Stabilization of Unstable Procedures: The Recursive Projection Method

Fixed-point iterative procedures for solving nonlinear parameter dependent problems can converge for some interval of parameter values and diverge as the parameter changes. The Recursive Projection Method (RPM), which stabilizes such procedures by computing a projection onto the unstable subspace is presented. On this subspace a Newton or special Newton iteration is performed, and the fixed-point iteration is used on the complement. As continuation in the parameter proceeds, the projection is efficiently updated, possibly increasing or decreasing the dimension of the unstable subspace. The method is extremely effective when the dimension of the unstable subspace is small compared to the dimension of the system. Convergence proofs are given and pseudo-arclength continuation on the unstable subspace is introduced to allow continuation past folds. Examples are presented for an important application of the RPM in which a “black-box” time integration scheme is stabilized, enabling it to compute unstable steady states. The RPM can also be used to accelerate iterative procedures when slow convergence is due to a few slowly decaying modes

Correlated Phenotypic Transitions to Competence in Bacterial Colonies

Genetic competence is a phenotypic state of a bacterial cell in which it is capable of importing DNA, presumably to hasten its exploration of alternate genes in its quest for survival under stress. Recently, it was proposed that this transition is uncorrelated among different cells in the colony. Motivated by several discovered signaling mechanisms which create colony-level responses, we present a model for the influence of quorum-sensing signals on a colony of B. Subtilis cells during the transition to genetic competence. Coupling to the external signal creates an effective inhibitory mechanism, which results in anti-correlation between the cycles of adjacent cells. We show that this scenario is consistent with the specific experimental measurement, which fails to detect some underlying collective signaling mechanisms. Rather, we suggest other parameters that should be used to verify the role of a quorum-sensing signal. We also study the conditions under which phenotypic spatial patterns may emerge

Gallium Arsenide preparation and QE Lifetime Studies using the ALICE Photocathode Preparation Facility

In recent years, Gallium Arsenide (GaAs) type photocathodes have become widely used as electron sources in modern Energy Recovery Linac based light sources such as the Accelerators and Lasers in Combined Experiments (ALICE) at Daresbury Laboratory and as polarised electron source for the proposed International Linear Collider (ILC). Once activated to a Low Electron Affinity (LEA) state and illuminated by a laser, these materials can be used as a high-brightness source of both polarised and un-polarised electrons. This paper presents an effective multi-stage preparation procedure including heat cleaning, atomic hydrogen cleaning and the activation process for a GaAs photocathode. The stability of quantum efficiency (QE) and lifetime of activated to LEA state GaAs photocathode have been studied in the ALICE load-lock photocathode preparation facility which has a base pressure in the order of 10^-11 mbar. These studies are supported by further experimental evidence from surface science techniques such as X-ray Photoelectron Spectroscopy (XPS) to demonstrate the processes at the atomic level.Comment: Presented at First International Particle Accelerator Conference, IPAC'10, Kyoto, Japan, from 23 to 28 May 201

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so

Quantum computation with trapped ions in an optical cavity

Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.Comment: 4 pages, 5 figures, REVTEX, second part modified, typos correcte

The doctor-patient relationship revisited. An analysis of the placebo effect.

An overview of prescientific medicine, evolution, and individual human development is presented in an attempt to discover the generic factors operating in all interpersonal therapies. We hypothesize that the placebo effect rests on the universal human need for a group and, by symbolic extension, a system

Dynamical phase transition for a quantum particle source

We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semiclassical limit.Comment: 24 pages; In the new version, we added several references concerning open quantum systems and present an extended result on linear particle production in the fermionic cas

Probing quantum and classical turbulence analogy through global bifurcations in a von K\'arm\'an liquid Helium experiment

We report measurements of the dissipation in the Superfluid Helium high REynold number von Karman flow (SHREK) experiment for different forcing conditions, through a regime of global hysteretic bifurcation. Our macroscopical measurements indicate no noticeable difference between the classical fluid and the superfluid regimes, thereby providing evidence of the same dissipative anomaly and response to asymmetry in fluid and superfluid regime. %In the latter case, A detailed study of the variations of the hysteretic cycle with Reynolds number supports the idea that (i) the stability of the bifurcated states of classical turbulence in this closed flow is partly governed by the dissipative scales and (ii) the normal and the superfluid component at these temperatures (1.6K) are locked down to the dissipative length scale.Comment: 5 pages, 5 figure