水力劈裂问题的态型近场动力学建模

将态型近场动力学理论引入水力劈裂问题的模拟。构建了能反映岩土类材料准脆性断裂特征的态型近场动力学本构模型,并在物质点间相互作用力模型中加入等效水压力项,以实现在新生裂纹面上跟踪施加水压力。同时,考虑裂纹面间的接触,引入物质点间的短程排斥力作用,并设计了相应的接触算法。通过自编程序将模型和算法应用于含初始裂纹、不含初始裂纹以及含坝基软弱结构面的混凝土重力坝在高水头作用下的水力劈裂过程模拟,并与扩展有限元等模拟结果对比,验证了本文模型和算法的可行性和准确性。     

Free (open) boundary condition: some experiences with viscous flow simulations

The free (or open) boundary condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, International Journal for Numerical Methods in Fluids, 1992; 14:587–608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been tested in several benchmark problems of viscous flow in fluid mechanics. The FEM is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal or non‐isothermal, steady‐state conditions, for Newtonian fluids. The effects of inertia, gravity, compressibility, pressure dependence of the viscosity, slip at the wall, and surface tension are all considered individually in the extrudate‐swell benchmark problem for a wide range of the relevant parameters. The present results extend previous ones regarding the applicability of the FBC and show cases where the FBC is inappropriate, namely in the extrudate‐swell problem with gravity or surface‐tension effects. Particular emphasis has been given to the pressure at the outflow, which is the most sensitive quantity of the computations. In all cases where FBC is appropriate, excellent agreement has been found in comparisons with results from very long domains. The formulation for Picard‐type iterations is given in some detail, and the differences with the Newton–Raphson formulation are highlighted regarding some computational aspects. Copyright © 2011 John Wiley & Sons, Ltd.     

重力匹配导航的影响模式分析

从重力场匹配导航的改进TERCOM算法入手,针对采样长度、采样间隔以及重力测量误差对匹配结果的影响进行了系统分析,并在此基础上利用海洋年度重力测量数据设计了准实时仿真试验,结果表明:(1)采样长度对匹配结果有重要的影响,采样长度与重力基准图的分辨率比值在10~20之间时,能够获得较好的匹配效果;(2)适当增加采样间隔可以在一定程度上提高匹配的整体精度,但增加了匹配失效的风险,实际应用中采样间隔以2~4 min为宜;(3)重力测量白噪声误差对匹配结果影响相对较大,过大的误差将不能得到有效匹配,水下重力测量误差最好能控制在2 mGal以内。     

Cosmological constant from quarks and torsion

We present a simple and natural way to derive the observed small, positive cosmological constant from the gravitational interaction of condensing fermions. In the Riemann‐Cartan spacetime, torsion gives rise to the axial–axial vector four‐fermion interaction term in the Dirac Lagrangian for spinor fields. We show that this nonlinear term acts like a cosmological constant if these fields have a nonzero vacuum expectation value. For quark fields in QCD, such a torsion‐induced cosmological constant is positive and its energy scale is only about 8 times larger than the observed value. Adding leptons to this picture could lower this scale to the observed value.     

Pseudoinstantons in Metric-Affine Field Theory

In abstract Yang–Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instanton is a spacetime whose connection is metric compatible and Riemann curvature irreducible (pseudoinstanton). We suggest a metric-affine action which is a natural generalization of the Yang–Mills action and for which pseudoinstantons are stationary points. We show that a spacetime with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum Einstein equation is a special case of our theory. We also find another pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the latter solution indicates the possibility of using it as a model for the neutrino.     

Neutrino Oscillations in Exotic Geometries and the Equivalence Principle Violation

Taking into account the violation of the equivalence principle, we analyze the propagation of neutrinos in the gravitational field generated by wormholes. The analysis is performed for massive and massless neutrinos. By using the constraints on the (negative) mass of wormholes, which is of the order of stellar-substellar masses, we determine constraints on f which characterizes the degree of violation of the equivalence principle.     

Equivalence Postulate and Quantum Origin of Gravitation

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation.     

Generalized Uncertainty Principle in a Simple Varying Speed of Light Model

In this paperwewill derive a generalized uncertainty principle (GUP) in a simple varying speed of light (VSL) model. First we will show that VSL is an immediate consequence of GUP. Then, within the framework of a simple VSL model, we will show that GUP can be expressed as a function of cosmological scale factor. This expression gives two main results: uncertainties in position and momentum are actually cosmological models dependent and these uncertainties depend on mass and momentum of the particle under consideration. The relationship between matter content of the Universe and the values of uncertainties in early stages of the evolution of the Universe will be discussed in a mini-superspace approach.