3,502 research outputs found
Exponential energy growth in adiabatically changing Hamiltonian Systems
Fermi acceleration is the process of energy transfer from massive objects in
slow motion to light objects that move fast. The model for such process is a
time-dependent Hamiltonian system. As the parameters of the system change with
time, the energy is no longer conserved, which makes the acceleration possible.
One of the main problems is how to generate a sustained and robust energy
growth. We show that the non-ergodicity of any chaotic Hamiltonian system must
universally lead to the exponential growth of energy at a slow periodic
variation of parameters. We build a model for this process in terms of a
Geometric Brownian Motion with a positive drift, and relate it to the entropy
increase
Fast Fermi Acceleration and Entropy Growth
Fermi acceleration is the process of energy transfer from massive objects in
slow motion to light objects that move fast. The model for such process is a
time-dependent Hamiltonian system. As the parameters of the system change with
time, the energy is no longer conserved, which makes the acceleration possible.
One of the main problems is how to generate a sustained and robust energy
growth. We show that the non-ergodicity of any chaotic Hamiltonian system must
universally lead to the exponential growth of energy at a slow periodic
variation of parameters. We build a model for this process in terms of a
Geometric Brownian Motion with a positive drift and relate it to the entropy
increase
Quantum States Allowing Minimum Uncertainty Product of angular position and momentum
We provide necessary and sufficient conditions for states to have an
arbitrarily small uncertainty product of the azimuthal angle and its
canonical moment . We illustrate our results with analytical examples
Explosive Synchronization is Discontinuous
Spontaneous explosive is an abrupt transition to collective behavior taking
place in heterogeneous networks when the frequencies of the nodes are
positively correlated to the node degree. This explosive transition was
conjectured to be discontinuous. Indeed, numerical investigations reveal a
hysteresis behavior associated with the transition. Here, we analyze explosive
synchronization in star graphs. We show that in the thermodynamic limit the
transition to (and out) collective behavior is indeed discontinuous. The
discontinuous nature of the transition is related to the nonlinear behavior of
the order parameter, which in the thermodynamic limit exhibits multiple fixed
points. Moreover, we unravel the hysteresis behavior in terms of the graph
parameters. Our numerical results show that finite size graphs are well
described by our predictions
Self-Synchronization in Duty-cycled Internet of Things (IoT) Applications
In recent years, the networks of low-power devices have gained popularity.
Typically these devices are wireless and interact to form large networks such
as the Machine to Machine (M2M) networks, Internet of Things (IoT), Wearable
Computing, and Wireless Sensor Networks. The collaboration among these devices
is a key to achieving the full potential of these networks. A major problem in
this field is to guarantee robust communication between elements while keeping
the whole network energy efficient. In this paper, we introduce an extended and
improved emergent broadcast slot (EBS) scheme, which facilitates collaboration
for robust communication and is energy efficient. In the EBS, nodes
communication unit remains in sleeping mode and are awake just to communicate.
The EBS scheme is fully decentralized, that is, nodes coordinate their wake-up
window in partially overlapped manner within each duty-cycle to avoid message
collisions. We show the theoretical convergence behavior of the scheme, which
is confirmed through real test-bed experimentation.Comment: 12 Pages, 11 Figures, Journa
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