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Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
In loop quantum gravity, partitioning graph introduces boundaries and entanglement between spin sub-networks, reflecting non-local degrees of freedom and correlation amongst spatial regions. This gives rise to the view of coarse-graining,…
In this paper, we explore classes of irrotational-fluid cosmological models in the context of f(R)-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f(R) gravitational Lagrangian. In particular,…
The similarity between Finsler and Riemann geometry is an intriguing starting point to extend general relativity. The lack of quadratic restriction over the line element (color) naturally generalize the Riemannian case and breaks the local…
The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical…
This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus on the spherical ambient space. The flows are designed to…
We propose a model to describe the quasistatic shearing of dry granular materials, which notably captures the differences in velocity profiles recently observed in 2 and 3-D Couette flow experiments. In our scheme, the steady-state flow is…
We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high resolution (10243) numerical simulations, we confirm the theory that the…
The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a…
In this letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and…
The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study the corresponding Cauchy problem with initial data of…
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse-graining extremely difficult. We here address this problem by…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…
In this contribution, we consider the equivalence between $f(R)$ gravity and scalar-tensor theories to study the evolution of scalar cosmological perturbations in the $1 + 3$ covariant formalism for the classes of shear-free cosmological…
We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by…
For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including…
The Vlasov equation is analyzed for coarse grained distributions resembling a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
This article provides non-trivial technical ingredients for the article "The quantitative hydrodynamic limit of the Kawasaki dynamics" by the same authors. In that work a quantitative version of the hydrodynamic limit is deduced using a…