Approximate Map Research Articles

Photodissociation dynamics in the first absorption band of pyrrole. II. Photofragment distributions for the 1A2(πσ*)←X̃1A1(ππ) transition.

The analysis of the total kinetic energy release (TKER) of the photofragments pyrrolyl + H-atom formed in the photodissociation of pyrrole in the low-lying state 1A2(πσ*) is presented. The TKER distributions contain complementary and often more precise information on the fragmentation process than the broad diffuse absorption spectra. The distributions are calculated quantum mechanically for the diabatic state 1A2(πσ*) either isolated or coupled to the ground electronic state at an exit channel conical intersection. The calculations use the novel ab initio quasi-diabatic potential energy matrix constructed in the work of Picconi and Grebenshchikov [J. Chem. Phys. 148, 104103 (2018)]. The approximate overlap integral-based adiabatic mapping approach is introduced with which the quantum mechanical TKER distributions can be efficiently and accurately reproduced. Finally, the calculated TKERs are compared with the experimental results. The main features of the measured vibrationally resolved distributions are reproduced, and the spectral peaks are assigned and interpreted in detail.

Controller Design of an Electric Power Steering System

This brief presents a new method of analyzing stability and design of a controller for an electric power steering (EPS) system. The most important task when designing a steering system is ensuring that the driver is pleased with how the steering feels. The way that the steering feels is dependent upon the assist torque map. The assist torque map is a one-to-one map between sensed driver torque and assist motor torque that varies with the cars speed. However, an assist torque map cannot be applied alone as an EPS controller because of high level of steering assist gain and nonlinearity of the torque map. Both elements of torque map can result in instability, which leads to vibration or divergence of the steering system. Therefore, an EPS system always needs to be designed with a stabilizing compensator and an assist torque map. The objective of designing a compensator is to stabilize the system with robustness and attenuate any unpleasant vibration. This brief presents a mechanical model of the EPS system and demonstrates a method to identify the model parameter. Based on the EPS model, stability of the system with an approximate linear torque map and nonlinear torque map is analyzed. Furthermore, criteria for designing the stabilizing compensator are suggested. Lead-lag compensators with different parameters are applied with the torque map in simulations, and vehicle experiments are performed to verify the theoretical analysis.

Optimal Perception Planning with Informed Heuristics Constructed from Visibility Maps

In this paper we consider the problem of motion planning for perception of a target position. A robot has to move to a position from where it can sense the target, while minimizing both motion and perception costs. The problem of finding paths for robots executing perception tasks can be solved optimally using informed search. In perception path planning, the solution when considering a straight line without obstacles is used as heuristic. In this work, we propose a heuristic that can improve the search efficiency. In order to reduce the node expansion using a more informed search, we use the robot Approximate Visibility Map (A-VM), which is used as a representation of the observability capability of a robot in a given environment. We show how the critical points used in A-VM provide information on the geometry of the environment, which can be used to improve the heuristic, increasing the search efficiency. The critical points allow a better estimation of the minimum motion and perception cost for targets in non-traversable regions that can only be sensed from further away. Finally, we show the contributed heuristic with improvements dominates the base PA* heuristic built on the euclidean distance, and then present the results of the performance increase in terms of node expansion and computation time.

Transport maps for β-matrix models in the multi-cut regime

We use the transport methods develop in [F. Bekerman, A. Figalli and A. Guionnet, Transport maps for [Formula: see text]-matrix models and universality, Commun. Math. Phys. 338(2) (2013) 589–619] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for [Formula: see text]-matrix models in the multi-cut regime. We construct an approximate transport map inbetween two probability measures from the fixed filling fraction model discussed in [G. Borot, A. Guionnet and K. K. Kozlowski, Large-N asymptotic expansion for mean field models with coulomb gas interaction, Int. Math. Res. Not. (2015)] and deduce from it universality in the initial model.

