Quadratic Expansion Research Articles

Robust topology optimization under multiple independent uncertainties of loading positions

SummaryThe topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain‐but‐bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient information to the topological variables can be evaluated efficiently upon an explicit quadratic expression as the loads deviate from their ideal application points. Based on the minimum (largest absolute) value of design sensitivities, which corresponds to the most sensitive compliance to the load position variations, a two‐level optimization algorithm within the non‐probabilistic approach is developed upon a gradient‐based optimization method. The proposed framework is then performed to achieve the robust optimal configurations of four benchmark examples, and the final designs are compared comprehensively with the traditional topology optimizations under the loading point fixation. It will be observed that the present methodology can provide a remarkably different structural layout with the auxiliary components in the design domain to counteract the load position uncertainties. The numerical results also show that the present robust topology optimization can effectively prevent the structural performance from a noticeable deterioration than the deterministic optimization in the presence of load position disturbances.

Characteristic Features of the Anomalous Magnetic Properties of Some Mixed Terbium–Yttrium Ferrite Garnets at Low Temperatures

This article is devoted to the experimental investigation of the occurrence of the so-called “low-temperature Belov point” T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> predicted previously for the mixed rare earth-yttrium iron garnet compounds RE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> possessing or not a magnetic compensation point T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">comp</sub> . Isothermal magnetizations MT(H) of two single crystals of Tb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-x</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> with rare-earth (RE) = Tb, and x = 1.98, 0.37, were measured in the 4.2-300 K range, using dc magnetic field H up to 100 kOe applied in one or more of the three main crystallographic directions. Anomalies are observed in the region of T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TbIG</sup> ≈ 58 K, the previous estimated value for TbIG (x = 3), in the temperature dependences of the paraprocess susceptibility χ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , the parameter |b| of the bH <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> term of the quadratic expansion of MT(H) curves, and other pertinent magnetic characteristics. For x = 1.98 with T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">comp</sub> = 137 K and when H is applied along (110), the χ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> - and |b|-maxima take place close to T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TbIG</sup> . The anisotropy of the χ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -data gives evidence for a spontaneous noncollinear structure around the easy axis of magnetization (111) at 4.2 K. For x = 0.37 which has no T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">comp</sub> point and when H is applied along (100), the χ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> - and |b|-maxima are clearly disturbed by the sign anomalies caused by the noncollinear structure instability mechanism due to the crossing of the Tb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> levels at the critical point T* = 16 K and by the lower continuous change from the easy axis <;100> to a low-symmetry angular phase (uuw) due to the first spontaneous spin reorientation phase transition at T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SR1</sub> = 40 K. When x decreases from 3 to 0.37, it is found that despite different anisotropy effects of the Tb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion, its magnetic moment m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tb</sub> close to T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TbIG</sup> is practically constant (~4.99 in μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> per Tb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> ion).

On even spin {mathcal{W}}_{infty }

We study the even spin {mathcal{W}}_{infty } which is a universal W -algebra for orthosymplectic series of mathcal{W} -algebras. We use the results of Fateev and Lukyanov to embed the algebra into {mathcal{W}}_{1+infty } . Choosing the generators to be quadratic in those of {mathcal{W}}_{1+infty } , we find that the algebra has quadratic operator product expansions. Truncations of the universal algebra include principal DrinfeǏd -Sokolov reductions of BC D series of simple Lie algebras, orthogonal and symplectic cosets as well as orthosymplectic Y -algebras of Gaiotto and Rapčák. Based on explicit calculations we conjecture a complete list of co-dimension 1 truncations of the algebra.

New extended thermodynamics balance equations for an electron gas confined in a metallic body

Sommerfeld’s theory of metal electrons suggests that the electrons in a metal can be described as a gas of free fermion particles confined inside the metallic body. In this paper a new extended thermodynamics model is proposed starting from this idea. The model includes both the stress tensor and a quadratic expansion of the distribution function in the neighborhhod of an equilibrium state. Such contributions were neglected in the original model proposed by Muller in 1976; so this new set of balance laws represents an improvement aimed at the description of non-equilibrium phenomena. The application to a simple case is briefly analysed.

Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations

We consider scalar-input control systems in the vicinity of an equilibrium, at which the linearized systems are not controllable. For finite dimensional control systems, the authors recently classified the possible quadratic behaviors. Quadratic terms introduce coercive drifts in the dynamics, quantified by integer negative Sobolev norms, which are linked to Lie brackets and which prevent smooth small-time local controllability for the full nonlinear system.In the context of nonlinear parabolic equations, we prove that the same obstructions persist. More importantly, we prove that two new behaviors occur, which are impossible in finite dimension. First, there exists a continuous family of quadratic obstructions quantified by fractional negative Sobolev norms or by weighted variations of them. Second, and more strikingly, small-time local null controllability can sometimes be recovered from the quadratic expansion. We also construct a system for which an infinite number of directions are recovered using a quadratic expansion.As in the finite dimensional case, the relation between the regularity of the controls and the strength of the possible quadratic obstructions plays a key role in our analysis.

Polynomial Reconstruction of the Reconnection Magnetic Field Observed by Multiple Spacecraft

AbstractWe describe methods for polynomial reconstruction of the magnetic field close to a cluster of spacecraft and apply that to reconstruction of the magnetic field observed during a magnetic reconnection event on 10 August 2017 by the Magnetospheric Multiscale spacecraft. Four different models are described, which vary in complexity between a 12‐parameter linear model, which has only linear variation with respect to the spatial coordinates, and a 27‐parameter quadratic model, which has the full quadratic expansion except that the second derivative with respect to the Minimum Directional Derivative minimum gradient coordinate has been neglected. In contrast to previous reconstruction techniques, these reconstructions can be found using only the magnetic field and current density measured at a single time by the cluster of spacecraft. The equations satisfying are satisfied exactly, while the equations specifying the model fields at the spacecraft locations are satisfied for most models in a best least squares sense. For this magnetotail event, the models have very small errors in magnetic field components ( 0.1 nT) at a distance from the nearest spacecraft on the order of the spacecraft separation, , here equal to 20.5 km. The magnetic structures found using the quadratic models are very time dependent, with a stretched field leading to plasmoid formation at one point in time.

Spatial Flow-Field Approximation Using Few Thermodynamic Measurements—Part I: Formulation and Area Averaging

AbstractOur investigation raises an important question that is of relevance to the wider turbomachinery community: how do we estimate the spatial average of a flow quantity given finite (and sparse) measurements? This paper seeks to advance efforts to answer this question rigorously. In this paper, we develop a regularized multivariate linear regression framework for studying engine temperature measurements. As part of this investigation, we study the temperature measurements obtained from the same axial plane across five different engines yielding a total of 82 datasets. The five different engines have similar architectures and therefore similar temperature spatial harmonics are expected. Our problem is to estimate the spatial field in engine temperature given a few measurements obtained from thermocouples positioned on a set of rakes. Our motivation for doing so is to understand key engine temperature modes that cannot be captured in a rig or in computational simulations, as the cause of these modes may not be replicated in these simpler environments. To this end, we develop a multivariate linear least-squares model with Tikhonov regularization to estimate the 2D temperature spatial field. Our model uses a Fourier expansion in the circumferential direction and a quadratic polynomial expansion in the radial direction. One important component of our modeling framework is the selection of model parameters, i.e., the harmonics in the circumferential direction. A training-testing paradigm is proposed and applied to quantify the harmonics.

