Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in eac...Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network,and apply the degree–degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.展开更多
Inspired by nature's self-similar designs,novel honeycomb-spiderweb based self-similar hybrid cellular structures are proposed here for efficient energy absorption in impact applications.The energy absorption is e...Inspired by nature's self-similar designs,novel honeycomb-spiderweb based self-similar hybrid cellular structures are proposed here for efficient energy absorption in impact applications.The energy absorption is enhanced by optimizing the geometry and topology for a given mass.The proposed hybrid cellular structure is arrived after a thorough analysis of topologically enhanced self-similar structures.The optimized cell designs are rigorously tested considering dynamic loads involving crush and high-velocity bullet impact.Furthermore,the influence of thickness,radial connectivity,and order of patterning at the unit cell level are also investigated.The maximum crushing efficiency attained is found to be more than 95%,which is significantly higher than most existing traditional designs.Later on,the first and second-order hierarchical self-similar unit cell designs developed during crush analysis are used to prepare the cores for sandwich structures.Impact tests are performed on the developed sandwich structures using the standard 9-mm parabellum.The influence of multistaging on impact resistance is also investigated by maintaining a constant total thickness and mass of the sandwich structure.Moreover,in order to avoid layer-wise weak zones and hence,attain a uniform out-of-plane impact strength,off-setting the designs in each stage is proposed.The sandwich structures with first and second-order self-similar hybrid cores are observed to withstand impact velocities as high as 170 m/s and 270 m/s,respectively.展开更多
We investigate the boundary effect of quark–gluon plasma(QGP)droplets and the self-similarity effect of hadrons on QGP–hadron phase transition.In intermediate-or low-energy collisions,when the transverse momentum is...We investigate the boundary effect of quark–gluon plasma(QGP)droplets and the self-similarity effect of hadrons on QGP–hadron phase transition.In intermediate-or low-energy collisions,when the transverse momentum is below quantum chromodynamics(QCD)scale,QGP cannot be produced.However,if the transverse momentum changes to a relatively large value,a smallscale QGP droplet is produced.The modified MIT bag model with the multiple reflection expansion method is employed to study the QGP droplet with the curved boundary effect.It is found that the energy density,entropy density and pressure of QGP with the influence are smaller than those without the influence.In the hadron phase,we propose the two-body fractal model(TBFM)to study the self-similarity structure,arising from resonance,quantum correlation and interaction effects.It is observed that the energy density,entropy density and pressure increase due to the self-similarity structure.We calculate the transverse momentum spectra of pions with the self-similarity structure influence,which show good agreement with experimental data.Considering both boundary effect and self-similarity structure influence,our model predicts an increase in the transition temperature compared to the scenarios without these two effects in the High Intensity heavy-ion Accelerator Facility(HIAF)energy region,2.2 GeV to approximately 4.5 GeV.展开更多
In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with ...In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.展开更多
This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=...This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.展开更多
In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption ...In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].展开更多
An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.
This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u t=div(u p-2u)-uq for 1<p<2 and q>in Rn× (0, ∞). It has ...This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u t=div(u p-2u)-uq for 1<p<2 and q>in Rn× (0, ∞). It has been proved that when 1<q<p-n/(n+1) there exists a unique self-similar very singular solution.展开更多
In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answ...Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.展开更多
In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle t...Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.展开更多
In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by ...In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.展开更多
With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction,...With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.展开更多
This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloc...This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.展开更多
We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-k...We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.展开更多
In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equat...In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.展开更多
A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension.It is proved that a random graph-directed self-similar set is regular a.e..
Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to ...The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61763009 and 72172025)。
文摘Research on the self-similarity of multilayer networks is scarce, when compared to the extensive research conducted on the dynamics of these networks. In this paper, we use entropy to determine the edge weights in each sub-network,and apply the degree–degree distance to unify the weight values of connecting edges between different sub-networks, and unify the edges with different meanings in the multilayer network numerically. At this time, the multilayer network is compressed into a single-layer network, also known as the aggregated network. Furthermore, the self-similarity of the multilayer network is represented by analyzing the self-similarity of the aggregate network. The study of self-similarity was conducted on two classical fractal networks and a real-world multilayer network. The results show that multilayer networks exhibit more pronounced self-similarity, and the intensity of self-similarity in multilayer networks can vary with the connection mode of sub-networks.
