We derive an analytical expression for the size distribution of monoatomic wires in the framework of a one-dimensional lattice gas model at thermodynamic equilibrium. The theoretical results are compared with the size distribution of one-dimensional Ag wires obtained via nucleation at the step edges of the Pt͑997͒ surface.
It is shown that the strain field of an edge dislocation in a smectic crystal must be described in the framework of nonlinear theory, even far away from the core region. We present an exact solution of this nonlinear problem. The result of the linear theory is recovered in the limit of large bending rigidity.
͓S1063-651X͑99͒50605-3͔PACS number͑s͒: 61.30. Jf, 61.72.Lk The strain field of point and linear defects in crystals decays with the distance from the defect, so that the long range distortion around the defects can be described within the framework of the linear theory of elasticity. The same approach has been used by de Gennes to describe edge dislocations in a smectic crystal ͓1͔. This linear theory is believed to be exact far from the dislocation core, and it is presented in text books on physics of liquid crystals and also in the more general context of the theory of elasticity ͑see, for example, ͓2,3͔͒. The intrinsic anisotropy of smectics, however, means that nonlinear effects can be important even for small strains, and the Helfrich instability ͓4͔, the corrugation of smectic layers in a stretched smectic film, is a well-known example.In this Rapid Communication we show that the linear theory of edge dislocations in smectics ͓1͔ is valid only in the limit bӶ, where b is the Burgers vector and is the length scale in the elastic energy functional. In the general case where bϳ nonlinearities must be taken into account to describe the asymptotic behavior even at large distances from the core. To the best of our knowledge this is the first instance where the asymptotic distortion field induced by the defect in a three-dimensional object must be treated by nonlinear theory. Moreover, we give an exact solution of the nonlinear equation for the displacement field around a dislocation.For small strains the distortion energy of a smectic is ͓2͔
Fϭ
The interaction between inclusions mediated by biological membranes undulations is analyzed. The interaction law is interpreted in terms of symmetries associated with inclusions. We show, in particular, that for a C3 and C3v symmetries the interaction law falls as 1/r3. We show that for completely isotropic inclusions, the dominant interaction vanishes to all orders, and the first contribution stems from the induced interaction which behaves as 1/r4. The same law holds for any other symmetry which is higher than C4. We introduce a straightforward method to compute these interactions. We point out important differences with results in the literature and explain the discrepancies.
We discuss crack propagation along the interface between two dissimilar
materials. The crack edge separates two states of the interface, ``stick'' and
``slip''. In the slip region we assume that the shear stress is proportional to
the sliding velocity, i.e. the linear viscous friction law. In this picture the
static friction appears as the Griffith threshold for crack propagation. We
calculate the crack velocity as a function of the applied shear stress and find
that the main dissipation comes from the macroscopic region and is mainly due
to the friction at the interface. The relevance of our results to recent
experiments,
Baumberger et al, Phys. Rev. Lett. 88, 075509 (2002), is discussed
The magnetic ordering in the mixed valence compound β-Na The low-temperature electron spin resonance (ESR) spectra and the static magnetization data obtained for the stoichiometric single crystals of β-Na0.33V2O5 indicate that this quasi-one-dimensional mixed valence compound demonstrates at TN = 22 K the phase transition into the canted antiferromagnetically ordered state. The spontaneous magnetization of 3.4 × 10 −3 µB per V 4+ ion was found to be oriented along the two-fold b axis of the monoclinic structure, the vector of antiferromagnetism is aligned with the a axis and the Dzyaloshinsky vector is parallel to the c-axis. The experimental data were successfully described in the frame of the macroscopic spin dynamics and the following values for the macroscopic parameters of the spin system were obtained: the Dzyaloshinsky field HD = 6 kOe, the energy gaps of two branches of the spin wave spectrum ∆1 = 48 GHz and ∆2 = 24 GHz.
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