Full Coordinates Research Articles

Enabling three-dimensional real-space analysis of ionic colloidal crystallization.

Structures of molecular crystals are identified using scattering techniques because we cannot see inside them. Micrometre-sized colloidal particles enable the real-time observation of crystallization with optical microscopy, but in practice this is still hampered by a lack of 'X-ray vision'. Here we introduce a system of index-matched fluorescently labelled colloidal particles and demonstrate the robust formation of ionic crystals in aqueous solution, with structures that can be controlled by size ratio and salt concentration. Full three-dimensional coordinates of particles are distinguished through in situ confocal microscopy, and the crystal structures are identified via comparison of their simulated scattering pattern with known atomic arrangements. Finally, we leverage our ability to look inside colloidal crystals to observe the motion of defects and crystal melting in time and space and to reveal the origin of crystal twinning. Using this platform, the path to real-time analysis of ionic colloidal crystallization is now 'crystal clear'.

Randomized block-coordinate adaptive algorithms for nonconvex optimization problems

Nonconvex optimization problems have always been one focus in deep learning, in which many fast adaptive algorithms based on momentum are applied. However, the full gradient computation of high-dimensional feature vector in the above tasks become prohibitive. To reduce the computation cost for optimizers on nonconvex optimization problems typically seen in deep learning, this work proposes a randomized block-coordinate adaptive optimization algorithm, named RAda, which randomly picks a block from the full coordinates of the parameter vector and then sparsely computes its gradient. We prove that RAda converges to a δ-accurate solution with the stochastic first-order complexity of O(1/δ2), where δ is the upper bound of the gradient’s square, under nonconvex cases. Experiments on public datasets including CIFAR-10, CIFAR-100, and Penn TreeBank, verify that RAda outperforms the other compared algorithms in terms of the computational cost.

Optimizing reaction coordinate by flux maximization in the transition path ensemble.

The transition path ensemble is a collection of reactive trajectories, all of which largely keep going forward along the transition channel from the reactant state to the product one, and is believed to possess the information necessary for the identification of reaction coordinates. Previously, the full coordinates (both position and momentum) of the snapshots in the transition path ensemble were utilized to obtain the reaction coordinate [W. Li and A. Ma, J. Chem. Phys. 144, 114103 (2016) and W. Li, J. Chem. Phys. 148, 084105 (2018)]. Here, with the conformational (or position) coordinates alone, it is suggested that a meaningful one-dimensional representation of the reaction coordinate can be obtained by maximizing the flux (the net number of transitions through the dividing surface) of a given coordinate in the transition path ensemble. In the application to alanine dipeptide in vacuum, dihedral angles ϕ and θ were identified to be the two best reaction coordinates, which was consistent with the results in the existing studies. A linear combination of these two coordinates gave a better reaction coordinate, which is highly correlated with the committor. Most importantly, the method obtained a linear combination of pairwise distances between heavy atoms, which was highly correlated with the committor as well. The standard deviation of the committor at the transition region defined by the optimized reaction coordinate is as small as 0.08. In addition, the effects of practical factors, such as the choice of transition path sub-ensembles and saving interval between frames in transition paths, on reaction coordinate optimization were also considered.

Unified Description of the Jahn-Teller Effect in Molecules with Only Cs Symmetry: Cyclohexoxy in Its Full 48-Dimensional Internal Coordinates.

The two lowest potential energy surfaces of cyclohexoxy which are coupled by conical intersections and the spin-orbit interaction are determined in the full 48-dimensional internal coordinate space using a feedforward neural network to fit a diabatic potential energy matrix. The electronic structure data are obtained at the multireference configuration interaction with single- and double-excitation level. Underlying parallels between these coupled surfaces and those of the alkoxy radicals methoxy and isopropoxy are established. Earlier work by Dillon and Yarkony is extended. While the parallels would have been challenging to appreciate using the concept of the Jahn-Teller active modes, they are readily seen in terms of two internal modes centered at the conical intersection: g the energy difference gradient vector and h the interstate coupling gradient vector. In other words, g and h vectors provide a unified description of the Jahn-Teller effect in molecules exhibiting C3v and quasi-C3v symmetries. A spectral simulation in the full 48-vibrational-internal coordinate space is reported. This spectrum is obtained using recently developed algorithms designed to increase the size of the systems that can be treated with a time-independent vibronic coupling approach.

Identification of Sagittarius stream members in angular momentum space with gaussian mixture techniques

ABSTRACT This paper uses Gaussian mixture techniques to dissect the Milky Way (MW) stellar halo in angular momentum space. Application to a catalogue of 5389 stars near the plane of the Sagittarius (Sgr) stream with full 6D phase-space coordinates supplied by Gaia EDR3 and SEGUE returns four independent dynamical components. The broadest and most populated corresponds to the smooth MW halo. The narrowest and faintest contains 40 stars of the Orphan stream. We find a component with little or no angular momentum likely associated with the Gaia-Sausage-Enceladus substructure. We also identify 925 stars and 7 globular clusters with probabilities $\gt 90{{\ \rm per\ cent}}$ to be members of the Sgr stream. Comparison against N-body models shows that some of these members trace the continuation of the leading/trailing tails in the Southern/Northern hemispheres. The new detections span ∼800° on the sky, thus wrapping the Galaxy twice.

Deep learning of multibody minimal coordinates

AbstractMultibody systems [1] are the state‐of‐the‐art tool to model complex mechanical mechanisms. However, they typically include redundant coordinates plus constraints, leading to differential algebraic equations for the dynamics which require dedicated integration schemes and control/estimation algorithms.In the deep learning field, autoencoders are a particular neural network class with a symmetric structure to perform a nonlinear dimensionality reduction. In fact, they can be seen as a non‐linear extension of principal component analysis [2].In this work, it is proposed to use an autoencoder to reduce a general multibody model to minimal coordinates, eliminating the constraints. The obtained decoder function is used to perform a non‐linear projection of the multibody coordinates: urn:x-wiley:16177061:media:PAMM202000348:pamm202000348-math-0001 where are respectively the encoder and decoder neural network functions, while are respectively the obtained minimal coordinates and reconstructed full multibody coordinates.The novelty is that the autoencoder training includes the multibody physics information [3]. In this way, the autoencoder does not only perform a dimensionality reduction of the original coordinates but can be used for model order reduction. The obtained reduced‐order model consists of ordinary differential equations (with respect to the original differential algebraic equations) and can be used to perform dynamic simulations and easily coupled with standard estimation algorithms for state‐estimation.A typical application example is a mechanism with closed‐loops, such as a car suspension, for which no analytical expression is available to reduce the full multibody model to minimal coordinates. The introduced physics‐informed neural network allows to reduce the model and combine it with an augmented extended Kalman filtering scheme [4], in order to estimate difficult‐to‐measure inputs or parameters in the system.In a first application, the model in combination with measured strut displacement or acceleration, allows to estimate the strut force, in addition to the body full coordinates in position, velocity and acceleration. The rationale is reported in the figure below.rationale.pngThe Flanders Innovation & Entrepreneurship Agency within the IMPROVED project and the AI impulse program of the Flemish Government are gratefully acknowledged for their support.

Deep learning for model order reduction of multibody systems to minimal coordinates

Among the proposed formulations for rigid multibody dynamics, the minimal coordinates approach permits to parametrize the system motion with the minimal amount of degrees of freedom without the need of additional constraints equations. This leads to a system of ordinary differential equations to describe the motion which enables a straightforward combination of the model with control or estimation algorithms. However, an explicit relation between the model full coordinates and a minimal number of parameters is not always available or easily obtainable, especially for spatial closed-loop mechanisms. In this work, we therefore propose to deploy deep learning to find an approximation of such motion mappings. More specifically, an autoencoder neural network architecture is exploited for the nonlinear dimensionality reduction from full to minimal coordinates. A novel neural-network training scheme is introduced, which exploits the multibody model dynamics information to optimize the decoder-function derivatives so that they represent the tangent space and the curvature of the minimal coordinates manifold. This scheme leads to an effective description of the motion manifold which can be used to express the dynamics in minimal coordinates. The approach is validated on two reference rigid body mechanisms.

Study of profilograph features for determining the geometric characteristics of products by laser scanning

The work is devoted to study of profilograph features for determining geometric characteristics of products by laser scanning. The control methods applied are implemented in science-based designs of technical means of control that can provide high accuracy of parameter measurement when profiling the surface of parts. The analysis of graphs of the metal sheet surface in full and Cartesian coordinates made it possible to determine the highest and lowest points of the surface, therefore to determine the profile of sheet undulation. For example, the height of metal sheet irregularities resulted from some deformations was 6,378 mm.

First Gaia dynamical model of the Milky Way disc with six phase space coordinates: a test for galaxy dynamics

ABSTRACT We construct the first comprehensive dynamical model for the high-quality subset of stellar kinematics of the Milky Way disc, with full 6D phase-space coordinates, provided by the Gaia Data Release 2. We adopt an axisymmetric approximation and use an updated Jeans Anisotropic Modelling (JAM) method, which allows for a generic shape and radial orientation of the velocity ellipsoid, as indicated by the Gaia data, to fit the mean velocities and all three components of the intrinsic velocity dispersion tensor. The Milky Way is the first galaxy for which all intrinsic phase space coordinates are available, and the kinematics are superior to the best integral-field kinematics of external galaxies. This situation removes the long-standing dynamical degeneracies and makes this the first dynamical model highly overconstrained by the kinematics. For these reasons, our ability to fit the data provides a fundamental test for both galaxy dynamics and the mass distribution in the Milky Way disc. We tightly constrain the volume average total density logarithmic slope, in the radial range 3.6–12 kpc, to be αtot = −2.149 ± 0.055 and find that the dark halo slope must be significantly steeper than αDM = −1 (NFW). The dark halo shape is close to spherical and its density is ρDM(R⊙) = 0.0115 ± 0.0020 M⊙ pc−3 (0.437 ± 0.076 GeV cm−3), in agreement with previous estimates. The circular velocity at the solar position vcirc(R⊙) = 236.5 ± 3.1 km s−1 (including systematics) and its gently declining radial trends are also consistent with recent determinations.

Damage detection in a fixed-fixed beam using natural frequency changes

This paper presents a damage detection technique which uses change in Frequency Response Function (FRF) and Modal Strain Energy (MSE) for damage detection in beam and truss like structures. It’s a robust approach for Structural Health Monitoring (SHM) using natural frequency for structural damage assessment. This technique couples FRF with Iterative Modal Strain Energy (IMSE) method to accurately localize and quantify the damage with only few frequencies, overcoming the limitation of mode shape based damage detection methods which requires mode shapes at full coordinates but damage is either over/underestimated. In the current approach, a damage detection algorithm is developed and validated by conducting numerical studies for a Fixed-Fixed beam, both noise-free and noise-effected cases are simulated. The numerical studies reveal that proposed algorithm is capable of identifying, localizing and quantifying the damage accurately at reduce computational cost.

\u201cFlashMap\u201d - A Semi-Automatic Tool for Rapid and Accurate Spatial Analysis of Marker Expression in the Subventricular Zone

The subventricular zone (SVZ) is a region of ongoing postnatal germinal activity that shows complex spatial heterogeneity. For instance, different SVZ microdomains contain neural stem cells that express distinct transcription factors and generate different glial and neuronal progenies. These unique characteristics call for the development of new methods to integrate a spatial dimension to histological analyses performed in this germinal region. We developed “FlashMap”, a semi-automatic software that allows the segmentation and rapid measurement of optical densities throughout the full SVZ coordinates. “FlashMap” generates easily readable two-dimensional heatmaps that can be superimposed onto three-dimensional reconstructions of the ventricular system for optimal spatial exploration. Accurate heatmaps can be obtained, even following serial section subsampling thereby reducing the amount of tissue and time required for histological analysis. We first illustrate the potential of “FlashMap” by spatially exploring the correlation of SVZ thickness and cellular density with germinal activity throughout its rostro-caudal coordinates. We then used “FlashMap” to analyse the spatial expression of the transcription factors Dlx2, Tbr2 and Hopx as well as of the immature neuronal marker Dcx, to demonstrate the suitability of this approach to explore the regional production of cells of distinct lineages by defined SVZ microdomains.

Determination of the location of air objects in polistatic radar system parasitising on radiation telecommunication systems

Currently, in areas of large cities there is a steady trend towards an increase in the spatial density of telecommunications systems. Saturation of the radio spectrum with analogue and digital systems used to solve problems of radio communication and television allows on their basis improving the technologies for semi-active radar detecting and determining the coordinates of air objects. The introduction of radar surveillance using transmitters not intended for radar purpose is often called a semi-active radar using outside or “parasitic” emission sources. The advantages of the systems are the minimization of the deployment costs, low operational energy costs, a low probability of establishing distortions, stealth operation, environmental friendliness and lack of requirements for radio frequency resource allocation. The relatively large elevations of the antennas of communication and television transmitters with the existing emitted power create favorable conditions for the detection of low altitude air objects. The digital signals of modern telecommunications systems have a spectrum width that provides acceptable resolution and accuracy for measuring the full range and angular coordinates. In general, a system of this type is a poly-static (multi-static) system consisting of one or more radiation sources and one or more receiving positions scattered in space. The promising task such systems solve along with airspace control is air traffic control. The article considers options for determining the rectangular coordinates of air objects in a system of bistatic radar stations using radio emission from external sources for target detection. The variants of the location of air objects with different composition of primary measurements of coordinates and a number of transmitting positions are considered. Analytical expressions are given for calculating the projections of the target velocity vector on the axis of the Cartesian coordinate system. The accuracy of airborne positioning for multi-static radar systems of this type is estimated.

