First-order Momentum Research Articles

Enhanced scattering from an almost-periodic optical temporal slab

We showcase the impact of almost-periodicity on the parametric amplification associated with the first-order momentum gap in photonic time-crystals with time-varying permittivity. Utilizing a vectorial coupled-wave theory approach, we rigorously analyze the scattering by a temporal slab of the considered medium. We pinpoint a critical regime wherein flaws in material tuning paradoxically enhance amplification due to the coupling of fewer, broader modes, resulting in a higher and broader pulselike amplification envelope. Additionally, we demonstrate that the intensity reflectances of time-reversed waves corresponding to secondary “Bragg” resonances achieve remarkably high levels of subharmonic parametric amplification, with the epsilon-near-zero regime serving as a preferred candidate for experimental implementation. Our counterintuitive findings highlight the potential of intentionally leveraging modulation desynchronization and impurities in the temporal unit cell of photonic time-crystals to enhance both the level and the bandwidth of amplification. Published by the American Physical Society 2024

UAdam: Unified Adam-Type Algorithmic Framework for Nonconvex Optimization.

Adam-type algorithms have become a preferred choice for optimization in the deep learning setting; however, despite their success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms, termed UAdam. It is equipped with a general form of the second-order moment, which makes it possible to include Adam and its existing and future variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. The approach is supported by a rigorous convergence analysis of UAdam in the general nonconvex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with a rate of O(1/T). Furthermore, the size of the neighborhood decreases as the parameter β1 increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also reveal the convergence conditions of vanilla Adam, together with the selection of appropriate hyperparameters. This provides a theoretical guarantee for the analysis, applications, and further developments of the whole general class of Adam-type algorithms. Finally, several numerical experiments are provided to support our theoretical findings.

Radial oscillations and dynamical instability analysis for linear-quadratic GUP-modified white dwarfs

A modification to the Heisenberg uncertainty principle is called the generalized uncertainty principle (GUP), which emerged due to the introduction of a minimum measurable length, common among phenomenological approaches to quantum gravity. One approach to GUP is called linear-quadratic GUP (LQGUP) which satisfies both the minimum measurable length and the maximum measurable momentum, resulting to an infinitesimal phase space volume proportional to the first-order momentum (1−αp)−4d3xd3p, where α is the still-unestablished GUP parameter. In this study, we explore the mass–radius relations of white dwarfs whose equation of state has been modified by LQGUP, and provide them with radial perturbations to investigate the dynamical instability arising from the oscillations. We find from the mass–radius relations that the main effect of LQGUP is to worsen the gravitational collapse by decreasing the mass of the relatively massive white dwarfs (including their limiting mass, while increasing their limiting radius). This effect gets more prominent with larger values of α. We then compare the results with available observational data. To further investigate the impact of the GUP parameter, a dynamical instability analysis of the white dwarf was conducted, and we find that instability sets in for all values of α. With increasing α, we also find that the central density at which instability occurs decreases, resulting to a lower maximum mass. This is in contrast to quadratic GUP, where instability only sets in below a critical value of the quadratic GUP parameter.

An Improved Adam Optimization Algorithm Combining Adaptive Coefficients and Composite Gradients Based on Randomized Block Coordinate Descent.

An improved Adam optimization algorithm combining adaptive coefficients and composite gradients based on randomized block coordinate descent is proposed to address issues of the Adam algorithm such as slow convergence, the tendency to miss the global optimal solution, and the ineffectiveness of processing high-dimensional vectors. The adaptive coefficient is used to adjust the gradient deviation value and correct the search direction firstly. Then, the predicted gradient is introduced, and the current gradient and the first-order momentum are combined to form a composite gradient to improve the global optimization ability. Finally, the random block coordinate method is used to determine the gradient update mode, which reduces the computational overhead. Simulation experiments on two standard datasets for classification show that the convergence speed and accuracy of the proposed algorithm are higher than those of the six gradient descent methods, and the CPU and memory utilization are significantly reduced. In addition, based on logging data, the BP neural networks optimized by six algorithms, respectively, are used to predict reservoir porosity. Results show that the proposed method has lower system overhead, higher accuracy, and stronger stability, and the absolute error of more than 86% data is within 0.1%, which further verifies its effectiveness.

A novel dense residual network based on Adam-S optimizer for fault diagnosis of bearings under different working conditions

In recent years, the residual network has been widely used in the field of intelligent diagnosis because of its powerful functioning. This paper proposes a novel dense residual network (DRNet) for the efficient fault diagnosis of rolling bearings, which combines the advantages of dense connections and residual learning to prevent the gradient disappearance and network degradation caused by network deepening. First, each sub-block in the dense network (DesNet) is deeply processed so that it has better nonlinear expressive ability to extract deep fault features. Then, the residual learning is embedded into each sub-block of the DesNet, so that each sub-block processed by deepening will not show the phenomenon of network degradation. Finally, an Adam-subtracted momentum optimization algorithm is proposed, which adds the first-order momentum and the second-order momentum of the previous gradient into the expression of the second-order momentum of the current gradient, which enhances the connection between the parameters in the two adjacent gradients in the Adam algorithm. It makes the algorithm more reliable and the gradient prediction more accurate. Without adding additional parameters, the training stability of the algorithm in complex environments is further improved. Experiments on two kinds of data sets under different working conditions are carried out many times, and in comparison with the random forest, support vector machine, dense network, residual network, AlexNet and DRNet-Adam. This proves the effectiveness and feasibility of the proposed model and optimization algorithm.

Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

Good representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions (0^circ and 45^circ with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy-top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy-top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to 17%. Additionally, we observe that the von Kármán coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique.

A new short-arc fitting method with high precision using Adam optimization algorithm

The high-precision short-arc measurement is a huge challenge in scientific research and engineering practice. The popular traditional least square fitting (TLSF) however fails to achieve the precise fitting parameters when the arc gets shorter. In this work, an inequation constrained fitting (ICF) method based on four-parameter circle equation is presented. Lagrangian multiplier and Karush-Kuhn-Tucker criteria are used to redefine the objective function. After that, Adam algorithm is utilized to solve the objective function in iterative way. Adam algorithm has a strong ability to resist noise pollution by virtue of modifying continually the first-order momentum and second-order momentum with average of gradients during the course of iteration. Finally, simulation and experimental results show that our ICF method is more robust and high-precision than TLSF and Hyper method, so it is very competent to measure short arcs with noise even their central angles are close to 5°.

Optimization of consistent two-equation models for thin film flows

Abstract A general study of consistent two-equation models for thin film flows is presented. In all models derived by the energy integral method or by an equivalent method, the energy of the system, apart from the kinetic energy of the mean flow, depends on the mean velocity. We show that in this case the model does not satisfy the principle of Galilean invariance. All consistent models derived by the momentum integral method are Galilean invariant but they admit an energy equation and a capillary energy only if the Galilean-invariant part of the first-order momentum flux does not depend on the mean velocity. We show that, both for theoretical and numerical reasons, two-equations models should be derived by a momentum integral method admitting an energy equation leading to the structure of the equations of fluids endowed with internal capillarity. Among all models fulfilling these conditions, those having the best properties are selected. The nonlinear properties are tested from the speed of solitary waves at the high Reynolds number limit while the linear properties are studied from the neutral stability curves and from the celerity of the kinematic waves along these curves. The latter criterion gives the best consistent way to write the second-order diffusive terms of the model. Optimized consistent two-equation models are then proposed and numerical results are compared to numerical and experimental results of the literature.

MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids

Abstract. We introduce MPAS-Albany Land Ice (MALI) v6.0, a new variable-resolution land ice model that uses unstructured Voronoi grids on a plane or sphere. MALI is built using the Model for Prediction Across Scales (MPAS) framework for developing variable-resolution Earth system model components and the Albany multi-physics code base for the solution of coupled systems of partial differential equations, which itself makes use of Trilinos solver libraries. MALI includes a three-dimensional first-order momentum balance solver (Blatter–Pattyn) by linking to the Albany-LI ice sheet velocity solver and an explicit shallow ice velocity solver. The evolution of ice geometry and tracers is handled through an explicit first-order horizontal advection scheme with vertical remapping. The evolution of ice temperature is treated using operator splitting of vertical diffusion and horizontal advection and can be configured to use either a temperature or enthalpy formulation. MALI includes a mass-conserving subglacial hydrology model that supports distributed and/or channelized drainage and can optionally be coupled to ice dynamics. Options for calving include “eigencalving”, which assumes that the calving rate is proportional to extensional strain rates. MALI is evaluated against commonly used exact solutions and community benchmark experiments and shows the expected accuracy. Results for the MISMIP3d benchmark experiments with MALI's Blatter–Pattyn solver fall between published results from Stokes and L1L2 models as expected. We use the model to simulate a semi-realistic Antarctic ice sheet problem following the initMIP protocol and using 2 km resolution in marine ice sheet regions. MALI is the glacier component of the Energy Exascale Earth System Model (E3SM) version 1, and we describe current and planned coupling to other E3SM components.

Collision detection algorithm for collaborative robots considering joint friction

This article proposes a collision detection algorithm without external sensors that can detect potential collisions in man–robot interaction. The algorithm is based on a modified first-order momentum deviation observer that also takes friction into account. The collision detection algorithm uses joint angles, angular velocities, and torques during the detection process, without any need to consider angular acceleration. The algorithm also uses an accurate friction model that is based on a Stribeck model with second-order Fourier series compensation. The friction model is applied in advance so that compensation can be made in real time during collision detection. Identification data are filtered through a first-order low-pass filter to reduce high-frequency noise. In order to verify the algorithm, a simulation and experiment were carried out using a collaborative robot experimental platform. The results confirmed that collisions can be detected by setting appropriate threshold values. Different possible responses can be implemented according to different response strategies, with the ultimate arbiter being that collision forces are kept strictly within ordinary human tolerances. This makes sure that safety can be preserved in man–robot interaction processes.

Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods.

Fluorescence molecular tomography (FMT) is a significant preclinical imaging modality that has been actively studied in the past two decades. It remains a challenging task to obtain fast and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden and the ill-posed nature of the inverse problem. We have recently studied a nonuniform multiplicative updating algorithm that combines with the ordered subsets (OS) method for fast convergence. However, increasing the number of OS leads to greater approximation errors and the speed gain from larger number of OS is limited. We propose to further enhance the convergence speed by incorporating a first-order momentum method that uses previous iterations to achieve optimal convergence rate. Using numerical simulations and a cubic phantom experiment, we have systematically compared the effects of the momentum technique, the OS method, and the nonuniform updating scheme in accelerating the FMT reconstruction. We found that the proposed combined method can produce a high-quality image using an order of magnitude less time.

Non-continuum effects on natural convection–radiation boundary layer flow from a heated vertical plate

Heat transfer by simultaneous radiation and natural convection through an optically thick fluid over a heated vertical plate has been studied with first-order momentum and thermal non-continuum boundary conditions. The radiant heat flux was treated using the Rosseland diffusion approximation. By solving the local non-similarity two-equation model, numerical solutions were obtained to examine the slip effects on the interaction between radiation and natural convection for a range of rarefied conditions and radiation effects. Results including slip velocity, temperature jump, skin friction, and heat transfer rate are presented graphically and discussed. In addition, an integral correlation is presented for the average Nusselt number as a function of the non-continuum conditions, radiation–conduction parameter, and flow properties.

A variationally derived, depth-integrated approximation to a higher-order glaciological flow model

AbstractAn approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.

Flow characteristics of bottom outlets with moving gates

This study investigates the discharge characteristics of a bottom outlet with a moving gate by Flow3D. Experimental results for a scale model outlet of the Aswan Dam, Egypt, were used. Two different flow features were found. Pressurized flow established if the flume was filled and then the gate was slowly opened. However, a free surface flow occurred if the gate was fully opened and the entire flume was slowly flooded with water. The numerical simulations successfully captured the two flow patterns as well as the discharges and water surface profiles. The discharges were predicted with sufficient accuracy using the first-order momentum advection scheme. In comparison with the k-ϵ turbulence model, the Re-Normalization Group model yields the best agreement with the experiments. The model performed with similar accuracy for both model and prototype cases.

Natural Convection over Vertical Plates: Local-Nonsimilarity Slip Flow Solutions

Natural convection over a vertical isothermal plate has been modeled with first-order momentum and thermal discontinuities at the wall. A local-nonsimilarity transformation has been applied and numerical solutions were obtained based on the three-equation model. The presence of nonequilibrium at the wall has been found to result in a nonsimilar boundary-layer problem. Nonsimilar velocity and temperature distributions within the boundary layer have been obtained. Results are presented which indicate the effects of nonequilibrium on wall slip velocity, temperature jump, wall shear stress, and boundary-layer thickness for both gaseous and liquid flows. Equations for predicting the drag and average Nusselt number have been formulated as an integral function of the nonequilibrium parameter. A reduction in heat transfer was predicted for more rarified gaseous flows with simultaneous momentum slip and thermal jump conditions. In liquids, without a thermal jump, heat transfer was found to increase relative to the respective no-slip value.

Slip effects on mixed convective flow and heat transfer from a vertical plate

Laminar mixed convection over an isothermal vertical plate has been modeled with first-order momentum and thermal discontinuities at the wall. Local non-similarity transformations, using two non-similarity variables, have been applied to study the mixed convection boundary layer problem. Numerical solutions were obtained for varying conditions in assisting flow based on the three-equation model. Non-similar velocity and temperature distributions within the boundary layer have been presented. Results are also presented for the effect of non-continuum upon wall slip velocity, temperature jump, wall shear stress and boundary layer thickness in both gaseous and liquid flows for Gr x / Re x 2 varying from 0.0001 to 8.0.

An analytic perturbation approach for classical spinning particle dynamics

A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson-Papapetrou-Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle's spin magnitude, it is shown how to obtain in general form an analytic representation of the particle's kinematic and dynamical degrees of freedom that is formally applicable to infinite order in the expansion. Within this formalism, it is possible to identify a classical analogue of radiative corrections to the particle's mass and spin due to spin-gravity interaction. The robustness of this approach is demonstrated by showing how to explicitly compute the first-order momentum and spin tensor components for arbitrary particle motion in a general space-time background. Potentially interesting applications based on this perturbation approach are outlined.

Quasi-Newtonian dust cosmologies

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function N (the relativistic acceleration scalar potential) which evolves along the reference congruence according to , we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearizing the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.

Soft-photon approximation for bound-state Compton scattering.

The transition amplitude for the inelastic scattering of a photon from a system of bound charged particles, with a single charge ejected, behaves at low-energy end of the scattered-photon spectrum as the inverse of the energy and is proportional to the on-shell matrix element corresponding to the process in which the soft photon is absent. The next term in the expansion in powers of the energy of the soft photon is derived here, and is expressed in terms of the same single-photon absorption amplitude. The correction takes the form of first-order momentum shifts in the arguments of the absorption amplitude; they enter in such a way as to leave this amplitude on the energy shell. This result is precisely what would be expected by analogy with Low's theorem [Phys. Rev. 110, 974 (1958)] on spontaneous bremsstrahlung. A nonrelativistic version of the theorem on bound-state Compton scattering is obtained through an asymptotic analysis of the configuration-space matrix element for this process, with the effect of a long-range Coulomb tail accounted for. Relativistic versions are derived as well, appropriate to particles of zero spin, and with spin effects included, based on the same type of gauge-invariance argument employed by Low. Analogous results are obtained from an external-field formulation in the weak-field limit.

Momentum Dependence of thekl3Decay Form Factors

When the formal solution to the algebra of currents is saturated with vector-meson resonances, the first-order momentum dependence of ${f}_{+}({q}^{2})$ is related to $\ensuremath{\Gamma}(\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+\ensuremath{\gamma})$ and is in agreement with experiments on ${{K}_{l3}}^{+}$ and ${{K}_{l3}}^{+}$ decays.