Related papers: Keep the Momentum: Conservation Laws beyond Euclid…
The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered…
For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two…
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…
The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring…
We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian Dynamics (MOND). We show that while there is a sense in which momentum is conserved, it is only if momentum is attributed to the gravitational…
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are…
We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to…
The angular momentum is conserved in fluids with a few exceptions such as ferrofluids. However it can be violated locally in fluid simulations to reduce computational costs. The effects of this violation are investigated using a…
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The…
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…