284 research outputs found
Incommensurate spin density modulation in a copper-oxide chain compound with commensurate charge order
Neutron diffraction has been used to determine the magnetic structure of
NaCuO, a stoichiometric compound containing chains based on
edge-sharing CuO plaquettes. The chains are doped with 2/5 hole per Cu site
and exhibit long-range commensurate charge order with an onset well above room
temperature. Below K, the neutron data indicate long-range collinear
magnetic order with a spin density modulation whose propagation vector is
commensurate along and incommensurate perpendicular to the chains. Competing
interchain exchange interactions are discussed as a possible origin of the
incommensurate magnetic order
A Codazzi-like equation and the singular set for smooth surfaces in the Heisenberg group
In this paper, we study the structure of the singular set for a
smooth surface in the -dimensional Heisenberg group . We
discover a Codazzi-like equation for the -area element along the
characteristic curves on the surface. Information obtained from this ordinary
differential equation helps us to analyze the local configuration of the
singular set and the characteristic curves. In particular, we can estimate the
size and obtain the regularity of the singular set. We understand the global
structure of the singular set through a Hopf-type index theorem. We also
justify that Codazzi-like equation by proving a fundamental theorem for local
surfaces in .Comment: 64 pages, 17 figure
A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution
We present a class of functions in which is variant
of the Knopp class of nowhere differentiable functions. We derive estimates
which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no is pointwise anywhere improvable to C^{0,\be} for any \be>\al.
In particular, all 's are nowhere differentiable with derivatives singular
distributions. furnishes explicit realizations of the functional
analytic result of Berezhnoi.
Recently, the author and simulteously others laid the foundations of
Vector-Valued Calculus of Variations in (Katzourakis), of
-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of
Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange
PDE" of Calculus of Variations in is the nonlinear nondivergence
form Aronsson PDE with as special case the -Laplacian.
Using , we construct singular solutions for these PDEs. In the
scalar case, we partially answered the open regularity problem of
Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the
solutions can not be rigorously interpreted by existing PDE theories and
justify our new theory of Contact solutions for fully nonlinear systems
(Katzourakis). Validity of arguments of our new theory and failure of classical
approaches both rely on the properties of .Comment: 5 figures, accepted to SeMA Journal (2012), to appea
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds
We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold,
where the L^2 norm of all second derivatives of the function involving
horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian.
Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE
in non-divergence form with bounded measurable coefficients. The method of
proof is through a Bochner technique. The Heisenberg group is seen to be en
extremal manifold for our inequality in the class of manifolds whose Ricci
curvature is non-negative.Comment: 13 page
Competing magnetic fluctuations in Sr3Ru2O7 probed by Ti doping
We report the effect of nonmagnetic Ti4+ impurities on the electronic and
magnetic properties of Sr3Ru2O7. Small amounts of Ti suppress the
characteristic peak in magnetic susceptibility near 16 K and result in a sharp
upturn in specific heat. The metamagnetic quantum phase transition and related
anomalous features are quickly smeared out by small amounts of Ti. These
results provide strong evidence for the existence of competing magnetic
fluctuations in the ground state of Sr3Ru2O7. Ti doping suppresses the low
temperature antiferromagnetic interactions that arise from Fermi surface
nesting, leaving the system in a state dominated by ferromagnetic fluctuations.Comment: 5 pages, 4 figures, 1 tabl
Effects of hydrostatic pressure on the magnetic susceptibility of ruthenium oxide Sr3Ru2O7: Evidence for pressure-enhanced antiferromagnetic instability
Hydrostatic pressure effects on the temperature- and magnetic field
dependencies of the in-plane and out-of-plane magnetization of the bi-layered
perovskite Sr3Ru2O7 have been studied by SQUID magnetometer measurements under
a hydrostatic helium-gas pressure. The anomalously enhanced low-temperature
value of the paramagnetic susceptibility has been found to systematically
decrease with increasing pressure. The effect is accompanied by an increase of
the temperature Tmax of a pronounced peak of susceptibility. Thus,
magnetization measurements under hydrostatic pressure reveal that the lattice
contraction in the structure of Sr3Ru2O7 promotes antiferromagnetism and not
ferromagnetism, contrary to the previous beliefs. The effects can be explained
by the enhancement of the inter-bi-layer antiferromagnetic spin coupling,
driven by the shortening of the superexchange path, and suppression, due to the
band-broadening effect, of competing itinerant ferromagnetic correlations.Comment: 11 pages, 4 figure
The mixed problem in L^p for some two-dimensional Lipschitz domains
We consider the mixed problem for the Laplace operator in a class of
Lipschitz graph domains in two dimensions with Lipschitz constant at most 1.
The boundary of the domain is decomposed into two disjoint sets D and N. We
suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary
and the Neumann data is in L^p(N). We find conditions on the domain and the
sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we
may find a unique solution to the mixed problem and the gradient of the
solution lies in L^p
Parturient perineal distensibility tolerance assessed by EPI-NO: an observational study
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