Shock statistics in higher-dimensional Burgers turbulence

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.Comment: 4 pages, 8 figure

Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figure

First-principle derivation of static avalanche-size distribution

We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an efficient and systematic method to compute the statistics of avalanche sizes and manifold displacements. The tree-level calculation, i.e. mean-field limit, is obtained by solving a saddle-point equation. Graphically, it can be interpreted as a the sum of all tree graphs. The 1-loop corrections are computed using results from the functional renormalization group. At the upper critical dimension the shock statistics is described by the Brownian Force model (BFM), the static version of the so-called ABBM model in the non-equilibrium context of depinning. This model can itself be treated exactly in any dimension and its shock statistics is that of a Levy process. Contact is made with classical results in probability theory on the Burgers equation with Brownian initial conditions. In particular we obtain a functional extension of an evolution equation introduced by Carraro and Duchon, which recursively constructs the tree diagrams in the field theory.Comment: 33 pages, 24 figure

Interference in disordered systems: A particle in a complex random landscape

We consider a particle in one dimension submitted to amplitude and phase disorder. It can be mapped onto the complex Burgers equation, and provides a toy model for problems with interplay of interferences and disorder, such as the NSS model of hopping conductivity in disordered insulators and the Chalker-Coddington model for the (spin) quantum Hall effect. The model has three distinct phases: (I) a {\em high-temperature} or weak disorder phase, (II) a {\em pinned} phase for strong amplitude disorder, and (III) a {\em diffusive} phase for strong phase disorder, but weak amplitude disorder. We compute analytically the renormalized disorder correlator, equivalent to the Burgers velocity-velocity correlator at long times. In phase III, it assumes a universal form. For strong phase disorder, interference leads to a logarithmic singularity, related to zeroes of the partition sum, or poles of the complex Burgers velocity field. These results are valuable in the search for the adequate field theory for higher-dimensional systems.Comment: 16 pages, 7 figure

Large N and Bosonization in Three Dimensions

Bosonization is normally thought of as a purely two-dimensional phenomenon, and generic field theories with fermions in D>2 are not expected be describable by local bosonic actions, except in some special cases. We point out that 3D SU(N) gauge theories on R^{1,1} x S^{1}_{L} with adjoint fermions can be bosonized in the large N limit. The key feature of such theories is that they enjoy large N volume independence for arbitrary circle size L. A consequence of this is a large N equivalence between these 3D gauge theories and certain 2D gauge theories, which matches a set of correlation functions in the 3D theories to corresponding observables in the 2D theories. As an example, we focus on a 3D SU(N) gauge theory with one flavor of adjoint Majorana fermions and derive the large-N equivalent 2D gauge theory. The extra dimension is encoded in the color degrees of freedom of the 2D theory. We then apply the technique of non-Abelian bosonization to the 2D theory to obtain an equivalent local theory written purely in terms of bosonic variables. Hence the bosonized version of the large N three-dimensional theory turns out to live in two dimensions.Comment: 30 pages, 2 tables. v2 minor revisions, references adde

Continuous Limit of Discrete Systems with Long-Range Interaction

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.Comment: 23 pages, LaTe

Localization of recombination proteins and Srs2 reveals anti-recombinase function in vivo

Homologous recombination (HR), although an important DNA repair mechanism, is dangerous to the cell if improperly regulated. The Srs2 “anti-recombinase” restricts HR by disassembling the Rad51 nucleoprotein filament, an intermediate preceding the exchange of homologous DNA strands. Here, we cytologically characterize Srs2 function in vivo and describe a novel mechanism for regulating the initiation of HR. We find that Srs2 is recruited separately to replication and repair centers and identify the genetic requirements for recruitment. In the absence of Srs2 activity, Rad51 foci accumulate, and surprisingly, can form in the absence of Rad52 mediation. However, these Rad51 foci do not represent repair-proficient filaments, as determined by recombination assays. Antagonistic roles for Rad52 and Srs2 in Rad51 filament formation are also observed in vitro. Furthermore, we provide evidence that Srs2 removes Rad51 indiscriminately from DNA, while the Rad52 protein coordinates appropriate filament reformation. This constant breakdown and rebuilding of filaments may act as a stringent quality control mechanism during HR

The Predatory Ecology of Deinonychus and the Origin of Flapping in Birds

Most non-avian theropod dinosaurs are characterized by fearsome serrated teeth and sharp recurved claws. Interpretation of theropod predatory ecology is typically based on functional morphological analysis of these and other physical features. The notorious hypertrophied ‘killing claw’ on pedal digit (D) II of the maniraptoran theropod Deinonychus (Paraves: Dromaeosauridae) is hypothesized to have been a predatory adaptation for slashing or climbing, leading to the suggestion that Deinonychus and other dromaeosaurids were cursorial predators specialized for actively attacking and killing prey several times larger than themselves. However, this hypothesis is problematic as extant animals that possess similarly hypertrophied claws do not use them to slash or climb up prey. Here we offer an alternative interpretation: that the hypertrophied D-II claw of dromaeosaurids was functionally analogous to the enlarged talon also found on D-II of extant Accipitridae (hawks and eagles; one family of the birds commonly known as “raptors”). Here, the talon is used to maintain grip on prey of subequal body size to the predator, while the victim is pinned down by the body weight of the raptor and dismembered by the beak. The foot of Deinonychus exhibits morphology consistent with a grasping function, supportive of the prey immobilisation behavior model. Opposite morphological trends within Deinonychosauria (Dromaeosauridae + Troodontidae) are indicative of ecological separation. Placed in context of avian evolution, the grasping foot of Deinonychus and other terrestrial predatory paravians is hypothesized to have been an exaptation for the grasping foot of arboreal perching birds. Here we also describe “stability flapping”, a novel behaviour executed for positioning and stability during the initial stages of prey immobilisation, which may have been pivotal to the evolution of the flapping stroke. These findings overhaul our perception of predatory dinosaurs and highlight the role of exaptation in the evolution of novel structures and behaviours