Related papers: The (small) vibrations of thin plates
The inclusion of the continuum in the study of weakly-bound three-body systems is discussed. A transformed harmonic oscillator basis is introduced to provide an appropriate discrete and finite basis for treating the continuum part of the…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
The three 3-brane system with both positive or negative tension is studied in a low energy regime by using gradient expansion method. The effective equations of motion on the brane is derived and in particular we examine, in the first…
[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes…
For a fluid of convex hard particles, characterized by a length scale $\sigma_\text{min}$ and an anisotropy parameter $\epsilon$, we develop a formalism allowing one to relate thermodynamic quantities to the body's shape. In a first step…
The purpose of this paper is to present a new mathematical model for the dynamics of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner-Mindlin plate theory, takes into account the…
The averaged resonant equations of motion for the planar circular restricted three-body problem are solved on the linearization basis taking into account also non-gravitational effects. The averaged resonant equations are derived from…
We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in…
The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…
A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…
It is demonstrated that the complex scaling method can be used in practical calculations to localize three-body resonances. Our model example emphasizes the fact that in three-body systems several essentially different asymptotic behaviors…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…
We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…
In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate…
I calculate the modes of vibration of membranes of arbitrary shape using a collocation approach based on Little Sinc Functions. The matrix representation of the PDE obtained using this method is explicit and it does not require the…
Viscoelastic microfluidic devices are promising for various microscale procedures such as particle sorting and separation. In this study, we perform three dimensional computational investigation of a particle in a viscoelastic channel flow…
The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic (EHD)…