Zero-Hopf bifurcation in the Van der Pol oscillator with delayed position and velocity feedback

In this paper, we consider the traditional Van der Pol oscillator with a forcing dependent on a delay in feedback. The delay is taken to be a nonlinear function of both position and velocity, which gives rise to many different types of bifurcations. In particular, we study the Zero-Hopf bifurcation that takes place at certain parameter values using methods of center manifold reduction of DDEs and normal form theory. We present numerical simulations that have been accurately predicted by the phase portraits in the Zero-Hopf bifurcation to confirm our numerical results and provide a physical understanding of the oscillator with the delay in feedback.     

Active stabilization of the resistive-wall mode in high-beta, low-rotation plasmas

The resistive-wall mode is actively stabilized in the National Spherical Torus Experiment in high-beta plasmas rotating significantly below the critical rotation speed for passive stability and in the range predicted for the International Thermonuclear Experimental Reactor. Variation of feedback stabilization parameters shows mode excitation or suppression. Stabilization of toroidal mode number unity did not lead to instability of toroidal mode number two. The mode can become unstable by deforming poloidally, an important consideration for stabilization system design.     

Definitive identification of lead(II)-amino acid adducts and the solid state structure of a lead-valine complex

Electrospray ionization mass spectra of lead(II) nitrate-amino acid mixtures enable unequivocal identification of lead complexes for each of the essential amino acids and a valine complex is reported as the first crystallographically characterized lead-amino acid complex.     

Flux expulsion and trapping in rotating discs of type II superconductors

The magnetic flux rotating in step with a type II superconducting disc is measured with orthogonal pick up coils for various previous magnetic histories vs H₀ applied ⊥ to the axis of rotation. For some initial magnetic states, flux expulsion, independent of the rate of rotation, occurs during the initial rotation. A simple model where flux lines leave the specimen against the magnetic pressure in the active region accounts for the observations.     

SAM‐II Riboswitch Samples at least Two Conformations in Solution in the Absence of Ligand: Implications for Recognition

Conformational equilibria are increasingly recognized as pivotal for biological function. Traditional structural analyses provide a static image of conformers in solution that sometimes present conflicting views. From ¹³C and ¹H chemical exchange saturation transfer experiments, in concert with ligation and selective labeling strategies, we show that in the absence of metabolite, a Mg²⁺ (0–0.5 mm )‐bound apo SAM‐II riboswitch RNA exists in a minor (≈10 %) partially closed state that rapidly exchanges with a predominantly (≈90 %) open form with a lifetime of ≈32 ms. The base and sugar (H6,C6, H1′,C1′) chemical shifts of C43 for the dominant conformer are similar to those of a free CMP, but those of the minor apo species are comparable to shifts of CMPs in helical RNA regions. Our results suggest that these transient, low populated states stabilized by Mg²⁺ will likely enhance rapid ligand recognition and, we anticipate, will play potentially ubiquitous roles in RNA signaling.     

The solubility of magnetite and the hydrolysis and oxidation of Fe2+ in water to 300°C

The solubility of carefully characterized magnetite, Fe₃O₄, in dilute aqueous solutions saturated with H₂ has been measured at temperatures from 100 to 300°C in a flow apparatus. Solution compositions included either HCl or NaOH molalities of up to 1 and 40 mmole-kg^?1, respectively, and H₂ molalities of 0.0779, 0.779, and 8.57 mmole-kg^?1. The dependence of the equilibrium solubility on the pH and reduction potential were fitted to a scheme of soluble ferrous and ferric species consisting of Fe²⁺, FeOH⁺, Fe(OH)₂, Fe(OH) ₃ ^? , Fe(OH)₃, and Fe(OH) ₄ ^? . Solubility products from the fit, corresponding to the reactions $$\tfrac{1}{3}Fe_3 O_4 + (2 - b)H^ + + \tfrac{1}{3}H_2 \rightleftharpoons Fe(OH)_b^{2 - b} + (4/3 - b)H_2 O$$ and $$\tfrac{1}{3}Fe_3 O_4 + (3 - b)H^ + \rightleftharpoons Fe(OH)_b^{3 - b} + \tfrac{1}{6}H_2 + (4/3 - b)H_2 O$$ were used to derive thermodynamic constants for each species. The extrapolared value for the Gibbs energy of formation of Fe²⁺ at 25°C is ?88.92±2.0 kJ-mole^?1, consistent with standard reduction potentials in the range E^o(Fe²⁺)=?0.47±0.01 V. The temperature coefficient of the equilibrium Fe molality, (?m(Fe, sat.)/?T)_{m(H2).m(NaOH)}, changes from negative to positive as the NaOH molality is increased to the point where Fe(OH) ₃ ^? and Fe(OH) ₄ ^? predominate.     

Classification and unfoldings of 1:2 resonant Hopf Bifurcation

In this paper, we study the bifurcations of periodic solutions from an equilibrium point of a differential equation whose linearization has two pairs of simple pure imaginary complex conjugate eigenvalues which are in 1:2 ratio. This corresponds to a Hopf-Hopf mode interaction with 1:2 resonance, as occurs in the context of dissipative mechanical systems. Using an approach based on Liapunov-Schmidt reduction and singularity theory, we give a framework in which to study these problems and their perturbations in two cases: no distinguished parameter, and one distinguished (bifurcation) parameter. We give a complete classification of the generic cases and their unfoldings. (Accepted May 26, 1995) – Communicated by M. Golubitsky