Trajectory generation for road vehicle obstacle avoidance using convex optimization

This paper presents a method for trajectory generation using convex optimization to find a feasible, obstacle-free path for a road vehicle. Consideration of vehicle rotation is shown to be necessary if the trajectory is to avoid obstacles specified in a fixed Earth axis system. The paper establishes that, despite the presence of significant non-linearities, it is possible to articulate the obstacle avoidance problem in a tractable convex form using multiple optimization passes. Finally, it is shown by simulation that an optimal trajectory that accounts for the vehicle’s changing velocity throughout the manoeuvre is superior to a previous analytical method that assumes constant speed

Equilibration between edge states in the fractional quantum Hall effect regime at high imbalances

We experimentally study equilibration between edge states, co-propagating at the edge of the fractional quantum Hall liquid, at high initial imbalances. We find an anomalous increase of the conductance between the fractional edge states at the filling factor $\nu=2/5$ in comparison with the expected one for the model of independent edge states. We conclude that the model of independent fractional edge states is not suitable to describe the experimental situation at $\nu=2/5$.Comment: 4 page

Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B.Comment: 4 pages, RevTe

Electron-phonon interactions on a single-branch quantum Hall edge

We consider the effect of electron-phonon interactions on edge states in quantum Hall systems with a single edge branch. The presence of electron-phonon interactions modifies the single-particle propagator for general quantum Hall edges, and, in particular, destroys the Fermi liquid even at integer filling. The effect of the electron-phonon interactions may be detected experimentally in the AC conductance or in the tunneling conductance between integer quantum Hall edges.Comment: 9 pages (revtex) + one postscript file with 2 figures. A complete postscript file with all figures + text (5 pages) is available from http://FY.CHALMERS.SE/~eggert/fqh.ps or by request from [email protected]

Boundary interactions changing operators and dynamical correlations in quantum impurity problems

Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation; this is the case for instance for the occupation probability $P(t)$ in the double well problem of dissipative quantum mechanics (DQM). We show in this paper how to handle this situation in the framework of integrable quantum field theories by introducing ``boundary interactions changing operators''. We determine the properties of these operators by using an axiomatic approach similar in spirit to what is done for form-factors. This allows us to obtain new exact results for $P(t)$; for instance, we find that that at large times (or small $g$), the leading behaviour for g < 1/2} is $P(t)\propto e^{-\Gamma t}\cos\Omega t$, with the universal ratio. $\Omega/\Gamma = \cot {\pi g}/{2(1-g)}$.Comment: 4 pages, revte

Magnetotunneling as a Probe of Luttinger-Liquid Behavior

A novel method for detecting Luttinger-liquid behavior is proposed. The idea is to measure the tunneling conductance between a quantum wire and a parallel two-dimensional electron system as a function of both the potential difference between them, $V$, and an in-plane magnetic field, $B$. We show that the two-parameter dependence on $B$ and $V$ allows for a determination of the characteristic dependence on wave vector $q$ and frequency $\omega$ of the {\it spectral function}, $A_{\rm LL}(q,\omega)$, of the quantum wire. In particular, the separation of spin and charge in the Luttinger liquid should manifest itself as singularities in the $I$-$V$-characteristic. The experimental feasibility of the proposal is discussed.Comment: Accepted for publication in Phys. Rev. Let

A Randomised, Blinded, Placebo-Controlled, Dose Escalation Study of the Tolerability and Efficacy of Filgrastim for Haemopoietic Stem Cell Mobilisation in Patients With Severe Active Rheumatoid Arthritis

