Local Potential Function Research Articles

Orbital eccentricities as indicators of stellar populations

Context.In previous work, we showed how the planar and vertical eccentricities of disc stars,eande′, could be used as indicators of the stars’ kinematic populations. For a local stellar sample drawn from theGaiaDR2 catalogue, these populations were represented geometrically in the eccentricity diagram,e′2vs.e2, approximately separated by straight lines.Aims.In the current work, we propose a new relationship between the star’s perpendicular velocity and its vertical eccentricity, allowing for a reevaluation of the critical vertical eccentricity and maximum height,zmax, specific to each population component.Methods.We approximated the local potential function to be consistent with the actual shape of the curve that relates the maximum vertical speed of a star and its maximum height. The curve corresponds to a non-linear restoring vertical force, where the stiffness decreases with an increase in the maximum height. The constants involved in this fitting, together with the population velocity dispersions, determine the specific region for each population in the eccentricity diagram.Results.The new classification determines 88% of the sample is made up of thin disc stars and 9% of thick disc stars, whereby 3% of the stars have been relabelled, by providing thinner thin and thick discs. Nested thin disc subsamples allow us to estimate Strömberg’s asymmetric drift equation, leading to a heliocentric velocity of the circular orbit ofVc ≈ −12.9 km s−1, an absolute rotation velocity of Θc ≈ 227 km s−1, and a rotation component of the Galactocentric velocity of the Sun at Θ⊙ ≈ 240 km s−1.Conclusions.The thin disc stars of our local sample are characterised based on values 0 ≤ e ≤ 0.32, 0 ≤ e′ ≤ 0.09, andzmax = 0.7 kpc. Disc stars satisfy 0 ≤ e ≤ 0.44, 0 ≤ e′ ≤ 0.18,zmax = 1.5 kpc. The maximum vertical peculiar velocity for disc stars is found to bew0 = 115 km s−1. The assumed potential provides a stellar density of the disc vanishing atz0 = 1.8 kpc. The approximate behaviour in the local disc is that a small decrease in the stiffness is associated with a relative decrease in the limiting velocity, which produces a thinner disc and a loss of stars in the local cylinder, both in a similar proportion to the limiting velocity.

Guaranteed Performance Design for Formation Tracking and Collision Avoidance of Multiple USVs With Disturbances and Unmodeled Dynamics

Searching and containing dynamic target like oil spillage in the ocean is a challenging task due to the natural time variance of the spread of the oil. The use of cooperative multi-marine vehicle systems in a cluttered environment for this purpose poses difficulties in sustaining formation pattern to pursue and contain the leakage. In this article, in order to provide realistic setup for the industrial applications of multi-marine vehicles systems, we present a novel approach for collision-free distributed formation control for a network of underactuated surface vessels (USVs). The proposed approach comprises two layers: A distributed coordination layer and a local fixed-time neural network control layer. In the first layer, formation leaders accomplish a specified formation configuration while tracking a desired trajectory from a tracking leader. The second control layer is to robustly drive the real USVs with parametric and nonparametric uncertainties to track their corresponding formation leaders. Because only parts of the formation leaders can acquire the states of the tracking leader, a distributed fixed-time estimator is proposed to obtain accurate estimations of the desired information for each USV in the network. Next, in order to effectively maneuver in cluttered environment, local path replanning-based repulsive potential function technique is proposed for each USV in the group formation to act on the formation leaders trajectories. Further, redesigned adaptive neural networks are integrated to compensate the model uncertainties. The stability of the proposed controller is verified by the Lyapunov direct method. Simulation studies of a hexagon formation are presented to illustrate the effectiveness of the proposed approach.

Three dimensional m‐quasi Einstein manifolds with degenerate Ricci tensor

AbstractIn this article we give a classification of three dimensional m‐quasi Einstein manifolds with two distinct Ricci‐eigen values. Our study provides explicit description of local and complete metrics and potential functions. We also describe the associated warped product Einstein manifolds in detail. For the proof we present a Codazzi tensor on any three dimensional m‐quasi Einstein manifold and use geometric properties of the tensor which help to analyze the m‐quasi Einstein equation effectively. A technical advance over preceding studies is made by resolving the case when the gradient of the potential function is not a Ricci‐eigen vector field.

