Approximate Point Research Articles

A Lagrangian Point Approximation-Based Immersed Boundary–Lattice Boltzmann Method for FSI Problems Involving Deformable Body

The proposed immersed boundary-lattice Boltzmann method (IB-LBM) with smoothed point interpolation method (S-PIM) has been verified to be an effective tool for simulating complex fluid–structure interaction (FSI) problems in previous works. LBM is employed as fluid solver with a simple solution process, S-PIM is used for largely deformable solids on the basis of gradient smoothing technique, and their combinations for FSI problems are achieved under the framework of immersed boundary method (IBM). IBM allows the coupling method to use a fixed fluid Euler mesh to avoid frequent mesh updates due to the movement or deformation of solids, whereas the introduction of fictitious fluid causes the internal mass effect and yields numerical errors. An extended Lagrangian point approximation approach has been proposed and introduced in IB-LBM with S-PIM to tackle this issue, and numerical experiments for FSI problems associated with rigid movement and large deformation of solids are investigated. It is verified that the accuracy and convergency properties of the present method are significantly improved compared with the original one in which the mass effect was not considered.

Delay Analysis of Wireless Federated Learning Based on Saddle Point Approximation and Large Deviation Theory

Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients’ private data. Driven by the ever increasing demand for model training of mobile applications or devices, a vast majority of FL tasks are implemented over wireless fading channels. Due to the time-varying nature of wireless channels, however, random delay occurs in both the uplink and downlink transmissions of FL. How to analyze the overall time consumption of a wireless FL task, or more specifically, a FL’s delay distribution, becomes a challenging but important open problem, especially for delay-sensitive model training. In this paper, we present a unified framework to calculate the approximate delay distributions of FL over arbitrary fading channels. Specifically, saddle point approximation, extreme value theory (EVT), and large deviation theory (LDT) are jointly exploited to find the approximate delay distribution along with its tail distribution, which characterizes the quality-of-service of a wireless FL system. Simulation results will demonstrate that our approximation method achieves a small approximation error, which vanishes with the increase of training accuracy.

Theoretical and Experimental Aspects of Influence of Temperature on Kinetics of Carbonaceous Materials Froth Flotation

ABSTRACT The relation between rate constant k 1 and absolute temperature T for graphite, anthracite, and coal floated with only frother was investigated using combined theoretical and empirical approaches. It was determined that the relation between lnk 1 and 1/T is curvilinear and requires a polynomial of a second degree for a sufficient approximation of the experimental data points. Therefore, the well-known Arrhenius empirical formula for chemical reactions, predicting a linear relation, cannot be used for relating lnk 1 and 1/T. Available in literature thermodynamic and kinetic considerations show that for chemical reactions and equilibrium processes the relation between the first order rate constant k 1 and absolute temperature T is lnk 1 = lnk −1-ΔHo /RT +ΔSo/R, where ΔHo is standard enthalpy change, ΔSo standard entropy change, R gas constant and k −1 is the rate constant of the reverse reaction, in our case the disintegration of the bubble-particle aggregate. Assuming that the performed batch flotation tests for a long time of flotation provide an equilibrium quantity called ultimate or maximum recovery, the values of enthalpy and entropy as well as reverse process rate constant k −1 were determined. It was found that k 1 depended on two constants (ΔHo and ΔSo) and two variables (1/T and k −1 = f(1/T)).

Asymptotics of $$\mathrm {SL}(2,{{\mathbb {C}}})$$ coherent invariant tensors

We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of $\mathrm{SL}(2,\mathbb{C})$ of the principal series, corresponding to generalized Clebsch-Gordan coefficients with $n\geq3$ legs. We find critical configurations of the quantum labels with a power-law decay of the invariants. They describe 3d polygons that can be deformed into one another via a Lorentz transformation. This is defined viewing the edge vectors of the polygons are the electric part of bivectors satisfying a (frame-dependent) relation between their electric and magnetic parts known as $\gamma$-simplicity in the loop quantum gravity literature. The frame depends on the SU(2) spin labelling the basis elements of the invariants. We compute a saddle point approximation using the critical points and provide a leading-order approximation of the invariants. The power-law is universal if the SU(2) spins have their lowest value, and $n$-dependent otherwise. As a side result, we provide a compact formula for $\gamma$-simplicity in arbitrary frames. The results have applications to the current EPRL model, but also to future research aiming at going beyond the use of fixed time gauge in spin foam models.

