Related papers: Kinematics of deformable media
We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…
A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…
This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold $\mathcal{M}$ under deformations. The second one is devoted to a similar study…
The kinematical quantities derived from the velocity field of a nongeodesic congruence are studied. We found the shear tensor components are finite in time but diverge at the event horizon of the spacetime located at $\rho = 0$. The surface…
We study the deformation and dewetting of liquid films under impinging gas jets using experimental, analytical and numerical techniques. We first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on…
An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The…
Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and…
In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial…
We present a new set of kinematic equations for front motion in bistable media. The equations extend earlier kinematic approaches by coupling the front curvature with the order parameter associated with a parity breaking front bifurcation.…
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport…