Large-scale structure of passive scalar turbulence

We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field by means of direct numerical simulations. We focus on scales larger than the characteristic length scale of scalar injection, yet smaller than the correlation length of the velocity. We show the existence of nontrivial long-range correlations in the form of new power laws for the decay of high-order coarse-grained scalar cumulants. This result contradicts the classical scenario of Gibbs equilibrium statistics that should hold in the absence of scalar flux. The breakdown of "thermal equilibrium" at large scales is traced back to the statistical geometry of turbulent dispersion of two scalar blobs. The numerical values obtained for the scaling exponents of the coarse-grained scalar cumulants are in agreement with recent theoretical results.     

Large scale structure in Bekenstein's theory of relativistic modified Newtonian dynamics

A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einstein's theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give modified Newtonian dynamics (MOND) in the weak-field nonrelativistic limit. We study the evolution of the Universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekenstein's theory of MOND.     

Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence

Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent intermittent field. Here we focus on Lagrangian passive scalar scaling exponents, and discuss their possible links with Eulerian passive scalar and mixed velocity-passive scalar structure functions. We provide different transformations between these scaling exponents, associated to different transformations linking space and time scales. We obtain four new explicit relations. Experimental data are needed to test these predictions for Lagrangian passive scalar scaling exponents.     

Fractal Iso-Contours of Passive Scalar in Two-Dimensional Smooth Random Flows

A passive scalar field was studied under the action of pumping, diffusion and advection by a 2D smooth flow with Lagrangian chaos. We present theoretical arguments showing that the scalar statistics are not conformally invariant and formulate a new effective semi-analytic algorithm to model scalar turbulence. We then carry out massive numerics of scalar turbulence, focusing on nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale r _d for scales exceeding r _d . The scalar isolines are found to be fractal/smooth at scales larger/smaller than the pumping scale. We characterize the statistics of isoline bending by the driving function of the Löwner map. That function is found to behave like diffusion with diffusivity independent of the resolution yet, most surprisingly, dependent on the velocity realization and time (beyond the time on which the statistics of the scalar is stabilized).     

Power-Law Expansion and Scalar Field Cosmology in Higher Derivative Theory

In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the scale factor. A number of evolutionary phases of the universe including the present accelerating phase are found to exist with scalar field in the higher derivative theory of gravitation. The properties of scalar field and other physical parameters are discussed in detail. We find that the equation of state parameter for matter and scalar field are same at late time in each case. We observe that a higher derivative term can hardly be a candidate to describe the presently observed accelerated expansion. It is only the hypothetical fluids, which provide the late time acceleration. It is also remarkable that the higher derivative theory does not effect the radiating model of scalar field cosmology.     

Communication modes in vector diffraction

The communication modes, which mathematically correspond to singular value decomposition, have proven a useful concept in optical scalar-field diffraction, with applications in resolution studies, image synthesis, and wave propagation. For optical near-field geometries the communication modes have to be extended to electromagnetic field accounting for the polarization properties. In this paper we present the vector-valued communication modes method based on the rigorous electric-field diffraction integral. As a special case the transverse-electric scalar field modes are obtained. The intensity and polarization properties of the leading electromagnetic communication modes in near-field arrangements with rectangular apertures are discussed in terms of the Stokes parameters. For small separations between the transmitting and receiving apertures the fundamental mode possesses a ring-shaped hollow structure. The polarization properties of the near-field modes show features on spatial scales smaller than the wavelength of light. The system symmetries lead to degenerate communication modes.     

Intermittency of temperature field in turbulent convection

The scaling behavior of the temperature structure functions in turbulent convection is found to be different for length scales below and above the Bolgiano scale. Both sets of the exponents are well described by log-Poisson statistics. The parameter beta(T) which measures the degree of intermittency is the same for the two regimes of scales and is consistent with the corresponding value for the passive scalar field. A balance between thermal forcing and nonlinear velocity advection, which is a key ingredient leading to Bolgiano scaling, is also checked.     

