Symmetry Principles for String Theory

The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing, and exhibit an infinite-dimensional supersymmetry algebra that includes space-time diffeomorphisms and an infinite number of spontaneously broken level-mixing symmetries. We review progress in this area, culminating in the identification of a weighted tensor algebra as a subalgebra of the full symmetry. We also briefly describe outstanding problems. Talk presented at the Gursey memorial conference, Istanbul, Turkey, June, 1994.Comment: 5 pages, Plain TeX, no figure

Testing an Optimised Expansion on Z_2 Lattice Models

We test an optimised hopping parameter expansion on various Z_2 lattice scalar field models: the Ising model, a spin-one model and lambda (phi)^4. We do this by studying the critical indices for a variety of optimisation criteria, in a range of dimensions and with various trial actions. We work up to seventh order, thus going well beyond previous studies. We demonstrate how to use numerical methods to generate the high order diagrams and their corresponding expressions. These are then used to calculate results numerically and, in the case of the Ising model, we obtain some analytic results. We highlight problems with several optimisation schemes and show for the best scheme that the critical exponents are consistent with mean field results to at least 8 significant figures. We conclude that in its present form, such optimised lattice expansions do not seem to be capturing the non-perturbative infra-red physics near the critical points of scalar models.Comment: 47 pages, some figures in colour but will display fine in B

Complexation of DNA with positive spheres: phase diagram of charge inversion and reentrant condensation

The phase diagram of a water solution of DNA and oppositely charged spherical macroions is studied. DNA winds around spheres to form beads-on-a-string complexes resembling the chromatin 10 nm fiber. At small enough concentration of spheres these "artificial chromatin" complexes are negative, while at large enough concentrations of spheres the charge of DNA is inverted by the adsorbed spheres. Charges of complexes stabilize their solutions. In the plane of concentrations of DNA and spheres the phases with positive and negative complexes are separated by another phase, which contains the condensate of neutral DNA-spheres complexes. Thus when the concentration of spheres grows, DNA-spheres complexes experience condensation and resolubilization (or reentrant condensation). Phenomenological theory of the phase diagram of reentrant condensation and charge inversion is suggested. Parameters of this theory are calculated by microscopic theory. It is shown that an important part of the effect of a monovalent salt on the phase diagram can be described by the nontrivial renormalization of the effective linear charge density of DNA wound around a sphere, due to the Onsager-Manning condensation. We argue that our phenomenological phase diagram or reentrant condensation is generic to a large class of strongly asymmetric electrolytes. Possible implication of these results for the natural chromatin are discussed.Comment: Many corrections to text. SUbmitted to J. Chem. Phy

Condensation transitions in a model for a directed network with weighted links

An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total out-strength condenses onto a single link; (ii) a phase in which a finite fraction of the total weight in the system is directed into a single node. A virtue of the model is that its dynamics can be mapped onto those of a zero-range process with many species of interacting particles -- an exactly solvable model of particles hopping between the sites of a lattice. This mapping, which is described in detail, guides the analysis of the steady state of the network model and leads to theoretical predictions for the conditions under which the different types of condensation may be observed. A further advantage of the mapping is that, by exploiting what is known about exactly solvable generalisations of the zero-range process, one can infer a number of generalisations of the network model and dynamics which remain exactly solvable.Comment: 23 pages, 8 figure

Factorised steady states for multi-species mass transfer models

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.Comment: 11 page

Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions.Comment: 4 pages. To appear in Physical Review Letter

Comparative effects of auxin and abscisic acid on growth, hydrogen ion efflux and gravitropism in primary roots of maize

In order to test the idea that auxin action on root growth may be mediated by H(+) movement, the correlation of auxin action on growth and H(+) movement in roots was examined along with changes in H(+) efflux patterns associated with the asymmetric growth which occurs during gravitropism. The effects of indoleacetic acid (IAA) and abscisic acid (AbA) on growth, H(+) secretion, and gravitropism in roots were compared. Results show a close correlation existent between H(+) efflux and growth in maize roots. In intact roots there is strong H(+) efflux from the elongation zone. Growth-promoting concentrations of IAA stimulate H(+) efflux. During gravitropism the H(+) efflux from the elongation zone becomes asymmetric; the evidence indicates that auxin redistribution contributes to the development of acid efflux asymmetry. That AbA stimulates root growth is reflected in its ability to stimulate H(+) efflux from apical root segments

Suppression of asymmetric acid efflux and gravitropism in maize roots treated with auxin transport inhibitors of sodium orthovanadate

In gravitropically stimulated roots of maize (Zea mays L., hybrid WF9 x 38MS), there is more acid efflux on the rapidly growing upper side than on the slowly growing lower side. In light of the Cholodny/Went hypothesis of gravitropism which states that gravitropic curvature results from lateral redistribution of auxin, the effects of auxin transport inhibitors on the development of acid efflux asymmetry and curvature in gravistimulated roots were examined. All the transport inhibitors tested prevented both gravitropism and the development of asymmetric acid efflux in gravistimulated roots. The results indicate that auxin redistribution may cause the asymmetry of acid efflux, a finding consistent with the Cholodny/Went hypothesis of gravitropism. As further evidence that auxin-induced acid efflux asymmetry may mediate gravitropic curvature, sodium orthovanadate, an inhibitor of auxin-induced H+ efflux was found to prevent both gravitropism and the development of asymmetric acid efflux in gravistimulated roots

Torsion pendulum measurements on viscoelastic materials during vacuum exposure

A torsional pendulum apparatus designed for testing in situ in vacuum, the dynamic mechanical properties of materials is described. The application of this apparatus to an experimental program to measure the effects of vacuum on the mechanical properties of two ablator materials (a foamed material and a filled elastomer) and a solid rocket propellant (a filled elastomer) is presented. Results from the program are discussed as to the effects of vacuum on the mechanical properties of these three materials. In addition, time-temperature-superposition, as a technique for accelerating vacuum induced changes in mechanical properties, is discussed with reference to the three materials tested in the subject program