基金the Science and Engineering Research Board(SERB),Department of Science and Technology,India,for funding this research through grant number SRG/2019/001581。
文摘Inspired by nature's self-similar designs,novel honeycomb-spiderweb based self-similar hybrid cellular structures are proposed here for efficient energy absorption in impact applications.The energy absorption is enhanced by optimizing the geometry and topology for a given mass.The proposed hybrid cellular structure is arrived after a thorough analysis of topologically enhanced self-similar structures.The optimized cell designs are rigorously tested considering dynamic loads involving crush and high-velocity bullet impact.Furthermore,the influence of thickness,radial connectivity,and order of patterning at the unit cell level are also investigated.The maximum crushing efficiency attained is found to be more than 95%,which is significantly higher than most existing traditional designs.Later on,the first and second-order hierarchical self-similar unit cell designs developed during crush analysis are used to prepare the cores for sandwich structures.Impact tests are performed on the developed sandwich structures using the standard 9-mm parabellum.The influence of multistaging on impact resistance is also investigated by maintaining a constant total thickness and mass of the sandwich structure.Moreover,in order to avoid layer-wise weak zones and hence,attain a uniform out-of-plane impact strength,off-setting the designs in each stage is proposed.The sandwich structures with first and second-order self-similar hybrid cores are observed to withstand impact velocities as high as 170 m/s and 270 m/s,respectively.
基金supported by the National Natural Science Foundation of China under Grant No.12175031Guangdong Provincial Key Laboratory of Nuclear Science under Grant No.2019B121203010。
文摘We investigate the boundary effect of quark–gluon plasma(QGP)droplets and the self-similarity effect of hadrons on QGP–hadron phase transition.In intermediate-or low-energy collisions,when the transverse momentum is below quantum chromodynamics(QCD)scale,QGP cannot be produced.However,if the transverse momentum changes to a relatively large value,a smallscale QGP droplet is produced.The modified MIT bag model with the multiple reflection expansion method is employed to study the QGP droplet with the curved boundary effect.It is found that the energy density,entropy density and pressure of QGP with the influence are smaller than those without the influence.In the hadron phase,we propose the two-body fractal model(TBFM)to study the self-similarity structure,arising from resonance,quantum correlation and interaction effects.It is observed that the energy density,entropy density and pressure increase due to the self-similarity structure.We calculate the transverse momentum spectra of pions with the self-similarity structure influence,which show good agreement with experimental data.Considering both boundary effect and self-similarity structure influence,our model predicts an increase in the transition temperature compared to the scenarios without these two effects in the High Intensity heavy-ion Accelerator Facility(HIAF)energy region,2.2 GeV to approximately 4.5 GeV.
基金supported by the NSFC(12271178,12171166)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J2022)the TCL Young Scholar(2024-2027).
文摘In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.
文摘This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.
基金supported in part by The 973 key Program(2006CB805902)Knowledge Innovation Funds of CAS(KJCX3-SYW-S03),People’s Republic of China+1 种基金supported in part by the Zheng Ge Ru Foundation and Hong Kong RGC Earmarked Research Grantsa research grant from the Center on Nonlinear Studies, Northwest University
文摘In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].
基金Supported by Natural Science Foundation of Zhejiang Province of China under Grant Nos.Y604106 and Y606182the Special Foundation of "University Talent Indraught Engineering" of Guangdong Province of China under Grant No.GDU2009109the Key Academic Discipline Foundation of Guangdong Shaoguan University under Gant No.KZ2009001
文摘An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.
基金TheKeyProjectofChineseMinistryofEducation (No .10 40 90 ) .
文摘This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u t=div(u p-2u)-uq for 1<p<2 and q>in Rn× (0, ∞). It has been proved that when 1<q<p-n/(n+1) there exists a unique self-similar very singular solution.
文摘In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
基金Supported by the Provincial Natural Science Young Foundation of Jiangxi, China (No. 2008GQS0071)
文摘Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.
基金Supported in part by the Foundations of the National Natural Science Committee(No.10572154)Jiangxi Province Natural Science Committee(No.0611005)the Foundation of Education Ministry, Jiangxi Province(No.[2006]239), China
文摘In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
文摘Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.
基金Sponsored by the NSFC (10871003, 10701008, 10726064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
文摘In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.
基金Project supported by the National Natural Science Foundations of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers (Grant No. 2009RC01)the Scientific Research and Developed Fund of Zhejiang Agricultural and Forestry University,China (Grant No. 2009FK42)
文摘With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.
基金supported in part by a grant from China Scholarship Councilthe National Natural Science Foundation of China(11301006)the Anhui Provincial Natural Science Foundation(1408085MA01)
文摘This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.
文摘We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.
基金supported by NSF of China (11071266)partially supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Educationpartially supported by the found of Chongqing Normal University (13XLB006)
文摘In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.
文摘A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension.It is proved that a random graph-directed self-similar set is regular a.e..
基金the National Natural Science Foundation of China
文摘Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
基金supported by the National Natural Science Founda-tion of China(Grant Nos.12122214,12272382,12293000,12293003,and 12293004)the Youth Innovation Promotion Association CAS(Grant No.2022019)High-level Innovation Research Institute Program of Guangdong Province(Grant Nos.2020B0909010003 and GARA2022002000).
文摘The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.
