Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence

We describe Lagrangian measurements of water droplets in grid generated wind tunnel turbulence at a Taylor Reynolds number of R(lambda)=250 and an average Stokes number (St) of approximately 0.1. The inertial particles are tracked by a high speed camera moving along the side of the tunnel at the mean flow speed. The standardized acceleration probability density functions of the particles have spread exponential tails that are narrower than those of a fluid particles (St approximately 0) and there is a decrease in the acceleration variance with increasing Stokes number. A simple vortex model shows that the inertial particles selectively sample the fluid field and are less likely to experience regions of the fluid undergoing the largest accelerations. Recent direct numerical simulations compare favorably with these first measurements of Lagrangian statistics of inertial particles in highly turbulent flows.     

Lagrangian theoretical framework of dynamics of nonholonomic systems

By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.     

A new assessment of the second-order moment of Lagrangian velocity increments in turbulence

The behaviour of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov 4/5-law into a relation predicting the linear (in time) scaling for the second-order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterisation of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for 3d turbulence, and for 2d turbulence in the inverse cascade regime. Such parameterisation supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small- and large timescales. When large-time saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterisation allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalised root mean squared acceleration as a function of the Reynolds number, without fitting parameters.     

Lagrangians forn point masses at the second post-Newtonian approximation of general relativity

We study the effect of an infinitesimal coordinate transformation on the Lagrangian and on the metric functional of a system ofn point masses. We show how to compute the Lagrangians ofn point masses at the second postNewtonian approximation of general relativity in different coordinate systems. The Lagrangians are shown to depend on the accelerations except in a special class of coordinates. This class includes the coordinates associated with the canonical formalism of Arnowitt, Deser, and Misner, but excludes most other coordinate systems used in the literature (notably the harmonic one).     

Acceleration correlations and pressure structure functions in high-reynolds number turbulence

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display K41 scaling in the inertial range.     

Nonlinear spinor theory and Weinberg's model

It is shown that the formalism for eliminating vacuum degeneracy can be used to reduce the Heisenberg-Ivanenko nonlinear spinor Lagrangian to a Weinberg-type model Lagrangian of the weak and electromagnetic interactions.     

Spatial Markov model of anomalous transport through random lattice networks

Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity.     

Tests for Varying G

In this note we consider a variable G cosmology which is consistent with observation and which had successfully predicted an ever expanding accelerating universe with a small cosmological constant amongst other things. Three further tests are proposed in this note: First, the inexplicable anomalous accelerations of the Pioneer spacecrafts can be explained. It is then shown that the observed shortening of the orbital periods of binary pulsars is in good agreement with this model. Finally, more general changes in orbital parameters are deduced, which may be observed in the future.     

Spiral Galaxy Rotation Curves Determined from Carmelian General Relativity

Equations of motion, in cylindrical co-ordinates, for the observed rotation of gases within the gravitational potential of spiral galaxies have been derived from Carmeli's Cosmological General Relativity theory. A Tully-Fisher type relation results and rotation curves are reproduced without the need for non-baryonic halo dark matter. Two acceleration regimes are discovered that are separated by a critical acceleration m s⁻². For accelerations larger than the critical value the Newtonian force law applies, but for accelerations less than the critical value the Carmelian regime applies. In the Newtonian regime the accelerations fall off as r ⁻², but in the Carmelian regime the accelerations fall off as r ⁻¹. This is new physics but is exactly what is suggested by Milgrom's phenomenological MOND theory.     

Quantum field theory for a system of interacting photons,electrons, and phonons

A Lagrangian in (1 + 3)-dimensional space-time which describes the interaction of photons, electrons, and phonons is proposed. This is a generalization of Rodriguez-Nuñez' model. This Lagrangian is also singular in the sense of Dirac. The path-integral quantization of this system is performed with the aid of the Dirac formalism for a singular Lagrangian and the method of functional integration. The phase-space generating functional of the Green function of this system is deduced. The Ward identities in canonical formalism for local symmetries are derived, and the Ward identities of proper vertices for this system are obtained. The conserved charges at the quantum level are also obtained. The effective Lagrangian in configuration space for the present model is derived in the case = const. Thus, the Feynman rule can be deduced immediately.     

Recent fluid deformation closure for velocity gradient tensor dynamics in turbulence: Timescale effects and expansions

In order to model pressure and viscous terms in the equation for the Lagrangian dynamics of the velocity gradient tensor in turbulent flows, Chevillard & Meneveau [L. Chevillard, C. Meneveau, Lagrangian dynamics and geometric structure of turbulence, Phys. Rev. Lett. 97 (174501) (2006) 1-4] introduced the Recent Fluid Deformation closure. Using matrix exponentials, the closure allows us to overcome the unphysical finite-time blow-up of the well-known Restricted Euler model. However, it also requires the specification of a decorrelation timescale of the velocity gradient along the Lagrangian evolution, and when the latter is chosen too short (or, equivalently, the Reynolds number is too high), the model leads to unphysical statistics. In the present paper, we explore the limitations of this closure by means of numerical experiments and analytical considerations. We also study the possible effects of using time-correlated stochastic forcing instead of the previously employed white-noise forcing. Numerical experiments show that reducing the correlation timescale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation timescale of the predicted evolution of the velocity gradient tensor. This observed inconsistency could explain the unrealistic predictions at increasing Reynolds numbers. We perform a series expansion of the matrix exponentials in powers of the decorrelation timescale, and we compare the full original model with a linearized version. The latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as a function of the second invariant of the velocity gradient tensor.     

Nonlinear Electrodynamics and NED-Inspired Chiral Solitons

A nonlinear electrodynamics Lagrangian is considered and the electric field associated to an electric point-like charge is derived. The corresponding expression for the total field energy which has finite value in our model, is obtained. The chiral form of the Lagrangian is also presented. Topological, finite-energy, spherically symmetric solutions of the chiral model are studied and some of their properties are discussed.     

New Mechanism for Mass Generation of Gauge Field

A new mechanism for mass generation of gauge field is discussed in this paper.By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations,the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian.This model is a renormalizable quantum model.     

On neutral currents in two-Z-boson gauge models

A systematic procedure is considered for the phenomenological analysis of neutral current interactions in an arbitrary two-Z-boson gauge model by means of a general neutral current effective Lagrangian. Expressions for two gauge boson masses and their mixing angle have been obtained directly through the effective Lagrangian parameters. A general classification of possible types of two-Z-boson gauge models is presented in accordance with the form of the effective Lagrangian.     

The teleparallel equivalent of general relativity

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.     

On adaptive-grid computations of variable stars

We show that the use of an implicit adaptive-grid technique is an efficient and up-to-date approach for the calculations of radial oscillations in variable stars. We chose as an illustrative example the radiative envelope of an RR Lyrae variable.

For the hydrostatic initial model we compare the Lagrangian ratioed zoning with an adaptive-grid rezoning. We show that the adaptive-grid yields an optimal distribution of the mesh points in the sense that the relevant physical features, the hydrogen and first and second helium ionization zones, are well resolved.

For the hydrodynamical evolution we present the full-amplitude model for both the Lagrangian and adaptive-grid computations. We perform a detailed comparison and show that the adaptive-grid method yields limit cycle solutions that are substantially improved over the Lagrangian grid model. This is due to the fact that the Lagrangian mesh sweeps through the ionization zones twice during one oscillation period, whereas the adaptive-mesh resolves them and tracks them continuously. The results are, in particular, smooth radial velocity and light curves.

Beyond a physically better defined solution we also observe larger time steps for the convergence towards the limit cycle and for the evolution during one period.