Adaptive strain prompting a pseudo-morphotropic phase boundary in ferroelectric (1- x)Na0.5Bi0.5TiO3−xBaTiO3

The understanding of the atomistic origin of the morphotropic phase boundary (MPB) occurring in composition-temperature phase diagrams of ferroelectric solid solutions is a key topic in material science because materials often exhibit anomalous properties at the MPB. Here we reveal mesoscopic-scale structural correlations for a leading Pb-free ferroelectric system, $(1\text{\ensuremath{-}}x){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_{3}\text{\ensuremath{-}}x{\mathrm{BaTiO}}_{3}$ (NBT-$x\mathrm{BT}$), by examining atomic pair distribution functions and Raman scattering data at ambient conditions. We demonstrate that the amplification of the piezoelectric properties of NBT-$x\mathrm{BT}$ at the MPB are predominantly driven by an easy switchability resulting from a progressive decoupling between strain and polarization as the Ba content increases from zero to the critical MPB composition. It was observed that as Ba content increases towards MPB, competing local correlations, such as A-site chemical order, antiferrodistortive correlations of correlated ${\mathrm{BO}}_{6}$ tilts, and antipolar Bi shifts, are reduced, which in turn renders favorable conditions for easy switching of local dipoles under external fields. In addition, the evolving characteristics of the atomic dynamics as a function of composition suggest that the local potential functions of the cations are not completely flat at the MPB. Altogether, our results reveal atomistic mechanisms responsible for the observed elevated MPB properties in the case of NBT-$x\mathrm{BT}$ which imply that the so-called MPB of NBT-$x\mathrm{BT}$ should not be categorized as originally introduced for Pb-containing solid solutions.

A femtoscopic correlation analysis tool using the Schr\xf6dinger equation (CATS)

We present a new analysis framework called “Correlation Analysis Tool using the Schrödinger equation” (CATS) which computes the two-particle femtoscopy correlation function C(k), with k being the relative momentum for the particle pair. Any local interaction potential and emission source function can be used as an input and the wave function is evaluated exactly. In this paper we present a study on the sensitivity of C(k) to the interaction potential for different particle pairs: p–p, p–mathrm {Lambda }, mathrm {K^-}–p, mathrm {K^+}–p, p–mathrm {Xi }^- and mathrm {Lambda }–mathrm {Lambda }. For the p–p Argonne v_{18} and Reid Soft-Core potentials have been tested. For the other pair systems we present results based on strong potentials obtained from effective Lagrangians such as chi EFT for p–mathrm {Lambda }, Jülich models for mathrm{K}(bar{mathrm{K}})–N and Nijmegen models for mathrm {Lambda }–mathrm {Lambda }. For the p–mathrm {Xi }^- pairs we employ the latest lattice results from the HAL QCD collaboration. Our detailed study of different interacting particle pairs as a function of the source size and different potentials shows that femtoscopic measurements can be exploited in order to constrain the final state interactions among hadrons. In particular, small collision systems of the order of 1 fm, as produced in pp collisions at the LHC, seem to provide a suitable environment for quantitative studies of this kind.

Automated segmentation of choroidal neovascularization in optical coherence tomography images using multi-scale convolutional neural networks with structure prior

Automated segmentation of choroidal neovascularization (CNV) in optical coherence tomography (OCT) images plays an important role for the treatment of CNV disease. This paper proposes multi-scale convolutional neural networks with structure prior to segment CNV from OCT data. The proposed framework consists of two stages. In the first stage, the structure prior learning method based on sparse representation-based classification and the local potential function is developed to capture the global spatial structure and local similarity structure prior. The obtained prior can be used to improve the distinctiveness between CNV and background patches. In the second stage, multi-scale CNN model with incorporation of the learned structure prior is constructed for CNV segmentation. In this stage, multi-scale analysis is used to capture effective contextual information, which is robust to varying sizes of CNV. The proposed method was evaluated on 15 spectral domain OCT data with CNV. The experimental results demonstrate the effectiveness of proposed method.

