Microscopic dissipation in a cohesionless granular jet impact

Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. We investigate the continuum limit of an unconfined, dense granular flow. To do this we use as a test system a two-dimensional dense cohesionless granular jet impinging upon a target. We simulate this via a timestep driven hard sphere method, and apply a mean-field theoretical approach to connect the macroscopic flow with the microscopic material parameters of the grains. We observe that the flow separates into a cone with an interior cone angle determined by the conservation of momentum and the dissipation of energy. From the cone angle we extract a dimensionless quantity $A-B$ that characterizes the flow. We find that this quantity depends both on whether or not a deadzone --- a stationary region near the target --- is present, and on the value of the coefficient of dynamic friction. We present a theory for the scaling of $A-B$ with the coefficient of friction that suggests that dissipation is primarily a perturbative effect in this flow, rather than the source of qualitatively different behavior.Comment: 9 pages, 11 figure

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.Comment: 19 pages, LaTex fil

Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields

This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action

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

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

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

Depinning of semiflexible polymers in (1+1) dimensions

We present a theoretical analysis of a simple model of the depinning of an anchored semiflexible polymer from a fixed planar substrate in (1+1) dimensions. We consider a polymer with a discrete sequence of pinning sites along its contour. Using the scaling properties of the conformational distribution function in the stiff limit and applying the necklace model of phase transitions in quasi-one-dimensional systems, we obtain a melting criterion in terms of the persistence length, the spacing between pinning sites, a microscopic effective length which characterizes a bond, and the bond energy. The limitations of this and other similar approaches are also discussed. In the case of force-induced unbinding, it is shown that the bending rigidity favors the unbinding through a ``lever-arm effect''

Algebra of Lax Connection for T-Dual Models

We study relation between T-duality and integrability. We develop the Hamiltonian formalism for principal chiral model on general group manifold and on its T-dual image. We calculate the Poisson bracket of Lax connections in T-dual model and we show that they are non-local as opposite to the Poisson brackets of Lax connection in original model. We demonstrate these calculations on two specific examples: Sigma model on S(2) and sigma model on AdS(2).Comment: 24 pages, references adde

Unique cellular organization in the oldest root meristem

Roots and shoots of plant bodies develop from meristems—cell populations that self-renew and produce cells that undergo differentiation—located at the apices of axes [1].The oldest preserved root apices in which cellular anatomy can be imaged are found in nodules of permineralized fossil soils called coal balls [2], which formed in the Carboniferous coal swamp forests over 300 million years ago [3, 4, 5, 6, 7, 8 and 9]. However, no fossil root apices described to date were actively growing at the time of preservation [3, 4, 5, 6, 7, 8, 9 and 10]. Because the cellular organization of meristems changes when root growth stops, it has been impossible to compare cellular dynamics as stem cells transition to differentiated cells in extinct and extant taxa [11]. We predicted that meristems of actively growing roots would be preserved in coal balls. Here we report the discovery of the first fossilized remains of an actively growing root meristem from permineralized Carboniferous soil with detail of the stem cells and differentiating cells preserved. The cellular organization of the meristem is unique. The position of the Körper-Kappe boundary, discrete root cap, and presence of many anticlinal cell divisions within a broad promeristem distinguish it from all other known root meristems. This discovery is important because it demonstrates that the same general cellular dynamics are conserved between the oldest extinct and extant root meristems. However, its unique cellular organization demonstrates that extant root meristem organization and development represents only a subset of the diversity that has existed since roots first evolved.</p

Origin of Pure Spinor Superstring

The pure spinor formalism for the superstring, initiated by N. Berkovits, is derived at the fully quantum level starting from a fundamental reparametrization invariant and super-Poincare invariant worldsheet action. It is a simple extension of the Green-Schwarz action with doubled spinor degrees of freedom with a compensating local supersymmetry on top of the conventional kappa-symmetry. Equivalence to the Green-Schwarz formalism is manifest from the outset. The use of free fields in the pure spinor formalism is justified from the first principle. The basic idea works also for the superparticle in 11 dimensions.Comment: 21 pages, no figure; v2: refs. adde