48 citations · 102 across the 9 of their papers we have counts for
9 papers
On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
In this paper we consider formal asymptotic algorithms for a class of meso-scale approximations for problems of vibration of elastic membranes, which contain clusters of small iner…
Vibrations and elastic waves in chiral multi-structures
Michael Nieves, Giorgio Carta, Ian Jones +2
We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An impor…
Asymptotic analysis of solutions to transmission problems in solids with many inclusions
Michael Nieves
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is ch…
Eigenvalue problem in a solid with many inclusions: asymptotic analysis
V. G. Maz'ya, A. B. Movchan, M. J. Nieves
We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions…
Meso-scale models and approximate solutions for solids containing clouds of voids
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale appr…
Localisation for a line defect in an infinite square lattice
D. J. Colquitt, M. J. Nieves, I. S. Jones +2
Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green'…
Propagation of Slepyan's crack in a non-uniform elastic lattice
Michael Nieves, Alexander Movchan, Ian Jones +1
We model and derive the solution for the problem of a Mode I semi-infinite crack propagating in a discrete triangular lattice with bonds having a contrast in stiffness in the princ…
Green's kernels for transmission problems in bodies with small inclusions
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are pr…
Mesoscale asymptotic approximations to solutions of mixed boundary value problems in perforated domains
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
We describe a method of asymptotic approximations to solutions of mixed boundary value problems for the Laplacian in a three-dimensional domain with many perforations of arbitrary…