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When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all…
We studied numerically the dynamics of colliding rigid bodies in a Newtonian fluid. The finite element method is used to solve the fluid-body interaction and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian framework. To…
We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
We present a sampling-based approach to reasoning about the caging-based manipulation of rigid and a simplified class of deformable 3D objects subject to energy constraints. Towards this end, we propose the notion of soft fixtures extending…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
This work develops a curvature-based geometric formulation of the Euler-Poisson equations by lifting the dynamics to the 3-sphere S^3 equipped with the left-invariant metric induced by the inertia tensor. For the inertia ratio I = (2,2,1)…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
The coupled dynamics of low lying modes, including the scissors mode, and various giant quadrupole resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom.…
Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…
We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at…
In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R^3 using the separation method. These solutions partly complement Yuen's irrotational and elliptic solutions in R^3 [Commun. Nonlinear…
We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in…