In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic fu...Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.展开更多
In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contrac...In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.展开更多
This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.展开更多
A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separati...A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separation and power-law spectral density,the more interesting phenomena predicted in coupled Luttinger liquids of neighboring 1D conductors have been rarely observed due to the difficulty in creating such structures.Recently,we have successfully grown close-packed carbon nanotube(CNT)arrays with uniform chirality,providing an ideal material system for studying the coupled Luttinger liquids.Here,we report on the observation of tunable hyperbolic plasmons in the coupled Luttinger liquids of CNT arrays using scanning near-field optical microscopy.These hyperbolic plasmons,resulting from the conductivity anisotropy in the CNT array,exhibit strong spatial confinement,in situ tunability,and a wide spectral range.Despite their hyperbolic wavefronts,the plasmon propagation in the axial direction still adheres to the Luttinger-liquid theory.Our work not only demonstrates a fascinating phenomenon in coupled Luttinger liquids for fundamental physics exploration,but also provides a highly confined and in situ tunable hyperbolic plasmon in close-packed CNT arrays for future nanophotonic devices and circuits.展开更多
Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exp...Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exploring homogeneous regions of temperature volatility and analyzing the driving factors.To investigate the regionalization of temperature volatility in China's mainland,a network constructed by the cosine similarity of temperature volatility series from China's mainland was embedded in hyperbolic space.Subsequently,we partitioned the network on the hyperbolic map using the critical gap method and then found eight regions in all.Ultimately,a network of communities was constructed while the interaction among communities was quantified.This yields a perspective of temperature volatility regionalization that can accurately reflect factors including altitude,climate type,and the geographic location of mountains.Further analysis demonstrates that the regionalization in the hyperbolic map is distinct from provinces and has a realistic basis:communities in southwest China show strong correlations due to the temperature sensitivity to altitude,and communities in northern China show a convergence in the area of Dingxi,Gansu,mainly owing to the strong temperature sensitivity to climate types.As a consequence,node distributions and community divisions in the hyperbolic map can offer new insights into the regionalization of temperature volatility in China's mainland.The results demonstrate the potential of hyperbolic embedding of complex networks in forecasting future node associations in real-world data.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
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
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
This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,t...This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.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
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
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
Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it i...Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce the vibration of the RSSFS simultaneously.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
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
基金supported by the National Natural Science Foundation of China(12371217)the Fundamental Research Funds for the Central Universities(2232022D-27).
文摘For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
基金financially supported by the National Natural Science Foundation of China (8225041038)the Sichuan Science and Technology Program (23NSFSC2916)the Fundamental Research Funds for the Central Universities, Southwest Minzu University (ZYN2024077)
文摘Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.
基金supported by the NSFC(12271122)the Fundamental Research Funds for the Central Universities.Han’s research was supported by the Fundamental Research Funds for the Central Universities(3072023GIP2401).
文摘In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
基金supported by the National Key R&D Program of China(Grant No.2021YFA1202902)the National Natural Science Foundation of China(Grant Nos.12374292 and 12074244)B.L.acknowledges support from the Development Scholarship for Outstanding Ph.D.of Shanghai Jiao Tong University.J.K.acknowledges support from the National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(Grant No.NRF-RS-2024-00454528).
文摘A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separation and power-law spectral density,the more interesting phenomena predicted in coupled Luttinger liquids of neighboring 1D conductors have been rarely observed due to the difficulty in creating such structures.Recently,we have successfully grown close-packed carbon nanotube(CNT)arrays with uniform chirality,providing an ideal material system for studying the coupled Luttinger liquids.Here,we report on the observation of tunable hyperbolic plasmons in the coupled Luttinger liquids of CNT arrays using scanning near-field optical microscopy.These hyperbolic plasmons,resulting from the conductivity anisotropy in the CNT array,exhibit strong spatial confinement,in situ tunability,and a wide spectral range.Despite their hyperbolic wavefronts,the plasmon propagation in the axial direction still adheres to the Luttinger-liquid theory.Our work not only demonstrates a fascinating phenomenon in coupled Luttinger liquids for fundamental physics exploration,but also provides a highly confined and in situ tunable hyperbolic plasmon in close-packed CNT arrays for future nanophotonic devices and circuits.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275179,12005079,and 41975100),the Shanghai Natural Science Foundation of China(Grant No.21ZR1443900),Natural Science Foundation of Jiangsu Province(Grant No.BK20220511),the funding for Scientific Research Startup of Jiangsu University(Grant No.4111710001),and the Joint Research Project for Meteorological Capacity Improvement(Grant No.22NLTSZ004).
文摘Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exploring homogeneous regions of temperature volatility and analyzing the driving factors.To investigate the regionalization of temperature volatility in China's mainland,a network constructed by the cosine similarity of temperature volatility series from China's mainland was embedded in hyperbolic space.Subsequently,we partitioned the network on the hyperbolic map using the critical gap method and then found eight regions in all.Ultimately,a network of communities was constructed while the interaction among communities was quantified.This yields a perspective of temperature volatility regionalization that can accurately reflect factors including altitude,climate type,and the geographic location of mountains.Further analysis demonstrates that the regionalization in the hyperbolic map is distinct from provinces and has a realistic basis:communities in southwest China show strong correlations due to the temperature sensitivity to altitude,and communities in northern China show a convergence in the area of Dingxi,Gansu,mainly owing to the strong temperature sensitivity to climate types.As a consequence,node distributions and community divisions in the hyperbolic map can offer new insights into the regionalization of temperature volatility in China's mainland.The results demonstrate the potential of hyperbolic embedding of complex networks in forecasting future node associations in real-world data.
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.
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 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.
文摘This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.
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.
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 by the Applied Basic Research Program of Liaoning Province,China(No.2023JH2/101300159)the National Natural Science Foundation of China(No.52275090).
文摘Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce the vibration of the RSSFS simultaneously.
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.