Inexact accelerated high-order proximal-point methods

In this paper, we present a new framework of bi-level unconstrained minimization for development of accelerated methods in Convex Programming. These methods use approximations of the high-order proximal points, which are solutions of some auxiliary parametric optimization problems. For computing these points, we can use different methods, and, in particular, the lower-order schemes. This opens a possibility for the latter methods to overpass traditional limits of the Complexity Theory. As an example, we obtain a new second-order method with the convergence rate Oleft( k^{-4}right) , where k is the iteration counter. This rate is better than the maximal possible rate of convergence for this type of methods, as applied to functions with Lipschitz continuous Hessian. We also present new methods with the exact auxiliary search procedure, which have the rate of convergence Oleft( k^{-(3p+1)/ 2}right) , where p ge 1 is the order of the proximal operator. The auxiliary problem at each iteration of these schemes is convex.

Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

We investigate the S3 free energy of mathcal{N} = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal frac{1}{6} log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures

The main aim of this work was to investigate a numerical error in determining limit state functions, which describe the extreme magnitudes of steel structures with respect to random variables. It was assisted here by the global version of the response function method (RFM). Various approximations of trial points generated on the basis of several hundred selected reference composite functions based on polynomials were analyzed. The final goal was to find some criterion—between approximation and input data—for the selection of the response function leading to relative a posteriori errors less than 1%. Unlike the classical problem of curve fitting, the accuracy of the final values of probabilistic moments was verified here as they can be used in further reliability calculations. The use of the criterion and the associated way of selecting the response function was demonstrated on the example of steel diagrid grillages. It resulted in quite high correctness in comparison with extended FEM tests.

Signatures of Bardasis-Schrieffer mode excitation in third-harmonic generated currents

We theoretically analyze the collective modes in unconventional superconductors focusing on Bardasis-Schrieffer (BS) mode and its contribution to the third harmonic generation currents. Starting from a model with competing superconducting pairing instabilities we add fluctuations of the fields beyond saddle point approximation and calculate their response to an applied pulsed electric field. To model phase fluctuations appropriately we take into account the effect of the long-range Coulomb interaction. While the phase mode is pushed into a plasmon frequency, as known from the literature, we show that the BS mode remains unaffected. Furthermore, it has a characteristic polarization dependence and, unlike the Higgs mode, generates a current in perpendicular direction to the applied field. We find that the Bardasis-Schrieffer excitations contribute a sizable signal to the third harmonic generated current, which is clearly distinguishable from the charge density fluctuations due to Cooper pair breaking effects and can be straightforwardly detected in experiment.

Generalized multiplicative nonlinear elastic matching distance measure and fixed point approximation

In this paper, inspired by the concept of nonlinear elastic matching, generalized metrics, and multiplicative triangle inequality, we propose a ‐multiplicative metric space in which we propose a generalized notion of a distance function, , with degree 2 is a distance of 3 points in generalizing the ordinary distance between 2 points and G‐metric between 3 points. We first discuss ‐multiplicative metric space mapping and later on the fundamental properties of ‐multiplicative metric are also discussed. Fundamental properties and several examples for the ‐multiplicative metric are also given. Moreover, topological properties on the ‐multiplicative metric space including the convergence of sequences and the continuity of mappings on the ‐multiplicative metric space are studied. Finally, we generalize some well‐known fixed point theorems including Banach contraction mapping as ‐multiplicative contraction mapping and proved some fixed point theorems on complete ‐multiplicative metric spaces. We prove the existence and uniqueness of a solution to a system of ‐multiplicative integral equations as an application. Our results generalize many pre‐existing results in literature.

