A new method of measuring the inhomogeneity in easy‐axis orientation and in the magnitude of the uniaxial anisotropy in thin ferromagneticfilms has been found. Correlation between the two can also be obtained by this...
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A new method of measuring the inhomogeneity in easy‐axis orientation and in the magnitude of the uniaxial anisotropy in thin ferromagneticfilms has been found. Correlation between the two can also be obtained by this method. Apparatus has been built to measure the probabilitydensity of finding a part of the film with a given easy‐axis orientation, as well as a given Hk , and to plot this probabilitydensity function on an x‐y recorder. The Hkprobabilitydensity function is found to be symmetric, contrary to popular belief. Measured values of easy‐axis inhomogeneity agree within experimental error with values obtained by conventional methods. Previous methods of measuringHkinhomogeneity, based on either radio‐frequency resonance linewidth or on reversible limit, are discussed and found to be questionable.
The problem of turbulence statistics described by the Lundgren-Monin-Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a...
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The problem of turbulence statistics described by the Lundgren-Monin-Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integro-differential equations for the multi-point probability density functions (pdf's) of velocity. A complete set of point transformations is derived for the one-point pdf's and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie-Backlund operator. Due to the one-way coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.
[1] Sea-surface slope probability density functions, which are usually fitted to a GramCharlier series, can be fit equally well by a bound wave/free wave model in which the distributions of bound and free waves are Ga...
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[1] Sea-surface slope probability density functions, which are usually fitted to a GramCharlier series, can be fit equally well by a bound wave/free wave model in which the distributions of bound and free waves are Gaussian. Bound waves are generated by longer waves on the surface and travel at nearly the phase speed of the long wave while free waves are generated directly by the wind and travel at their intrinsic phase speed. These two types of short surface waves can usually be separated in measurements that yield their velocities. The integrals over the two distributions yield the probabilities of finding bound or free waves on the surface. We show that the probability of finding bound waves on the ocean is comparable to that in a wind-wave tank and much larger than the probability of whitecapping. The mean slopes of the two distributions yield the mean tilts of bound or free waves. We show that the mean tilt of the bound waves is similar to that in a wind-wave tank and close to that necessary to explain Doppler shifts in microwave backscatter from the sea surface at high incidence angles. Finally, the widths of the two distributions yield the variance of sea-surface slopes at the locations of bound and free waves. We show that these are larger at sea than in a wind-wave tank, which explains why bound waves at sea have not been recognized previously in sea-surface slope probability distributions.
probability density functions for the orthogonal components of the radius of gyration, , of a random‐flight chain were computed using an indirect numerical integration algorithm which was based upon a multiple convol...
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probability density functions for the orthogonal components of the radius of gyration, , of a random‐flight chain were computed using an indirect numerical integration algorithm which was based upon a multiple convolution proposed by Forsman and Hughes. Computations were performed for relatively long chains of 100–1000 statistical segments . By using a reduced radius of gyrationthe distributions converged to a limiting function at about , except for extremely small radii, . Additional computations using the one‐dimensional distributions yielded the corresponding probability densities for both the two‐ and three‐dimensional (polar) radii. The computed functions were in excellent agreement with all their limiting properties previously determined by analytical methods.
In this paper, first the probability density functions (PDFs) of the states of Chua's circuit have been estimated using B-spline functions and then the state entropies of Chua's circuit with respect to the bif...
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In this paper, first the probability density functions (PDFs) of the states of Chua's circuit have been estimated using B-spline functions and then the state entropies of Chua's circuit with respect to the bifurcation parameter have been obtained. The results of the proposed B-spline density estimator have been compared with the results obtained from the Parzen density estimator.
The assumed joint probabilitydensity function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-sc...
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The assumed joint probabilitydensity function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PDF families are based on the double Gaussian form and the remaining two are the single Gaussian and a Double Delta Function (analogous to a mass flux model). The assumed PDF method is tested for grid sizes as small as 0.4 km to as large as 204.8 km. In addition, studies are performed for PDF sensitivity to errors in the input moments and for how well the PDFs diagnose some higher-order moments. In general, the double Gaussian PDFs more accurately represent SGS cloud structure and turbulence moments in the boundary layer compared to the single Gaussian and Double Delta Function PDFs for the range of grid sizes tested. This is especially true for small SGS cloud fractions. While the most complex PDF, Lewellen-Yoh, better represents shallow convective cloud properties (cloud fraction and liquid water mixing ratio) compared to the less complex Analytic Double Gaussian 1 PDF, there appears to be no advantage in implementing Lewellen-Yoh for deep convection. However, the Analytic Double Gaussian 1 PDF better represents the liquid water flux, is less sensitive to errors in the input moments, and diagnoses higher order moments more accurately. Between the Lewellen-Yoh and Analytic Double Gaussian 1 PDFs, it appears that neither family is distinctly better at representing cloudy layers. However, due to the reduced computational cost and fairly robust results, it appears that the Analytic Double Gaussian 1 PDF could be an ideal family for SGS cloud and turbulence representation in coarse-g
A comment is made on the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669675].
A comment is made on the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669675].
A response is given to to Olczak's comment about the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669675].
A response is given to to Olczak's comment about the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669675].
Capillary imbibition in periodically constricted tubes (PCTs) plays a critical role in multiple natural and technological processes, where the control of autonomous flows is intrinsically linked to the geometric archi...
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Capillary imbibition in periodically constricted tubes (PCTs) plays a critical role in multiple natural and technological processes, where the control of autonomous flows is intrinsically linked to the geometric architecture of the imbibition space. Here we present analytical expressions for the effective radius (r(eff)) of PCTs with different wave shapes and analyze how geometric parameters influence the infiltration dynamics. Our analysis reveals that r(eff) is strongly dependent on the ratio of maximum to minimum radii (alpha) and, for stepped geometries, on the relative segment length proportion (gamma). Increasing alpha enhances r(eff) up to a critical value, beyond which a strong reduction is observed: for alpha>> 2, approximately, the infiltration velocity progressively decreases. This counterintuitive behavior arises from the interplay between hydrodynamic resistance and capillary driving forces. We evaluated the effect on different geometries, achieving different r(eff) that can be analytically predicted by closed-form expressions. The model was also validated against previously reported experimental data. These findings underline the potential of geometric design to optimize capillary-driven flows, providing a framework for tailoring PCTs to specific applications in microfluidics, porous media, and related fields.
Reducing fuel consumption for future airplanes is a critical issue. One solution is to design airplanes with a large wing aspect ratio to increase the lift. However, such wings are sensitive to loads induced by gusts....
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Reducing fuel consumption for future airplanes is a critical issue. One solution is to design airplanes with a large wing aspect ratio to increase the lift. However, such wings are sensitive to loads induced by gusts. A technique consists of using adaptive wings that modify their shape according to the gust measured ahead of the airplane (the so-called feed-forward gust load alleviation). The gust is typically measured using a wind lidar at the nose of the airplane. To determine the three-dimensional wind field, the lidar is addressed along different axes to obtain the projections of the wind along each of them. In this paper, we present a methodology for reconstructing a gust immersed in wind turbulence from the lidar measurements. The proposed estimation methods are based on the Bayesian filtering theory. Considering simplified models, numerical simulations show the feasibility of such a reconstruction.
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