1,083 research outputs found
Frictional shear cracks
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
Nonlinear Two-Dimensional Green's Function in Smectics
The problem of the strain of smectics subjected to a force distributed over a
line in the basal plane has been solved
Fracture and Friction: Stick-Slip Motion
We discuss the stick-slip motion of an elastic block sliding along a rigid
substrate. We argue that for a given external shear stress this system shows a
discontinuous nonequilibrium transition from a uniform stick state to uniform
sliding at some critical stress which is nothing but the Griffith threshold for
crack propagation. An inhomogeneous mode of sliding occurs, when the driving
velocity is prescribed instead of the external stress. A transition to
homogeneous sliding occurs at a critical velocity, which is related to the
critical stress. We solve the elastic problem for a steady-state motion of a
periodic stick-slip pattern and derive equations of motion for the tip and
resticking end of the slip pulses. In the slip regions we use the linear
viscous friction law and do not assume any intrinsic instabilities even at
small sliding velocities. We find that, as in many other pattern forming
system, the steady-state analysis itself does not select uniquely all the
internal parameters of the pattern, especially the primary wavelength. Using
some plausible analogy to first order phase transitions we discuss a ``soft''
selection mechanism. This allows to estimate internal parameters such as crack
velocities, primary wavelength and relative fraction of the slip phase as
function of the driving velocity. The relevance of our results to recent
experiments is discussed.Comment: 12 pages, 7 figure
High-Field Low-Frequency Spin Dynamics
The theory of exchange symmetry of spin ordered states is extended to the
case of high magnetic field. Low frequency spin dynamics equation for
quasi-goldstone mode is derived for two cases of collinear and noncollinear
antiferromagnets.Comment: 2 page
Transfer matrix solution of the Wako-Sait\^o-Mu\~noz-Eaton model augmented by arbitrary short range interactions
The Wako-Sait{\^o}-Mu\~noz-Eaton (WSME) model, initially introduced in the
theory of protein folding, has also been used in modeling the RNA folding and
some epitaxial phenomena. The advantage of this model is that it admits exact
solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002)
which facilitates the study of realistic systems. However, a shortcoming of the
model is that it accounts only for interactions within continuous stretches of
native bonds or atomic chains while neglecting interstretch (interchain)
interactions. But due to the biopolymer (atomic chain) flexibility, the
monomers (atoms) separated by several non-native bonds along the sequence can
become closely spaced. This produces their strong interaction. The inclusion of
non-WSME interactions into the model makes the model more realistic and
improves its performance. In this study we add arbitrary interactions of finite
range and solve the new model by means of the transfer matrix technique. We can
therefore exactly account for the interactions which in proteomics are
classified as medium- and moderately long-range ones.Comment: 15 pages, 2 figure
Elastic domains in antiferromagnets
We consider periodic domain structures which appear due to the magnetoelastic
interaction if the antiferromagnetic crystal is attached to an elastic
substrate. The peculiar behavior of such structures in an external magnetic
field is discussed. In particular, we find the magnetic field dependence of the
equilibrium period and the concentrations of different domains
Unified continuum approach to crystal surface morphological relaxation
A continuum theory is used to predict scaling laws for the morphological
relaxation of crystal surfaces in two independent space dimensions. The goal is
to unify previously disconnected experimental observations of decaying surface
profiles. The continuum description is derived from the motion of interacting
atomic steps. For isotropic diffusion of adatoms across each terrace, induced
adatom fluxes transverse and parallel to step edges obey different laws,
yielding a tensor mobility for the continuum surface flux. The partial
differential equation (PDE) for the height profile expresses an interplay of
step energetics and kinetics, and aspect ratio of surface topography that
plausibly unifies observations of decaying bidirectional surface corrugations.
The PDE reduces to known evolution equations for axisymmetric mounds and
one-dimensional periodic corrugations.Comment: 5 pages, 1 figur
Random matrices, non-backtracking walks, and orthogonal polynomials
Several well-known results from the random matrix theory, such as Wigner's
law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of
non-backtracking walks on a certain graph. Orthogonal polynomials with respect
to the limiting spectral measure play a role in this approach.Comment: (more) minor change
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