws). In practical terms the corrections are very small although X-ray and optic experimental techniques have progressed to the point where observations of such very small effects are not hopeless.

Possible types of liquid-crystalline order in systems consisting of rod-shaped or diskotic, as well as structurally more complicated, molecules are examined. Special attention is devoted to new liquid-crystalline phases. Their basic physical properties are analyzed. The phase diagrams and the peculiarities of the critical behavior are investigated in each case. Analogies to some well known problems in the physics of the condensed state are discussed.