24,194 research outputs found
Non-standard discretization of biological models
We consider certain types of discretization schemes for differential equations with quadratic nonlinearities, which were introduced by Kahan, and considered in a broader setting by Mickens. These methods have the property that they preserve important structural features of the original systems, such as the behaviour of solutions near to fixed points, and also, where appropriate (e.g. for certain mechanical systems), the property of being volume-preserving, or preserving a symplectic/Poisson structure. Here we focus on the application of Kahan's method to models of biological systems, in particular to reaction kinetics governed by the Law of Mass Action, and present a general approach to birational discretization, which is applied to population dynamics of Lotka-Volterra type
Investigating Biological Matter with Theoretical Nuclear Physics Methods
The internal dynamics of strongly interacting systems and that of
biomolecules such as proteins display several important analogies, despite the
huge difference in their characteristic energy and length scales. For example,
in all such systems, collective excitations, cooperative transitions and phase
transitions emerge as the result of the interplay of strong correlations with
quantum or thermal fluctuations. In view of such an observation, some
theoretical methods initially developed in the context of theoretical nuclear
physics have been adapted to investigate the dynamics of biomolecules. In this
talk, we review some of our recent studies performed along this direction. In
particular, we discuss how the path integral formulation of the molecular
dynamics allows to overcome some of the long-standing problems and limitations
which emerge when simulating the protein folding dynamics at the atomistic
level of detail.Comment: Prepared for the proceedings of the "XII Meeting on the Problems of
Theoretical Nuclear Physics" (Cortona11
A Regularized Boundary Element Formulation for Contactless SAR Evaluations within Homogeneous and Inhomogeneous Head Phantoms
This work presents a Boundary Element Method (BEM) formulation for
contactless electromagnetic field assessments. The new scheme is based on a
regularized BEM approach that requires the use of electric measurements only.
The regularization is obtained by leveraging on an extension of Calderon
techniques to rectangular systems leading to well-conditioned problems
independent of the discretization density. This enables the use of highly
discretized Huygens surfaces that can be consequently placed very near to the
radiating source. In addition, the new regularized scheme is hybridized with
both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers
accelerated with fast matrix-vector multiplication schemes. This allows for
rapid and effective dosimetric assessments and permits the use of inhomogeneous
and realistic head phantoms. Numerical results corroborate the theory and
confirms the practical effectiveness of all newly proposed formulations
Thermodynamics and Phase Transitions of Electrolytes on Lattices with Different Discretization Parameters
Lattice models are crucial for studying thermodynamic properties in many
physical, biological and chemical systems. We investigate Lattice Restricted
Primitive Model (LRPM) of electrolytes with different discretization parameters
in order to understand thermodynamics and the nature of phase transitions in
the systems with charged particles. A discretization parameter is defined as a
number of lattice sites that can be occupied by each particle, and it allows to
study the transition from the discrete picture to the continuum-space
description. Explicit analytic and numerical calculations are performed using
lattice Debye-H\"{u}ckel approach, which takes into account the formation of
dipoles, the dipole-ion interactions and correct lattice Coulomb potentials.
The gas-liquid phase separation is found at low densities of charged particles
for different types of lattices. The increase in the discretization parameter
lowers the critical temperature and the critical density, in agreement with
Monte Carlo computer simulations results. In the limit of infinitely large
discretization our results approach the predictions from the continuum model of
electrolytes. However, for the very fine discretization, where each particle
can only occupy one lattice site, the gas-liquid phase transitions are
suppressed by order-disorder phase transformations.Comment: Submitted to Molecular Physic
First-order phase transition of the tethered membrane model on spherical surfaces
We found that three types of tethered surface model undergo a first-order
phase transition between the smooth and the crumpled phase. The first and the
third are discrete models of Helfrich, Polyakov, and Kleinert, and the second
is that of Nambu and Goto. These are curvature models for biological membranes
including artificial vesicles. The results obtained in this paper indicate that
the first-order phase transition is universal in the sense that the order of
the transition is independent of discretization of the Hamiltonian for the
tethered surface model.Comment: 22 pages with 14 figure
- …