Formation Shape Control Based on Distance Measurements Using Lie Bracket Approximations

We study the problem of distance-based formation control in autonomous multi-agent systems in which only distance measurements are available. This means that the target formations as well as the sensed variables are both determined by distances. We propose a fully distributed distance-only control law, which requires neither a time synchronization of the agents nor storage of measured data. The approach is applicable to point agents in the Euclidean space of arbitrary dimension. Under the assumption of infinitesimal rigidity of the target formations, we show that the proposed control law induces local uniform asymptotic stability. Our approach involves sinusoidal perturbations in order to extract information about the negative gradient direction of each agent's local potential function. An averaging analysis reveals that the gradient information originates from an approximation of Lie brackets of certain vector fields. The method is based on a recently introduced approach to the problem of extremum seeking control. We discuss the relation in the paper.

Development of Quantum Local Potential Function Networks Based on Quantum Assimilation and Subspace Division.

The centers and radii of radial basis functions (RBFs) greatly affect the approximation capability of RBF networks (RBFNs). Traditional statistics-based approaches are widely used, but they may lack adaptivity to different data structures. Quantum clustering (QC), derived from quantum mechanics and the Schrödinger equation, demonstrates excellent capability in finding the structure and conformity toward data distribution. In this paper, a novel neural networks model called quantum local potential function networks (QLPFNs) is proposed. The QLPFN inherits the outstanding properties of QC by constructing the waves and the potential functions, and the level of data concentration can be discovered to obtain the inherent structures of the given data set. The local potential functions form the basic components of the QLPFN structure, which are automatically generated from the subsets of training data following specific subspace division procedures. Therefore, the QLPFN model in fact incorporates the level of data concentration as a computation technique, which is different from the classical RBFN model that exhibits radial symmetry toward specific centers. Some application examples are given in this paper to show the effectiveness of the QLPFN model.

Direct mapping of microscopic polarization in ferroelectricx(BiScO3)−(1−x)(PbTiO3)throughout its morphotropic phase boundary

Pair distribution functions of ferroelectric $x{\mathrm{BiScO}}_{3}\text{\ensuremath{-}}(1\ensuremath{-}x){\mathrm{PbTiO}}_{3}$, obtained from neutron total scattering data, were examined and modeled utilizing the reverse Monte Carlo technique to depict exclusively the local structure of this compound throughout its reported morphotropic phase boundary (MPB). Microscopic polarizations due to the cation shifts have been mapped out from the refined crystal structure as a function of composition in order to reveal individual cation behavior driven by the composition. Direct evidences are provided for large static displacements of the cations $(\ensuremath{\sim}0.2\ensuremath{-}0.5\phantom{\rule{0.28em}{0ex}}\AA{})$, local cation ordering between Ti and Sc, and a categorical change of favored polarization directions of the cations at the conjuncture of the MPB. Apart from Sc, all cations have demonstrated an apparent transition from a relatively defined directional distribution to a broad and random distribution at $x={x}_{\mathrm{MPB}}$, suggesting a flattening of the local potential function for them. These features can further be correlated with the general concept of structural instability of a ferroelectric system at the MPB, which is often linked to the manifestation of enhanced physical properties.