Reversible Image Watermarking Algorithm Based on Quadratic Difference Expansion

To improve the visual quality and embedding rate of existing reversible image watermarking algorithms, a reversible image watermarking algorithm based on quadratic difference expansion is proposed. First, the pixel points with grayscale values 0 and 255 in the original image are removed, and then, the half-scrambled watermark information is embedded into the original image using linear difference expansion. Finally, the remaining half of the watermark information is embedded into the previously generated watermarked image by the quadratic difference expansion, meanwhile the removed pixel points with grayscale values 0 and 255 in the image are merged, and the final watermarked image is generated accordingly. The experimental results show that the algorithm has both a high embedding rate and a high visual quality, which can completely recover the original image. Compared with other difference expansion watermarking algorithms, it has certain advantages without having to consider the smoothness of the embedded image region.

Finite strip method applied to steady heat conduction and thermal radiation in a planar slab: absorbing ̶ emitting gray material and parallel diffuse surfaces

This paper addresses a new finite strip method for the analysis of simultaneous heat conduction and thermal radiation in a planar slab with diffuse surfaces and filled with an absorbing and emitting material considered as a gray medium. The gray material is discretized into a finite number of strips where the temperature is approximated with quadratic expansions in local coordinates whose coefficients are unknowns inside each strip. The finite strip method consists in a set of discrete equations corresponding to energy balance equations united to the compatibility conditions of both temperature and heat flux between consecutive strips. The gray material is articulated with different combinations of thermal and optical properties. Numerical results for the temperature fields and the conductive, radiative and total heat fluxes are presented in graphical and tabular forms and they compared favorably with equivalent results employing standard calculation techniques. The three main features attributable to the finite strip method are simplicity, quick calculation, good convergence and quality results.

Robust topology optimization under load position uncertainty

SummaryThe topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain‐but‐bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single‐level optimization approach is suggested by using a popular gradient‐based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs.

A New Ring Current Model for Saturn

AbstractThe ring current of Saturn is obtained by taking the curl of the observed magnetic field. An analytical model of this ring current can then be obtained by fitting it to a lognormal in ρ and a Gaussian in z. Local time dependence is included as a harmonic expansion in ϕ for coefficients of the lognormal; radial dependence is included as a quadratic expansion in ρ of the width of the Gaussian. In this model, the ring current peaks at ~0.25 MA/RS2 at ~10 RS on the nightside near ~1 hr. The ring current strength minimizes at ~0.17 MA/RS2 on the dayside near ~16 hr. The cross‐sectional shape of the ring current is a teardrop extending from ~5 to ~20 RS or more.

The clustering of theSDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the anisotropic baryon acoustic oscillations with redshift weights

We present an anisotropic analysis of Baryon Acoustic Oscillation (BAO) signal from the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample. The sample consists of 147,000 quasars distributed over a redshift range of $0.8 < z < 2.2$. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement $D_M$ at $z = 2.2$ and Hubble parameter $H$ at $z=0.8$. We parameterize the distance-redshift relation, relative to a fiducial model, as a quadratic expansion. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine $D_M(z=1) = 3405\pm305 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=1) = 120.7\pm 7.3 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ and $D_M(z=2) = 5325\pm249 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=2) = 189.9\pm 32.9 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.

Temperature Resistant Binary SLES/Nonionic Surfactant Mixtures at the Air/Water Interface.

Surface compositions of adsorbed monolayers at the air/water interface, formed from binary surfactant mixtures in equilibrium, have been studied using neutron reflectivity at three discrete temperatures: 10, 25, and 40 °C. The binary compositions studied are sodium lauryl dodecyl ether sulfate (SLES EO3)/C12E n, where n = 6 and 8, at a fixed concentration of 2 mM with and without the addition of 0.1 M NaCl. Without NaCl, the nonionic surfactant dominates at the interface and nonideal mixing behavior is observed. This is modeled using the pseudophase approximation with a quadratic expansion of the free energy of mixing. The addition of 0.1 M NaCl screens the charge interaction between the surfactants and drives the surface composition of each system closer to that of the bulk composition. However, model fits to both the micelles and surface layers suggest that nonideal mixing is still taking place, although it is difficult to establish the extent of nonideality due to the limited data quality. The effect of temperature changes on the surface adsorption and composition of the surfactant mixtures is minimal and within error, with and without NaCl, but the critical micelle concentrations are significantly affected. This indicates the dominant influence of steric hindrances and surfactant charge interactions in determining interfacial behavior for these surfactants, relative to the temperature changes. The study also highlights the delicate effect of a relatively small change in the number of EO groups on mixing behavior.

