2,533 research outputs found
A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem
A computational procedure that allows the detection of a new type of
high-dimensional chaotic saddle in Hamiltonian systems with three degrees of
freedom is presented. The chaotic saddle is associated with a so-called
normally hyperbolic invariant manifold (NHIM). The procedure allows to compute
appropriate homoclinic orbits to the NHIM from which we can infer the existence
a chaotic saddle. NHIMs control the phase space transport across an equilibrium
point of saddle-centre-...-centre stability type, which is a fundamental
mechanism for chemical reactions, capture and escape, scattering, and, more
generally, ``transformation'' in many different areas of physics. Consequently,
the presented methods and results are of broad interest. The procedure is
illustrated for the spatial Hill's problem which is a well known model in
celestial mechanics and which gained much interest e.g. in the study of the
formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys
Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium
The paper deals with the problem of existence of a convergent "strong" normal
form in the neighbourhood of an equilibrium, for a finite dimensional system of
differential equations with analytic and time-dependent non-linear term. The
problem can be solved either under some non-resonance hypotheses on the
spectrum of the linear part or if the non-linear term is assumed to be (slowly)
decaying in time. This paper "completes" a pioneering work of Pustil'nikov in
which, despite under weaker non-resonance hypotheses, the nonlinearity is
required to be asymptotically autonomous. The result is obtained as a
consequence of the existence of a strong normal form for a suitable class of
real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page
Dynamical epidemic suppression using stochastic prediction and control
We consider the effects of noise on a model of epidemic outbreaks, where the
outbreaks appear. randomly. Using a constructive transition approach that
predicts large outbreaks, prior to their occurrence, we derive an adaptive
control. scheme that prevents large outbreaks from occurring. The theory
inapplicable to a wide range of stochastic processes with underlying
deterministic structure.Comment: 14 pages, 6 figure
Enhancing Pilot Training Through Virtual Reality: Recognizing and Mitigating Aviation Visual and Vestibular Illusions
Aviation illusions, arising from sensory misinterpretations, can lead to critical pilot errors. The study aims to evaluate VR training\u27s efficacy in recognizing and managing these illusions. Embry-Riddle Aeronautical University (ERAU) subject matter experts and the Extended Reality Lab developed the Virtual Reality Aviation Illusion Trainer (VRAIT) software program to provide users a complete VR experience and training on visual and vestibular illusions. This study investigated the effectiveness of integrating virtual reality (VR) technology in pilot training, focusing on the VRAIT motion-based visual and vestibular illusion training. Conducted with participants from Embry-Riddle Aeronautical University, the research assesses pre-training and post-training knowledge scores and self-efficacy. Motion-based VR training significantly improved knowledge and self-efficacy scores. Pre-training knowledge scores (M = 64.36, SD = 12.71) increase to post-training scores (M = 79.41, SD = 15.02), indicating significant knowledge enhancement (t(214) = -12.433, p \u3c .001). Similarly, pre-training self-efficacy scores (M = 5.50, SD = 2.01) significantly increased to post-training scores (M = 8.31, SD = 1.55), highlighting self-efficacy improvements (t(214) = -17.712, p \u3c .001). Participants experienced minimal simulator sickness, suggesting a well-tolerated training duration and sequence. Additionally, participants reported a high level of enjoyment and technological satisfaction with the training. The study contributes to VR training methodologies, emphasizing the potential of motion-based VR training to enhance aviation education. This research demonstrated that motion-based VR training effectively enhanced pilot knowledge and self-efficacy in recognizing and managing aviation illusions. The findings underscore VR\u27s potential in enhancing visual and vestibular illusion training outcomes
Isomerization dynamics of a buckled nanobeam
We analyze the dynamics of a model of a nanobeam under compression. The model
is a two mode truncation of the Euler-Bernoulli beam equation subject to
compressive stress. We consider parameter regimes where the first mode is
unstable and the second mode can be either stable or unstable, and the
remaining modes (neglected) are always stable. Material parameters used
correspond to silicon. The two mode model Hamiltonian is the sum of a
(diagonal) kinetic energy term and a potential energy term. The form of the
potential energy function suggests an analogy with isomerisation reactions in
chemistry. We therefore study the dynamics of the buckled beam using the
conceptual framework established for the theory of isomerisation reactions.
When the second mode is stable the potential energy surface has an index one
saddle and when the second mode is unstable the potential energy surface has an
index two saddle and two index one saddles. Symmetry of the system allows us to
construct a phase space dividing surface between the two "isomers" (buckled
states). The energy range is sufficiently wide that we can treat the effects of
the index one and index two saddles in a unified fashion. We have computed
reactive fluxes, mean gap times and reactant phase space volumes for three
stress values at several different energies. In all cases the phase space
volume swept out by isomerizing trajectories is considerably less than the
reactant density of states, proving that the dynamics is highly nonergodic. The
associated gap time distributions consist of one or more `pulses' of
trajectories. Computation of the reactive flux correlation function shows no
sign of a plateau region; rather, the flux exhibits oscillatory decay,
indicating that, for the 2-mode model in the physical regime considered, a rate
constant for isomerization does not exist.Comment: 42 pages, 6 figure
Direct transition to high-dimensional chaos through a global bifurcation
In the present work we report on a genuine route by which a high-dimensional
(with d>4) chaotic attractor is created directly, i.e., without a
low-dimensional chaotic attractor as an intermediate step. The high-dimensional
chaotic set is created in a heteroclinic global bifurcation that yields an
infinite number of unstable tori.The mechanism is illustrated using a system
constructed by coupling three Lorenz oscillators. So, the route presented here
can be considered a prototype for high-dimensional chaotic behavior just as the
Lorenz model is for low-dimensional chaos.Comment: 7 page
Internal displacement reactions in multicomponent oxides: Part II. Oxide solid solutions of wide composition range
As models of internal displacement reactions in oxide solid solutions, the following reactions were studied at 1273 K as a function of time: Fe + NixMg1-x)O = Ni + (FexMg1-x)O Fe + (Co0.5Mg0.5)O = Co + (Fe0.5Mg0.5)O In both reactions, Ni or Co in the starting oxide is displaced by Fe and the γ-(Ni-Fe) or (Co-Fe) alloy is precipitated. In the reaction zone, composition gradients develop in both product phases, viz., the oxide and the alloy precipitate. The Ni (or Co) concentration of the alloy precipitate increases towards the reaction front. In the product oxide, the "inert" Mg diffuses toward the reaction front along with the Fe, while the Ni (or Co) diffusion is in the opposite direction, towards the Fe/boundary. The shape of the composition profiles for Mg and Fe in the product oxide suggests that cross-coefficient terms in the generalized flux equations contribute significantly to the cation flux. The parabolic rate constants of reactions involving Fe/(NixMg1-x)O decrease by nearly four orders of magnitude when x decreases from 1 to 0.1
Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition
We re-examine the prototypical roaming reaction—hydrogen atom roaming in formaldehyde decomposition—from a phase space perspective. Specifically, we address the question “why do trajectories roam, rather than dissociate through the radical channel?” We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well
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