Related papers: Tensorial conservation law for nematic polymers
For every mapping of a perturbed spacetime onto a background and with any vector field $\xi$ we construct a conserved covariant vector density $I(\xi)$, which is the divergence of a covariant antisymmetric tensor density, a…
It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum…
An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves.…
The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with…
In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level…
Ionic electro-active polymer (Nafion for example) can be used as sensor or actuator. To this end, a thin film of the water-saturated material is sandwiched between two electrodes. Water saturation causes a quasi-complete dissociation of the…
The properties of the canonical symmetry of the nonlinear Schr\"odinger equation are investigated. The densities of the local conservation laws for this system are shown to change under the action of the canonical symmetry by total space…
Quantum electrodynamics (QED) deals with the relativistic interaction of bosonic gauge fields and fermionic charged particles. In QED, global conservation laws of angular momentum for light-matter interactions are well-known. However, local…
A significant effort in condensed matter physics is dedicated to the search for exotic arrangements of electric dipoles in crystals. Non-collinear dipolar arrangements mimicking magnetic spin textures, such as polar vortices and skyrmions,…
Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics.…
Relations between the kinematical tensors (the expansion, the shear, and the vorticity) and the polarization modes of gravitational waves are studied within the context of metric theories of gravity by considering freely falling test…
We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L 1 initial data, general self-adjoint pure jump L{\'e}vy operators, and locally Lipschitz nonlinearities of…
Living polymers composed of non-covalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can…
We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $ \frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u) $ as elements of the characteristic cohomology of the associated exterior differential…
Relaxor ferroelectrics exhibit exceptional dielectric and electromechanical properties, yet their microscopic origins remain elusive due to the interplay of hierarchical polar structures and chemical complexity. While models based on polar…
Wave interactions with magnetized particles underly many plasma heating and current drive technologies. Typically, these interactions are modeled by bounce-averaging the quasilinear Kennel-Engelmann diffusion tensor over the particle orbit.…
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
The various methods to derive Einstein conservation laws and the relevant definitions of energy-momentum tensor density for gravitational fields are studied in greater detail. It is shown that these methods are all equivalent. The study on…
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at…