Error estimates for the space-semidiscrete approximation of solutions of the wave equation in polygons G ⊂ R are presented. Based on corner asymptotics of solutions of the wave equation, it is shown that for continuous, simplicial Lagrangian Finite Elements of polynomial degree p ≥ 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of G, the...

The motion of inertial (i.e., finite-size) particles is analyzed in a three-dimensional unsteady simulation of Hurricane Isabel. As established recently, the long-term dynamics of inertial particles in a fluid is governed by a reduced-order inertial equation, obtained as a small perturbation of passive fluid advection on a globally attracting slow manifold in the phase space of particle motions...

The internal motions of DNA immersed in bio-fluid are investigated. The interactions between the fragments of DNA and the surrounding bio-fluid are modeled using the gauge fluid lagrangian. In the model, the bio-fluid is coupled to the standard gauge invariant bosonic lagrangian describing the DNA. It is shown that at non-relativistic limit various equation of motions, from the well-known Sine-...

In recent works of the author [Found. Phys. 36 (2006) 1701–1717; Math. Comput. Simul. 74 (2007) 93–103], the argument has een made that Hertz’s equations of electrodynamics reflect the material invariance (indifference) of the latter. Then the principle of aterial invariance was postulated in lieu of Lorentz covariance, and the respective absolute medium was named themetacontinuum. Here, we go ...

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi’s method by applying it to the same equation studied by Musielak et al. with their own method [Musielak ZE, Roy D and Swift LD. Method to derive Lagrangian and Hamiltonian for a nonlinear dynami...

For design optimization tasks, quite often a so-called one-shot approach is used. It augments the solution of the state equation with a suitable adjoint solver yielding approximate reduced derivatives that can be used in an optimization iteration to change the design. The coordination of these three iterative processes is well established when only the state equation is considered as equality c...

In a series of papers, we proved theorems characterizing the value function in exit time optimal control as the unique viscosity solution of the corresponding Bellman equation that satisfies appropriate side conditions. The results applied to problems which satisfy a positivity condition on the integral of the Lagrangian. This positive integral condition assigned a positive cost to remaining ou...

Using the Lagrangian formalism, with a simple trial function for dissipative optical two-dimensional 2D soliton beams, we show that there are two disjoint sets of stationary soliton solutions of the complex cubicquintic Ginzburg-Landau equation, with concave and convex phase profiles, respectively. These correspond to continuously self-focusing and continuously self-defocusing types of 2D solit...

The paper introduces the approach to construction of the Lagrangian of the field (fields). This approach is based solely on the metric function of the Finsler space: the Lagrangian is constructed as the unit divided by the volume swept by the unit vector running through all the points of the indicatrix in the tangent space under the assumption of the tangent space being Euclidean. For the space...

In this article an evaluation of two semi-analytical techniques is carried out, considering the quality and accuracy of these techniques in reproducing the ground-level concentration values of passive pollutant of the advection-diffusion equation by the Laplace transform technique. The second is a Lagrangian model based on solution of the Langevin equation through the Picard Iterative Method. T...