Search results for " diffusion"
showing 10 items of 521 documents
Can histographic analysis of apparent diffusion coefficient help discriminate between benign and malignant nodes in head and neck squamous cell carci…
2011
Objective: To investigate histographic analysis of apparent diffusion coefficient (ADC) measurements as discriminators of benign from malignant lymph nodes in patients with head and neck (H&N) squamous cell carcinoma (SCC) Materials and Methods: Seventeen patients with H&N SCC staged for nodal disease using anatomical MRI, contrast enhanced CT and ultrasound ± fine needle aspiration gave informed consent for additional MR diffusion weighted imaging (DWI). Axial DWI was performed by short tau inversion recovery (STIR) echo planar imaging and trace weighted images obtained b 0, 50, 100, 300, 600 and 1000. Image analysis was conducted using Jim 5.0. Nodal disease and contralateral benign nodal…
Technology standard diffusion and negative network externalities: a lesson from the third Browser War
2009
This paper presents a new model for technology standard diffusion that highlights the importance of negative network externalities in some fields of technology product such as web browsers. Again, as often happened in this research field, motivation and suggestion for such a research has been acquired from the evolution of the web browser war. So, in the paper, the main literature concerning standard diffusion has been reviewed in conjunction with web browser evolution, and the necessity of a new development of technology standard diffusion models is highlighted and supported by empirical evidences.
Jump-diffusion models of German stock returns
1991
This paper discusses the statistical properties of jump-diffusion processes and reports on parameter estimates for the DAX stock index and 48 German stocks with traded options. It is found that a Poisson-type jump-diffusion process can explain the high levels of kurtosis and skewness of observed return distributions of German stocks. Furthermore, we demonstrate that the return dynamics of the DAX include a statistically significant jump component except for a few sample subperiods. This finding is seen to be inconsistent with asset pricing models assuming that the jump component of the stock's return is unsystematic and diversifiable in the market portfolio.
On fractional diffusion and continuous time random walks
2003
Abstract A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.
Ergodicity for a stochastic Hodgkin–Huxley model driven by Ornstein–Uhlenbeck type input
2013
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by a variant of the classical Hodgkin-Huxley model. Using the existence of an accessible point where the weak Hoermander condition holds and the fact that the coefficients of the system are analytic, we show that the system is non-degenerate. The existence of a Lyapunov function allows to deduce the existence of (at most a finite number of) extremal invariant measures for the process. As a consequence, the complexity of the system is drastically reduced in c…
Graphical representation of some duality relations in stochastic population models
2007
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with logistic growth (cf. math/0509612). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.
Rare events and scaling properties in field-induced anomalous dynamics
2012
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long sp…
Phase transformation kinetics in d-dimensional grains-containing systems: diffusion-type model
1998
Abstract An analytical approach to the phase transformation in d-dimensional grains-containing complex systems is offered. It is based on considering the mechanism of surface material exchange among neighbouring grains as the so-called state-dependent diffusion process, where the diffusion function is related to the magnitude of the grain boundary. The approach proposed deals with the kinetics of that ensemble under circumstances of a volume increase of the new phase or microstructure. Probabilistic characteristics of the process are derived and analyzed. A comparison with 2D modelling of similar kind is presented for the 3D case, and some possible practical realizations of the situation un…
Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime
2016
The diffusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker-Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The effect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results.
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
2011
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set of invariant measures in the small-noise limit. The aim of this study is essentially to point out that this statement leads to the existence, as the noise intensity is small, of one unique…