In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamicall...In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.展开更多
Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f i...Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.展开更多
Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent prob...Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.展开更多
Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be...Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be used to construct near-field radiative modulators with excellent modulation effects.However,in practical applications,natural hyperbolic materials need to be deposited on the substrate,and the influence of substrate on modulation effect has not been studied yet.In this work,we investigate the influence of substrate effect on near-field radiative modulator based onα-MoO_(3).The results show that compared to the situation without a substrate,the presence of both lossless and lossy substrate will reduce the modulation contrast(MC)for different film thicknesses.When the real or imaginary component of the substrate permittivity increases,the mismatch of hyperbolic phonon polaritons(HPPs)weakens,resulting in a reduction in MC.By reducing the real and imaginary components of substrate permittivity,the MC can be significantly improved,reaching 4.64 forε_(s)=3 at t=10 nm.This work indicates that choosing a substrate with a smaller permittivity helps to achieve a better modulation effect,and provides guidance for the application of natural hyperbolic materials in the near-field radiative modulator.展开更多
Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagati...Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.展开更多
Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of ...Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.展开更多
The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework i...The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.展开更多
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy ...In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.展开更多
Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to sca...Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.展开更多
We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a ...We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.展开更多
In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume fram...In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.展开更多
Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the k...Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the knowledge graph increases exponentially with the depth of the tree,whereas the distances of nodes in Euclidean space are second-order polynomial distances,whereby knowledge embedding using graph neural networks in Euclidean space will not represent the distances between nodes well.This paper introduces a novel approach called hyperbolic hierarchical graph attention network(H2GAT)to rectify this limitation.Firstly,the paper conducts knowledge representation in the hyperbolic space,effectively mitigating the issue of exponential growth of nodes with tree depth and consequent information loss.Secondly,it introduces a hierarchical graph atten-tion mechanism specifically designed for the hyperbolic space,allowing for enhanced capture of the network structure inherent in the knowledge graph.Finally,the efficacy of the proposed H2GAT model is evaluated on benchmark datasets,namely WN18RR and FB15K-237,thereby validating its effectiveness.The H2GAT model achieved 0.445,0.515,and 0.586 in the Hits@1,Hits@3 and Hits@10 metrics respectively on the WN18RR dataset and 0.243,0.367 and 0.518 on the FB15K-237 dataset.By incorporating hyperbolic space embedding and hierarchical graph attention,the H2GAT model successfully addresses the limitations of existing hyperbolic knowledge embedding models,exhibiting its competence in knowledge graph completion tasks.展开更多
In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyp...In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.展开更多
In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary ...In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.展开更多
Predicting potential facts in the future,Temporal Knowledge Graph(TKG)extrapolation remains challenging because of the deep dependence between the temporal association and semantic patterns of facts.Intuitively,facts(...Predicting potential facts in the future,Temporal Knowledge Graph(TKG)extrapolation remains challenging because of the deep dependence between the temporal association and semantic patterns of facts.Intuitively,facts(events)that happened at different timestamps have different influences on future events,which can be attributed to a hierarchy among not only facts but also relevant entities.Therefore,it is crucial to pay more attention to important entities and events when forecasting the future.However,most existing methods focus on reasoning over temporally evolving facts or mining evolutional patterns from known facts,which may be affected by the diversity and variability of the evolution,and they might fail to attach importance to facts that matter.Hyperbolic geometry was proved to be effective in capturing hierarchical patterns among data,which is considered to be a solution for modelling hierarchical relations among facts.To this end,we propose ReTIN,a novel model integrating real-time influence of historical facts for TKG reasoning based on hyperbolic geometry,which provides low-dimensional embeddings to capture latent hierarchical structures and other rich semantic patterns of the existing TKG.Considering both real-time and global features of TKG boosts the adaptation of ReTIN to the ever-changing dynamics and inherent constraints.Extensive experiments on benchmarks demonstrate the superiority of ReTIN over various baselines.The ablation study further supports the value of exploiting temporal information.展开更多
We investigated the spin splitting of vortex beam on the surface of biaxial natural hyperbolic materials(NHMs)rotated by an angle with respect to the incident plane. An obvious asymmetry of spatial shifts produced by ...We investigated the spin splitting of vortex beam on the surface of biaxial natural hyperbolic materials(NHMs)rotated by an angle with respect to the incident plane. An obvious asymmetry of spatial shifts produced by the left-handed circularly(LCP) component and right-handed circularly polarized(RCP) component is exhibited. We derived the analytical expression for in-and out-of-plane spatial shifts for each spin component of the vortex beam. The orientation angle of the optical axis plays a key role in the spin splitting between the two spin components, which can be reflected in the simple expressions for spatial shifts without the rotation angle. Based on an α-MoO_(3) biaxial NHM, the spatial shifts of the two spin components with the topological charge were investigated. As the topological charge increases, the spatial shifts also increase;in addition, a tiny spatial shift close to zero can be obtained if we control the incident frequency or the polarization of the reflected beams. It can also be concluded that the maximum of the spin splitting results from the LCP component at p-incidence and the RCP component at s-incidence in the RB-Ⅱ hyperbolic frequency band. The effect of the incident angle and the thickness of the α-MoO_(3) film on spin splitting is also considered. These results can be used for manipulating infrared radiation and optical detection.展开更多
Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning thi...Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.展开更多
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluate...This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.展开更多
We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different clas...We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.展开更多
文摘In this paper,a new efficient,and at the same time,very simple and general class of thermodynamically compatiblefinite volume schemes is introduced for the discretization of nonlinear,overdetermined,and thermodynamically compatiblefirst-order hyperbolic systems.By construction,the proposed semi-discrete method satisfies an entropy inequality and is nonlinearly stable in the energy norm.A very peculiar feature of our approach is that entropy is discretized directly,while total energy conservation is achieved as a mere consequence of the thermodynamically compatible discretization.The new schemes can be applied to a very general class of nonlinear systems of hyperbolic PDEs,including both,conservative and non-conservative products,as well as potentially stiff algebraic relaxation source terms,provided that the underlying system is overdetermined and therefore satisfies an additional extra conservation law,such as the conservation of total energy density.The proposed family offinite volume schemes is based on the seminal work of Abgrall[1],where for thefirst time a completely general methodology for the design of thermodynamically compatible numerical methods for overdetermined hyperbolic PDE was presented.We apply our new approach to three particular thermodynamically compatible systems:the equations of ideal magnetohydrodynamics(MHD)with thermodynamically compatible generalized Lagrangian multiplier(GLM)divergence cleaning,the unifiedfirst-order hyperbolic model of continuum mechanics proposed by Godunov,Peshkov,and Romenski(GPR model)and thefirst-order hyperbolic model for turbulent shallow waterflows of Gavrilyuk et al.In addition to formal mathematical proofs of the properties of our newfinite volume schemes,we also present a large set of numerical results in order to show their potential,efficiency,and practical applicability.
基金supported by the Grant No.20-16367/NRPU/RD/HEC/20212021。
文摘Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52204258 and 52106099)the Postdoctoral Research Foundation of China (Grant No.2023M743779)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No.2022QN1017)the Key Research Development Projects in Xinjiang Uygur Autonomous Region (Grant No.2022B03003-3)the Shandong Provincial Natural Science Foundation (Grant No.ZR2020LLZ004)。
文摘Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.
基金Project supported by the National Natural Science Foundation of China (Grant No.52106099)the Natural Science Foundation of Shandong Province of China (Grant No.ZR2022YQ57)the Taishan Scholars Program。
文摘Relative rotation between the emitter and receiver could effectively modulate the near-field radiative heat transfer(NFRHT)in anisotropic media.Due to the strong in-plane anisotropy,natural hyperbolic materials can be used to construct near-field radiative modulators with excellent modulation effects.However,in practical applications,natural hyperbolic materials need to be deposited on the substrate,and the influence of substrate on modulation effect has not been studied yet.In this work,we investigate the influence of substrate effect on near-field radiative modulator based onα-MoO_(3).The results show that compared to the situation without a substrate,the presence of both lossless and lossy substrate will reduce the modulation contrast(MC)for different film thicknesses.When the real or imaginary component of the substrate permittivity increases,the mismatch of hyperbolic phonon polaritons(HPPs)weakens,resulting in a reduction in MC.By reducing the real and imaginary components of substrate permittivity,the MC can be significantly improved,reaching 4.64 forε_(s)=3 at t=10 nm.This work indicates that choosing a substrate with a smaller permittivity helps to achieve a better modulation effect,and provides guidance for the application of natural hyperbolic materials in the near-field radiative modulator.
文摘Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.
基金support via NSF grants NSF-19-04774,NSF-AST-2009776,NASA-2020-1241NASA grant 80NSSC22K0628.DSB+3 种基金HK acknowledge support from a Vajra award,VJR/2018/00129a travel grant from Notre Dame Internationalsupport via AFOSR grant FA9550-20-1-0055NSF grant DMS-2010107.
文摘Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.
文摘The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
基金supported by the NSFC grant 12101128supported by the NSFC grant 12071392.
文摘In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.
基金supported by the National Natural Science Foundation of China-China State Railway Group Co.,Ltd.Railway Basic Research Joint Fund (Grant No.U2268217)the Scientific Funding for China Academy of Railway Sciences Corporation Limited (No.2021YJ183).
文摘Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.
基金partially supported by NSF Grants DMS-1854434,DMS-1952644,and DMS-2151235 at UC Irvinesupported by NSF Grants DMS-1924935,DMS-1952339,DMS-2110145,DMS-2152762,and DMS-2208361,and DOE Grants DE-SC0021142 and DE-SC0002722.
文摘We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.
基金supported in part by the NSF grant DMS-2208438.The work of M.Herty was supported in part by the DFG(German Research Foundation)through 20021702/GRK2326,333849990/IRTG-2379,HE5386/18-1,19-2,22-1,23-1under Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612+1 种基金The work of A.Kurganov was supported in part by the NSFC grant 12171226the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design,China(No.2019B030301001).
文摘In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.
基金the Beijing Municipal Science and Technology Program(No.Z231100001323004).
文摘Utilizing graph neural networks for knowledge embedding to accomplish the task of knowledge graph completion(KGC)has become an important research area in knowledge graph completion.However,the number of nodes in the knowledge graph increases exponentially with the depth of the tree,whereas the distances of nodes in Euclidean space are second-order polynomial distances,whereby knowledge embedding using graph neural networks in Euclidean space will not represent the distances between nodes well.This paper introduces a novel approach called hyperbolic hierarchical graph attention network(H2GAT)to rectify this limitation.Firstly,the paper conducts knowledge representation in the hyperbolic space,effectively mitigating the issue of exponential growth of nodes with tree depth and consequent information loss.Secondly,it introduces a hierarchical graph atten-tion mechanism specifically designed for the hyperbolic space,allowing for enhanced capture of the network structure inherent in the knowledge graph.Finally,the efficacy of the proposed H2GAT model is evaluated on benchmark datasets,namely WN18RR and FB15K-237,thereby validating its effectiveness.The H2GAT model achieved 0.445,0.515,and 0.586 in the Hits@1,Hits@3 and Hits@10 metrics respectively on the WN18RR dataset and 0.243,0.367 and 0.518 on the FB15K-237 dataset.By incorporating hyperbolic space embedding and hierarchical graph attention,the H2GAT model successfully addresses the limitations of existing hyperbolic knowledge embedding models,exhibiting its competence in knowledge graph completion tasks.
文摘In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.
基金Projects supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No.G2002CB312101)
文摘In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.
基金Major Key Project of Pengcheng Laboratory,Grant/Award Number:PCL2022A03。
文摘Predicting potential facts in the future,Temporal Knowledge Graph(TKG)extrapolation remains challenging because of the deep dependence between the temporal association and semantic patterns of facts.Intuitively,facts(events)that happened at different timestamps have different influences on future events,which can be attributed to a hierarchy among not only facts but also relevant entities.Therefore,it is crucial to pay more attention to important entities and events when forecasting the future.However,most existing methods focus on reasoning over temporally evolving facts or mining evolutional patterns from known facts,which may be affected by the diversity and variability of the evolution,and they might fail to attach importance to facts that matter.Hyperbolic geometry was proved to be effective in capturing hierarchical patterns among data,which is considered to be a solution for modelling hierarchical relations among facts.To this end,we propose ReTIN,a novel model integrating real-time influence of historical facts for TKG reasoning based on hyperbolic geometry,which provides low-dimensional embeddings to capture latent hierarchical structures and other rich semantic patterns of the existing TKG.Considering both real-time and global features of TKG boosts the adaptation of ReTIN to the ever-changing dynamics and inherent constraints.Extensive experiments on benchmarks demonstrate the superiority of ReTIN over various baselines.The ablation study further supports the value of exploiting temporal information.
基金Project supported by the Natural Science Foundation of Heilongjiang Province of China (Grant No. LH2022F041)。
文摘We investigated the spin splitting of vortex beam on the surface of biaxial natural hyperbolic materials(NHMs)rotated by an angle with respect to the incident plane. An obvious asymmetry of spatial shifts produced by the left-handed circularly(LCP) component and right-handed circularly polarized(RCP) component is exhibited. We derived the analytical expression for in-and out-of-plane spatial shifts for each spin component of the vortex beam. The orientation angle of the optical axis plays a key role in the spin splitting between the two spin components, which can be reflected in the simple expressions for spatial shifts without the rotation angle. Based on an α-MoO_(3) biaxial NHM, the spatial shifts of the two spin components with the topological charge were investigated. As the topological charge increases, the spatial shifts also increase;in addition, a tiny spatial shift close to zero can be obtained if we control the incident frequency or the polarization of the reflected beams. It can also be concluded that the maximum of the spin splitting results from the LCP component at p-incidence and the RCP component at s-incidence in the RB-Ⅱ hyperbolic frequency band. The effect of the incident angle and the thickness of the α-MoO_(3) film on spin splitting is also considered. These results can be used for manipulating infrared radiation and optical detection.
基金supported in part by the National Natural Science Foundation of China under Grants No.62027803,No.61601096,No.61971111,and No.61801089in part by the Science and Technology Program under Grants No.8091C24,No.2021JCJQJJ0949,and No.2022JCJQJJ0784in part by the Industrial Technology Development Program under Grant No.2020110C041.
文摘Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.
基金the Institute of Applied Physics and Computational Mathematics,Beijing,for the hospitality and support.The second author is supported by the NSFC(Nos.11771054,12072042,91852207)the Sino-German Research Group Project(No.GZ1465)the National Key Project GJXM92579.
文摘This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.
基金the author was partially funded by the SNF project 200020_175784.
文摘We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.
