Deep Global Multiple-Scale and Local Patches Attention Dual-Branch Network for Pose-Invariant Facial Expression Recognition

Pose-invariant facial expression recognition(FER)is an active but challenging research topic in computer vision.Especially with the involvement of diverse observation angles,FER makes the training parameter models inconsistent from one view to another.This study develops a deep global multiple-scale and local patches attention(GMS-LPA)dual-branch network for pose-invariant FER to weaken the influence of pose variation and selfocclusion on recognition accuracy.In this research,the designed GMS-LPA network contains four main parts,i.e.,the feature extraction module,the global multiple-scale(GMS)module,the local patches attention(LPA)module,and the model-level fusion model.The feature extraction module is designed to extract and normalize texture information to the same size.The GMS model can extract deep global features with different receptive fields,releasing the sensitivity of deeper convolution layers to pose-variant and self-occlusion.The LPA module is built to force the network to focus on local salient features,which can lower the effect of pose variation and self-occlusion on recognition results.Subsequently,the extracted features are fused with a model-level strategy to improve recognition accuracy.Extensive experimentswere conducted on four public databases,and the recognition results demonstrated the feasibility and validity of the proposed methods.

The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles

In this paper,the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles.When considering solving sloshing problems with baffles by using boundary integral methods,degenerate geometry and problems of numerical instability are inevitable.To avoid numerical instability,the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance.Again,the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme.A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems(IBVPs)at each time step.More importantly,the parameters of the algorithm,namely,the T-complete function,dissipation factor,and time step,can obtain a linear relationship.The boundary noise interference and energy conservation are successfully overcome,and the accuracy of the boundary value problem is also improved.Finally,benchmark cases are used to verify the correctness of the numerical algorithm.The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.

A NON-ISOTROPIC MULTIPLE-SCALE TURBULENCE MODEL

This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.

Multiple-scale temporal variations and fluxes near a hydrothermal vent over the Southwest Indian Ridge

A deep-ocean mooring system was deployed 100 m away from an active hydrothermal vent over the Southwest Indian Ridge （SWIR）, where the water depth is about 2,800 m. One year of data on ocean temperature 50 m away from the ocean floor and on velocities at four levels （44 m, 40 m, 36 m, and 32 m away from the ocean floor） were collected by the mooring system. Multiple- scale variations were extracted from these data： seasonal, tidal, super-tidal, and eddy scales. The semidiumal tide was the strongest tidal signal among all the tidal constituents in both currents and temperature. With the multiple-scale variation presented in the data, a new method was developed to decompose the data into five parts in terms of temporal scales： time-mean, seasonal, tidal, super-tidal, and eddy. It was shown that both eddy and tidal heat （momentum） fluxes were characterized by variation in the bottom topography： the tidal fluxes of heat and momentum in the along-isobath direction were much stronger than those in the cross-isobath direction. For the heat flux, eddy heat flux was stronger than tidal heat flux in the cross-isobath direction, while eddy heat flux was weaker in the along-isobath direction. For the momentum flux, the eddy momentum flux was weaker than tidal momentum flux in both directions. The eddy momen^m fluxes at the four levels had a good relationship with the magnitude of mean currents： it increased with the mean current in an exponential relationship.

Introduction to the JES Special Issue on “Multiple-Scale Geodynamics of Continental Interiors”

A major mission of geosciences is to characterize the composition, structure and geodynamic history of the earth＇s continental interiors. Because the evidence for such studies is spread over different disciplines and in different spatial and temporal scales, advances in understanding the geodynamics of continental interiors often require a multi-disciplinary approach to examine the multiplescale nature of the subjects.

A viscoelastic nonlinear energy sink with an electromagnetic energy harvester:Narrow-band random response

Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.

BIFURCATION OF THE ELECTROMECHANICALLY COUPLED SUBSYNCHRONOUS TORSIONAL OSCILLATING SYSTEM WITH HYSTERETIC BEHAVIOR

In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior of couplings in the shaft systems is considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf bifurcation point are analyzed.

Nonlinear free vibration of piezoelectric cylindrical nanoshells

The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then,the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.

HARMONIC, SUBHARMONIC, SUPERHARMONIC, SIMULTANEOUS SUB/SUPER HARMONIC AND COMBINATION RESONANCES OF SELF-EXCITED TWO COUPLED SECOND ORDER SYSTEMS TO MULTI-FREQUENCY EXCITATION

Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.

