1,416 research outputs found
Exchange of stability as a function of system size in a nonequilibrium system
In equilibrium systems with short-ranged interactions, the relative stability
of different thermodynamic states generally does not depend on system size (as
long as this size is larger than the interaction range). Here, we use a large
deviations approach to show that, in contrast, different states can exchange
stability as system size is varied in a driven, bistable reaction-diffusion
system. This striking effect is related to a shift from a spatially uniform to
a nonuniform transition state and should generically be possible in a wide
range of nonequilibrium physical and biological systems.Comment: 7 pages, 4 figures. Supporting Material included in same file with
main tex
A linear domain decomposition method for partially saturated flow in porous media
The Richards equation is a nonlinear parabolic equation that is commonly used
for modelling saturated/unsaturated flow in porous media. We assume that the
medium occupies a bounded Lipschitz domain partitioned into two disjoint
subdomains separated by a fixed interface . This leads to two problems
defined on the subdomains which are coupled through conditions expressing flux
and pressure continuity at . After an Euler implicit discretisation of
the resulting nonlinear subproblems a linear iterative (-type) domain
decomposition scheme is proposed. The convergence of the scheme is proved
rigorously. In the last part we present numerical results that are in line with
the theoretical finding, in particular the unconditional convergence of the
scheme. We further compare the scheme to other approaches not making use of a
domain decomposition. Namely, we compare to a Newton and a Picard scheme. We
show that the proposed scheme is more stable than the Newton scheme while
remaining comparable in computational time, even if no parallelisation is being
adopted. Finally we present a parametric study that can be used to optimize the
proposed scheme.Comment: 34 pages, 13 figures, 7 table
Dissortative From the Outside, Assortative From the Inside: Social Structure and Behavior in the Industrial Trade Network
It is generally accepted that neighboring nodes in financial networks are
negatively assorted with respect to the correlation between their degrees. This
feature would play an important 'damping' role in the market during downturns
(periods of distress) since this connectivity pattern between firms lowers the
chances of auto-amplifying (the propagation of) distress. In this paper we
explore a trade-network of industrial firms where the nodes are suppliers or
buyers, and the links are those invoices that the suppliers send out to their
buyers and then go on to present to their bank for discounting. The network was
collected by a large Italian bank in 2007, from their intermediation of the
sales on credit made by their clients. The network also shows dissortative
behavior as seen in other studies on financial networks. However, when looking
at the credit rating of the firms, an important attribute internal to each
node, we find that firms that trade with one another share overwhelming
similarity. We know that much data is missing from our data set. However, we
can quantify the amount of missing data using information exposure, a variable
that connects social structure and behavior. This variable is a ratio of the
sales invoices that a supplier presents to their bank over their total sales.
Results reveal a non-trivial and robust relationship between the information
exposure and credit rating of a firm, indicating the influence of the neighbors
on a firm's rating. This methodology provides a new insight into how to
reconstruct a network suffering from incomplete information.Comment: 10 pages, 10 figures, To appear in conference proceedings of the
IEEE: HICSS-4
- …