We apply a nonlinear-nonlocal field theory for numerical calculation of quasistatic fracture. The model is given by regularized nonlinear pairwise potential in peridynamic formulation. function an explicit formula with first and second derivatives. This fact allows us to write the entries tangent stiffness matrix explicitly thereby saving computational costs during assembly matrix. validate our...

In this article we define a level set method for a scalar conservation law with a diffusive flux on an evolving hypersurface Γ (t) contained in a domain Ω ⊂ Rn+1. The partial differential equation is solved on all level set surfaces of a prescribed time dependent function Φ whose zero level set is Γ (t). The key idea lies in formulating an appropriate weak form of the conservation law with resp...

In this paper, I explore the exponential Rosenbrock-type method of order two. It is an explicit method that solves stiff ODEs. The method linearizes the equation with each step, then uses a matrix exponential to solve the linearized equation exactly. Previous research has identified stability bounds and convergence results. In this paper, I explore the stiffness capabilities of this second orde...

A formula is derived for stiffness of a polymer chain in terms of the distribution function of end-to-end vectors. This relationship is applied to calculate the stiffness of Gaussian chains (neutral and carrying electric charges at the ends), chains modeled as self-avoiding random walks, as well as semi-flexible (worm-like and Dirac) chains. The effects of persistence length and Bjerrum’s lengt...

Efficiency of numerical integration methods for a biologically detailed neuron model is examined. Because of the wide range of time constants, neuron equations are considered stiff. Stiffness is a property of a system in which the time step required to maintain stability for an explicit method is much smaller than the time step required to achieve a desired level of accuracy. Traditional explic...

K e y w o r d s O r d i n a r y differential equations, Initial value problems, Runge-Kut ta methods, Stiffness detection, Symbolic computation, Computer algebra systems, Computer generation of numerical methods. 1. I N T R O D U C T I O N A framework for explicit Runge-Kutta methods is being implemented as part of an ongoing overhaul of MATHEMATICA~S differential equation solver NDSolve. One o...

Previous work has shown that virtual fixtures applied to cooperative manipulation systems improve performance in tracking tasks. However, if a user wishes to move away from the nominal path, the stiffness of the virtual fixture should be adjusted to increase the level of user control. Our experiments show that modifying the stiffness of a soft virtual fixture can improve a user’s performance, m...

We derive an implicit-explicit (IMEX), realizability-preserving first-order scheme for moment models with Lipschitz-continuous source terms. In contrast to the fully-explicit schemes in [3, 42] the time step does not depend on the physical parameters, removing the stiffness from the system. Furthermore, a wider class of collision operators (e.g. the Laplace-Beltrami operator) can be used. The d...