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981.
The development of a compact fourth-order finite volume method for solutions of the Navier–Stokes equations on staggered grids is presented. A special attention is given to the conservation laws on momentum control volumes. A higher-order divergence-free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes. Three forms of the nonlinear correction for staggered grids are proposed and studied. The accuracy of each approximation is assessed comparatively in Fourier space. The importance of higher-order approximations of pressure is discussed and numerically demonstrated. Fourth-order accuracy of the complete scheme is illustrated by the doubly-periodic shear layer and the instability of plane-channel flow. The efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations. The proposed scheme is highly accurate and efficient. At the same level of accuracy, the fourth-order scheme can be ten times faster than the second-order counterpart. This gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost. 相似文献
982.
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated
in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not
possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require
symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory,
wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field
theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having
to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum
field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot
vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing
vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of
a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than
the natural scales of the theory.
Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation. 相似文献
983.
984.
Yingzhou Li Haizhao Yang Lexing Ying 《Applied and Computational Harmonic Analysis》2018,44(3):737-758
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of size with a product of sparse matrices, each of which contains nonzero entries. We also propose efficient algorithms for constructing this factorization when either (i) a fast algorithm for applying the kernel matrix and its adjoint is available or (ii) every entry of the kernel matrix can be evaluated in operations. For the kernel matrices of multidimensional Fourier integral operators, for which the complementary low-rank property is not satisfied due to a singularity at the origin, we extend this factorization by combining it with either a polar coordinate transformation or a multiscale decomposition of the integration domain to overcome the singularity. Numerical results are provided to demonstrate the efficiency of the proposed algorithms. 相似文献
985.
利用复合Nd:YAG实现600 mW高效紧凑型蓝光激光器 总被引:15,自引:7,他引:8
报道了采用复合Nd: YAG晶体, LBO腔内倍频, 简单的平凹谐振腔结构实现大功率LDA泵浦条件下高效率蓝光激光器. 利用大功率泵浦情况下晶体的热透镜效应实现最优模式匹配, 在可吸收泵浦功率为15.09W时, 激光器的473nm蓝光功率输出达600mW, 光-光转化效率达3.98%. 相似文献
986.
Let MC denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?C∈B(K,H)σr(MC) are, respectively, characterized completely, where σc(·) denotes the continuous spectrum, σp(·) denotes the point spectrum and σr(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given. 相似文献
987.
We present the method of proving the reconstructibility of graph classes based on the new type of decomposition of graphs — the operator decomposition. The properties of this decomposition are described. Using this decomposition we prove the following. Let P and Q be two hereditary graph classes such that P is closed with respect to the operation of join and Q is closed with respect to the operation of disjoint union. Let M be a module of graph G with associated partition (A,B,M), where A∼M and B⁄∼M, such that G[A]∈P, G[B]∈Q and G[M] is not (P,Q)-split. Then the graph G is reconstructible. 相似文献
988.
In this paper, it is shown that the Berezin-Toeplitz operator Tg is compact or in the Schatten class Sp of the Segal-Bargmann space for 1?p<∞ whenever (vanishes at infinity) or , respectively, for some s with , where is the heat transform of g on Cn. Moreover, we show that compactness of Tg implies that is in C0(Cn) for all and use this to show that, for g∈BMO1(Cn), we have is in C0(Cn) for some s>0 only if is in C0(Cn) for alls>0. This “backwards heat flow” result seems to be unknown for g∈BMO1 and even g∈L∞. Finally, we show that our compactness and vanishing “backwards heat flow” results hold in the context of the weighted Bergman space , where the “heat flow” is replaced by the Berezin transform Bα(g) on for α>−1. 相似文献
989.
It is proved that the Wiener algebra of functions on a connected compact abelian group whose Bohr-Fourier spectra are contained in a fixed subsemigroup of the (additive) dual group, is projective free. The semigroup is assumed to contain zero and have the property that it does not contain both a nonzero element and its opposite. The projective free property is proved also for the algebra of continuous functions with the same condition on their Bohr-Fourier spectra. As an application, the connected components of the set of factorable matrices are described. The proofs are based on a key result on homotopies of continuous maps on the maximal ideal spaces of the algebras under consideration. 相似文献
990.
Kenny De Commer 《Journal of Functional Analysis》2010,258(10):3362-1079
We provide a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes). This also gives examples of cocycle twists where the underlying C∗-algebra of the quantum group changes. 相似文献