577 research outputs found
Comparison of topologies on *-algebras of locally measurable operators
We consider the locally measure topology on the *-algebra
of all locally measurable operators affiliated with a von
Neumann algebra . We prove that coincides with
the -topology on if
and only if the algebra is -finite and a finite algebra.
We study relationships between the topology and various
topologies generated by faithful normal semifinite traces on .Comment: 21 page
Front propagation in geometric and phase field models of stratified media
We study front propagation problems for forced mean curvature flows and their
phase field variants that take place in stratified media, i.e., heterogeneous
media whose characteristics do not vary in one direction. We consider phase
change fronts in infinite cylinders whose axis coincides with the symmetry axis
of the medium. Using the recently developed variational approaches, we provide
a convergence result relating asymptotic in time front propagation in the
diffuse interface case to that in the sharp interface case, for suitably
balanced nonlinearities of Allen-Cahn type. The result is established by using
arguments in the spirit of -convergence, to obtain a correspondence
between the minimizers of an exponentially weighted Ginzburg-Landau type
functional and the minimizers of an exponentially weighted area type
functional. These minimizers yield the fastest traveling waves invading a given
stable equilibrium in the respective models and determine the asymptotic
propagation speeds for front-like initial data. We further show that
generically these fronts are the exponentially stable global attractors for
this kind of initial data and give sufficient conditions under which complete
phase change occurs via the formation of the considered fronts
Instabilities and disorder of the domain patterns in the systems with competing interactions
The dynamics of the domains is studied in a two-dimensional model of the
microphase separation of diblock copolymers in the vicinity of the transition.
A criterion for the validity of the mean field theory is derived. It is shown
that at certain temperatures the ordered hexagonal pattern becomes unstable
with respect to the two types of instabilities: the radially-nonsymmetric
distortions of the domains and the repumping of the order parameter between the
neighbors. Both these instabilities may lead to the transformation of the
regular hexagonal pattern into a disordered pattern.Comment: ReVTeX, 4 pages, 3 figures (postscript); submitted to Phys. Rev. Let
Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films
We analyze the electric current and magnetic field driven domain wall motion
in perpendicularly magnetized ultrathin ferromagnetic films in the presence of
interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and
in-plane uniaxial anisotropies. We obtain exact analytical Walker-type
solutions in the form of one-dimensional domain walls moving with constant
velocity due to both spin-transfer torques and out-of-plane magnetic field.
These solutions are embedded into a larger family of propagating solutions
found numerically. Within the considered model, we find the dependencies of the
domain wall velocity on the material parameters and demonstrate that adding
in-plane anisotropy may produce domain walls moving with velocities in excess
of 500 m/s in realistic materials under moderate fields and currents.Comment: 6 pages, 2 figure
Non-meanfield deterministic limits in chemical reaction kinetics far from equilibrium
A general mechanism is proposed by which small intrinsic fluctuations in a
system far from equilibrium can result in nearly deterministic dynamical
behaviors which are markedly distinct from those realized in the meanfield
limit. The mechanism is demonstrated for the kinetic Monte-Carlo version of the
Schnakenberg reaction where we identified a scaling limit in which the global
deterministic bifurcation picture is fundamentally altered by fluctuations.
Numerical simulations of the model are found to be in quantitative agreement
with theoretical predictions.Comment: 4 pages, 4 figures (submitted to Phys. Rev. Lett.
Translation of Muratov, E. A. 1966. Kroveparazit roda \u3ci\u3eNuttallia\u3c/i\u3e Franca ot domovoi myshi (\u3ci\u3eMus musculus\u3c/i\u3e Lin.) [= A blood parasite of the genus \u3ci\u3eNuttallia\u3c/i\u3e from the house mouse, \u3ci\u3eMus musculus\u3c/i\u3e]. \u3ci\u3eDokl. Tadzhik SSR\u3c/i\u3e 9(5): 34-47
Translation number 27, College of Veterinary Medicine, University of Illinois, Urbana, Illinois, United States (4 pages)
Translation of Muratov, E. A. 1966. Kroveparazit roda Nuttallia Franca ot domovoi myshi (Mus musculus Lin.) [= A blood parasite of the genus Nuttallia from the house mouse, Mus musculus]. Dokl. Tadzhik SSR 9(5): 34-47
Translated from Russian to English by Frederick K. Plous, Jr., and edited by Norman D. Levin
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