Search results for "Diffusion process"
showing 10 items of 44 documents
Calculation of small-angle neutron scattering by macromolecules in the semicrystalline state
1980
The conformation of macromolecules in the semicrystalline state has been studied by various authors with respect to the validity of the adjacent re-entry — or switchboard model by application of small-angle neutron scattering. Analytical as well as Monte-Carlo calculations show that the experimental results for melt crystallized polyethylene and isotactic polypropylene can be interpreted on the basis of the solidification model. In this model it is assumed that crystallization occurs by straightening of coil sequences without a long range diffusion process.
Dynamic self-assembly of photo-switchable nanoparticles
2012
Nanoparticles functionalized with photo-switchable ligands can be assembled into a broad range of structures by controlled light exposure. In particular, alternating light exposures provide the means to control formation of assemblies of various sizes and symmetries. Here, we use scaling arguments and Kinetic Monte Carlo simulations to study the evolution of reversible aggregates in a solution of periodically irradiated photo-switchable nanoparticles. Scaling estimates of the characteristic size and the mean separation of aggregates agree with the simulations. The transition probabilities in the Kinetic Monte Carlo scheme are derived from a renormalized master equation of the diffusion proc…
Modelling of electromagnetic heating and mixing conditions in glass melt output equipment
2011
PurposeThe purpose of this paper is to investigate the outlet of a special glass melting system, which is used to control melt flow and modify flow pattern.Design/methodology/approachNumerical calculations in ANSYS and ANSYS CFX were used to study electromagnetic, thermal, hydrodynamic and chemical mixing processes, results are validated by comparison with experimental data.FindingsObtained results show that investigated approach can improve glass melt chemical homogeneity significantly – Lorentz force driven melt movement in conjunction with diffusion process ensures good mixing quality.Research limitations/implicationsThe mixing in glass melt is present only in azimuthal direction (in cyl…
On first exit times and their means for Brownian bridges
2017
For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), \,\, h>0,$ behaves as $O(h^2)$ when $h \downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.
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…
Fractional Brownian motion and Martingale-differences
2004
Abstract We generalize a result of Sottinen (Finance Stochastics 5 (2001) 343) by proving an approximation theorem for the fractional Brownian motion, with H> 1 2 , using martingale-differences.
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…
On a set of data for the membrane potential in a neuron
2006
We consider a set of data where the membrane potential in a pyramidal neuron is measured almost continuously in time, under varying experimental conditions. We use nonparametric estimates for the diffusion coefficient and the drift in view to contribute to the discussion which type of diffusion process is suitable to model the membrane potential in a neuron (more exactly: in a particular type of neuron under particular experimental conditions).
Anomalous surface diffusion of protons on lipid membranes.
2014
AbstractThe cellular energy machinery depends on the presence and properties of protons at or in the vicinity of lipid membranes. To asses the energetics and mobility of a proton near a membrane, we simulated an excess proton near a solvated DMPC bilayer at 323 K, using a recently developed method to include the Grotthuss proton shuttling mechanism in classical molecular dynamics simulations. We obtained a proton surface affinity of −13.0 ± 0.5 kJ mol−1. The proton interacted strongly with both lipid headgroup and linker carbonyl oxygens. Furthermore, the surface diffusion of the proton was anomalous, with a subdiffusive regime over the first few nanoseconds, followed by a superdiffusive re…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …