4,689 research outputs found
Loss of energy concentration in nonlinear evolution beam equations
Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we
introduce the notion of solutions with a prevailing mode for the nonlinear
evolution beam equation in bounded
space-time intervals. We give a new definition of instability for these
particular solutions, based on the loss of energy concentration on their
prevailing mode. We distinguish between two different forms of energy transfer,
one physiological (unavoidable and depending on the nonlinearity) and one due
to the insurgence of instability. We then prove a theoretical result allowing
to reduce the study of this kind of infinite-dimensional stability to that of a
finite-dimensional approximation. With this background, we study the occurrence
of instability for three different kinds of nonlinearities and for some
forcing terms , highlighting some of their structural properties and
performing some numerical simulations
Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
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