2,567 research outputs found
How to be causal: time, spacetime, and spectra
I explain a simple definition of causality in widespread use, and indicate
how it links to the Kramers Kronig relations. The specification of causality in
terms of temporal differential eqations then shows us the way to write down
dynamical models so that their causal nature /in the sense used here/ should be
obvious to all. To extend existing treatments of causality that work only in
the frequency domain, I derive a reformulation of the long-standing Kramers
Kronig relations applicable not only to just temporal causality, but also to
spacetime "light-cone" causality based on signals carried by waves. I also
apply this causal reasoning to Maxwell's equations, which is an instructive
example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B,
cause classification/frames (not in EJP); v7 - unusual model case; v8 add
reference
Pulse-driven quantum dynamics beyond the impulsive regime
We review various unitary time-dependent perturbation theories and compare
them formally and numerically. We show that the Kolmogorov-Arnold-Moser
technique performs better owing to both the superexponential character of
correction terms and the possibility to optimize the accuracy of a given level
of approximation which is explored in details here. As an illustration, we
consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure
Open strings in relativistic ion traps
Electromagnetic plane waves provide examples of time-dependent open string
backgrounds free of corrections. The solvable case of open strings in
a quadrupolar wave front, analogous to pp-waves for closed strings, is
discussed. In light-cone gauge, it leads to non-conformal boundary conditions
similar to those induced by tachyon condensates. A maximum electric gradient is
found, at which macroscopic strings with vanishing tension are pair-produced --
a non-relativistic analogue of the Born-Infeld critical electric field. Kinetic
instabilities of quadrupolar electric fields are cured by standard atomic
physics techniques, and do not interfere with the former dynamic instability. A
new example of non-conformal open-closed duality is found. Propagation of open
strings in time-dependent wave fronts is discussed.Comment: 43 pages, 11 figures, Latex2e, JHEP3.cls style; v2: one-loop
amplitude corrected, open-closed duality proved, refs added, miscellaneous
improvements, see historical note in fil
Asymptotic Symmetries in the Gauge Fixing Approach and the BMS Group
These notes are an introduction to asymptotic symmetries in gauge theories,
with a focus on general relativity in four dimensions. We explain how to impose
consistent sets of boundary conditions in the gauge fixing approach and how to
derive the asymptotic symmetry parameters. The different procedures to obtain
the associated charges are presented. As an illustration of these general
concepts, the examples of four-dimensional general relativity in asymptotically
(locally) (A)dS and asymptotically flat spacetimes are covered. This
enables us to discuss the different extensions of the Bondi-Metzner-Sachs-van
der Burg (BMS) group and their relevance for holography, soft gravitons
theorems, memory effects, and black hole information paradox. These notes are
based on lectures given at the XV Modave Summer School in Mathematical Physics.Comment: 56 pages, 2 figures, published versio
Dynamic loads analysis system (DYLOFLEX) summary. Volume 1: Engineering formulation
The DYLOFLEX computer program system expands the aeroelastic cycle from that in the FLEXSTAB computer program system to include dynamic loads analyses involving active controls. Two aerodynamic options exist within DYLOFLEX. The analyst can formulate the problem with unsteady aerodynamics calculated using the doublet lattice method or with quasi-steady aerodynamics formulated from either FLEXSTAB or doublet lattice steady state aerodynamics with unsteady effects approximated by indicial lift growth functions. The equations of motion are formulated assuming straight and level flight and small motions. Loads are calculated using the force summation technique. DYLOFLEX consists of nine standalone programs which can be linked with each other by magnetic files used to transmit the required data between programs
Positive Solutions for a Second-Order p
The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u,  00 and μ>0 are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of λ>0 and μ>0. The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by Ding and Wang
Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations
Mathematical formulation of guidance equations and solutions for orbital space mission
On the Various Extensions of the BMS Group
The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry
group of radiating asymptotically flat spacetimes. It has recently received
renewed interest in the context of the flat holography and the infrared
structure of gravity. In this thesis, we investigate the consequences of
considering extensions of the BMS group in four dimensions with superrotations.
In particular, we apply the covariant phase space methods on a class of first
order gauge theories that includes the Cartan formulation of general relativity
and specify this analysis to gravity in asymptotically flat spacetime.
Furthermore, we renormalize the symplectic structure at null infinity to obtain
the generalized BMS charge algebra associated with smooth superrotations. We
then study the vacuum structure of the gravitational field, which allows us to
relate the so-called superboost transformations to the velocity kick/refraction
memory effect. Afterward, we propose a new set of boundary conditions in
asymptotically locally (A)dS spacetime that leads to a version of the BMS group
in the presence of a non-vanishing cosmological constant, called the
-BMS asymptotic symmetry group. Using the holographic renormalization
procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we
construct the phase space of -BMS and show that it reduces to the one
of the generalized BMS group in the flat limit.Comment: PhD Thesis, 204 pages, 2 figure
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