Autologous haemopoietic stem cell transplantation (HSCT) represents a potential therapy for severe rheumatoid arthritis (RA). As a prelude to clinical trails, the safety and efficacy of haemopoietic stem cell (HSC) mobilisation required investigation as colony-stimulating factors (CSFs) have been reported to flare RA. A double-blind, randomised placebo-controlled dose escalation study was performed. Two cohorts of eight patients fulfilling strict eligibility criteria for severe active RA (age median 40 years, range 24-60 years; median disease duration 10.5 years, range 2-18 years) received filgrastim (r-Hu-methionyl granulocyte(G)-(SF) at 5 and 10 microg/kg/day, randomised in a 5:3 ratio with placebo. Patients were unblinded on the fifth day of treatment and those randomised to filgrastim underwent cell harvesting (leukapheresis) daily until 2 X 10^6/kg CD34+ cells (haemopoietic stem and progenitor cells) were obtained. Patients were assessed by clinical and laboratory parameters before, during and after filgrastim administration. RA flare was defined as an increase of 30% or more in two of the following parameters: tender joint count, swollen joint count or pain score. Efficacy was assessed by quantitation of CD34+ cells and CFU-GM. One patient in the 5 microg/kg/day group and two patients in the 10 microg/kg/day group fulfilled criteria for RA flare, although this did not preclude successful stem cell collection. Median changes in swollen and tender joint counts were not supportive of filgrastim consistently causing exacerbation of disease, but administration of filgrastim at 10 microg/kg/day was associated with rises in median C-reactive protein and median rheumatoid factor compared with placebo. Other adverse events were well recognised for filgrastim and included bone pain (80%) and increases in alkaline phosphatase (four-fold) and lactate dehydrogenase (two-fold). With respect to efficacy, filgrastim at 10 microg/kg/day was more efficient with all patients (n = 5) achieving target CD34+ cell counts with a single leukapheresis (median = 2.8, range = 2.3-4.8 X 10^6/kg, median CFU-GM = 22.1, range = 4.2-102.9 X 10^4/kg), whereas 1-3 leukaphereses were necessary to achieve the target yield using 5 microg/kg/day. We conclude that filgrastim may be administered to patients with severe active RA for effective stem cell mobilisation. Flare of RA occurs in a minority of patients and is more likely with 10 than 5 microg/kg/day. However, on balance, 10 microg/kg/day remains the dose of choice in view of more efficient CD34+ cell mobilisation

A unified framework for the Kondo problem and for an impurity in a Luttinger liquid

We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values, respectively, in standard or cyclic representations of the quantum group $SU(2)_q$. This unification is powerful, and allows us to find new results for both models. For the anisotropic Kondo problem, we find exact expressions (in the presence of a magnetic field) for all the coefficients in the ``Anderson-Yuval'' perturbative expansion. Our expressions hold initially in the very anisotropic regime, but we show how to continue them beyond the Toulouse point all the way to the isotropic point using an analog of dimensional regularization. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the non-equilibrium conductance for all values of the Luttinger coupling.Comment: 36 pages (22 in double-page format), 7 figures in uuencoded file, uses harvmac and epsf macro

Nonuniversal behavior of scattering between fractional quantum Hall edges

Among the predicted properties of fractional quantum Hall states are fractionally charged quasiparticles and conducting edge-states described as chiral Luttinger liquids. In a system with a narrow constriction, tunneling of quasi-particles between states at different edges can lead to resistance and to shot noise. The ratio of the shot noise to the backscattered current, in the weak scattering regime, measures the fractional charge of the quasi-particle, which has been confirmed in several experiments. However, the non-linearity of the resistance predicted by the chiral Luttinger liquid theory was apparently not observed in some of these cases. As a possible explanation for these discrepancies, we consider a model where a smooth edge profile leads to formation of additional edge states. Coupling between the current carrying edge mode and the additional phonon like mode can lead to {\it nonuniversal} exponents in the current-voltage characteristic, while preserving the ratio between shot noise and the back-scattered current, for weak backscattering. For special values of the coupling, one may obtain a linear I-V behavior.Comment: 10 pages, 3 figure

Resonance in a Tomonaga-Luttinger liquid

We study a homogeneous Tomonaga-Luttinger liquid with backscattering potential. A perturbative computation of the conductance at and near resonance is given. We find that the backscattering of one electron dominates that of two electrons for an interaction parameter $K\geq 1/3$ and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot-noise in FQHE, where the charge 1/3 and not $2*1/3$ is measured on resonance.Comment: 15 pages, three Figures. v2: Definite version, Citations added, presentation improved. To appear in Phys. Rev. B, Rapid Co