Uncertainty quantification for multiscale disk forging of polycrystal materials using probabilistic graphical model techniques

The mechanical properties of a deformed workpiece are sensitive to the initial microstructure before processing commences. Generally, the initial microstructure is random in nature and location specific. The location-dependence of the microstructure dramatically increases the dimensionality of the stochastic input and thus leads to the “curse of dimensionality” in stochastic deformation problems. In this work, a graph-theoretic approach is used to address the stochastic multiscale deformation problem and compute the propagation of the initial microstructure uncertainty to the forged disk properties. Following the finite element representation of the multiscale deformation problem, a graphical representation is introduced with nodes in the graph representing the macro- and meso- scale random variables and links between nodes modeling the dependence relations between variables at each scale and across scales. Model reduction techniques are employed locally in the graph to represent the initial random microstructure. Then the conditional distribution of the multi-output mechanical responses on the low-dimensional representation of the initial microstructure is factorized into a product of local potential functions. An expectation-maximization algorithm is used to learn the non-parametric representation of these potentials using a set of training data. A non-parametric loopy belief propagation method is applied to perform uncertainty quantification tasks. The non-parametric nature of the model is able to capture non-Gaussian features of the responses. The developed framework can be used as a surrogate model to predict the mechanical response fields for any input microstructure realization as well as our confidence on such predictions. A multiscale disk forging example of FCC nickel is presented to demonstrate the accuracy and efficiency of the constructed framework for addressing uncertainty quantification problems in multiscale deformation processes.

A nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media

A probabilistic graphical model approach to uncertainty quantification for flows in random porous media is introduced. Model reduction techniques are used locally in the graph to represent the random permeability. Then the conditional distribution of the multi-output responses on the low dimensional representation of the permeability field is factorized into a product of local potential functions. An expectation–maximization algorithm is used to learn the nonparametric representation of these potentials using the given input/output data. We develop a nonparametric belief propagation method for uncertainty quantification by employing the loopy belief propagation algorithm. The nonparametric nature of our model is able to capture non-Gaussian features of the response. The proposed framework can be used as a surrogate model to predict the responses for new input realizations as well as our confidence on these predictions. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed framework for solving uncertainty quantification problems in flows through porous media using stationary and non-stationary permeability fields.

Preservation of Formation Tracking under Incomplete Information and Chaotic Path-following

This paper presents a formation tracking strategy based on local potential functions and the leader-followers scheme for a group of point robots moving in the space. A leader robot is chosen to follow a prescribed trajectory whilst the rest, considered as followers, are formed in an open chain configuration. The formation convergence and the path following, including chaotic trajectories, are guaranteed if every follower robot measures exactly the velocity of the next robot and the leader knows the velocity of the marching path. Then, we analyze the preservation of the formation using approximations of the velocities of robots and the chaotic path. These restrictions appear in real implementations in robots equipped by position sensors only and where the velocities functions are approximated by online numerical methods.

Decentralized Formation Control of Multi-agent Robot Systems based on Formation Graphs

Formation control is an important issue of motion coordination of Multi-agent Robots Systems. The goal is to coordinate a group of agents to achieve a desired formation pattern. The control strategies are decentralized because every robot does not possess information about the positions and goals of all the other robots. Based on the formation graphs properties and the local potential functions approach, we obtain a formal result about global convergence to the desired pattern for any formation graph. Also, we characterize the topologies of the formation graphs where the centroid of positions remains stationary. Finally, the control approach is extended to the case of unicycle-type robots.

Trajectory Tracking Control and Obstacle Avoidance for a Differentially Driven Mobile Robot

AbstractIn this paper a Vector Field Orientation control algorithm for a differentially-driven mobile platform in an environment with obstacles is presented. The goal is to track the desired trajectory. Collision avoidance is assured using the local artificial potential function (APF) method. A proof of stability and convergence for the algorithm is presented. Effectiveness of the algorithm is illustrated with experiments on a real robot. The paper also presents how the parameters of the control algorithm influence effectiveness of the method in practice.

AFM + Raman Microscopy + SNOM + Tip-Enhanced Raman: Instrumentation and Applications

Atomic Force Microscopy (AFM) has developed into a very powerful tool for characterization of surfaces and nanoscale objects. Many physical properties of an object can be studied by AFM with nanometer-scale resolution. Local stiffness, elasticity, conductivity, capacitance, magnetization, surface potential and work function, friction, piezo response—these and many other physical properties can be studied with over 30 AFM modes. What is typically lacking in information provided by AFM studies is the chemical composition of the sample and information about its crystal structure. To obtain this information other characterization techniques are required, such as Raman and fluorescence microscopy. The Raman effect (inelastic light scattering) provides extensive information about sample chemical composition, quality of crystal structure, crystal orientation, presence of impurities and defects, and so on. Information provided by Raman and fluorescence spectroscopy is complementary to the information obtained by AFM. So it is a natural requirement in many research fields to integrate these techniques in one piece of equipment—to provide comprehensive physical, chemical, and structural characterization of the same object. Of course, for routine studies of various samples, it is important to be able to obtain AFM and Raman/fluorescence images of exactly the same sample area, preferably with the same sample scan.

Motion constraint Markov network model for multi-target tracking

A typical Markov network for modeling the interaction among targets can handle the error merge problem, but it suffers from the labeling problem due to the blind competition among collaborative trackers. In this paper, we propose a motion constraint Markov network model for multi-target tracking. By augmenting the typical Markov network with an ad hoc Markov chain which carries motion constraint prior, this proposed model can overcome the blind competition and direct the label to the corresponding target even in the case of severe occlusion. In addition, the motion constraint prior is formulated as a local potential function and can be easily incorporated in the joint distribution representation of the novel model. Experimental results demonstrate that our model is superior to other methods in solving the error merge and labeling problems simultaneously and efficiently.

Energy-switching potential energy surface for the water molecule revisited: A highly accurate singled-sheeted form

A global ab initio potential energy surface is proposed for the water molecule by energy-switching/merging a highly accurate isotope-dependent local potential function reported by Polyansky et al. [Science 299, 539 (2003)] with a global form of the many-body expansion type suitably adapted to account explicitly for the dynamical correlation and parametrized from extensive accurate multireference configuration interaction energies extrapolated to the complete basis set limit. The new function mimics also the complicated Sigma/Pi crossing that arises at linear geometries of the water molecule.

Decentralized formation control of mobile agents: A unified framework

This paper studies the formation control problem for systems consisting of multiple mobile agents that are described by first-order differential equations and second-order differential equations respectively. The following issues are investigated: bounded input, disturbance, and time delay. In derivation of the main results, a blend of graph-theoretic and system-theoretic tools is employed, where local potential functions and LaSalle’s Invariant Principle play central roles. Finally, numerical examples which support the analytical results very well are also included.

On the construction of hybrid potential energy functions for the treatment of local anharmonicity in molecular vibrations†

This paper reports a process by which a local, accurate, and intrinsically anharmonic potential function may be joined with a larger harmonic oscillator representation of the remainder of a molecule to build a hybrid potential energy function. Such functions find use in chemical dynamics in which there is local anharmonic bond breaking and forming, but the remainder of the molecular system behaves essentially as a set of harmonic oscillators. In constructing such a potential, for malonaldehyde as an example, it is assumed that the harmonic-limit potential can be found for the system using a given data set of the Cartesian forces and force constants derived with the use of a computational quantum chemistry program. The Pulay transformation is used to establish a set of internal coordinate forces and force constants consistent with the local model potential function. The success (i.e. faithfulness) of the construction of the hybrid potential strongly depends on the choice of internal coordinates. The Pulay transformation together with the vibrational projection analysis of Grafton and Wheeler allows one to see the strengths or weaknesses of particular choices of internal coordinates. †Approved for Public Release. Distribution Unlimited. Dedicated to Péter Pulay on the occasion of the celebration of his scientific achievements: Budapest, 24 May–3 June 2007.

Local effective potential theory: Nonuniqueness of potential and wave function

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model system wave function. According to nondegenerate ground state HKS-DFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKS-DFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrained-search version of HKS-DFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via Q-DFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlation-kinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of Q-DFT reaffirms that there can be no equivalent to the ground state HKS-DFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlation-kinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke's atom. The work of others is also discussed.