13,296 research outputs found
Second order splitting of a class of fourth order PDEs with point constraints
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments
Interleukin-1ß enhances capsaicin-induced neurogenic vasodilatation in the rat skin
No abstract available
Quantum Phase Transition in a Multi-Level Dot
We discuss electronic transport through a lateral quantum dot close to the
singlet-triplet degeneracy in the case of a single conduction channel per lead.
By applying the Numerical Renormalization Group, we obtain rigorous results for
the linear conductance and the density of states. A new quantum phase
transition of the Kosterlitz-Thouless type is found, with an exponentially
small energy scale close to the degeneracy point. Below , the
conductance is strongly suppressed, corresponding to a universal dip in the
density of states. This explains recent transport measurements.Comment: 4 pages, 5 eps figures, published versio
Generalized Symmetries of Impulsive Gravitational Waves
We generalize previous \cite{AiBa2} work on the classification of
() symmetries of plane-fronted waves with an impulsive profile. Due
to the specific form of the profile it is possible to extend the group of
normal-form-preserving diffeomorphisms to include non-smooth transformations.
This extension entails a richer structure of the symmetry algebra generated by
the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure
Dependence of the 0.5(2e2/h) conductance plateau on the aspect ratio of InAs quantum point contacts with in-plane side gates
The observation of a 0.5 conductance plateau in asymmetrically biased quantum
point contacts with in-plane side gates has been attributed to the onset of
spin-polarized current through these structures. For InAs quantum point
contacts with the same width but longer channel length, there is roughly a
fourfold increase in the range of common sweep voltage applied to the side
gates over which the 0.5 conductance plateau is observed when the QPC aspect
ratio (ratio of length over width of the narrow portion of the structure) is
increased by a factor 3. Non-equilibrium Green s function simulations indicate
that the increase in the size of the 0.5 conductance plateau is due to an
increased importance, over a larger range of common sweep voltage, of the
effects of electron-electron interactions in QPC devices with larger aspect
ratio. The use of asymmetrically biased QPCs with in-plane side gates and large
aspect ratio could therefore pave the way to build robust spin injectors and
detectors for the successful implementation of spin field effect transistorsComment: 30 pages, 9 figure
On mechanisms that enforce complementarity
In a recent publication Luis and Sanchez-Soto arrive at the conclusion that
complementarity is universally enforced by random classical phase kicks. We
disagree. One could just as well argue that quantum entanglement is the
universal mechanism. Both claims of universality are unjustified, however.Comment: 4 page
ADM and Bondi four-momenta for the ultrarelativistic Schwarzschild black hole
We argue that it is possible to assign Bondi as well as ADM four-momentum to
the ultrarelativistic limit of the Schwarzschild black hole in agreement to
what is expected on physical grounds: The Bondi-momentum is lightlike and equal
to the ADM-momentum up to the retarded time when particle and radiation escape
to infinity and drops to zero thereafter, leaving flat space behind.Comment: Changes in the expression used for the ADM four-momentum without
altering the result, correction of some minor typing error
Head-on collision of ultrarelativistic charges
We consider the head-on collision of two opposite-charged point particles
moving at the speed of light. Starting from the field of a single charge we
derive in a first step the field generated by uniformly accelerated charge in
the limit of infinite acceleration. From this we then calculate explicitly the
burst of radiation emitted from the head-on collision of two charges and
discuss its distributional structure. The motivation for our investigation
comes from the corresponding gravitational situation where the head-on
collision of two ultrarelativistic particles (black holes) has recently aroused
renewed interest.Comment: 4 figures, uses the AMSmat
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