An empirical relationship between seismic bedrock depth and fundamental frequency for Değirmendere (Kocaeli-Turkey)

Sediments’ thickness is one of the important parameters in seismic hazard assessment. This study aims to establish a new empirical relationship to determine the overburden layer thickness on seismic bedrock by using a relationship between the fundamental frequencies obtained from microtremor measurements and seismic bedrock depth obtained from microgravity measurements and subsequently produce an approximate seismic bedrock depth distribution map for the study area. In this context, ambient noise analyses were performed to estimate the fundamental frequency of the ground. Within this scope, noise measurements at 43 points were established in the study area. Determined fundamental frequencies and seismic bedrock depths obtained by microgravity measurements were iteratively processed to calculate the best-fitting exponential function for the empirical depth–frequency relation. This relation was established as $$m = 338.2 \cdot f_{0}^{ - 0.6558}$$ (m is seismic bedrock depth, f 0 is fundamental frequency) for the study area.

Lower semicontinuity of solution mappings for parametric fixed point problems with applications

In this paper, we establish the lower semicontinuity of the solution mapping and the approximate solution mapping for parametric fixed point problems under some suitable conditions. As applications, the lower semicontinuity result applies to the parametric vector quasi-equilibrium problem, and allows to prove the existence of solutions for generalized Stackelberg games.

Robust Cross-correlation-based Measurement of Clump Sizes in Galaxies

Abstract Stars form in molecular complexes that are visible as giant clouds ( ) in nearby galaxies and as giant clumps ( ) in galaxies at redshifts –3. Theoretical inferences on the origin and evolution of these complexes often require robust measurements of their characteristic size, which is hard to measure at limited resolution and often ill-defined due to overlap and quasi-fractal substructure. We show that maximum and luminosity-weighted sizes of clumps seen in star formation maps (e.g., Hα) can be recovered statistically using the two-point correlation function (2PCF) if an approximate stellar surface density map is taken as the normalizing random field. After clarifying the link between Gaussian clumps and the 2PCF analytically, we design a method for measuring the diameters of Gaussian clumps with realistic quasi-fractal substructure. This method is tested using mock images of clumpy disk galaxies at different spatial resolutions and perturbed by Gaussian white noise. We find that the 2PCF can recover the input clump scale at accuracy, as long as this scale is larger than the spatial resolution. We apply this method to the local spiral galaxy NGC 5194, as well as to three clumpy turbulent galaxies from the DYNAMO-HST sample. In both cases, our statistical measurements of Hα clump size agree with previous measurements and with the estimated Jeans lengths. However, the new measurements are free from subjective choices when fitting individual clumps.

Painlevé–Kuratowski stability of approximate efficient solutions for perturbed semi-infinite vector optimization problems

This paper is concerned with the stability of semi-infinite vector optimization problems (SIVOP) under functional perturbations of both objective functions and constraint sets. First, we establish the Berge-lower semicontinuity and Painleve–Kuratowski convergence of the constraint set mapping. Then, using the obtained results, we obtain sufficient conditions of Painleve–Kuratowski stability for approximate efficient solution mapping and approximate weakly efficient solution mapping to the (SIVOP). Furthermore, an application to the traffic network equilibrium problems is also given.

Investigation of thermal acoustic oscillations in a superconducting linac cryogenic system

During the commissioning stage of a superconducting linear accelerator (linac) three major cryogenic systems were seen to generate thermal acoustic oscillations (TAO): the cryostat liquid helium level sensor interface, the pre-cooling line and the cryogenic distribution valve box with associated transfer tube. By using Rott’s stability curves, published by other researchers elsewhere, an approximate map of the oscillations in the cryogenic systems under investigation was created for both straight and U-shaped tubes. This investigation confirmed that all systems under consideration fall within the critical range and that damping of TAO would be needed to achieve stable operation conditions. The geometry and hence the temperature distribution within the cryogenic system of the accelerator facility could not be altered arbitrarily. Possible TAO damping techniques were narrowed to two options: (a) adding restrictions at the cold end and (b) control of the helium gas pressure. In all systems, before modifications, pressure oscillations were clearly observed within the frequency range 0.25–47Hz. In two systems TAO were observed with no liquid helium present at the cold end. The TAO investigations provided solutions that resulted in a substantial improvement in the performance of the linac cryogenic and RF stabilization systems, under test.

Enhancement of Digital PID Controller Performance for Blood Glucose Level of Diabetic Patients using Disparate Tuning Techniques

Objectives: To design digital PID controller by using CHR-I and CHR-II tuning techniques, as it helps in finding out the tuning parameters of controllers for a specific system. Transformation of analog to digital PID controller using various transformation techniques like first order hold method, impulse-invariant mapping, Tustin approximation and zero-pole mapping equivalents and also the mathematical modeling of blood glucose level, such that a system injects the exact amount of insulin into the body of diabetic patient to maintain his/her glucose level to the normal range. Method/Statistical Analysis: The differential equation of the blood glucose level is formulated and then it is converted to three-dimensional Laplace equation using forward Laplace transform. Using the Laplace transform the differential equation of the blood glucose is converted into a s-domain equation. Then, using the s-domain equation as the equation of the system and the Tuning techniques, CHR-I and CHR-II, the tuning parameters (Kp, Ki and Kd) are acquired. Then, it is converted into digital, i.e. in z-domain, by applying disparate transformation techniques. Findings: On analyzing the acquired equation, it is depicted that on tuning the controller with CHR-I tuning technique the system exhibits zero overshoot which is most reliable and efficient for diabetic patient. Also, a considerable settling time of 6.3362 seconds is also achieved. Application/Improvement: Therefore, a system that can inject the exact amount of insulin into the patient's blood and bring the blood glucose level to the normal range, by automatically calculating the amount of insulin required, from the available status of blood glucose level, is being achieved.

Existence and stability of solutions to inverse variational inequality problems

In this paper, two new existence theorems of solutions to inverse variational and quasi-variational inequality problems are proved using the Fan-Knaster-Kuratowski-Mazurkiewicz (KKM) theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Upper semicontinuity and lower semicontinuity of the solution mapping and the approximate solution mapping to the parametric inverse variational inequality problem are also discussed under some suitable conditions. An application to a road pricing problem is given.

Weak sharp solutions of mixed variational inequalities in Banach spaces

In this paper, using the approximate duality mapping, we introduce the definition of weak sharpness of the solution set to a mixed variational inequality in Banach spaces. In terms of the primal gap function associated to the mixed variational inequality, we give several characterizations of the weak sharpness.

Heterogeneous out-of-equilibrium nonlinear q-voter model with zealotry.

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in Mellor etal. [Europhys. Lett. 113, 48001 (2016)EULEEJ0295-507510.1209/0295-5075/113/48001]. In this model, each individual supports one of two parties and is either a susceptible voter of type q_{1} or q_{2}, or is an inflexible zealot. At each time step, a q_{i}-susceptible voter (i=1,2) consults a group of q_{i} neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever q_{1}≠q_{2} and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the nonequilibrium stationary state of the system in terms of its probability distribution, nonvanishing currents, and unequal-time two-point correlation functions. We also study the switching time properties of the model by exploiting an approximate mapping onto the model of Mobilia [Phys. Rev. E 92, 012803 (2015)PLEEE81539-375510.1103/PhysRevE.92.012803] that satisfies the detailed balance, and we outline some properties of the model near criticality.

An efficient hybrid scheme for fast and accurate inversion of airborne transient electromagnetic data

Airborne transient electromagnetic (TEM) methods target a range of applications that all rely on analysis of extremely large datasets, but with widely varying requirements with regard to accuracy and computing time. Certain applications have larger intrinsic tolerances with regard to modelling inaccuracy, and there can be varying degrees of tolerance throughout different phases of interpretation. It is thus desirable to be able to tune a custom balance between accuracy and compute time when modelling of airborne datasets. This balance, however, is not necessarily easy to obtain in practice. Typically, a significant reduction in computational time can only be obtained by moving to a much simpler physical description of the system, e.g. by employing a simpler forward model. This will often lead to a significant loss of accuracy, without an indication of computational precision.We demonstrate a tuneable method for significantly speeding up inversion of airborne TEM data with little to no loss of modelling accuracy. Our approach introduces an approximation only in the calculation of the partial derivatives used for minimising the objective function, rather than in the evaluation of the objective function itself. This methodological difference is important, as it introduces no further approximation in the physical description of the system, but only in the process of iteratively guiding the inversion algorithm towards the solution. By means of a synthetic study, we demonstrate how our new hybrid approach provides inversion speed-up factors ranging from ~3 to 7, depending on the degree of approximation. We conclude that the results are near identical in both model and data space. A field case confirms the conclusions from the synthetic examples: that there is very little difference between the full nonlinear solution and the hybrid versions, whereas an inversion with approximate derivatives and an approximate forward mapping differs significantly from the other results.