Assessing the accuracy of integral equation theories for nano-sized hydrophobic solutes in water.

Integral equation theories provide an efficient route for computing the solvation free energy (SFE) of molecular systems in water. The accuracy of those theories is usually tested against small molecules via comparison of SFE with reference data. However, tests against larger molecules in the nanometer regime are scarce in literature despite recent applications to such systems. Here, we thus study the accuracy and validity of a commonly used integral equation theory, namely, a three-dimensional reference interaction site model (3D-RISM), by considering the following problems: (1) solvation of a small to large Lennard-Jones particle, (2) binding of planar hydrophobic systems with varying size and hydrophobicity, and (3) self-assembly of amphiphilic molecules into a nanocapsule. The energy representation method is also utilized for comparison. The results show that the 3D-RISM method works successfully for small molecules, while the accuracy degrades systematically with system size and hydrophobicity. The size-dependent error in SFE does not cancel adequately between two solute configurations, resulting in a substantial error in the free energy difference. It is also shown that the free energy profiles for hydrophobic association exhibit a fictitious high-energy barrier, suggesting that care must be taken for studying such systems. The numerical difficulties observed above are discussed based on the relation between hypernetted-chain approximation, classical density functional theory with quadratic expansion, and the size-dependent error arising from the cavity region of the system.

Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

SummaryThe Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a posteriori the effects of the imperfections in the reduced nonlinear equations. The state‐of‐art treatment of geometrical imperfections is accurate only for small imperfection amplitudes and linear pre‐critical behaviour. This work enlarges the validity of the method to a wider range of practical problems through a new approach, which accurately takes into account the imperfection without losing the benefits of the a posteriori treatment. A mixed solid‐shell finite element is used to build the discrete model. A large number of numerical tests, regarding nonlinear buckling problems, modal interaction, unstable post‐critical and imperfection sensitive structures, validates the proposal. Copyright © 2017 John Wiley &amp; Sons, Ltd.

A novel quadratic polynomial expansion of nonlinear scattering function for RF power amplifier modeling

AbstractThe design of high‐performance radio frequency power amplifiers requires accurate and simple characterization of power transistors. Behavioral modeling technique provides an efficient and convenient way to tackle this issue. This study presents a novel behavioral model, which is based on quadratic polynomial expansion of nonlinear scattering function with high‐order components included. This method was implemented in Computer Aided Design (CAD) program with the help of the frequency‐domain defined device component. The comparisons of the output voltage are presented and discussed under different load impedance and input power on a practical circuit operating at 20 GHz, and the results show that the model is capable of accurately characterizing the strong nonlinear behavior the device expressed while the fundamental and harmonic frequency load impedance located anywhere inside the Smith Chart.

A three-dimensional nodal neutron kinetics code with a higher-accuracy algorithm for reactor core in hexagonal-z geometry

A nodal neutron kinetics model with a higher-accuracy algorithm for three-dimensional multi-group neutron diffusion calculation is developed for transient analysis of reactor core in hexagonal-z geometry. The spatial discretization technique is based on a high order nodal expansion method for hexagonal-z geometry. In this method, one dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four order polynomial expansion respectively. The partially-integrated radial and axial leakages are both approximated by the quadratic polynomial. The time discretization technique is based on a fully implicit scheme combined with a Runge-Kutta method for solving the neutron flux and delayed neutron precursor equations. A flux weighting method is adopted to calculate homogenized multi-group cross sections for transient analysis of control rod ejection accident. The described numerical methods are implemented into the computer code HNHEXK. This code is tested with one static benchmark problem and several kinetic benchmark problems. The numerical results show that the current method has a good agreement with the reference.