Large-scale–small-scale duality and the cosmological constant

We study a model of quantum cosmology originating from a classical model of gravitation where a self-interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical signature changing solutions, one at large scales and the other at small scales. It is possible to fine-tune the physics in both scales with an infinitesimal effective cosmological constant.     

Charged perfect fluid and scalar field coupled to gravity

Charged perfect fluid with vanishing Lorentz force and massless scalar field is studied for the case of stationary cylindrically symmetric spacetime. The scalar field can depend both on radial and longitudinal coordinates. Solutions are found and classified according to scalar field gradient and magnetic field relationship. Their physical and geometrical properties are examined and discussion of particular cases, directly generalizing Gödel-type spacetimes, is presented.     

The effect of subgrid-scale models on the entrainment of a passive scalar in a turbulent planar jet

Classical large-eddy simulation (LES) modelling assumes that the passive subgrid-scale (SGS) models do not influence large-scale quantities, even though there is now ample evidence of this in many flows. In this work, direct numerical simulation (DNS) and large-eddy simulations of turbulent planar jets at Reynolds number Re_H = 6000 including a passive scalar with Schmidt number Sc = 0.7 are used to study the effect of several SGS models on the flow integral quantities e.g. velocity and scalar jet spreading rates. The models analysed are theSmagorinsky, dynamic Smagorinsky, shear-improved Smagorinsky and the Vreman. Detailed analysis of the thin layer bounding the turbulent and non-turbulent regions – the so-called turbulent/non-turbulent interface (TNTI) – shows that this region raises new challenges for classical SGS models. The small scales are far from equilibrium and contain a high fraction of the total kinetic energy and scalar variance, but the situation is worse for the scalar than for the velocity field. Both a-priori and a-posteriori (LES) tests show that the dynamic Smagorinsky and shear-improved models give the best results because they are able to accurately capture the correct statistics of the velocity and passive scalar fluctuations near the TNTI. The results also suggest the existence of a critical resolution Δ_x, of the order of the Taylor scale λ, which is needed for the scalar field. Coarser passive scalar LES i.e. Δ_x ≥ λ results in dramatic changes in the integral quantities. This fact is explained by the dynamics of the small scales near the jet interface.     

Bosonization in (1 + 1) dimensions: An elementary analysis

The expression of a free, massless, Fermi field in terms of scalar field components in a Lorentz basis is obtained. The infrared “disease” of the scalar field is seen to play a positive role in enforcing the fermionic selection rules. Particular attention is paid to the Poincaré transformation properties, both of the Fermi construct and of the Bose constituents. The way that two charge operators are contained in the scalar theory, and the necessary enlargement of the (indefinite metric) space on which the scalar field acts, are discussed in detail.     

Palatini form of 1/R gravity

It has been suggested that the Universe's recent acceleration is due to a contribution to the gravitational action proportional to the reciprocal of the Ricci scalar. Although the original version of this theory disagrees with solar system observations, a modified Palatini version, in which the metric and connection are treated as independent variables, has been suggested as a viable model of the cosmic acceleration. We show that this theory is equivalent to a scalar-tensor theory in which the scalar field kinetic energy term is absent from the action. Integrating out the scalar field gives rise to additional interactions among the matter fields of the standard model of particle physics at an energy scale of order 10(-3) eV (the geometric mean of the Hubble and the Planck scales), and so the theory is excluded by, for example, electron-electron scattering experiments.     

平面对称标量场的静态时空

本文求出零质量标量场产生的平面对称度规的静态通解,并研究了它的对称性、奇异性等整体特性,发现平面对称情况与球对称不同,标量场的引入与否,其时空的奇异性没有本质差别。 关键词：     

Changing alpha with time: implications for fifth-force-type experiments and quintessence

If the recent observations suggesting a time variation of the fine structure constant are correct, they imply the existence of an ultralight scalar particle. This particle inevitably couples to nucleons through the alpha dependence of their masses and thus mediates an isotope-dependent long-range force. The strength of the coupling is within a couple of orders of magnitude of the existing experimental bounds for such forces. The new force can be potentially measured in precision experimental tests of the equivalence principle. Because of a coincidence of the required time scales, the scalar field can at the same time play the role of a quintessence field.     

Conserved scalar mixing in a confined-opposed-jets flow

The focus of this paper is on the mixing of a conserved passive scalar for Sc = 1 (Sc is the Schmidt number) in axisymmetric turbulence for which the initial injections of turbulent kinetic energy and scalar variance are similar. Two confined-opposed-jets (COJ) are experimentally studied through simultaneous PIV (particle image velocimetry) and PLIF (planar laser induced fluorescence) measurements, for different flow regimes. One-point transport equation for the scalar variance is assessed through experimental data, along the common axis of the two opposed jets, and different physical phenomena are revealed (production, diffusion, dissipation). The production of scalar variance is equilibrated by the diffusion term (～75%) and the mean dissipation of the scalar variance (～25%). To further assess the scalar behaviour at each scale in this anisotropic, but axisymmetric, flow, a scale-by-scale scalar variance budget equation is derived for axisymmetric turbulence. This equation reduces to Yaglom's 4/3 law, under additional restrictions. The equation is assessed through experimental data, in the impingement region between the two COJ. In particular, the anisotropic energy transfer along different directions is quantified. It is shown that for scales smaller than the size of the central region, Δ, the cascade of the scalar variance is completely inhibited, independently of the particular direction. For scales larger than Δ, the apparent aspect of the energy transfer is that of an inverse cascade, with positive values of the scalar variance transfer. Nonetheless, inhomogeneity of the flow and mixing at those scales is directly responsible for these positive values.     

Scalar and neutrino fields in the Gödel universe

Some properties of the Gödel universe are demonstrated, such as closed timelike lines, and new coordinates are found. The scalar and neutrino field equations are solved and the eigenvalue spectra are calculated. The scalar field has a discrete spectrum, but the neutrino field has, in addition, a continuous spectrum due to the coupling of neutrino spin and rotation in the Gōdel universe. The mode solutions do not form a complete set for either the scalar or neutrino fields; therefore, a quantum field theory cannot be constructed in the usual manner.     

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通过使用一排16根冷线探头排在多个空间点同时测量微加热圆柱的尾流温度场, 用小波分析技术对瞬时温度场的时间序列信号进行多尺度分析, 目的是研究不同尺度脉动温度对总体温度场的贡献.直径为d = 12.7 mm 的圆柱产生了被测的尾流, 对应的雷诺数为5500, 测量区域位于下游距离为2d 和 20d 之间. 基于小波多尺度分辨技术, 尾流温度场被分解为不同温度脉动特征尺度的小波分量. 通过分析这些小波分量的瞬时温度等值线图, 能够直接观测到不同特征尺度的涡结构运动特征和湍流间歇过程. 特别地, 我们在近场区从原始信号分解获得的高频区域中发现了K-H涡的存在. 不同尺度的温度方差沿流向的变化表明, 在下游距离为x=3d和 20d之间, 中等尺度的结构比大尺度和小尺度结构对总的温度均方根的贡献更大. 不同尺度的自相关函数表明, 大尺度和中等尺度的结构显示出较大的相关性, 而高频的小波分量则更快地失去了原有的拟序性. 关键词： 湍流尾流 被动标量 小波分析     

Self-gravitating wave fields in a Gödel space

The properties of self-gravitating wave fields with integral spin (scalar and vector), compatible with a Gödel type space, are investigated. The simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Gödel's metric are solved. For the scalar field, the solutions are obtained for different types of interaction Lagrangians for the gravitational and scalar fields. It is shown that for a massive vector field the relations obtained between the constants lead, within the scope of the strong gravitation theory, to the classical expression for the spin of elementary particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–63, October, 1981.The authors are grateful to the participants of the theoretical seminar conducted by D. Ivanenko for discussing the results of this work.     

A mechanism for reducing the value of the cosmological constant

A mechanism is presented for relaxing an initially large, positive cosmological constant to a value near zero. This is done by introducing a scalar field whose vacuum energy compensates for the initial cosmological constant. The compensating sector involves small mass scales but no unnatural fine-tuning of parameters. It is not clear how to incorporate this mechanism into a realistic cosmology.     

Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.