共查询到19条相似文献,搜索用时 171 毫秒
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在引入非保守非惯性系的基础上对不可逆过程建立非保守系等效性假设,在引入广域度规的基础上对具有复杂行为的时空建立非保守系协变性假设;利用密度分布的不均匀度h(ρ)和粗粒熵S(ρtε)及推导的多标度因数η*计算式,引入非保守惯性质量和非保守引力质量.分析表明,新结果使引力理论与非平衡态统计理论和非线性动力学达到应有的谐和,发展并修正广义相对论.
关键词:
时空关系
耗散系统
不可逆性
可拓展广义相对论
非保守引力质量 相似文献
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本文讨论了无机材料科学中存在的自相似分形特性.在一定尺度范围内,许多材料具有统计的自相似分形几何,其静态几何性质可用分形几何的质量标度指数D──分形维数来描述.由分形几何造成对经典欧几里德几何表征动力学性质的偏离,可用指数Di──分形子维数来描述.D和Di是分形结构的两个重要参数,且Df≤D≤d. 相似文献
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为探讨分形基底结构对生长表面标度行为的影响, 本文采用Kinetic Monte Carlo(KMC)方法模拟了刻蚀模型(etching model)在谢尔宾斯基箭头和蟹状分形基底上刻蚀表面的动力学行为. 研究表明,在两种分形基底上的刻蚀模型都表现出很好的动力学标度行为, 并且满足Family-Vicsek标度规律. 虽然谢尔宾斯基箭头和蟹状分形基底的分形维数相同, 但模拟得到的标度指数却不同, 并且粗糙度指数 α与动力学指数z也不满足在欧几里得基底上成立的标度关系α+z=2. 由此可以看出, 标度指数不仅与基底的分形维数有关, 而且和分形基底的具体结构有关. 相似文献
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提出了一种方便、科学有效的利用气体吸附法测定二氧化硅干凝胶等多孔材料分形维数(表面分形维数和孔分布分形维数)的方法,不需要进行一系列的吸附/脱附实验,只需要利用单一气体的一次吸附/脱附实验得出的样品孔分布、比表面数据,与不同的标尺进行关联,即可同时获得表面分形维数和孔分布分形维数.通过误差分析和校正,保证了结果的可靠性.用上述方法测定了二氧化硅干凝胶的分形维数,以FHH法和SAXS法对所得结果进行了比较和验证,并对吸附/脱附过程所得结果的差异进行了初步分析.
关键词:
分形维数
气体吸附
二氧化硅
干凝胶 相似文献
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以6种具有典型特征的生成元构造了6个具有相同rms粗糙度的规则表面,用变分法计算了这些表面的分形维数,结果表明,分形维数可以将具有相同rms粗糙度的表面区分开来,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。
关键词:
粗糙度
分形维数
多重分形谱 相似文献
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一、分形理论的基本内容分形是对没有特征长度但有某种意义下的自相似性的形体和结构的总称。分形体系是具有无标度性的自相似结构。自相似结构可用分形维数来表示,这个维数可以是分数,或是一个连续变化的数。分形维数是描述分形的重要参数,有多种定义和计算方法。一般地,如把一个D维几何物体的尺寸放大L倍,就得到LD个原来的几何图像。令LD=K,则有D=lnKlnL上式可作为豪斯道夫维数的定义,并且能毫无困难地推广到非整数的范围。分形几何中的主要角色是由传统数学中的“病态”结构所扮演的,如科契曲线、谢尔品斯基海绵等,它们都具有严格的自相似结构,属于有规分形。 相似文献
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Yoshiharu Sato Kazuaki Sugawa Michiaki Kawaguchi 《Reports on Mathematical Physics》1979,16(1):111-119
The differential geometrical consideration of the parameter space, especially as a Riemannian geometry, was initiated by C.R. Rao in 1945. This approach appears to be important for the problem of estimation and test of hypotheses as well as for applications to physical problems. It has been shown that the parameter spaces of univariate normal distribution, univariate exponential distribution and multinomial distribution are Riemannian spaces of constant curvature. In the present paper the discussion is confined to the parameter space of the two-dimensional normal distribution. It has been shown that in general the parameter space is not necessarily of a constant curvature and that, if the correlation coefficient vanishes, the parameter space becomes an Einstein space. In addition, some invariant quantities, as sectional curvature, mean curvature and scalar curvature, have been calculated. 相似文献
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分别用狭义和广义相对论解出了爱因斯坦转盘上的热平衡流体系统内固有温度对柱坐标的依赖关系T0(ρ).结果表明,运动温度的收缩只与子系统的速度有关而与加速度无关.考虑到引力场中坐标温度的均恒性,爱因斯坦转盘与早期宇宙的时空对偶性直接给出宇宙介质固有温度反比于标度因子R(t)的结论.
关键词:
热平衡
弯曲时空
坐标温度
早期宇宙 相似文献
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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos. 相似文献
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《Journal of Geometry and Physics》2006,56(8):1294-1325
Given a geometry defined by the action of a Lie-group on a flat manifold, the Fels–Olver moving frame method yields a complete set of invariants, invariant differential operators, and the differential relations, or syzygies, they satisfy. We give a method that determines, from minimal data, the differential equations the frame must satisfy, in terms of the curvature and evolution invariants that are associated to curves in the given geometry. The syzygy between the curvature and evolution invariants is obtained as a zero curvature relation in the relevant Lie-algebra. An invariant motion of the curve is uniquely associated with a constraint specifying the evolution invariants as a function of the curvature invariants. The zero curvature relation and this constraint together determine the evolution of curvature invariants.Invariantizing the formal symmetry condition for curve evolutions yield a syzygy between different evolution invariants. We prove that the condition for two curvature evolutions to commute appears as a differential consequence of this syzygy. This implies that integrability of the curvature evolution lifts to integrability of the curve evolution, whenever the kernel of a particular differential operator is empty. We exhibit various examples to illustrate the theorem; the calculations involved in verifying the result are substantial. 相似文献
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Darlan A. Moreira Gilberto Corso 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(5):120
The Lucena network (LN) is the dual of a multifractal partition of the square. We analyzethe relation between the typical topologic distance l and the number ofvertices Nof the LN. The multifractal partition has one parameter ρ which controls thegeometrical asymmetry of the multifractal. In the limit of ρ → 1 the blocks of thepartition are squared, the connections amont the blocks are short range, the LN is moreregular and the relation l ∝ √N is observed. For the limit ρ → 0 the blocks arestrongly asymmetric, long range connections appear, and the topologic distance followsl ∝(log?N)α, a weak smallworld phenomenon. For any network size we calculate analytically the size of the minimumdistance lmin (ρ → 0) and the maximaldistance lmax (ρ → 1). The distance in theweak small world regime is calculated using the number of vertices inside a radius oflength land taking into account the network average connectivity and the exponent α. 相似文献
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Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated. 相似文献
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Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated. 相似文献