An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are analyzed. An adaptive hybrid least squares batch filter based on linearization of the orbital equation and unscented transformation of the measurement equation is...

We derive the detailed balance condition as a solution to the Hamilton-Jacobi equation in the Hořava-Lifshitz gravity. This result leads us to propose the existence of the d-dimensional quantum field theory on the future boundary of the (d + 1)dimensional Hořava-Lifshitz gravity from the viewpoint of the holographic renormalization group. We also obtain a Ricci flow equation of the boundary the...

is derived for surface gravity waves with nearly-elliptic front, generalising the cylindrical KP equation for nearly-concentric waves. We discuss transformations between the derived equation and two existing versions of the KP equation, for nearly-plane and nearly-concentric waves. The transformations are used to construct important classes of exact solutions of the derived equation and corresp...

The evolution of scale-invariant gravity waves from the early universe is analyzed using an equation of state which smoothly interpolates between the radiation dominated era and the present matter dominated era. We find that for large wavenumbers the standard scale-invarant wavefunction for the gravity wave severely underestimates the actual size of the gravity wave. Moreover, there is a defini...

The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves. MSC: 35Q35, 35Q53, 3...

We derive an analytic solution for the capillary rise of liquids in a cylindrical tube or a porous medium in terms of height h as a function of time t. The implicit t(h) solution by Washburn is the basis for these calculations and the Lambert W function is used for its mathematical rearrangement. The original equation is derived out of the 1D momentum conservation equation and features viscous ...

We consider the gravity in the system consisting of the Bogomol’nyi-Prasad-Sommerfield (BPS) D3-brane embedded in the flat background geometry, produced by the solutions of the supergravity. The effective action for this system is represented by the sum of the Hilbert-Einstein and DBI actions. We derive the Wheeler-De Witt equation for this system and obtain analytical solutions in some special...

in many countries, leveling networks are established for height determination which is one of the most important topics in geodesy. in these networks, the sum of the leveled height differences between a and b will not be equal to the difference in the orthometric heights ha and hb. the reason is that the leveling increment ?n, as we henceforth denote it, is different from the corresponding incr...

The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions (2 ≃ d ≤ 4). It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbativelly ǫ-expanded calculations in 2 + ǫ gravity theory remains in d = 4. Hence it is possible that quantum gravity is an asymptotically safe theory ...