Semiclassical treatment of quantum propagation with nonlinear classical dynamics: A third-order thawed Gaussian approximation.

The time-dependent WKB approximation for a coherent state is expanded to third order around a guiding real trajectory, allowing for the novel treatment of nonlinearity in its semiclassical dynamics, which is generally present in all physical systems far from the classical regime. The result is a closed-form solution consisting of a linear combination of Airy functions and their derivatives multiplied by an exponential. The expression's ability to capture nonlinearity is demonstrated by examining the autocorrelation of initial coherent states in anharmonic systems with few to many contributing periodic orbits. Its accuracy is compared to the quadratic expansion and found to be superior in regimes of ℏ where the curvature begins to be significant, as expected. Moreover, the expression is shown to be a real-trajectory uniformization over two coalescing saddle points that are emblematic of significant curvature. This extends real-trajectory time-dependent wave-packet semiclassical methods to highly anharmonic systems for the first time and establishes their regime of validity.

Analysis and Design for the Moderately Deep Postbuckling Behavior of Composite Plates

It is widely acknowledged that tracking the postbuckling response of structures made from thin plates can be problematical. Such difficulty is associated with highly nonlinear effects, including mode jumping, imperfection sensitivity, and their combined interactions. Two widely used techniques that are currently used involve path following and asymptotic expansion. The former is often implemented in commercial finite element codes but can prove unreliable at representing branch switching. The latter is a relatively quick technique due to its recursive linear nature but is only reliable in the vicinity of bifurcations. Due to the overall complex nonlinearity, analytical closed-form solutions do not exist for path following and exist rarely for quadratic asymptotic expansions where simple forms have been adopted. This paper presents an analytical-based approach that enables the efficient optimal design of “moderately deep” nonlinear postbuckling behavior of laminated composite plates under uniaxial or biaxial loading. It provides a closed-form solution that more reliably reflects a deeper postbuckling response than the state of the art. Subsequently, highly efficient postbuckling optimization is attributed to the newly derived closed-form solution and a recent two-level optimization framework.

Redshift weights for baryon acoustic oscillations: application to mock galaxy catalogues

Large redshift surveys capable of measuring the Baryon Acoustic Oscillation (BAO) signal have proven to be an effective way of measuring the distance-redshift relation in cosmology. Building off the work in Zhu et al. (2015), we develop a technique to directly constrain the distance-redshift relation from BAO measurements without splitting the sample into redshift bins. We parametrize the distance-redshift relation, relative to a fiducial model, as a quadratic expansion. We measure its coefficients and reconstruct the distance-redshift relation from the expansion. We apply the redshift weighting technique in Zhu et al. (2015) to the clustering of galaxies from 1000 QuickPM (QPM) mock simulations after reconstruction and achieve a 0.75% measurement of the angular diameter distance $D_A$ at $z=0.64$ and the same precision for Hubble parameter H at $z=0.29$. These QPM mock catalogs are designed to mimic the clustering and noise level of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12). We compress the correlation functions in the redshift direction onto a set of weighted correlation functions. These estimators give unbiased $D_A$ and $H$ measurements at all redshifts within the range of the combined sample. We demonstrate the effectiveness of redshift weighting in improving the distance and Hubble parameter estimates. Instead of measuring at a single 'effective' redshift as in traditional analyses, we report our $D_A$ and $H$ measurements at all redshifts. The measured fractional error of $D_A$ ranges from 1.53% at $z=0.2$ to 0.75% at $z=0.64$. The fractional error of $H$ ranges from 0.75% at $z=0.29$ to 2.45% at $z = 0.7$. Our measurements are consistent with a Fisher forecast to within 10% to 20% depending on the pivot redshift. We further show the results are robust against the choice of fiducial cosmologies, galaxy bias models, and RSD streaming parameters.