Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Observation via one-dimensional 13Calpha NMR of local conformational substates in thermal unfolding equilibria of a synthetic analog of the GCN4 leucine zipper.

Synthesis of a 33-residue, capped leucine zipper analogous to that in GCN4 is reported. Histidine and arginine residues are mutated to lysine to reduce the unfolding temperature. CD and ultracentrifugation studies indicate that the molecule is a two-stranded coiled coil under benign conditions. Versions of the same peptide are made with 99% 13Calpha at selected sites. One-dimensional 13C NMR spectra are assigned by inspection and used to study thermal unfolding equilibria over the entire transition from 8 to 73 degrees C. Spectra at the temperature extremes establish the approximate chemical shifts for folded and unfolded forms at each labeled site. Resonances for each amino acid appear at both locations at intermediate T, indicating that folded and unfolded forms interconvert slowly (> >2 ms) on the NMR time scale. Moreover, near room temperature, the structured form's resonance is double at several, but not all, sites, indicating at least two slowly interconverting, structured, local conformational substates. Analysis of the dynamics is possible. For example, near room temperature at the Val-9, Ala-24, and Gly-31 positions, the equilibrium constant for interconversion of the two structured forms is near unity and the time scale is > or= 10-20 ms.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Variation in per capita interaction strength: Thresholds due to nonlinear dynamics and nonequilibrium conditions

I measured the strength of interaction between a marine herbivore and its growing resource over a realistic range of absolute and relative abundances. The herbivores (hermit crabs: Pagurus spp.) have slow and/or weak functional and numerical responses to epiphytic diatoms (Isthmia nervosa), which show logistic growth in the absence of consumers. By isolating this interaction in containers in the field, I mimicked many of the physical and biological variables characteristic of the intertidal while controlling the densities of focal species. The per capita effects of consumers on the population dynamics of their resource (i.e., interaction strength) were defined by using the relationship between hermit crab density and proportional change in the resource. When this relationship is fit by a Weibull function, a single parameter distinguishes constant interaction strength from one that varies as a function of density. Constant interaction strength causes the proportion of diatoms to fall linearly or proportionally as hermit crab density increases whereas per capita effects that increase with density cause an accelerating decline. Although many mathematical models of species interactions assume linear dynamics and invariant parameters, at least near equilibrium, the per capita effects of hermit crabs on diatoms varied substantially, apparently crossing a threshold from weak to strong when consumption exceeded resource production. This threshold separates a domain of coexistence from one of local extinction of the resource. Such thresholds may help explain trophic cascades, resource compensation, and context-dependent interaction strengths, while indicating a way to predict trophic effects, despite nonlinearities, as a function of vital rates.

Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Solution 19F nuclear Overhauser effects in structural studies of the cytoplasmic domain of mammalian rhodopsin

19F nuclear Overhauser effects (NOEs) between fluorine labels on the cytoplasmic domain of rhodopsin solubilized in detergent micelles are reported. Previously, high-resolution solution 19F NMR spectra of fluorine-labeled rhodopsin in detergent micelles were described, demonstrating the applicability of this technique to studies of tertiary structure in the cytoplasmic domain. To quantitate tertiary contacts we have applied a transient one-dimensional difference NOE solution 19F NMR experiment to this system, permitting assessment of proximities between fluorine labels specifically incorporated into different regions of the cytoplasmic face. Three dicysteine substitution mutants (Cys-140–Cys-316, Cys-65–Cys-316, and Cys-139–Cys-251) were labeled by attachment of the trifluoroethylthio group through a disulfide linkage. Each mutant rhodopsin was prepared (8–10 mg) in dodecylmaltoside and analyzed at 20°C by solution 19F NMR. Distinct chemical shifts were observed for all of the rhodopsin 19F labels in the dark. An up-field shift of the Cys-316 resonance in the Cys-65–Cys-316 mutant suggests a close proximity between the two residues. When analyzed for 19F-19F NOEs, a moderate negative enhancement was observed for the Cys-65–Cys-316 pair and a strong negative enhancement was observed for the Cys-139–Cys-251 pair, indicating proximity between these sites. No NOE enhancement was observed for the Cys-140–Cys-316 pair. These NOE effects demonstrate a solution 19F NMR method for analysis of tertiary contacts in high molecular weight proteins, including membrane proteins.