Energy Cascade in a Nonlinear Mechanistic Model of Turbulence

Energy transfer plays an essential role in many natural and engineering processes which include different scales. Understanding how the energy cascade (which refers to the energy transfer among the different scales) works is of primary importance. One notable example is the energy cascade in turbulent flow whose kinetic energy is transferred from large eddies to smaller ones. Below a threshold scale the energy is dissipated due to viscous friction. We introduce a nonlinear phenomenological mechanistic model of turbulence which consists of masses connected by springs arranged in a binary tree structure. To represent the various scales, the masses are gradually decreased in lower levels. The bottom level of the model consists of nonlinear energy sinks to provide dissipation. Based on previous research, we choose the system parameters and analyze its behavior for simple impulsive excitations. The decay of the total mechanical energy and the discrete energy spectrum of the system are compared for different impulse magnitudes. It is demonstrated that the dissipation is much more significant compared to the linear model, if the input energy is large enough. The energy spectra are compared with that of the linear model. We find that the energy spectrum of the nonlinear model better highlights the cut-off feature of the Kolmogorov spectrum

Vascular endothelial growth factor directly inhibits primitive neural stem cell survival but promotes definitive neural stem cell survival

There are two types of neural stem cells (NSCs). Primitive NSCs [leukemia inhibitory factor (LIF) dependent but exogenous fibroblast growth factor (FGF) 2 independent] can be derived from mouse embryonic stem (ES) cells in vitro and from embryonic day 5.5 (E5.5) to E7.5 epiblast and E7.5-E8.5 neuroectoderm in vivo. Definitive NSCs (LIF independent but FGF2 dependent) first appear in the E8.5 neural plate and persist throughout life. Primitive NSCs give rise to definitive NSCs. Loss and gain of functions were used to study the role of vascular endothelial growth factor (VEGF)-A and its receptor, Flk1, in NSCs. The numbers of Flk1 knock-out mice embryo-derived and ES cell-derived primitive NSCs were increased because of the enhanced survival of primitive NSCs. In contrast, neural precursor-specific, Flk1 conditional knock-out mice-derived, definitive NSCs numbers were decreased because of the enhanced cell death of definitive NSCs. These effects were not observed in cells lacking Flt1, another VEGF receptor. In addition, the cell death stimulated by VEGF-A of primitive NSC and the cell survival stimulated by VEGF-A of definitive NSC were blocked by Flk1/Fc-soluble receptors and VEGF-A function-blocking antibodies. These VEGF-A phenotypes also were blocked by inhibition of the downstream effector nuclear factor kappa B (NF-kappa B). Thus, both the cell death of primitive NSC and the cell survival of definitive NSC induced by VEGF-A stimulation are mediated by bifunctional NF-kappa B effects. In conclusion, VEGF-A function through Flk1 mediates survival (and not proliferative or fate change) effects on NSCs, specifically

A causal statistical family of dissipative divergence type fluids

In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for all states outside equilibrium for which the theory preserves this statistical interpretation condition. This subclass includes the usual equilibrium distributions, namely Boltzmann, Bose or Fermi distributions, according to the statistics used, suitably generalized outside equilibrium. Therefore this gives a simple proof that they are causal in a neighborhood of equilibrium. We also find a bigger set of dissipative divergence type theories which are only pseudo-statistical, in the sense that the third rank tensor of the fluid theory has the symmetry and trace properties of a third momentum of an statistical distribution, but the energy-momentum tensor, while having the form of a second momentum distribution, it is so for a different distribution function. This set also contains a subclass (including the one already mentioned) of manifestly causal theories.Comment: LaTex, documentstyle{article

Multi-jet cross sections in deep inelastic scattering at next-to-leading order

We present the perturbative prediction for three-jet production cross section in DIS at the NLO accuracy. We study the dependence on the renormalization and factorization scales of exclusive three-jet cross section. The perturbative prediction for the three-jet differential distribution as a function of the momentum transfer is compared to the corresponding data obtained by the H1 collaboration at HERA.Comment: 5 pages, 3 figure

Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics

In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz, which generalizes the well-known Hwa-Bjorken solution, we obtain a wide class of new exact, explicit and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects (i.e. the work done by the pressure and the modified change of the volume elements) into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, 1+1 dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we show that this general solution is stable for perturbations.Comment: 34 pages, 8 figures, detailed write-up of http://arxiv.org/abs/nucl-th/0605070