Ca2+ -induced orientation of tandem collagen binding domains from clostridial collagenase ColG permits two opposing functions of collagen fibril formation and retardation.

The full atomic coordinates of the tandem CBD and its corresponding structure factor amplitudes have been deposited in the Protein Data Bank (PDB accession code 5IKU). Small-angle X-ray scattering data and corresponding ab initio models have been submitted to the Small Angle Scattering Biological Data Bank (SASBDB). Accession codes CL2, collagenase module 2, CN2, CP2 are assigned to envelopes for tandem CBD at -log[Ca2+ ] (pCa) 3, 4, 5, and 6, respectively. Accession code DC64 was assigned to the complex of polycystic kidney disease-CBD1-CBD2 with mini-collagen.

GaiaData Release 2

Context.The secondGaiadata release (GaiaDR2) contains high-precision positions, parallaxes, and proper motions for 1.3 billion sources as well as line-of-sight velocities for 7.2 million stars brighter thanGRVS= 12 mag. Both samples provide a full sky coverage.Aims.To illustrate the potential ofGaiaDR2, we provide a first look at the kinematics of the Milky Way disc, within a radius of several kiloparsecs around the Sun.Methods.We benefit for the first time from a sample of 6.4 million F-G-K stars with full 6D phase-space coordinates, precise parallaxes (σϖ∕ϖ≤ 20%), and precise Galactic cylindrical velocities (median uncertainties of 0.9-1.4 km s-1and 20% of the stars with uncertainties smaller than 1 km s-1on all three components). From this sample, we extracted a sub-sample of 3.2 million giant stars to map the velocity field of the Galactic disc from ~5 kpc to ~13 kpc from the Galactic centre and up to 2 kpc above and below the plane. We also study the distribution of 0.3 million solar neighbourhood stars (r< 200 pc), with median velocity uncertainties of 0.4 km s-1, in velocity space and use the full sample to examine how the over-densities evolve in more distant regions.Results. GaiaDR2 allows us to draw 3D maps of the Galactocentric median velocities and velocity dispersions with unprecedented accuracy, precision, and spatial resolution. The maps show the complexity and richness of the velocity field of the galactic disc. We observe streaming motions in all the components of the velocities as well as patterns in the velocity dispersions. For example, we confirm the previously reported negative and positive galactocentric radial velocity gradients in the inner and outer disc, respectively. Here, we see them as part of a non-axisymmetric kinematic oscillation, and we map its azimuthal and vertical behaviour. We also witness a new global arrangement of stars in the velocity plane of the solar neighbourhood and in distant regions in which stars are organised in thin substructures with the shape of circular arches that are oriented approximately along the horizontal direction in theU−Vplane. Moreover, in distant regions, we see variations in the velocity substructures more clearly than ever before, in particular, variations in the velocity of the Hercules stream.Conclusions. GaiaDR2 provides the largest existing full 6D phase-space coordinates catalogue. It also vastly increases the number of available distances and transverse velocities with respect toGaiaDR1.GaiaDR2 offers a great wealth of information on the Milky Way and reveals clear non-axisymmetric kinematic signatures within the Galactic disc, for instance. It is now up to the astronomical community to explore its full potential.

Vibration analysis of composite airfoil blade using orthotropic thin shell bending theory

In this paper, starting with the thin shell theory, the governing partial differential equation of motion for the transverse deflection of a rotating pre-twisted airfoil is derived. Strain-displacement relationships include the effect of warping of the cross-section due to twist-bend coupling effect introduced as a result of varying stagger angle and camber radius of the blade. The equation of motion, thus derived, is used to formulate the free vibration of a typical turbo-machinery cantilevered airfoil by considering it as an anisotropic shell in full curvilinear coordinates subjected to a centrifugal force field. The analytical derivation considers both the stress-stiffening as well as stress-softening effects of the centrifugal forces on the spinning airfoil. The fourth-order partial differential equation characterizing the flexural motion of the airfoil is transformed into a matrix- eigenvalue form using a Rayleigh-Ritz technique. The blade deformations are represented by a set of “admissible” sinusoidal trial functions, which fully satisfy all the clamped-end constraints as well as the free-edge boundary conditions. The numerical results presented in a non-dimensional parametric form are directly applicable in determining the static and running frequencies of typical composite blades used in the fan module of an aeroengine.

