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Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…
We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The…
Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance $r$ and a third body a distance $\rho$…
In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the…
We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient…
Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system…
Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame functions are applicable to diverse areas such as boundary value problems in ellipsoidal…
We develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in $\mathbb{R}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in…
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to…
Accurate state estimation for flexible robotic systems poses significant challenges, particularly for platforms with dynamically deforming structures that invalidate rigid-body assumptions. This paper addresses this problem and enables the…
We study the equilibrium of hyperelastic solids subjected to kinematic constraints on many small regions, which we call perforations. Such constraints on the displacement $u$ are given in the quite general form $u(x) \in F_x$, where $F_x$…
We investigate the mechanical properties of a layered material with interlayer friction. We propose a model that contains lateral elasticity and interlayer friction to obtain the response function both in the Fourier and real spaces. By…
A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion…
The problem of determining the thermomechanical characteristics of the system of closely spaced bodies considered by many authors. For scalar problems, such as problems of heat, electrostatic, etc., the localization effect was found (so…