Practicing Law in the Twenty-First Century in a Twentieth (Nineteenth) Century Straightjacket: Something has to Give

Article published in the Michigan State Law Review

On Projections to the Pure Spinor Space

A family of covariant non-linear projections from the space of SO(10) Weyl spinors onto the space of pure SO(10) Weyl spinors is presented. The Jacobian matrices of these projections are related to a linear projector which was previously discussed in pure spinor string literature and which maps the antighost to its gauge invariant part. Only one representative of the family leads to a Hermitian Jacobian matrix and can itself be derived from a scalar potential. Comments on the SO(1,9) case are given as well as on the non-covariant version of the projection map. The insight is applied to the ghost action of pure spinor string theory, where the constraints on the fields can be removed using the projection, while introducing new gauge symmetries. This opens the possibility of choosing different gauges which might help to clarify the origin of the pure spinor ghosts. Also the measure of the pure spinor space is discussed from the projection point of view. The appendix contains the discussion of a toy model which served as a guideline for the pure spinor case.Comment: 35+32 pages (main part+ appendix). Changes from version 2 to version 3: Reference [11] added. Equation numbers include now the section number in order to match the published version in JHEP. Changes from version 1 to version 2: Two references added about the derivation of the pure spinor string from a classical action; last equation in footnote 2 rewritten; 3 minor changes in the tex

Emergence of foams from the breakdown of the phase field crystal model

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams, and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously-reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.Comment: 4 pages, 4 figure

Shadows, currents and AdS fields

Conformal totally symmetric arbitrary spin currents and shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal boost symmetries is obtained. Gauge invariant differential constraints for currents and shadow fields are obtained. AdS/CFT correspondence for currents and shadow fields and the respective normalizable and non-normalizable solutions of massless totally symmetric arbitrary spin AdS fields is studied. The bulk fields are considered in modified de Donder gauge that leads to decoupled equations of motion. We demonstrate that leftover on-shell gauge symmetries of bulk fields correspond to gauge symmetries of boundary currents and shadow fields, while the modified de Donder gauge conditions for bulk fields correspond to differential constraints for boundary conformal currents and shadow fields. Breaking conformal symmetries, we find interrelations between the gauge invariant formulation of the currents and shadow fields and the gauge invariant formulation of massive fields.Comment: v3: 31 pages, RevTeX4. Appendix D devoted to modified de Donder gauge in AdS(d+1) x S(d+1) added. Footnotes 10, 21 added. Typos correcte

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.Comment: 4 pages, 3 figure

Courant-like brackets and loop spaces

We study the algebra of local functionals equipped with a Poisson bracket. We discuss the underlying algebraic structures related to a version of the Courant-Dorfman algebra. As a main illustration, we consider the functionals over the cotangent bundle of the superloop space over a smooth manifold. We present a number of examples of the Courant-like brackets arising from this analysis.Comment: 20 pages, the version published in JHE

Flow profiling of a surface acoustic wave nanopump

The flow profile in a capillary gap and the pumping efficiency of an acoustic micropump employing Surface Acoustic Waves is investigated both experimentally and theoretically. Such ultrasonic surface waves on a piezoelectric substrate strongly couple to a thin liquid layer and generate an internal streaming within the fluid. Such acoustic streaming can be used for controlled agitation during, e.g., microarray hybridization. We use fluorescence correlation spectroscopy and fluorescence microscopy as complementary tools to investigate the resulting flow profile. The velocity was found to depend on the applied power somewhat weaker than linearly and to decrease fast with the distance from the ultrasound generator on the chip.Comment: 12 pages 20 figure

Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.Comment: 5 pages, 3 figures; added comments on system size scaling and turbulence analogy, added error estimates of data collapse parameters. Slightly enhanced from the version which will appear in PR

Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure