Krylov subspace projection method and its application on oil reservoir simulation

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｐｒｏｂｌｅｍｓｏｆｅｎｇｉｎｅｅｒｉｎｇｉｎｔｅｒｅｓｔ,ｉｎｃｌｕｄｉｎｇｐｒｏｂｌｅｍｓｏｆｏｉｌｒｅｓｅｒｖｏｉｒｓｉｍｕｌａｔｉｏｎ,ｌｅａｄｔｏｔｈｅｔａｓｋｏｆｓｏｌｖｉｎｇａｓｙｓｔｅｍｏｆｌｉｎｅａｒｅｑｕａｔｉｏｎｓＡｘ=ｆ,(1)ｗｈｅｒｅＡｉｓａｎｎ×ｎ,ｒｅａｌ,ｌａｒｇｅｓｐａｒｓｅ,ｎｏｎ＿ＳＰＤｍａｔｒｉｘ.Ｔｈｅｄｉｒｅｃｔｄｅｃｏｍｐｏｓｉｔｉｏｎｍｅｔｈｏｄｉｓｍｏｓｔｅｆｆｉｃｉｅｎｔｓｏｌｖｅｒｗｈｅｎｎｉｓｓｍａｌｌ.Ｈｏｗｅｖｅｒ…     

Electromagnetic tomography (EMT): Theoretical analysis of the forward problem

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｍｉｄ＿1 980’ｓ,ａｔｏｍｏｇｒａｐｈｉｃｉｍａｇｉｎｇｔｅｃｈｎｉｑｕｅｓｕｉｔｅｄｔｏｉｎｄｕｓｔｒｉａｌｐｒｏｃｅｓｓｄｅｔｅｃｔｉｏｎ ,ＰｒｏｃｅｓｓＴｏｍｏｇｒａｐｈｙ[1],ｗａｓｒａｐｉｄｌｙｄｅｖｅｌｏｐｅｄｉｎｔｈｅＵＫ ,ＵＳＡ ,ｅｔｃ .ｗｉｔｈｓｕｃｃｅｓｓｆｕｌａｐｐｌｉｃａｔｉｏｎｓｏｆＣＴｔｅｃｈｎｉｑｕｅｔｏｍｅｄｉｃａｌｄｉａｇｎｏｓｉｓ .Ｉｎｐａｒｔｉｃｕｌａｒ,ａｓａｎｅｗｍｅｍｂｅｒｗｉｔｈｉｎｔｈｅｆａｍｉｌｙｏｆｔｈｅ…     

Linearized inverse scattering for elastic parameters in a half-space with reflection data

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｌｔｉｐａｒａｍｅｔｅｒｉｎｖｅｒｓｅｓｃａｔｔｅｒｉｎｇｆｏｒｅｌａｓｔｉｃｍｅｄｉｕｍｉｓａｆｏｕｎｄａｔｉｏｎａｌｐｒｏｂｌｅｍｉｎｓｅｉｓｍｏｌｏｇｙａｎｄｎｏｎｄｅｓｔｒｕｃｔｉｖｅｔｅｓｔｉｎｇ .ＷｉｔｈｉｎｔｈｅＢｏｒｎａｐｐｒｏｘｉｍａｔｉｏｎ ,ｔｈｉｓｐｒｏｂｌｅｍｈａｓｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｂｙｓｅｖｅｒａｌａｕｔｈｏｒｓ.Ｂｌａｃｋｌｅｄｇｅｅｔａｌ.[1]ｈａｖｅｅｘｔｅｎｄｅｄｔｈｅＸ＿ｒａｙｔｏｍｏｇｒａｐｈｙｓｃｈｅｍｅｔｏｔｈｅｄ…     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

An analytic and application to state space reconstruction about chaotic time series

The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.     

ON THE CRITICAL POINTS OF THE MAP Fp:X→‖AXB-C‖pp

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A^- such that (AA^-)^*=AA^- and B has a generalized inverse B^- such that (B^-B)^*=B^-B,the general characteristic forms for the critical points of the map F_p:X^→‖AXB-C‖_p^p(1p=2. Similarly, the same question has been discussed for several operators.     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

1　ＴｈｅＦｌｏｗＭｏｄｅｌｏｆＰｏｗｅｒ＿ＬａｗＦｌｕｉｄｉｎＲａｄｉｃａｌＦｒａｃｔａｌＲｅｓｅｒｖｏｉｒＴｈｅｔｒａｎｓｉｅｎｔｆｌｏｗｏｆｐｏｗｅｒ＿ｌａｗｆｌｕｉｄｉｎｒａｄｉｃａｌｆｒａｃｔａｌｒｅｓｅｒｖｏｉｒｉｓｓｔｕｄｉｅｄｉｎＲｅｆ.[1 ] ,ａｎｄａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｏｆＬａｐｌａｃｅｓｐａｃｅｉｓｄｅｒｉｖｅｄ .ＩｎＲｅｆ.[2 ] ,ｔｈｅｔｒａｎｓｉｅｎｔｅｌｌｉｐｔｉｃａｌｆｌｏｗｉｓｒｅｓｅａｒｃｈｅｄｏｎｍｏｄｅｌｏｆｅｘｐａｎｄｉｎｇｒｅｃｔａｎｇｌｅ .Ｔ…     

SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｓｙｍｐｔｏｔｉｃｅｘｐａｎｓｉｏｎｍａｔｃｈｅｄｍｅｔｈｏｄｗａｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆＰｌａｎｄｔｌ’ｓＢｏｕｎｄａｒｙＬａｙｅｒｓＴｈｅｏｒｙ[1- 3].Ｉｎ 1 960’ｓｌａｔｅｒ,ｔｈｅｖａｌｉｄｍａｔｃｈｅｄｐｒｉｎｃｉｐｌｅｓｗｅｒｅａｄｖａｎｃｅｄｂｙＶａｎＤｙｋｅａｎｄＫａｐｌｕｎ[4 ,5 ],ｒｅｓｐｅｃｔｉｖｅｌｙ .Ｂｕｔｔｈｅａｐｐｌｉｃａｂｌｅｒａｎｇｅｏｆｔｈｅｍｅｔｈｏｄｗａｓｒｅｓｔｒｉｃｔｅｄｂｙｔｈｅｄｉｆｆｉｃｕｌｔｙｔｈ…     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｔｈｅｓｐｅｃｉａｌｓｕｐｅｒｉｏｒｉｔｙｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓｔｅｃｈｎｏｌｏｇｙｉｎｖａｒｉｏｕｓｅｎｇｉｎｅｅｒｉｎｇｔｅｃｈｎｉｑｕｅｓｆｉｅｌｄｓ,ｓｕｃｈａｓｏｐｔｉｍｉｚａｔｉｏｎ ,ａｓｓｏｃｉａｔｉｖｅｍｅｍｏｒｉｅｓ,ｐａｔｔｅｒｎｒｅｃｏｇｎｉｔｉｏｎ ,ｓｉｇｎａｌｐｒｏｃｅｓｓｉｎｇａｎｄａｕｔｏｍａｔｉｃｃｏｎｔｒｏｌ,ｔｈｅｒｅｈａｓｂｅｅｎｉｎｃｒｅａｓｉｎｇｉｎｔｅｒｅｓｔｉｎｔｈｅｉｎｖｅｓｔｉｇａｔｉ…