Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach

By employing Hopf's functional method, we find the exact characteristic functional for a simple nonlinear dynamical system introduced by Orszag. Steady-state equal-time statistics thus obtained are compared to direct numerical simulation. The solution is both non-trivial and strongly non-Gaussian.Comment: 6 pages and 2 figure

Singularities and the distribution of density in the Burgers/adhesion model

We are interested in the tail behavior of the pdf of mass density within the one and $d$-dimensional Burgers/adhesion model used, e.g., to model the formation of large-scale structures in the Universe after baryon-photon decoupling. We show that large densities are localized near ``kurtoparabolic'' singularities residing on space-time manifolds of codimension two ($d \le 2$) or higher ($d \ge 3$). For smooth initial conditions, such singularities are obtained from the convex hull of the Lagrangian potential (the initial velocity potential minus a parabolic term). The singularities contribute {\em \hbox{universal} power-law tails} to the density pdf when the initial conditions are random. In one dimension the singularities are preshocks (nascent shocks), whereas in two and three dimensions they persist in time and correspond to boundaries of shocks; in all cases the corresponding density pdf has the exponent -7/2, originally proposed by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional forced Burgers turbulence. We also briefly consider models permitting particle crossings and thus multi-stream solutions, such as the Zel'dovich approximation and the (Jeans)--Vlasov--Poisson equation with single-stream initial data: they have singularities of codimension one, yielding power-law tails with exponent -3.Comment: LATEX 11 pages, 6 figures, revised; Physica D, in pres

Familiäre Kavernome des Zentralnervensystems: Eine klinische und genetische Studie an 15 deutsche Familien

Zusammenfassung: 1928 beschrieb Hugo Friedrich Kufs erstmalig eine Familie mit zerebralen, retinalen und kutanen Kavernomen. Mittlerweile wurden über 300 weitere Familien beschrieben. Ebenfalls wurden drei Genloci 7q21-q22 (mit dem Gen CCM1), 7p15-p13 (Gen CCM2) und 3q25.2-q27 (Gen CCM3) beschrieben, in denen Mutationen zu Kavernomen führen. Das Genprodukt von CCM1 ist das Protein Krit1 (Krev Interaction Trapped 1), das über verschiedene Mechanismen mit der Angiogenese interagiert. Das neu entdeckte CCM2-Gen enkodiert ein Protein, das möglicherweise eine dem Krit1 ähnliche Funktion in der Regulation der Angiogenese hat. Das CCM3-Gen wurde noch nicht beschrieben. In dieser Arbeit werden sowohl die klinischen und genetischen Befunde bei 15 deutschen Familien beschriebe

Endoscopically Based Endonasal and Transnasal Lasersurgery

The endoscopically based endonasal and transnasal laser surgery is a surgical procedure, which offers the ENT-specialist a safe and effective method to cure or to improve a number of diseases of the upper and middle airways. Coagulative lasers are used in contact and noncontact mode. Their light is mainly absorbed by hemoglobin but rarely by water. The laser–tissue interaction is performed via flexible glass fibers. For the delivery of the laser beam we use specially designed applicator sheaths, which incorporate the endoscope, the laser fiber and the suction channel. The procedure is controlled online via the endoscopic image on the monitor (“video-endoscopy”). The patient suffers less trauma using this treatment compared to the standard endoscopic surgery and the procedure is much quicker. Pre- and post-operative rhinomanometric and rhinoresistometric measurements reveal that the air flow rate of the nose can be improved effectively

Variational bounds on the energy dissipation rate in body-forced shear flow

A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations.Comment: 15 pages, 7 figure

A note on the extension of the polar decomposition for the multidimensional Burgers equation

It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such solutions have polar singularities on complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys. Rev. E (Rapid Comm.

Burgers velocity fields and dynamical transport processes

We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_t\rho =-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $\rho$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive matter transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium.Comment: Latex fil

Statistical properties of the Burgers equation with Brownian initial velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its $n$-point correlations. In the same limit, we derive the $n-$point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.Comment: 42 pages, published in J. Stat. Phy

Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur