22,255 research outputs found
Calculus on surfaces with general closest point functions
The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs
Topological derivation of shape exponents for stretched exponential relaxation
In homogeneous glasses, values of the important dimensionless
stretched-exponential shape parameter beta are shown to be determined by magic
(not adjusted) simple fractions derived from fractal configuration spaces of
effective dimension d* by applying different topological axioms (rules) in the
presence (absence) of a forcing electric field. The rules are based on a new
central principle for defining glassy states: equal a priori distributions of
fractal residual configurational entropy. Our approach and its beta estimates
are fully supported by the results of relaxation measurements involving many
different glassy materials and probe methods. The present unique topological
predictions for beta typically agree with observed values to ~ 1% and indicate
that for field-forced conditions beta should be constant for appreciable ranges
of such exogenous variables as temperature and ionic concentration, as indeed
observed using appropriate data analysis. The present approach can also be
inverted and used to test sample homogeneity and quality.Comment: Original 13 pages lengthened to 21 pages (longer introduction, added
references and discussion of new experimental data published since original
submission
Imaging crystal orientations in multicrystalline silicon wafers via photoluminescence
We present a method for monitoring crystal orientations in chemically polished and unpassivated multicrystalline silicon wafers based on band-to-band photoluminescence imaging. The photoluminescence intensity from such wafers is dominated by surface recombination, which is crystal orientation dependent. We demonstrate that a strong correlation exists between the surface energy of different grain orientations, which are modelled based on first principles, and their corresponding photoluminescence intensity. This method may be useful in monitoring mixes of crystal orientations in multicrystalline or so-called “cast monocrystalline” wafers.H. C. Sio acknowledges scholarship support from
BT Imaging and the Australian Solar Institute, and the
Centre for Advanced Microscopy at ANU for SEM access.
This work has been supported by the Australian Research
Council
Magneto-electric coupling in zigzag graphene nanoribbons
Zigzag graphene nanoribbons can have magnetic ground states with
ferromagnetic, antiferromagnetic, or canted configurations, depending on
carrier density. We show that an electric field directed across the ribbon
alters the magnetic state, favoring antiferromagnetic configurations. This
property can be used to prepare ribbons with a prescribed spin-orientation on a
given edge.Comment: 4 pages, 5 figure
Magnetic interactions of substitutional Mn pairs in GaAs
We employ a kinetic-exchange tight-binding model to calculate the magnetic
interaction and anisotropy energies of a pair of substitutional Mn atoms in
GaAs as a function of their separation distance and direction. We find that the
most energetically stable configuration is usually one in which the spins are
ferromagnetically aligned along the vector connecting the Mn atoms. The
ferromagnetic configuration is characterized by a splitting of the topmost
unoccupied acceptor levels, which is visible in scanning tunneling microscope
studies when the pair is close to the surface and is strongly dependent on pair
orientation. The largest acceptor splittings occur when the Mn pair is oriented
along the symmetry direction, and the smallest when they are oriented
along . We show explicitly that the acceptor splitting is not simply
related to the effective exchange interaction between the Mn local moments. The
exchange interaction constant is instead more directly related to the width of
the distribution of all impurity levels -- occupied and unoccupied. When the Mn
pair is at the (110) GaAs surface, both acceptor splitting and effective
exchange interaction are very small except for the smallest possible Mn
separation.Comment: 25 figure
Chern number spins of Mn acceptor magnets in GaAs
We determine the effective total spin of local moments formed from
acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern
numbers. We find that when individual Mn atoms are close to the sample surface,
the total spin changes from to , due to quenching of the
acceptor orbital moment. For Mn pairs in bulk, the total depends on the
pair orientation in the GaAs lattice and on the separation between the Mn
atoms. We point out that Berry curvature variation as a function of local
moment orientation can profoundly influence the quantum spin dynamics of these
magnetic entities.Comment: 4 pages, 3 figure
Magnetic properties of substitutional Mn in (110) GaAs surface and subsurface layers
Motivated by recent STM experiments, we present a theoretical study of the
electronic and magnetic properties of the Mn-induced acceptor level obtained by
substituting a single Ga atom in the (110) surface layer of GaAs or in one of
the atoms layers below the surface. We employ a kinetic-exchange tight-binding
model in which the relaxation of the (110) surface is taken into account. The
acceptor wave function is strongly anisotropic in space and its detailed
features depend on the depth of the sublayer in which the Mn atom is located.
The local-density-of-states (LDOS) on the (110) surface associated with the
acceptor level is more sensitive to the direction of the Mn magnetic moment
when the Mn atom is located further below the surface. We show that the total
magnetic anisotropy energy of the system is due almost entirely to the
dependence of the acceptor level energy on Mn spin orientation, and that this
quantity is strongly dependent on the depth of the Mn atom.Comment: 14 pages, 13 figure
Non-equilibrium Entanglement and Noise in Coupled Qubits
We study charge entanglement in two Coulomb-coupled double quantum dots in
thermal equilibrium and under stationary non-equilibrium transport conditions.
In the transport regime, the entanglement exhibits a clear switching threshold
and various limits due to suppression of tunneling by Quantum Zeno localisation
or by an interaction induced energy gap. We also calculate quantum noise
spectra and discuss the inter-dot current correlation as an indicator of the
entanglement in transport experiments.Comment: 4 pages, 4 figure
On the Distribution of a Second Class Particle in the Asymmetric Simple Exclusion Process
We give an exact expression for the distribution of the position X(t) of a
single second class particle in the asymmetric simple exclusion process (ASEP)
where initially the second class particle is located at the origin and the
first class particles occupy the sites {1,2,...}
- …