The vast majority of lattice Boltzmann algorithms produce a non-Galilean invariant viscous stress. This defect arises from the absence of a term in the third moment, the equilibrium heat flow tensor, proportional to the cube of the fluid velocity. This moment cannot be specified independently of the lower moments on the standard lattices such as D2Q9, D3Q15, D3Q19 or D3Q27. A partial correction...

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velociti...

We define and discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)dimensional gravity, the Galilean limit is not trivial. Depending on the topology of spacetime there are typically finitely many topological degrees of freedom as well as topological interactions of Aharonov-Bohm type between massive...

In the history of sciences, some apparently independent questions often have received the same answer. For example, the questions “What does make apples fall off trees?”, “What does make planets revolve around the Sun?”, “What does make matter hold together in a star?” all have received the same answer: “gravity”. When this happens, we can say that the concepts used in this answer structure a f...

In this paper, symmetry properties of the basic equations atmospheric motion are proposed. The results on symmetries show that invariant under space-time translation transformation, Galilean transformations and scaling transformations. Eight one-parameter subgroups eight group solutions demonstrated. Three types nontrivial similarity invariants With help perturbation method, we derive second-or...