Molecular dynamics study of deformation and fracture of Bi-segregated copper bicrystals

The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement (GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11 and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Pseudo-molecular dynamics study of grain boundary segregation

The segregation of bismuth atoms on the [101] tilt copper grain boundaries Σ3 ( ) 70.53°, Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° has been studied by pseudo-molecular dynamics using the empiricalN-body potentials. The relationship between bismuth segregation and grain boundary structure has been discussed in detail. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Resolvent Estimates and Maximal Regularity in Weighted L q -spaces of the Stokes Operator in an Infinite Cylinder

Let be an infinite cylinder of , n ≥ 3, with a bounded cross-section of C ^1,1-class. We study resolvent estimates and maximal regularity of the Stokes operator in for 1 < q, r < ∞ and for arbitrary Muckenhoupt weights ω ∈ A _r with respect to x′ ∈ Σ. The proofs use an operator-valued Fourier multiplier theorem and techniques of unconditional Schauder decompositions based on the -boundedness of the family of solution operators for a system in Σ parametrized by the phase variable of the one-dimensional partial Fourier transform. Supported by the Gottlieb Daimler- und Karl Benz-Stiftung, grant no. S025/02-10/03.     

Topological Semi-Conjugacies Between Adding Machines

Let K = (k ₁, k ₂, . . .) be a sequence of positive integers, and be a topological group with a metric and an additive operation given. The adding machine f _K is the addition-by-one map on Σ _K . Buescu and Stewart (Ergodic Theory Dynam Syst 15:271–290, 1995), Block and Keesling (Topology Appl 140:151–161, 2004) and Banks (Ergodic Theory Dynam Syst 17:505–529, 1997) obtained several equivalent conditions for which two adding machines are topologically conjugate, respectively. In this paper, we have a further discussion about semi-conjugate relationship between adding machines, and give some necessary and sufficient conditions for an adding machine to be semi-conjugate to another one. Moveover, we also prove that a transitive translation on a compact subgroup of Σ _K is isometrically conjugate to an adding machine. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

Vortices for a Rotating Toroidal Bose–Einstein Condensate

We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid torus of revolution in with starshaped cross-section. We show that for angular speeds ω_ε = O(|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the torus.     

Eigenvalue integral relation and stability condition for a mode

In this paper, we point out that for a static system the eigenvalue integral relation (iσ)²I+^iσΦ+Σ=0 derived from an eigenequation only gives the sufficiency of condition gZ>0 for the stability of a certain mode, but it can not provide the necessity to the condition in general. Three theorems presented in this paper show that under some conditions, Π>0 makes the mode stable, while Π<0 makes the mode unstable. The project supported by the National Natural Science Foundation of China.     

Surface selections and topological constraint evaluations for flow field analyses

The isolated singular points (nodes, saddles) of a continuous vector field (e.g., velocity, shear stress, pressure gradient, vorticity, etc.) that are overlaid on a given surface must be compatible with the Euler characteristic of that surface, X_surface. All surfaces can be fashioned from a sphere plus handles plus holes, and X_surface=2–holes–2handles=nodes–saddles. This establishes an a priori constraint for the nodes and saddles that can be tested against the observed vector field to determine whether the experimental (or computational) observations are compatible with the known constraint. Numerous examples, including a clarification of, and a correction to, published results are given.

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A Variational Approach to the Fredholm Alternative for the p-Laplacian near the First Eigenvalue

We are concerned with the existence of a weak solution to the degenerate quasi-linear Dirichlet boundary value problem

The generalized variational principles about blending energy form of non-linear elasticity

First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(E_ij) and complementary strain energy function Σc(S_ij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function Σch_k! and blending strain energy function Σh_k!. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity.     

Positive periodic solution of a neutral predator-prey system

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Properties of parallel — surfaces coordinate systems

Summary The paper is devoted to the study of the basic properties of the set of parallel-surfaces coordinate (p.s.c.) system previously introduced by the author for the most appropriate formulation of the differential form of the balance equations in fluid dynamic problems, where a «direction field» plays a fundamental role. This field is usually defined by the unit normal to a given surface S either known or unknown a-priori.To properly exploit the invariant properties enjoyed by both holonomic and anholonomic sets of basic vectors are introduced in E ₃ , the latter ones resting on the coordinate vectors of the variety V ₂ (0)=S. The corresponding tensor algebra and tensor calculus are based on an appropriate affine connection of E ₃ reducing to the metric connections for holonomic basis vectors. They are developed and suitably commented upon in the paper.

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Sommario Il presente lavoro deriva le proprietà fondamentali dell'insieme di sistemi di coordinate in cui una delle famiglie di superfici coordinate è la famiglia di superfici parallele ad una data superficie S, nota o meno a-priori. Tali sistemi di coordinate sono stati precedentemente introdotti dall'autore per la formulazione più appropriata delle equazioni differenziali del bilancio per problemi fluidodinamici in cui un «campo di direzioni», definito dal versore normale ad S, gioca un ruolo fondamentale.Per sfruttare nel modo più adeguato le proprietà di invarianza godute da, vengono introdotti in E ₃ sistemi di vettori base sia olonomici che anolonomici, questi ultimi basati sui vettori coordinati della varietà V ₂ (0)=S. L'algebra tensoriale corrispondente ed il calcolo tensoriale basato su una opportuna connessione affine di E ₃ riducentesi a quella metrica per sistemi olonomici, vengono sviluppati e commentati evidenziando i vantaggi offerti dall'insieme.

