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11.
采用分子动力学模拟的方法研究了Cu50Ni50合金在不同冷却速度下的凝固过程,利用均方位移、径向分布函数和结构可视化等方法分析其微观结构.并对凝固模型进行拉伸模拟,通过应力应变曲线和直观结构变化分析其性能.研究表明:冷却速度对Cu50Ni50合金凝固形成的结构有较大影响,随着冷却速度的升高,凝固形成的结构中晶体含量减少,在较低的冷却速度下,如冷却1×1012K/s时,Cu50Ni50合金凝固形成晶体结构;在较高的冷却速度下,如1×1014K/s时,Cu50Ni50合金凝固形成非晶体结构,且非晶Cu50Ni50合金的抗拉性能要优于晶体Cu50Ni50合金. 相似文献
12.
13.
In this paper, the effect ofmaterial anisotropy on void nucleation and growth inincompressible nonlinearly elastic solids is examined. A bifurcation problem is considered for a solid sphere composed of an incompressible homogeneous nonlinearly elastic material which is transversely isotropic about the radial direction. Under a uniform radial tensile dead-load, a branch of radially symmetric configurations involving a traction-free internal cavity bifurcates from the undeformed configuration at sufficiently large loads. Closed form analytic solutions are obtained for a specific material model, which may be viewed as a generalization of the classic neo-Hookean model to anisotropic materials. In contrast to the situation for a neo-Hookean sphere, bifurcation here may occur locally either to the right (supercritical) or to the left (subcritical), depending on the degree of anisotropy. In the latter case, the cavity has finite radius on first appearance. Such a discontinuous change in stable equilibrium configurations is reminiscent of the snap-through buckling phenomenon of structural mechanics. Such dramatic cavitational instabilities were previously encountered by Antman and Negrón-Marrero [3] for anisotropiccompressible solids and by Horgan and Pence [17] forcomposite incompressible spheres. 相似文献
14.
A class of similarity solutions is obtained for radial motions of spherical and cylindrical bodies made of a certain type of compressible hyperelastic materials. The equations satisfied by the infinitesimal generators of the symmetry group of the unified governing first order field equations for spheres and cylinders are found. It is shown that these equations admit a special class of solutions which generate a five-parameter group of transformations. The form of the strain energy function corresponding to the resulting symmetry group is evaluated. The similarity variable is determined and ordinary differential equations satisfied by similarity solutions are obtained. Numerical solutions are given for a Ko material which falls into the class of admissible materials. 相似文献
15.
Darya Apushkinskaya Michael Bildhauer Martin Fuchs 《Journal of Mathematical Fluid Mechanics》2005,7(2):261-297
We consider the stationary flow of a generalized Newtonian fluid which is modelled by an anisotropic dissipative potential f. More precisely, we are looking for a solution
of the following system of nonlinear partial differential equations
Here
denotes the pressure, g is a system of volume forces, and the tensor T is the gradient of the potential f. Our main hypothesis imposed on f is the existence of exponents 1 < p q0 < such that
holds with constants , > 0. Under natural assumptions on p and q0 we prove the existence of a weak solution u to the problem (*), moreover we prove interior C1,-regularity of u in the two-dimensional case. If n = 3, then interior partial regularity is established. 相似文献
((*)) |
16.
Zachary Cline 《Journal of Pure and Applied Algebra》2019,223(8):3635-3664
Let q be an nth root of unity for and let be the Taft (Hopf) algebra of dimension . In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial -module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of . We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel . 相似文献
17.
For wide classes of locally convex spaces, in particular, for the space of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of ‐spaces have led us to introduce quasi‐ ‐spaces, a class of locally convex spaces containing ‐spaces that preserves subspaces, countable direct sums and countable products. Regular ‐spaces as well as their strong duals are quasi‐ ‐spaces. Hence the space of distributions provides a concrete example of a quasi‐ ‐space not being a ‐space. We show that has a fundamental bounded resolution if and only if is a quasi‐ ‐space if and only if the strong dual of is a quasi‐ ‐space if and only if X is countable. If X is metrizable, then is a quasi‐ ‐space if and only if X is a σ‐compact Polish space. 相似文献
18.
Alberto Cattaneo 《Mathematische Nachrichten》2019,292(10):2137-2152
We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for . 相似文献
19.
D.R. Baños F. Cordoni G. Di Nunno L. Di Persio E.E. Røse 《Journal of Differential Equations》2019,266(9):5772-5820
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate -type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation. 相似文献
20.
Lukas Katthän 《Journal of Pure and Applied Algebra》2019,223(3):1227-1245
Let be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution of . In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on . We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive.On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general.Finally, we show that it is enough to modify the last map of to ensure that it admits the structure of a DG algebra. 相似文献