10,264 research outputs found
Covariant Canonical Gauge theory of Gravitation resolves the Cosmological Constant Problem
The covariant canonical transformation theory applied to the relativistic
theory of classical matter fields in dynamic space-time yields a new (first
order) gauge field theory of gravitation. The emerging field equations embrace
a quadratic Riemann curvature term added to Einstein's linear equation. The
quadratic term facilitates a momentum field which generates a dynamic response
of space-time to its deformations relative to de Sitter geometry, and adds a
term proportional to the Planck mass squared to the cosmological constant. The
proportionality factor is given by a dimensionless parameter governing the
strength of the quadratic term. In consequence, Dark Energy emerges as a
balanced mix of three contributions, (A)dS curvature plus the residual vacuum
energy of space-time and matter. The Cosmological Constant Problem of the
Einstein-Hilbert theory is resolved as the curvature contribution relieves the
rigid relation between the cosmological constant and the vacuum energy density
of matter
Front speed enhancement by incompressible flows in three or higher dimensions
We study, in dimensions , the family of first integrals of an
incompressible flow: these are functions whose level surfaces are
tangent to the streamlines of the advective incompressible field. One main
motivation for this study comes from earlier results proving that the existence
of nontrivial first integrals of an incompressible flow is the main key
that leads to a "linear speed up" by a large advection of pulsating traveling
fronts solving a reaction-advection-diffusion equation in a periodic
heterogeneous framework. The family of first integrals is not well understood
in dimensions due to the randomness of the trajectories of and
this is in contrast with the case N=2. By looking at the domain of propagation
as a union of different components produced by the advective field, we provide
more information about first integrals and we give a class of incompressible
flows which exhibit `ergodic components' of positive Lebesgue measure (hence
are not shear flows) and which, under certain sharp geometric conditions, speed
up the KPP fronts linearly with respect to the large amplitude. In the proofs,
we establish a link between incompressibility, ergodicity, first integrals, and
the dimension to give a sharp condition about the asymptotic behavior of the
minimal KPP speed in terms the configuration of ergodic components.Comment: 34 pages, 3 figure
Real-time simulation of three-dimensional shoulder girdle and arm dynamics
Electrical stimulation is a promising technology for the restoration of arm function in paralyzed individuals. Control of the paralyzed arm under electrical stimulation, however, is a challenging problem that requires advanced controllers and command interfaces for the user. A real-time model describing the complex dynamics of the arm would allow user-in-the-loop type experiments where the command interface and controller could be assessed. Real-time models of the arm previously described have not included the ability to model the independently controlled scapula and clavicle, limiting their utility for clinical applications of this nature. The goal of this study therefore was to evaluate the performance and mechanical behavior of a real-time, dynamic model of the arm and shoulder girdle. The model comprises seven segments linked by eleven degrees of freedom and actuated by 138 muscle elements. Polynomials were generated to describe the muscle lines of action to reduce computation time, and an implicit, first-order Rosenbrock formulation of the equations of motion was used to increase simulation step-size. The model simulated flexion of the arm faster than real time, simulation time being 92% of actual movement time on standard desktop hardware. Modeled maximum isometric torque values agreed well with values from the literature, showing that the model simulates the moment-generating behavior of a real human arm. The speed of the model enables experiments where the user controls the virtual arm and receives visual feedback in real time. The ability to optimize potential solutions in simulation greatly reduces the burden on the user during development
Spectral gap of segments of periodic waveguides
We consider a periodic strip in the plane and the associated quantum
waveguide with Dirichlet boundary conditions. We analyse finite segments of the
waveguide consisting of periodicity cells, equipped with periodic boundary
conditions at the ``new'' boundaries. Our main result is that the distance
between the first and second eigenvalue of such a finite segment behaves like
.Comment: 3 page
Canonical Transformation Path to Gauge Theories of Gravity
In this paper, the generic part of the gauge theory of gravity is derived,
based merely on the action principle and on the general principle of
relativity. We apply the canonical transformation framework to formulate
geometrodynamics as a gauge theory. The starting point of our paper is
constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and
vector fields, which is supposed to be form-invariant under (global) Lorentz
transformations. Following the reasoning of gauge theories, the corresponding
locally form-invariant system is worked out by means of canonical
transformations. The canonical transformation approach ensures by construction
that the form of the action functional is maintained. We thus encounter amended
Hamiltonian systems which are form-invariant under arbitrary spacetime
transformations. This amended system complies with the general principle of
relativity and describes both, the dynamics of the given physical system's
fields and their coupling to those quantities which describe the dynamics of
the spacetime geometry. In this way, it is unambiguously determined how spin-0
and spin-1 fields couple to the dynamics of spacetime.
A term that describes the dynamics of the free gauge fields must finally be
added to the amended Hamiltonian, as common to all gauge theories, to allow for
a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is
outside of the scope of gauge theory as presented in this paper. It accounts
for the remaining indefiniteness of any gauge theory of gravity and must be
chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of
the gauge theory of gravity is shown to be at least quadratic in the conjugate
momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of
General Relativity.Comment: 16 page
Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model
We study a continuous matrix-valued Anderson-type model. Both leading
Lyapunov exponents of this model are proved to be positive and distinct for all
ernergies in except those in a discrete set, which leads to
absence of absolutely continuous spectrum in . This result is an
improvement of a previous result with Stolz. The methods, based upon a result
by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a
criterion by Goldsheid and Margulis, allow for singular Bernoulli
distributions
Preheating after N-flation
We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass
distribution, equal energy initial conditions at the beginning of inflation and
equal axion-matter couplings, where matter is taken to be a single, massless
bosonic field. By numerical analysis we find that preheating via parametric
resonance is suppressed, indicating that the old theory of perturbative
preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity
parameters and the scalar spectral index computed for N-flation are similar to
those in single field inflation (at least within an observationally viable
parameter region), our results suggest that the physics of preheating can
differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo
- …