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11.
Risky asset models with the dependence through fractal activity time are described. The construction of the fractal activity time is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. The model features both tractable dependence structure and desired marginal distributions of the returns from the generalized hyperbolic class: the Variance Gamma and normal inverse Gaussian. These distributions provide good fit to real financial data. Pricing formulae for the proposed models are derived. 相似文献
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We compute the temperature profile near a laterally growing uniformly sheared viscous layer, a melt of the host material. A similarity variable is identified and an analytical solution is found for the temperature field and phase boundary trajectory for the case of uniform sliding. A numerical method for the iterative solution of this non-linear Stefan problem is implemented. In the case of a chemically reactive material with an Arrhenius dependence of the reaction rate on temperature we compute the ignition times. The dependence of the ignition time on the sliding velocity and latent heat of the material is determined numerically. 相似文献
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We investigate the long-time behavior of solutions to the classical mean-field model for coarsening by Lifshitz–Slyozov and Wagner (LSW). In the original work (Lifshitz and Slyozov, 1961; Wagner 1961) convergence of solutions to a uniquely determined self-similar solution was predicted. However, it is by now well known (Giron et al., 1998; Niethammer and Pego 1999 2001) that the long-time behavior of solutions depends sensitively on the initial data. In Niethammer and Pego (1999 2001) a necessary criterion for convergence to any self-similar solution which behaves like a finite power at the end of its (compact) support is given. It says that the data have to be regularly varying at the end of their support with the same power. This criterion is also shown to be sufficient if the power is sufficiently small and for data which are close to self-similar. In this article we extend the local stability result to the whole range of self-similar solutions with compact support. Our first main result establishes global stability of self-similar solutions with not too large power. The proof relies on a global contraction argument for the spreading of characteristics. In addition, we also establish upper and lower bounds for the coarsening rates of the system for a suitable class of initial data whose variation is bounded at the end of the support but not necessarily regular. 相似文献
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C. R. Tench T. M. Fromhold P. B. Wilkinson M. J. Carter R. P. Taylor A. P. Micolich R. Newbury 《Physica E: Low-dimensional Systems and Nanostructures》2000,7(3-4)
We report quantum-mechanical calculations which replicate the self-similar magnetoconductance fluctuations observed in recent experiments on semiconductor Sinai billiards. We interpret these fluctuations by considering the mixed stable-chaotic classical dynamics of electrons in the billiard. In particular, we show that the fluctuation patterns are dominated by individual stable orbits. The scaling characteristics of the self-similar fluctuations depend on the geometry of the associated stable orbit. We find that our analysis is insensitive to the details of the potential landscape, and is applicable to real devices with a wide range of soft-wall profiles. We show that our analysis also provides a possible explanation for the distinct series of magnetoconductance fluctuations observed in recent experiments on carbon nanotubes. 相似文献
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While a general consensus exists that the morphogenesis of living organisms has its roots in genetically encoded information, there is a big debate about the physical mechanisms that actually mediate its control. In embryo development, cells stop proliferating at homeostasis, a target state in terms of physical conditions that can represent, for instance, the shape and size of an organ. However, while control of mitosis is local, the spatial dimension of a tissue is a global information. How do single cells get aware of that at the same time? Which is their communication mechanism? While morphogen factors are demonstrated to play a key role in morphogenesis, and in particular for shape emergence, they seem unable to produce a global control on size by themselves and, conversely, many recent experiments suggest that active mechanics plays a role. Here we focus on a paradigmatic larval structure: the imaginal disc that will become the wing of the fruit fly. By a formalization of theoretical conjectures in terms of simple mathematical models, we show that inhomogeneous stress, likely dictated by morphogenetic patterns, is an admissible mechanism to convey locally the global information of organ size. 相似文献
16.
From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U∧c(t) = U0(t/t0)m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations. 相似文献
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We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity
that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance
of the local conductivity. Using perturbation expansions up to third order and fourth order in obtained from the moment equation approach, we construct the general functional dependence of the scalar hydraulic conductivity
in the regime where is of order 1 and larger than 1. Comparison with available numerical simulations show that the proposed method provides reasonable
improvements over available expansions. 相似文献
20.
Experiment on mechanical strength of porous trabecular bone shows power law dependence on the density of the structure. Physical structure and mechanical properties of the trabecular network are modelled here with a fractal lattice network of elastic springs having a strain based fracture criteria. An analysis of the model system supports the power law and shows that lacunarity is an important parameter in differentiating the mechanical strength of trabecular bones of same density. 相似文献