     

Iterative approximation with errors of fixed point for a class of nonlinear operator with a bounder range

Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X, define S: X → X by Sx =f−Tx+x, for all x ε X. Let {a_n} _n=0 ^∞ , {β_n} _n=0 ^∞ be two real sequences in (0, 1) satisfying:

A Note on the Existence of Solutions to the Oseen System in Lipschitz Domains

We study the boundary-value problem associated with the Oseen system in the exterior of m Lipschitz domains of an euclidean point space We show, among other things, that there are two positive constants and α depending on the Lipschitz character of Ω such that: (i) if the boundary datum a belongs to L^q(∂Ω), with q ∈ [2,+∞), then there exists a solution (u, p), with and u ∈ L^∞(Ω) if a ∈ L^∞(∂Ω), expressed by a simple layer potential plus a linear combination of regular explicit functions; as a consequence, u tends nontangentially to a almost everywhere on ∂Ω; (ii) if a ∈ W^1-1/q,q(∂Ω), with then ∇u, p ∈ L^q(Ω) and if a ∈ C^0,μ(∂Ω), with μ ∈ [0, α), then also, natural estimates holds.     

Molecular dynamics studies on the local disordering of Σ3 and Σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5°(Σ11), 129.5°(Σ11), 70.5°(Σ3) and 109.5°(Σ3) at various tempratures. The GB structures are found to start local disordering at about 0.5T _m (T _m is the melting point of aluminium) for 50.5°(Σ11), 0.32T _m for 129.5° (Σ11) and 0.38T _m for 70.5°(Σ3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5°(Σ3), this disordering has not been found even when temperature increases up to 0.9T _m . The project supported by the National Natural Science Foundation of China and Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Academia Sinica.     

The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities

Heat and mass transfer characteristics of the self-similar boundary layer flows induced by continuous surfaces stretched with rapidly decreasing power law velocities U_w x^m, m < –1 are considered for mixed convection flow. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, dimensionless injection/suction velocity f_w, and the mixed convection parameter = s Gr/Re² are studied. These parameters have great effects on velocity and temperature profiles, heat transfer coefficient, and skin friction coefficient at the moving surface. Results show that similarity solutions exist only when the condition n = 2m – 1 is satisfied. Critical values of , Nu/Re^0.5 and C_f Re^0.5 are obtained for predominate natural convection for different Prandtl numbers at m = –2, –6 and n = –5, and –13 respectively. Results also show that the effect of buoyancy is more significant for weak than for strong suction. Furthermore, critical Prandtl numbers where f_w profiles have minimums are obtained for m = –2 and –6. Finally, critical values of , C_f Re^0.5 are also obtained for predominate natural convection for both m = –2 and –6.     

Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis

Variable fluid property continuity, Navier–Stokes and energy equations are solved for roughness induced forced convective laminar-transitional flow in a micropipe. Influences of Reynolds number, heat flux and surface roughness, on the momentum-energy transport mechanisms and second-law of thermodynamics, are investigated for the ranges of Re = 1–2,000, Q = 5–100 W/m² and ε = 1–50 μm. Numerical investigations put forward that surface roughness accelerates transition with flatter velocity profiles and increased intermittency values (γ); such that a high roughness of ε = 50 μm resulted in transitional character at Re _tra = 450 with γ = 0.136. Normalized friction coefficient (C _f^*) values showed augmentation with Re, as the evaluated C _f^* are 1.006, 1.028 and 1.088 for Re = 100, 500 and 1,500, respectively, at ε = 1 μm, the corresponding values rise to C _f^* = 1.021, 1.116 and 1.350 at ε = 50 μm. Heat transfer rates are also recorded to rise with Re and ε; moreover the growing influence of ε on Nusselt number with Re is determined by the Nu _ε=50 μm/Nu _ε=1 μm ratios of 1.086, 1.168 and 1.259 at Re = 500, 1,000 and 1,500. Thermal volumetric entropy generation values decrease with Re and ε in heating; however the contrary is recorded for frictional volumetric entropy generation data, where the augmentations in are more considerable when compared with the decrease rates of      

Compact Molecule of Beryllium

The interaction potential for beryllium atoms is calculated using the Ritz variational method with molecular wave functions as trial functions. The results of calculations for Be₂ molecules in the ¹_g ⁺ state, which from the well–known data is considered ground, coincide with the results of previous studies. Similar calculations for the ³_u ⁺ state show that the minimum energy for this state is reached at horter internuclear distance and is lower than that for the ¹_g ⁺ state.     

Scalar Minimizers with Fractal Singular Sets

Lack of regularity of local minimizers for convex functionals with non-standard growth conditions is considered. It is shown that for every >0 there exists a function aC() such that the functional admits a local minimizer uW^1,p() whose set of non-Lebesgue points is a closed set with dim()>N–p–, and where 1<p<N<N+<q<+.     

Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space

This paper uses a variational approach to establish existence of solutions (σ _t , v _t ) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ ₀, σ _T are prescribed in , the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer of the action when the time interval [0,T] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σ _t in . When σ _t  = δ _y(t) is a Dirac mass, the Euler–Poisson system reduces to . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure Appl Math, to appear) as a Hamiltonian system. WG gratefully acknowledges the support provided by NSF grants DMS-02-00267, DMS-03-54729 and DMS-06-00791. TN gratefully acknowledges the postdoctoral support provided by NSF grants DMS-03- 54729 and the School of Mathematics. AT gratefully acknowledges the support provided by the School of Mathematics.     

The Semigeostrophic Equations Discretized in Reference and Dual Variables

We study the evolution of a system of n particles in . That system is a conservative system with a Hamiltonian of the form , where W ₂ is the Wasserstein distance and μ is a discrete measure concentrated on the set . Typically, μ(0) is a discrete measure approximating an initial L ^∞ density and can be chosen randomly. When d  =  1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that the limiting densities are absolutely continuous with respect to the Lebesgue measure. When converges to a measure concentrated on a special d–dimensional set, we obtain the Vlasov–Monge–Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov–Poisson system.