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The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
We describe a method to address efficiently problems of two-phase flow in the regime of low particle Reynolds number and negligible Brownian motion. One of the phases is an incompressible continuous fluid and the other a discrete…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 2, we derive and analyse governing equations for rapidly…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\bf g}=\rho{\bf V}$, where $\rho,\: {\bf g}$ and ${\bf V}$ are the mass density, the momentum density and the local velocity field,…
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…
A new analytical approach to derive an approximate equation of state and the virial coefficients for simple fluids is presented. Starting from the usual expression of the partition function, we first perform a Fourier transformation, and…
In this paper we calculate the Bogoliubov coefficients and the energy density of the stochastic gravitational wave background for a universe that undergoes inflation followed by radiation domination and matter domination, using a formalism…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
We provide an alternative unified approach for proving the Pythagorean theorem (in dimension $2$ and higher), the law of sines and the law of cosines, based on the concept of shape derivative. The idea behind the proofs is very simple: we…
Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
Dynamics of collisionless plasma described by the Poisson-Vlasov equations is connected with the Hamiltonian motions of particles and their symmetries. The Poisson equation is obtained as a constraint arising from the gauge symmetries of…
We follow-up on our works devoted to homogenization theory for linear second-order elliptic equations with coefficients that are perturbations of periodic coefficients. We have first considered equations in divergence form in [6, 7, 8]. We…
We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the…
We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
The coefficients of different combinations of terms of the liquid drop model have been determined by a least square fitting procedure to the experimental atomic masses. The nuclear masses can also be reproduced using a Coulomb radius taking…