Fast Solving the Cauchy Problems of Poisson Equation in an Arbitrary Three-Dimensional Domain

In this paper we propose a novel two-stage method to solve the threedimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary.The solution is decomposed into a particular solution and a homogeneous solution.In the first stage a multiple-scale polynomial method(MSPM)is used to approximate the forcing term and then the formula of Tsai et al.[Tsai,Cheng,and Chen(2009)]is used to obtain the corresponding closed-form solution for each polynomial term.Then in the second stage we use a multiple/scale/direction Trefftz method(MSDTM)to find the solution of Laplace equation,of which the directions are uniformly distributed on a unit circle 1,and the scales are determined a priori by the collocation points on boundary.Two examples of 3D data interpolation,and several numerical examples of direct and inverse Cauchy problems in complex domain confirm the efficiency of the MSPM and the MSDTM.

Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic aonlineax equation of motion with damping is established by employing Hamilton＇s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve axe analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.

Modulational instability for a self-attractive two-component Bose-Einstein condensate

By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings. PART II: The Second Order Contribution

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings

The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .

Multi-scale habitat selection and impacts of climate change on the distribution of four sympatric meso-carnivores using random forest algorithm

Background:The habitat resources are structured across different spatial scales in the environment,and thus animals perceive and select habitat resources at different spatial scales.Failure to adopt the scale-dependent framework in species habitat relationships may lead to biased inferences.Multi-scale species distribution models(SDMs)can thus improve the predictive ability as compared to single-scale approaches.This study outlines the importance of multi-scale modeling in assessing the species habitat relationships and may provide a methodological framework using a robust algorithm to model and predict habitat suitability maps(HSMs)for similar multi-species and multi-scale studies.Results:We used a supervised machine learning algorithm,random forest(RF),to assess the habitat relationships of Asiatic wildcat(Felis lybica ornata),jungle cat(Felis chaus),Indian fox(Vulpes bengalensis),and golden-jackal(Canis aureus)at ten spatial scales(500-5000 m)in human-dominated landscapes.We calculated out-of-bag(OOB)error rates of each predictor variable across ten scales to select the most influential spatial scale variables.The scale optimization(OOB rates)indicated that model performance was associated with variables at multiple spatial scales.The species occurrence tended to be related strongest to predictor variables at broader scales(5000 m).Multivariate RF models indicated landscape composition to be strong predictors of the Asiatic wildcat,jungle cat,and Indian fox occurrences.At the same time,topographic and climatic variables were the most important predictors determining the golden jackal distribution.Our models predicted range expansion in all four species under future climatic scenarios.Conclusions:Our results highlight the importance of using multiscale distribution models when predicting the distribution and species habitat relationships.The wide adaptability of meso-carnivores allows them to persist in human-dominated regions and may even thrive in disturbed habitats.These meso-carnivores are among the few species that may benefit from climate change.

Numerical Simulation of Non-Linear Schrodinger Equations in Arbitrary Domain by the Localized Method of Approximate Particular Solution

The aim of this paper is to propose a fast meshless numerical scheme for the simulation of non-linear Schrodinger equations.In the proposed scheme,the implicit-Euler scheme is used for the temporal discretization and the localized method of approximate particular solution(LMAPS)is utilized for the spatial discretization.The multiple-scale technique is introduced to obtain the shape parameters of the multiquadric radial basis function for 2D problems and the Gaussian radial basis function for 3D problems.Six numerical examples are carried out to verify the accuracy and efficiency of the proposed scheme.Compared with well-known techniques,numerical results illustrate that the proposed scheme is of merits being easy-to-program,high accuracy,and rapid convergence even for long-term problems.These results also indicate that the proposed scheme has great potential in large scale problems and real-world applications.

A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions

In this study,the polynomial expansion method(PEM)and the polynomial method of particular solutions(PMPS)are applied to solve a class of linear elliptic partial differential equations(PDEs)in two dimensions with constant coefficients.In the solution procedure,the sought solution is approximated by the Pascal polynomials and their particular solutions for the PEM and PMPS,respectively.The multiple-scale technique is applied to improve the conditioning of the resulted linear equations and the accuracy of numerical results for both of the PEM and PMPS.Some mathematical statements are provided to demonstrate the equivalence of the PEM and PMPS bases as they are both bases of a certain polynomial vector space.Then,some numerical experiments were conducted to validate the implementation of the PEM and PMPS.Numerical results demonstrated that the PEM is more accurate and well-conditioned than the PMPS and the multiple-scale technique is essential in these polynomial methods.

A Novel Envelope Soliton Solution to the Granular Crystal Model

A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.