1. Ground Motion Models • describe ground motion caused by earthquakes given event and site related predictor variables • a popular model, based on physical principles, is the so-called stochastic model a • because of its complexity, a surrogate model is often used instead • usually a regression function is fitted through data generated by the stochastic model; the functional form is derived fr...

Higher order gradient continuum theories have often been proposed as models for solids that exhibit localization of deformation (in the form of shear bands) at sufficiently high levels of strain. These models incorporate a length scale for the localized deformation zone and are either postulated or justified from micromechanical considerations. Of interest here is the consistent derivation of s...

A new Reynolds stress anisotropy closure that includes nonlocal and nonequilibrium effects in turbulent flows has been obtained from a recently proposed nonlocal anisotropy formulation. This formulation is based on a new nonlocal derivation of the rapid pressurestrain correlation, which rigorously accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gra...

Acknowledging that what is currently defined as ‘pressure’ should not have reason to exist without the existence of a gravity field, the connection between thermodynamics and gravity can be easily made clear. Comprehensive thermo-gravitational equilibrium conditions may be defined without raising any doubt about the validity of the conventional thermodynamic and gravitational equilibrium condit...

We consider a family of sixth-order Boussinesq equations in one space dimension with an arbitrary nonlinearity. The equation was originally derived for one-dimensional lattice model considering higher order effects, and later it re-derived the context nonlinear nonlocal elasticity. In sense wave propagation solids, nonlinearity function is connected stress-strain relation physical model. Consid...

We show how a unified method, due to Webb and Infante, of tackling many nonlocal boundary value problems, can be applied to nonlocal versions of some recently studied higher order boundary value problems. In particular, we give some explicit examples and calculate the constants that are required by the theory.

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal similarities inherently existing in images by treating each patch of a color image as a 3D tensor consisting of not only horizontal and vertical but also spectral dimen...

Following a study of the existing algorithms for image-based homing, and their strengths and weaknesses, a new, adaptive controller was designed. The controller achieves homing through gradient descent of the RMS surface by modelling C. Elegans chemotaxis with a first-order function. The controller parameters were evolved in a simulated environment, and were then tested and evaluated both in si...

The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known about higher order elliptic equations in the general setting. In this paper we introduce new integral identities that allow to investigate the sol...

in this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. for this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. from the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...