Application of the WNN-Based SCG Optimization Algorithm for Predicting Soft Soil Foundation Engineering Settlement

Settlement prediction in soft soil foundation engineering is a newer technique. Predicting soft soil settling has long been one of the most challenging techniques due to difficulties in soft soil engineering. To overcome these challenges, the wavelet neural network (WNN) is mostly used. So, after assessing its estimate performance, two elements, early parameter selection and system training techniques, are chosen to optimize the traditional WNN difficulties of readily convergence to the local infinitesimal point, low speed, and poor approximation performance. The number of hidden layer nodes is determined using a self-adaptive adjustment technique. The wavelet neural network (WNN) is coupled with the scaled conjugate gradient (SCG) to increase the feasibility and accuracy of the soft fundamental engineering settlement prediction model, and a better wavelet network for the soft ground engineering settlement prediction is suggested in this paper. Furthermore, we have proposed the technique of locating the early parameters based on autocorrelation. The settlement of three types of traditional soft foundation engineering, including metro tunnels, highways, and high-rise building foundations, has been predicted using our proposed model. The findings revealed that the model is superior to the backpropagation neural network and the standard WNN for solving problems of approximation performance. As a result, the model is acceptable for soft foundation engineering settlement prediction and has substantial project referential value.

Weak and Strong Convergence Theorems for Common Attractive Points of Widely More Generalized Hybrid Mappings in Hilbert Spaces

In this work, we study iterative methods for the approximation of common attractive points of two widely more generalized hybrid mappings in Hilbert spaces and obtain weak and strong convergence theorems without assuming the closedness for the domain. A numerical example supporting our main result is also presented. As a consequence, our main results can be applied to solving a common fixed point problem.

Power and Rate Adaptive Pushing Over Fading Channels

Proactive caching is capable of reducing access latency and improving network throughput, thereby attracting attention from both industry and academia. However, the energy efficiency (EE) of proactive caching over fading channels has not been well studied yet. In this paper, we aim at presenting an energy-efficient content pushing policy by carefully adapting the transmit rate and power in pushing and on-demand delivery phases, while assuring delivery delay constraints. To this end, the average delay, delay-outage probability, and EE are analyzed for a general adaptive pushing policy based on the saddle point approximation. According to these results, we formulate EE maximization problems under average delay and delay-outage constraints, respectively, for two special types of adaptive pushing policies, namely, opportunistic pushing and water-filling-based pushing. Due to the high complexity of the grid search for solving the formulated problems, suboptimal algorithms are presented based on gradient descent and golden section search methods. Moreover, we mathematically derive the scaling property and numerically obtain request probability and delivery delay thresholds for content pushing. Simulations show that the presented pushing policies achieve higher EE than on-demand transmissions, especially when the content item is popular and the tolerable delivery delay is small.

Wave function of simple universes analytically continued from negative to positive potentials

We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.

Nut Unfastening by Robotic Surface Exploration

In this paper, we present a novel concept and primary investigations regarding automated unfastening of hexagonal nuts by means of surface exploration with a compliant robot. In contrast to the conventional industrial approaches that rely on custom-designed motorised tools and mechanical tool changers, we propose to use robot fingers to position, grasp and unfasten unknown random-sized hexagonal nuts, which are arbitrarily positioned in the robot’s task space. Inspired by how visually impaired people handle unknown objects, in this work, we use information observed from surface exploration to devise the unfastening strategy. It combines torque monitoring with active compliance for the robot fingers to smoothly explore the object’s surface. We implement a shape estimation technique combining scaled iterative closest point and hypotrochoid approximation to estimate the location as well as contour profile of the hexagonal nut so as to accurately position the gripper fingers. We demonstrate this work in the context of dismantling an electrically driven vehicle battery pack. The experiments are conducted using a seven degrees of freedom (DoF)–compliant robot fitted with a two-finger gripper to unfasten four different sized randomly positioned hexagonal nuts. The obtained results suggest an overall exploration and unfastening success rate of 95% over an average of ten trials for each nut.

