This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines...This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines content and the percentage of fractured coarse aggregates were identified as direct indicators of the resilient modulus susceptibility to changes in water content.The results showed that the percentage of fractured coarse aggregates particles(FR)has a more significant impact on the resilient modulus(Er)of crushed granular materials used in pavement construction than the combined indicator of the fines content and sample volumetrics(nf).Crushed granular materials with a higher percentage of fractured coarse aggregates are relatively insensitive to changes in the degree of saturation,but become more sensitive as the fine fraction porosity decreases.An adjusted model was proposed based on the existing formulation,but considers a complex parameter to describe and adjust the sensitivity of base granular materials to variations in moisture content with respect to fabrication charac-teristics,fines content and volumetric properties.The model shows that the variation of Er values is below10%for fully crushed granular materials.However,it reaches approximately±12%for materials with 75%of crushed coarse aggregates andþ40%and-25%for materials with FR=50%.This model could help select good ag-gregates characteristics and adjust grain-size distribution for environments where significant moisture content variations can occur in the pavement system,such as in the Province of Quebec(Canada).As it is based on pa-rameters that can be easily determined or estimated,it also represents a valuable tool for detailed design and analysis that can consider material characteristics.展开更多
Based on the theory of pattern recognition, the concept of closeness degree between fuzzy sets is brought into the condition assessment of long span bridges. Using the fuzzy analytic hierarchy process （FAHP）, a math...Based on the theory of pattern recognition, the concept of closeness degree between fuzzy sets is brought into the condition assessment of long span bridges. Using the fuzzy analytic hierarchy process （FAHP）, a mathematical model of a multi-objective assessment of a long span suspension bridge is set up. An example is given to show the procedure in the synthetical condition assessment of the Runyang Suspension Bridge, which includes the hierarchical division, the definition of factor weights and fuzzy membership functions, and the calculation of closeness degrees, etc. The assessment combines both the data from the health monitoring system and the manual tests. The classification of evaluation items as well as the calculation of deterministic and nondeterministic items is presented. Compared with the traditional method of point rating, this method can better describe the discreteness of monitoring data and the fuzziness in the condition assessment.展开更多
In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri...In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.展开更多
In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary part...In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares （MLS） interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetra- tion through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-treatment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.展开更多
In this note,we show a sharp lower bound of min{Σ_(i=1)^(k)dG(u_(i)):u1u2...uk is a path of(2-)connected G}on its order such that(k-1)-iterated line graphs L^(k-1)(G)are hamiltonian.
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ...The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.展开更多
A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate th...A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix’s method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.展开更多
Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v...Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v∈V(G).In this paper,we prove that every graph G with n≥2(b+1)(a+b) vertices has all(a,b)-parity factors if δ(G)≥(b^(2)-b)/a,and for any two nonadjacent vertices u,v ∈V(G),max{d_(G)(u),d_(G)(v)}≥bn/a+b.Moreover,we show that this result is best possible in some sense.展开更多
An example is presented to introduce the concept of implicit continuity proposed as contrasted with the explicit continuity.A sufficient and necessary condition of the implicit continuity is given and proved in forms ...An example is presented to introduce the concept of implicit continuity proposed as contrasted with the explicit continuity.A sufficient and necessary condition of the implicit continuity is given and proved in forms of implicit system.This condition also offers the solution of initial values at the points where the dynamic system is discontinuous.Some discussions are contributed to the physical significance of implicit continuity.展开更多
文摘This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines content and the percentage of fractured coarse aggregates were identified as direct indicators of the resilient modulus susceptibility to changes in water content.The results showed that the percentage of fractured coarse aggregates particles(FR)has a more significant impact on the resilient modulus(Er)of crushed granular materials used in pavement construction than the combined indicator of the fines content and sample volumetrics(nf).Crushed granular materials with a higher percentage of fractured coarse aggregates are relatively insensitive to changes in the degree of saturation,but become more sensitive as the fine fraction porosity decreases.An adjusted model was proposed based on the existing formulation,but considers a complex parameter to describe and adjust the sensitivity of base granular materials to variations in moisture content with respect to fabrication charac-teristics,fines content and volumetric properties.The model shows that the variation of Er values is below10%for fully crushed granular materials.However,it reaches approximately±12%for materials with 75%of crushed coarse aggregates andþ40%and-25%for materials with FR=50%.This model could help select good ag-gregates characteristics and adjust grain-size distribution for environments where significant moisture content variations can occur in the pavement system,such as in the Province of Quebec(Canada).As it is based on pa-rameters that can be easily determined or estimated,it also represents a valuable tool for detailed design and analysis that can consider material characteristics.
基金The National Natural Science Foundation of China(No50608017,50538020)
文摘Based on the theory of pattern recognition, the concept of closeness degree between fuzzy sets is brought into the condition assessment of long span bridges. Using the fuzzy analytic hierarchy process （FAHP）, a mathematical model of a multi-objective assessment of a long span suspension bridge is set up. An example is given to show the procedure in the synthetical condition assessment of the Runyang Suspension Bridge, which includes the hierarchical division, the definition of factor weights and fuzzy membership functions, and the calculation of closeness degrees, etc. The assessment combines both the data from the health monitoring system and the manual tests. The classification of evaluation items as well as the calculation of deterministic and nondeterministic items is presented. Compared with the traditional method of point rating, this method can better describe the discreteness of monitoring data and the fuzziness in the condition assessment.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No. 41074100)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No. NCET-10-0812)
文摘In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
基金supported by the National Natural Science Foundation of China(51276192)
文摘In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares （MLS） interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetra- tion through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-treatment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.
基金Supported by the National Natural Science Foundation of China(11871099).
文摘In this note,we show a sharp lower bound of min{Σ_(i=1)^(k)dG(u_(i)):u1u2...uk is a path of(2-)connected G}on its order such that(k-1)-iterated line graphs L^(k-1)(G)are hamiltonian.
基金Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3)
文摘The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
文摘A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix’s method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.
基金supported by the National Natural Science Foundation of China (No.12271425 and No.11871391)。
文摘Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v∈V(G).In this paper,we prove that every graph G with n≥2(b+1)(a+b) vertices has all(a,b)-parity factors if δ(G)≥(b^(2)-b)/a,and for any two nonadjacent vertices u,v ∈V(G),max{d_(G)(u),d_(G)(v)}≥bn/a+b.Moreover,we show that this result is best possible in some sense.
文摘An example is presented to introduce the concept of implicit continuity proposed as contrasted with the explicit continuity.A sufficient and necessary condition of the implicit continuity is given and proved in forms of implicit system.This condition also offers the solution of initial values at the points where the dynamic system is discontinuous.Some discussions are contributed to the physical significance of implicit continuity.
