14,425 research outputs found
Internal relaxation time in immersed particulate materials
We study the dynamics of the solid to liquid transition for a model material
made of elastic particles immersed in a viscous fluid. The interaction between
particle surfaces includes their viscous lubrication, a sharp repulsion when
they get closer than a tuned steric length and their elastic deflection induced
by those two forces. We use Soft Dynamics to simulate the dynamics of this
material when it experiences a step increase in the shear stress and a constant
normal stress. We observe a long creep phase before a substantial flow
eventually establishes. We find that the typical creep time relies on an
internal relaxation process, namely the separation of two particles driven by
the applied stress and resisted by the viscous friction. This mechanism should
be relevant for granular pastes, living cells, emulsions and wet foams
The dynamics of financial stability in complex networks
We address the problem of banking system resilience by applying
off-equilibrium statistical physics to a system of particles, representing the
economic agents, modelled according to the theoretical foundation of the
current banking regulation, the so called Merton-Vasicek model. Economic agents
are attracted to each other to exchange `economic energy', forming a network of
trades. When the capital level of one economic agent drops below a minimum, the
economic agent becomes insolvent. The insolvency of one single economic agent
affects the economic energy of all its neighbours which thus become susceptible
to insolvency, being able to trigger a chain of insolvencies (avalanche). We
show that the distribution of avalanche sizes follows a power-law whose
exponent depends on the minimum capital level. Furthermore, we present evidence
that under an increase in the minimum capital level, large crashes will be
avoided only if one assumes that agents will accept a drop in business levels,
while keeping their trading attitudes and policies unchanged. The alternative
assumption, that agents will try to restore their business levels, may lead to
the unexpected consequence that large crises occur with higher probability
A Bendixson-Dulac theorem for some piecewise systems
The Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. We apply it to three different Liénard piecewise differential systems ¨ x+f±(x)˙ x+x = 0. The first is linear, the second is rational and the last corresponds to a particular extension of the cubic van der Pol oscillator. In all cases, the systems present regions in the parameter space with no limit cycles and others having at most one
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