We develop several formal analogies between the logistic equation and spatially homogeneous isotropic relativistic cosmology described by Einstein–Friedmann equations. These produce an effective Lagrangian Hamiltonian new symmetries for equation.

The interaction between large internal motion of DNA surrounded by bio-fluid is investigated. The phenomenon is modelled using the relativistic Navier-Stokes lagrangian describing the bio-fluid coupled to the standard Klein-Gordon lagrangian describing the DNA. It is shown that the equation of motion at non-relativistic limit, |~v| ≪ c, reproduces the well-known SineGordon equation. The effect ...

In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to th...

For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

We study the one-point probability distribution functions (PDFs) of the peculiar velocity and the density fluctuation in a cosmological fluid. Within the perturbative approach to the structure formation scenario, the effect of “pressure” has recently been an area of research interest. The velocity dispersion of the cosmological fluid creates effective “pressure” or viscosity terms. From this vi...

Fast response tracer flux measurements are compared against flux footprint predictions from both a Lagrangian stochastic simulation and an analytical solution to the equation of diffusion over a canopy of intermediate roughness. A turbulent tracer flux experiment was conducted over a peach orchard for a range of mildly unstable to very unstable conditions. For this purpose, a line source was us...

We consider the lagrangian L = F (R) in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein’s theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians and scale-invariant field equations. L is scale-invariant for F = c1R k+1 and a divergence for F = c2R. The field equation is scale-invariant not only for ...

Chemical bonding is a well understood quantum phenomena with the accuracy of Schrodinger based predictions determined by the computing power applied [1]. The hydrogen molecule ion, H2, is the most studied and theoretically understood molecule, with no unexplained observations. Thus, to understand how two deuterons could possibly fuse to He, a more fundamental approach than the Schrodinger equat...