Gravitational helicity interaction

For gravitational deflections of massless particles of given helicity from a classical rotating body, we describe the general relativity corrections to the geometric optics approximation. We compute the corresponding scattering cross sections for neutrinos, photons and gravitons to lowest order in the gravitational coupling constant. We find that the helicity coupling to spacetime geometry modifies the ray deflection formula of the geometric optics, so that rays of different helicity are deflected by different amounts. We also discuss the validity range of the Born approximation.Comment: 16 pages, 1 figure, to be published in Nuclear Physics

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Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks

Abstract. We analyze the scaling behaviors of two field-scale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q) of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ(q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn), stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm or tfGn functions

On the identification of Dragon Kings among extreme-valued outliers

Abstract. Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges

Some Properties of Tensor Multiplets in Six-Dimensional Supergravity

We review some results on the complete coupling between tensor and vector multiplets in six-dimensional $(1,0)$ supergravity.Comment: 6 pages, LateX. Contribution to the Proceedings of "String Duality, II", Trieste, april 199

Factor analysis of Hungarian hydrophysical data to predict soil water retention characteristics

We explore the information associated with soil water retention included in the large scale soil maps of Hungary. We employed factor analysis to investigate tire role of different commonly measured soil properties - namely -,and and clay content, organic matter content, pH and CaCO3 content - on determining soil water retention at different pF values (pF0, pF2.5, pF4.2 and pF6.2). Analyses were performed oil all the samples of the database, that contains 382 1 soil horizons of diverse soil types, as well as a selection of the horizons belonging to Chernozem soils of the database. Results show considerable differences of water retention characteristics of Chernozems, mainly at pF0. This suggests that a separate analysis for different soil types might be appropriate in order to characterize the impact of measured soil properties on water retention

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly het-erogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead-(or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance (sigma(2)(Y) << 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing sigma(2)(Y) . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of sigma(2)(Y) up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of under-standing of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios. (C) 2022 Elsevier Ltd. All rights reserved

A Gaussian-Mixture based stochastic framework for the interpretation of spatial heterogeneity in multimodal fields

We provide theoretical formulations enabling characterization of spatial distributions of variables (such as, e.g., conductivity/permeability, porosity, vadose zone hydraulic parameters, and reaction rates) that are typical of hydrogeological and/or geochemical scenarios associated with randomly heterogeneous geomaterials and are organized on various scales of heterogeneity. Our approach and ensuing formulations embed the joint assessment of the probability distribution of a target variable and its associated spatial increments, DY, taken between locations separated by any given distance (or lag). The spatial distribution of Y is interpreted through a bimodal Gaussian mixture model. The modes of the latter correspond to an indicator random field which is in turn related to the occurrence of different processes and/or geomaterials within the domain of observation. The distribution of each component of the mixture is governed by a given length scale driving the strength of its spatial correlation. Our model embeds within a unique theoretical framework the main traits arising in a stochastic analysis of these systems. These include (i) a slight to moderate asymmetry in the distribution of Y and (ii) the occurrence of a dominant peak and secondary peaks in the distribution of DY whose importance changes with lag together with the moments of the distribution. This causes the probability distribution of increments to scale with lag in way that is consistent with observed experimental patterns. We analyze the main features of the modeling and parameter estimation framework through a set of synthetic scenarios. We then consider two experimental datasets associated with different processes and observation scales. We start with an original dataset comprising microscale reaction rate maps taken at various observation times. These are evaluated from AFM imaging of the surface of a calcite crystal in contact with a fluid and subject to dissolution. Such recent high resolution imaging techniques are key to enhance our knowledge of the processes driving the reaction. The second dataset is a well established collection of Darcy-scale air-permeability data acquired by Tidwell and Wilson (1999) [Water Resour Res, 35, 3375-3387] on a block of volcanic tuff through minipermeameters associated with various measurement scales

Torsional strengthening of thin-walled tubular reinforced concrete structures using NSM-CFRP laminates: experimental work

Torsional strengthening of thin walled tubular reinforced concrete elements, such as bridge box girders and spandrel beams, has received only limited attention, and investigations generally focus on the use of conventional strengthening methods such as span shortening, steel encasing, member enlargement, shotcrete etc. However, research on the use of innovative fibre reinforced polymers (FRP) as near surface mounted (NSM) reinforcement for torsional strengthening is still very limited and more work should be undertaken to examine the full potential of the NSM technique over more traditional solutions. The current paper assesses experimentally, four different strengthening configurations using NSM technique applied on three faces of two beams using straight CFRP laminates, and on four faces of two beams using special L-CFRP laminates. The results show that the proposed strengthening configurations can effectively control crack propagation and increase the torsional moment carrying capacity of the RC element, thus resulting in increased performance and durability.Marie Curie Initial Training Network “Endure” for the grant received and also the Portuguese Foundation for Science and Technology for the current FCT grant. The author would also like to extend the acknowledgements to the industries CASAIS and CiviTest for performing the experimental work. The authors acknowledge the support provided by the FCT for the project StreColesf, POCI-01-0145- FEDER-02948

Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media

Equations governing flow and transport in randomly heterogeneous porous media are stochastic and scale dependent. In the moment equation (ME) method, exact deterministic equations for the leading moments of state variables are obtained at the same support scale as the governing equations. Computable approximations of the MEs can be derived via perturbation expansion in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for standard deviation smaller than one. Here, we consider steady-state saturated flow in a porous medium with random second-order stationary conductivity field. We show it is possible to identify a support scale, $\eta*$, where the typically employed approximate formulations of MEs yield accurate (statistical) moments of a target state variable. Therefore, at support scale $\eta*$ and larger, MEs present an attractive alternative to slowly convergent Monte Carlo (MC) methods whenever lead-order statistical moments of a target state variable are needed. We also demonstrate that a surrogate model for statistical moments can be constructed from MC simulations at larger support scales and be used to accurately estimate moments at smaller scales, where MC simulations are expensive and the ME method is not applicable