Modelling Three-Dimensional Winds on a NW Pacific Region of Mexico Using Boundary-Fitted Grids

In this study, the momentum equations describing an atmospheric flow over a NW Pacific region of Mexico are solved numerically. In order to capture the complex flow-topography interactions with detail, a combination of a numerical wind model in full 3D curvilinear coordinates, along with a high resolution boundary-fitted grid is used. Boundary conditions were obtained from ten years (2002-2012) of measured offshore wind data. Prevailing winds from April to September during that period of observations were selected for the simulations. For the cases analyzed, it was found that at the points of the study region (PSS, PSM, PM), wind speed increased about 10% to 20% of its offshore values, while inland they decreased about 86% to 96%. This spatial behavior agreed very well with the observed local winds. A coastal jet (CJ), 35 km long with speeds about 1.5 - 2 m/s, emanating from PSS was found for NNW winds. Modeled winds were also used to compute wind stresses, wind stress curl, and CUI fields. Wind stress values agreed very well to those reported in the literature. High values of wind stress curl, and CUI were found at the lee of the points (PSS, PSM, PM). Indirect estimations of sea surface currents were about 15 - 20 cm/s offshore and 5 - 10 cm/s at the coast.

Non‐intrusive reduced order modelling with least squares fitting on a sparse grid

SummaryThis paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps, taking only a set of full model solution snapshots as the training data during the construction. Thus, neither the physical details nor further numerical simulations of the original PDE model are required by this methodology, and the level of non‐intrusiveness is improved compared with existing reduced order models. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients. This model can be applied to a wide range of physical and engineering scenarios, and we test it on a couple of problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high‐fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude. Copyright © 2016 John Wiley & Sons, Ltd.

Pointcatcher software: analysis of glacial time-lapse photography and integration with multitemporal digital elevation models

ABSTRACTTerrestrial time-lapse photography offers insight into glacial processes through high spatial and temporal resolution imagery. However, oblique camera views complicate measurement in geographic coordinates, and lead to reliance on specific imaging geometries or simplifying assumptions for calculating parameters such as ice velocity. We develop a novel approach that integrates time-lapse imagery with multitemporal DEMs to derive full three-dimensional coordinates for natural features tracked throughout a monoscopic image sequence. This enables daily independent measurement of horizontal (ice flow) and vertical (ice melt) velocities. By combining two terrestrial laser scanner surveys with a 73 days sequence from Sólheimajökull, Iceland, variations in horizontal ice velocity of ~10% were identified over timescales of ~25 days. An overall decrease of ~3.0 m surface elevation showed asynchronous rate changes with the horizontal velocity variations, demonstrating a temporal disconnect between the processes of ice surface lowering and mechanisms of glacier movement. Our software, ‘Pointcatcher’, is freely available for user-friendly interactive processing of general time-lapse sequences and includes Monte Carlo error analysis and uncertainty in projection onto DEM surfaces. It is particularly suited for analysis of challenging oblique glacial imagery, and we discuss good features to track, both for correction of camera motion and for deriving ice velocities.

Subaperture stitching test of large steep convex spheres.

Limited by the aperture and f/number of the transmission sphere (TS), large convex spheres with very small R/number (ratio of the radius of curvature to the aperture) cannot be tested in a single measurement with a standard interferometer. We present the algorithm and troubleshooting for subaperture stitching test of a half meter-class convex sphere with R/0.61. Totally 90 off-axis subapertures are arranged on 5 rings around the central one. Since the subaperture is so small, its surface error is comparable with that of the TS reference error. Hence a self-calibrated stitching algorithm is proposed to separate the reference error from the measurements. Another serious problem is the nonlinear mapping between the subaperture's local coordinates and the full aperture's global coordinates. The nonlinearity increases remarkably with the off-axis angle. As a result, we cannot directly remove power from the full aperture error map as we usually do. Otherwise incorrect spherical aberration will be generated. We therefore propose the sphericity assessment algorithm to match the stitched surface error with a best-fit sphere. The residual is true surface error which can be used for corrective figuring or for tolerance assessment. The self-calibrated stitching and troubleshooting are demonstrated experimentally.

Self-dual chiral boson: augmented superfield approach

We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above transformations, we invoke the (dual-)horizontality conditions, (anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that are defined on the (2, 2)-dimensional supermanifold. The latter is parameterized by the bosonic variable x^\mu\,(\mu = 0,\, 1) and a pair of Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0 and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is such that, instead of the full (2, 2) dimensional superspace coordinates (x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional super-subspace variables (t, \theta, \bar\theta) for its description. This is a novel observation in the context of superfield approach to BRST formalism. The application of the dual-horizontality condition, in the derivation of a set of proper (anti-)co-BRST symmetries, is also one of the new ingredients of our present endeavor where we have exploited the augmented version of superfield formalism which is geometrically very intuitive.