Critical exponents for higher order phase transitions: Landau theory and RG flow

In this work, we define and calculate critical exponents associated with higher order thermodynamic phase transitions. Such phase transitions can be classified into two classes: with or without a local order parameter. For phase transitions involving a local order parameter, we write down the Landau theory and calculate critical exponents using the saddle point approximation. Further, we investigate fluctuations about the saddle point and demarcate when such fluctuations dominate over saddle point calculations by introducing the generalized Ginzburg criteria. We use Wilsonian renormalization group (RG) to derive scaling forms for observables near criticality and obtain scaling relations between the critical exponents. Afterwards, we find out fixed points of the RG flow using the one-loop beta function and calculate critical exponents about the fixed points for third and fourth order phase transitions.

A zeroth order method for stochastic weakly convex optimization

In this paper, we consider stochastic weakly convex optimization problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with a larger constant, and report some numerical results showing the effectiveness of the approach.

Photogalvanic effect in silicene

Silicene has introduced itself as an outstanding novel material, which seeks its meritorious place among common spintronic devices like Cu and Ag. In this work, photogalvanic effect in silicene is studied within the semi-classical approach and beyond Dirac point approximation. Normal electric field plays the role of effective pseudo-magnetic field which breaks the inversion symmetry and splits the conduction and valence bands. The interplay between this external field and intrinsic spin-orbit coupling provides spin-valley locking in silicene. Spin-valley locking in silicene makes this material superior to its carbon counterpart, graphene. Since the absorption of the polarized photons is not equivalent at both of the valleys, spin-valley locking leads to a spin-polarized photocurrent injection.

An Analysis on Polygonal Approximation Techniques for Digital Image Boundary

Polygonal approximation (PA) techniques have been widely applied in the field of pattern recognition, classification, shape analysis, identification, 3D reconstruction, medical imaging, digital cartography, and geographical information system. In this paper, we focus on some of the key techniques used in implementing the PA algorithms. The PA can be broadly divided into three main category, dominant point detection, threshold error method with minimum number of break points and break points approximation by error minimization. Of the above three methods, there has been always a tradeoff between the three classes and optimality, specifically the optimal algorithm works in a computation intensive way with a complexity ranges from O (N2) to O (N3).The heuristic methods approximate the curve in a speedy way, however they lack in the optimality but have linear time complexity. Here a comprehensive review on major PA techniques for digital planar curve approximation is presented.

Pseudomyopia and Its Association With Anxiety.

Pseudomyopia is an inappropriately excessive accommodation of the eye due to overstimulation or ciliary spasm, which leads to a marked approximation of the far point. Common symptoms of pseudomyopia include eye strain or fatigue, and it is classified as organic or functional. The latter is due to eye strain and functional increase in the ciliary tonus. Pseudomyopia can vary from being a transient condition or continue to progress to myopia. Head trauma is the most common cause followed by psychiatric illnesses, neurologic diseases, and drug-induced causes. There is an association between psychological stress-inducing events and pseudomyopia as it affects the autonomic nervous system. The human body counteracts anxiety by activating the parasympathetic nervous system, causing ciliary muscle contraction. Underlying psychiatric diseases in pseudomyopia patients have been reported in the past in multiple studies. Generalized anxiety disorder is the most common psychiatric illness associated with pseudomyopia with a positive correlation between anxiety-somatization scores and accommodation amount of the eye. It is strongly advised that a psychiatric consultation should be included in the multidisciplinary evaluation of every case. If patients have coexisting anxiety disorders, a multidisciplinary approach using psychiatric consultations, work environment changes, ocular exercises, and cycloplegic drugs can be used. This review aims to shed light on the association of psychiatric disorders such as anxiety with pseudomyopia.

Fixed Point Approximation of Monotone Nonexpansive Mappings in Hyperbolic Spaces

Fixed points of monotone α -nonexpansive and generalized β -nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.