Manipulating spin-dependent splitting of vector abruptly autofocusing beam by encoding cosine-azimuthal variant phases.

We report the realization of spin-dependent splitting of vector abruptly autofocusing beam (AAB) by encoding cosine-azimuthal variant phases. By employing the local spatial frequency (LSF), we reveal an approximation mapping relationship between focal field intensity of the two spin components and the pertinent phase distribution of input field. As well as theoretical analysis, we present experimental demonstrations of this guidance. Special focal field intensity, polarization and phase are realized by consciously managing the cosine-azimuthal variant phase. This distinctive focal field of vector AAB may have a broad range of applications in harnessing the spin-orbit coupling, optical trapping and laser machining.

A single-image retrieval method for edge illumination X-ray phase-contrast imaging: Application and noise analysis

PurposeEdge illumination (EI) X-ray phase-contrast imaging (XPCI) has been under development at University College London in recent years, and has shown great potential for both laboratory and synchrotron applications. In this work, we propose a new acquisition and processing scheme. Contrary to existing retrieval methods for EI, which require as input two images acquired in different setup configurations, the proposed approach can retrieve an approximate map of the X-ray phase from a single image, thus significantly simplifying the acquisition procedure and reducing data collection times. MethodsThe retrieval method is analytically derived, based on the assumption of a quasi-homogeneous object, i.e. an object featuring a constant ratio between refractive index and absorption coefficient. The noise properties of the input and retrieved images are also theoretically analyzed under the developed formalism. The method is applied to experimental synchrotron images of a biological object. ResultsThe experimental results show that the method can provide high-quality images, where the “edge” signal typical of XPCI images is transformed to an “area” contrast that enables an easier interpretation of the sample geometry. Moreover, the retrieved images confirm that the method is highly stable against noise. ConclusionsWe anticipate that the developed approach will become the method of choice for a variety of applications of EI XPCI, thanks to its ability to simplify the acquisition procedure and reduce acquisitions time and dose to the sample. Future work will focus on the adaptation of the method to computed tomography and to polychromatic radiation from X-ray tubes.

Shortcut to adiabaticity in spinor condensates

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel $m=0$, is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.

A New Localization Algorithm Based on Taylor Series Expansion for NLOS Environment

Abstract In Non-Line-Of-Sight (NLOS) environment, location accuracy of Taylorseries expansion location algorithm degrades greatly. A new Taylor-series expansion location algorithm based on self-adaptive Radial-Basis-Function (RBF) neural network is proposed in this paper, which can reduce the impact on the positioning accuracy of NLOS effectively on the basis of the measurement error correction. RBF neural network has a faster learning characteristic and the ability of approximate arbitrary nonlinear mapping. In the process of studying, RBF neural network adjusts to the quantity of the nodes according to corresponding additive strategy and removing strategy. The newly-formed network has a simple structure with high accuracy and better adaptive ability. After correcting the error, reuse Taylor series expansion location algorithm for positioning. The simulation results indicate that the proposed algorithm has high location accuracy, the performance is better than RBF-Taylor algorithm, LS-Taylor algorithm, Chan algorithm and LS algorithm in NLOS environment.

The approximate conformal mapping onto simply and doubly connected domains

A new method of approximate conformal mapping of the unit disk onto a simply connected domain and of an annulus onto a doubly connected domain with smooth boundaries is presented. The method is based on integral equations solution which is reduced to a linear system solution and does not require iterations. The mapping function has the form of a Taylor or a Laurent polynomial defined on the unit disk or on the annulus, respectively. The method is easily computable.

Approximate Conformal Mappings and Elasticity Theory

Here, we present the new method of approximate conformal mapping of the unit disk to a one-connected domain with smooth boundary without auxiliary constructions and iterations. The mapping function is a Taylor polynomial. The method is applicable to elasticity problems solution.