9,150 research outputs found
Nonlinear dynamics of microtubules - A new model
In the present paper we describe a model of nonlinear dynamics of
microtubules (MT) assuming a single longitudinal degree of freedom per tubulin
dimer. This is a longitudinal displacement of a dimer at a certain position
with respect to the neighbouring one. A nonlinear partial differential
equation, describing dimer`s dynamics within MT, is solved both analytically
and numerically. It is shown that such nonlinear model can lead to existence of
kink solitons moving along the MTs. Internal electrical field strength is
calculated using two procedures and a perfect agreement between the results is
demonstrated. This enabled estimation of total energy, kink velocity and kink
width. To simplify the calculation of the total energy we proved a useful
theorem.Comment: 14 pages, 4 figure
Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts
In this paper, we study the benefits of using polyharmonic splines and node
layouts with smoothly varying density for developing robust and efficient
radial basis function generated finite difference (RBF-FD) methods for pricing
of financial derivatives. We present a significantly improved RBF-FD scheme and
successfully apply it to two types of multidimensional partial differential
equations in finance: a two-asset European call basket option under the
Black--Scholes--Merton model, and a European call option under the Heston
model. We also show that the performance of the improved method is equally high
when it comes to pricing American options. By studying convergence,
computational performance, and conditioning of the discrete systems, we show
the superiority of the introduced approaches over previously used versions of
the RBF-FD method in financial applications
Quantum Mechanical Operator of Time
The self adjoint operator of time in non-relativistic quantum mechanics is
found within the approach where the ordinary Hamiltonian is not taken to be
conjugate to time. The operator version of the reexpressed Liouville equation
with the total Hamiltonian, consisting of the part that is a conventional
function of coordinate and momentum and the part that is conjugate to time, is
considered. The von Neumann equation with quantized time is found and discussed
from the point of view of exact time measurement.Comment: 9 page
Embedding technology to support the development of problem-solving skills in geotechnical design students
- ā¦