Ellipsoidal Tubes Research Articles

Crystals of Ni6L12 Ellipsoidal Tubes as Single-Crystal-to-Single-Crystal Adsorption Matrix: Penetrative Study of Self-Assembled Crystals vs Guest-Exchanged Crystals.

Informative similarities/differences between self-assembled and single-crystal-to-single-crystal (SCSC) guest-exchanged crystals based on both the molecular structure and adsorption nature are observed. The self-assembly of Ni(ClO4)2 with a dicyclopentyldi(pyridine-3-yl)silane bidentate ligand (L) in a mixture of toluene and acetonitrile gives rise to purple crystals consisting of double-stranded ellipsoidal tubes, [Ni6(ClO4)4(CH3CN)8L12]·8ClO4·4CH3CN·5C7H8. The coordinated acetonitriles as well as the solvates are removed at 170 °C to transform the purple crystals into blue crystals of [Ni(ClO4)2L2]n that return to the original crystals in the mixture of toluene and acetonitrile. Further, the toluene and acetonitrile solvates of the original crystals are replaced by o-, m-, and p-xylene isomers within 5 min in a SCSC manner. In the present study, SCSC xylene-exchanged crystals were compared with crystals obtained from direct self-assembly in a mixture of each xylene isomer and acetonitrile.

A novel approach to construct self-assembled 3D MEMS arrays

The paper presents the design and technological fabrication process of Yin or Yang-shaped, micron-sized electromechanical system (MEMS) elements displaying asymmetric hollow cylinders with two different curvatures of the cylinder shell. By adapting the process steps, two neighboring shutter MEMS elements can either be attached to each other to create asymmetric hollow cylinders or remain disconnected to form curled cylindrical or ellipsoidal tubes or tube fractions. A novel 3D self-organization process has been developed to connect two neighboring shutter elements, exploiting surface tension forces via a sequential drying process. The process conditions have been analyzed and optimized to fabricate the two different geometries of the MEMS elements. The resulting MEMS system elements were characterized by focused ion beam and scanning electron microscopy. The contribution of Casimir force, van der Waals force, and other physical interfacial forces are discussed in the formation of the asymmetric hollow cylinders.

Monocular Vision-Based Localization and Pose Estimation with a Nudged Particle Filter and Ellipsoidal Confidence Tubes

This paper proposes a nudged particle filter for estimating the pose of a camera mounted on flying robots collecting a video sequence. The nudged particle filter leverages two image-to-pose and pose-to-image neural networks trained in an auto-encoder fashion with a dataset of pose-labeled images. Given an image, the retrieved camera pose using the image-to-pose network serves as a special particle to nudge the set of particles generated from the particle filter while the pose-to-image network serves to compute the likelihoods of each particle. We demonstrate that such a nudging scheme effectively mitigates low likelihood samplings during the particle propagation step. Ellipsoidal confidence tubes are constructed from the set of particles to provide a computationally efficient bound on localization error. When an ellipsoidal tube self-intersects, the probability volume of the intersection can be significantly shrunken using a novel Dempster–Shafer probability mass assignment algorithm. Starting from the intersection, a loop closure procedure is developed to move backward in time to shrink the volumes of the entire ellipsoidal tube. Experimental results using the Georgia Tech Miniature Autonomous Blimp platform are provided to demonstrate the feasibility and effectiveness of the proposed algorithms in providing localization and pose estimation based on monocular vision.

Numerical analysis of heat transfer enhancement and flow characteristics inside cross-combined ellipsoidal dimple tubes

The heat transfer and flow characteristics have been numerically investigated in the cross-combined dimple tube with the k-ε model, and the enhancement model based on composite-shape surface technologies is established for the first time. The results indicate that the heat transfer index, friction factor and performance evaluation criteria increase tremendously by comparing with the single ellipsoidal dimple tube at considered operating conditions. In particular, the heat transfer enhancement rises by 18.8–48.3%, and an average of 24.8%, when compared with the traditional single ellipsoidal tube. 3D simulation is carried out to elaborate the influence mechanism of dimples on the thermal performance and concludes that dimples can further enhance heat transfer through changing temperature distribution and increasing the gradient of the core region at the dimple section. The concave surface profile can disturb steady flow and boundary layer development to enhance the mixture of hot fluid and cold fluid. Additionally, the effects of geometric parameters on thermal and hydraulic performances are discussed to reveal that the larger quantity and volume of dimples lead to a better comprehensive thermo-hydraulic performance.

Control and Estimation in Linear Time-Varying Systems Based on Ellipsoidal Reachability Sets

Linear continuous or discrete time-varying systems in which the sum of a quadratic form of the initial state and the integral or sum of quadratic forms of a disturbance on a finite horizon is bounded above by a given value are considered. It is demonstrated that the reachability set of such a continuous- or discrete-time system is an evolving ellipsoid, and its ellipsoid matrix satisfies a linear matrix differential or difference equation, respectively. The optimal ellipsoidal observer and identification algorithm that yield the best ellipsoidal estimates of the system’s state and unknown parameters are designed. In addition, the optimal controllers ensuring that the system’s state will fall into a target set or that the system’s trajectory will stay within the ellipsoidal tube are designed. A connection between the optimal ellipsoidal observer and the Kalman filter is established. Some illustrative examples for the Mathieu equation, which describes the parametric oscillations of a linear oscillator, are given.

Ellipsoidal reachable sets of linear time-varying continuous and discrete systems in control and estimation problems

The paper is devoted to reachable sets of linear time-varying continuous or discrete systems under uncertain initial states and disturbances with a bounded uncertainty measure. The uncertainty measure is the sum of a quadratic form of the initial state and the integral/sum over the finite-time interval from a quadratic form of the disturbance. It is shown that the reachable set of the system under this assumption is an evolving ellipsoid with a matrix being a solution to the linear matrix differential or difference equation. This result is used to synthesize optimal observers and estimators providing the minimal ellipsoidal sets as the estimates of the system state and unknown parameters, respectively, as well as optimal controllers steering the system state into a final target ellipsoidal set or keeping the entire system trajectory in a prescribed ellipsoidal tube under all admissible initial states and disturbances. The relationships between the optimal ellipsoidal observer and the Kalman filter as well as between the optimal ellipsoidal estimator and the recursive least weighted squares algorithm are established. Numerical modeling with the Mathieu equation for parametric vibrations of a linear oscillator illustrates the results.

Control and Filtering Problems for Linear Time-Varying Systems Based on Ellipsoidal Reachable Sets

The paper is devoted to reachable sets of linear time-varying continuous systems under uncertain initial states and disturbances with a bounded uncertainty measure. The uncertainty measure is the sum of a quadratic form of the initial state and the integral over the finite-time interval from a quadratic form of the disturbance. It is shown that the reachable set of the system under this assumption is an evolving ellipsoid with a matrix being a solution to the linear matrix differential equation. This result is used to synthesize the optimal observer providing the minimal ellipsoidal set as the estimate of the system state, as well as optimal controllers steering the system state into a final target ellipsoidal set or keeping the entire system trajectory in a prescribed ellipsoidal tube under all admissible initial states and disturbances. The relationship between the optimal ellipsoidal observer and the Kalman filter are established. Numerical modeling with the Mathieu equation for parametric vibrations of a linear oscillator illustrates the results.

Ellipsoidal Reachability Sets of Linear Time-Varying Systems in Estimation and Control Problems

We consider a linear time-varying system with an initial state and disturbance that are known imprecisely and satisfy a common constraint. The constraint is the sum of a quadratic form of the initial state and the time integral of a quadratic form of the disturbance, and these quadratic forms are allowed to be degenerate. We obtain a linear matrix differential Lyapunov equation describing the evolution of the ellipsoidal reachability set. In the problem of estimating the state based on output observations, this result is used to find the minimum-size ellipsoidal set of admissible system states, which is determined by the optimal observer and by the reachability set of the corresponding observation error equation. A method for control law synthesis ensuring that the system state reaches the target set or the system trajectory remains in a given ellipsoidal tube is proposed. Illustrative examples are given for the Mathieu equation, which describes parametric oscillations of a linear oscillator.

Hamiltonian Formalism in Team Control Problems

We consider the target control synthesis problem for a team of single-type plants performing a common motion to a target set under the condition that the team members do not collide with each other. In the process of motion, the team members must stay inside a virtual container forming a standard motion (tube) and avoiding the obstacles known in advance by reconfiguration. The general scheme for solving this problem, which reduces the original problem to a series of subproblems, is given, and Hamiltonian formalism is used for a detailed consideration of the subproblems of terminal control of ellipsoidal tubes, the container motions between moving external obstacles, and the evolution of the team inside the virtual container.

Numerical study of shell and tube heat exchanger with different cross-section tubes and combined tubes

Shell and tube heat exchangers are used in various industrial processes, and are one of the most commonly used heat exchangers. A shell and tube heat exchanger with a 25% baffle cut was used in this study. Tubes of different cross-sections (circular, elliptical with an attack angle of 90° and elliptical with an attack angle of 0°) were studied. A combined model of a shell and tube heat exchanger with elliptical tubes with an attack angle of 90° and circular tubes was introduced. A heat exchanger with ellipsoidal tubes near the shell with an attack angle of 90° and circular tubes in the center of the shell showed the highest heat transfer compared with the shell and tube heat exchangers with circular tubes and elliptical tubes with an attack angle of 90° and 0°. The pressure drop in the tube and shell side was also investigated for all five cases in this study. The effect of the location of tubes on heat transfer was investigated. It was shown that tubes located near the shell have a greater impact on heat transfer compared with tubes located in the center of the shell.

Kinematic formula for heterogeneous Gaussian related fields

We provide a generalization of the Gaussian Kinematic Formula (GKF) in Taylor et al. (2006) for multivariate, heterogeneous Gaussian-related fields. The fields under consideration, f=F∘y, are non-Gaussian fields built out of smooth, independent Gaussian fields y=(y1,y2,..,yK) with heterogeneity in distribution amongst the individual building blocks. Our motivation comes from potential applications in the analysis of Cosmological Data (CMB). Specifically, future CMB experiments will be focusing on polarization data, typically modeled as isotropic vector-valued Gaussian related fields with independent, but non-identically distributed Gaussian building blocks; this necessitates such a generalization. Extending results (Taylor et al., 2006) to these more general Gaussian relatives with distributional heterogeneity, we present a generalized Gaussian Kinematic Formula (GKF). The GKF in this paper decouples the expected Euler characteristic of excursion sets into Lipschitz Killing Curvatures (LKCs) of the underlying manifold and certain Gaussian Minkowski Functionals (GMFs). These GMFs arise from Gaussian volume expansions of ellipsoidal tubes as opposed to the usual tubes in the Euclidean volume of tube formulae. The GMFs form a main contribution of this work that identifies this tubular structure and a corresponding volume of tubes expansion in which the GMFs appear.

Numerical Controlled Process of Tube Sheet on Phthalic Anhydride Switch Condenser

Phthalic anhydride switch condenser was imported, failure occurred many times after put in use. There are ellipsoidal winged tubes in them and the holes on tube sheet are ellipsoidal too, which is very difficult to manufacture. Established mathematics model, analyzed the mathematic relation, compiled NC program, realized the numerical controlled process of ellipsoidal hole on MITSUBISHI MCV-1700 machining center, and realized domestic manufacture of phthalic anhydride switch condenser. Analyzed the error of process and selected proper cutter too. Machining center was imported in 1990’s, which CPU is only on 80386 levels, when the NC program is complex, the velocity of calculate will lower than the feed of end mill. The program is compiled with EIA code, which is difficult for most of engineers, took a common PC as program editor to compile program with Quick BASIC, then more technicians can compile program. This improved the procession of process and enlarged the range of machining center.

Heat Transfer Conditions in Flow Across a Bundle of Cylindrical and Ellipsoidal Tubes

ABSTRACT Transient numerical simulations of fluid and heat flow are performed for a number of heat exchanger segments with cylindrical and ellipsoidal form of tubes in a staggered arrangement. Based on the recorded time distributions of velocity and temperature, time-average values of Reynolds number, drag coefficient, and Stanton number are calculated. The drag coefficient and the Stanton number are smaller for the ellipsoidal tubes than for the cylindrical tubes. With an increasing hydraulic diameter, the difference between the two forms of tubes diminishes. To validate the selected numerical approach, the calculated time-average values are compared with experimental data. The time-average values are further used to construct the drag coefficient and the Stanton number as polynomial functions of Reynolds number and hydraulic diameter. The polynomial functions obtained are to be used as input correlations for a heat exchanger integral model.

Ellipsoidal Techniques for Reachability Under State Constraints

The paper presents a scheme to calculate approximations of reach sets and tubes for linear control systems with time-varying coefficients, bounds on the controls, and constraints on the state. The scheme provides tight external approximations by ellipsoid-valued tubes. The tubes touch the reach tubes from the outside at each point of their boundary so that the surface of the reach tube is totally covered by curves that belong to the approximating tubes. The result is an exact parametric representation of reach tubes through families of external ellipsoidal tubes. The parameters that characterize the approximating ellipsoids are solutions of ordinary differential equations with coefficients given partly in explicit analytical form and partly through the solution of a recursive optimization problem. The scheme combines the calculation of external approximations of infinite sums and intersections of ellipsoids, and suggests an approach to calculate reach sets of hybrid systems.

On Ellipsoidal Techniques for Reachability Analysis. Part II: Internal Approximations Box-valued Constraints

Following Part I, this article continues to describe the calculation of the reach sets and tubes for linear control systems with time-varying coefficients and ellipsoidal hard bounds on the controls and initial states. It deals with parametrized families of internal ellipsoidal approximations constructed such that they touch the reach sets at every point of their boundary at any instant of time. The reach tubes are thus touched internally by ellipsoidal tubes along some curves. The ellipsoidal tubes are chosen here in such a way that the touching curves do not intersect and that the boundary of the reach tube would be entirely covered by such curves. This allows exact parametric representation of reach tubes through unions of tight internal ellipsoidal tubes as compared with earlier methods based on constructing one or several isolated approximating tubes. The method of external and internal ellipsoidal approximations is then propagated to systems with box-valued hard bounds on the controls and initial states. It appears that the proposed technique may well work for nonellipsoidal, box-valued constraints. This broadens the range of applications of the approach and opens new routes to the arrangement of efficient numerical algorithms.

REACHABILITY UNDER STATE CONSTRAINTS - THE ELLIPSOIDAL TECHNIQUE

This report describes the calculation of the reach sets and tubes with hard bounds on the controls and state space variables, with an emphasis on linear nonautonomous systems. The topic is important in the verification of hybrid systems and navigation problems, in set-membership estimation, robust control synthesis and related fields. The suggested scheme for linear systems relies on external approximations by ellipsoidal-valued tubes and induces a smaller computational burden compared with other methods of reach set calculation. In particular such approximations may be expressed through ordinary differential equations with coefficients given in explicit analytical form. This results in exact parametric representation of reach tubes through families of external ellipsoidal tubes. A tight approximation partly requires an online solution of a recurrent optimization problem. Applications to target problems relevant for verification of complex systems are finally indicated.

On Ellipsoidal Techniques for Reachability Analysis. Part I: External Approximations

The paper describes the calculation of the reach sets and tubes for linear control systems with time-varying coefficients and ellipsoidal hard bounds on the controls and initial states. This is achieved by parametrized families of external and internal ellipsoidal approximations constructed such that they touch the reach sets at every point of their boundary at any instant of time (both from outside and inside, respectively). The surface of the reach tube would then be entirely covered by curves that belong to the approximating tubes. It is further shown how such approximations may be expressed through ordinary differential equations with coefficients given in explicit analytical form. This allows exact parametric representation of reach tubes through families of external and internal ellipsoidal tubes as compared with earlier methods based on constructing one or several isolated approximating tubes. The approach opens new routes to the arrangement of efficient numerical algorithms. The present Part I deals with external approximations.

Ellipsoidal techniques for reachability analysis: internal approximation

For the reach tube of a linear time-varying system with ellipsoidal bounds on the control variable consider the following approximation problem. Find a tight ellipsoid-valued tube inside the reach tube that touches it along any prespecified smooth curve on the boundary. We construct this ellipsoidal tube, and show that if the given curve is itself a system trajectory, the tube can be calculated recursively, with minimum computational burden.

Algorithms for state bounding in large‐scale systems

AbstractA class of linear and time‐invariant large‐scale systems under unknown input signals and measurement errors is considered. No assumptions about statistical properties of the unknown quantities are made. the uncertainty is modelled through bounds that define ellipsoids in which lie unknown initial conditions and unknown ellipsoidal tubes containing signal trajectories. the state estimation problem consists of determining on‐line the smallest sets in the state space in which the unknown system state lies. Two hierarchical estimation algorithms are proposed and compared, namely the ‘completely decentralized with interaction measurements’ (CDIM) algorithm and the two‐level hierarchical with interaction measurements (THIM) algorithm. the THIM algorithm leads to smaller estimating sets owing to additional co‐ordinator‐level information.