in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

Hinge-based Ankle Foot Orthosis (HAFO) is one of the most common non-surgical solutions for the foot drop. In conventional HAFOs, the ankle joint is almost locked, and plantar flexion is restricted due to the high stiffness of the hinge mechanism. This often leads to a rigid walking gate cycle, poor muscle activity, and muscle atrophy. Since the ankle torque-angle loop has a non-linear profile,...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

The feasibility of reconstructing total spring precipitation for the South Platte River basin from treering chronologies using artificial neural networks is explored. The use of artificial neural networks allows a comparison of reconstructions resulting from both linear and nonlinear models. Both types of models produced reconstructions that explained more than 40% of the variation in spring pr...

Time evolution of the probability density is investigated for initially quiescent dynamical systems exposed suddenly to random excitations. A variety of dynamical systems is considered, including the usual linear oscillator, and nonlinear oscillators of hardening spring, of softening spring, and of the van del Pol type. The random excitations are assumed to be stationary stochastic processes, s...

A horse's legs are compressed during the stance phase, storing and then returning elastic strain energy in spring-like muscle-tendon units. The arrangement of the muscle-tendon units around the lever-like joints means that as the leg shortens the muscle-tendon units are stretched. The forelimb anatomy means that the leg can be conceptually divided into two springs: the proximal spring, from the...

We model small deviations from linear mechanical behaviour of a loaded vertically suspended helical spring. A Taylor expansion of the elasticity equations governing the axial extension of the spring is used to determine the relative magnitudes of linear and (quadratic and cubic) nonlinear terms in the force–extension relationship. This relationship is the basis for the derivation of a model for...

Mass-spring systems are of special interest for soft tissue modeling in surgical simulation due to their ease of implementation and real-time behavior. However, the parameter identification (masses, spring constants, mesh topology) still remains a challenge. In previous work, we proposed an approach based on the training of mass-spring systems according to known reference models. Our initial fo...