126 research outputs found
Elastic properties of small-world spring networks
We construct small-world spring networks based on a one dimensional chain and
study its static and quasistatic behavior with respect to external forces.
Regular bonds and shortcuts are assigned linear springs of constant and
, respectively. In our models, shortcuts can only stand extensions less
than beyond which they are removed from the network. First we
consider the simple cases of a hierarchical small-world network and a complete
network. In the main part of this paper we study random small-world networks
(RSWN) in which each pair of nodes is connected by a shortcut with probability
. We obtain a scaling relation for the effective stiffness of RSWN when
. In this case the extension distribution of shortcuts is scale free with
the exponent -2. There is a strong positive correlation between the extension
of shortcuts and their betweenness. We find that the chemical end-to-end
distance (CEED) could change either abruptly or continuously with respect to
the external force. In the former case, the critical force is determined by the
average number of shortcuts emanating from a node. In the latter case, the
distribution of changes in CEED obeys power laws of the exponent with
.Comment: 16 pages, 14 figures, 1 table, published versio
Biased random satisfiability problems: From easy to hard instances
In this paper we study biased random K-SAT problems in which each logical
variable is negated with probability . This generalization provides us a
crossover from easy to hard problems and would help us in a better
understanding of the typical complexity of random K-SAT problems. The exact
solution of 1-SAT case is given. The critical point of K-SAT problems and
results of replica method are derived in the replica symmetry framework. It is
found that in this approximation for .
Solving numerically the survey propagation equations for K=3 we find that for
there is no replica symmetry breaking and still the SAT-UNSAT
transition is discontinuous.Comment: 17 pages, 8 figure
Biology helps to construct weighted scale free networks
In this work we study a simple evolutionary model of bipartite networks which
its evolution is based on the duplication of nodes. Using analytical results
along with numerical simulation of the model, we show that the above
evolutionary model results in weighted scale free networks. Indeed we find that
in the one mode picture we have weighted networks with scale free distributions
for interesting quantities like the weights, the degrees and the weighted
degrees of the nodes and the weights of the edges.Comment: 15 pages, 7 figures, Revte
Ising Model on Edge-Dual of Random Networks
We consider Ising model on edge-dual of uncorrelated random networks with
arbitrary degree distribution. These networks have a finite clustering in the
thermodynamic limit. High and low temperature expansions of Ising model on the
edge-dual of random networks are derived. A detailed comparison of the critical
behavior of Ising model on scale free random networks and their edge-dual is
presented.Comment: 23 pages, 4 figures, 1 tabl
Simplifying Random Satisfiability Problem by Removing Frustrating Interactions
How can we remove some interactions in a constraint satisfaction problem
(CSP) such that it still remains satisfiable? In this paper we study a modified
survey propagation algorithm that enables us to address this question for a
prototypical CSP, i.e. random K-satisfiability problem. The average number of
removed interactions is controlled by a tuning parameter in the algorithm. If
the original problem is satisfiable then we are able to construct satisfiable
subproblems ranging from the original one to a minimal one with minimum
possible number of interactions. The minimal satisfiable subproblems will
provide directly the solutions of the original problem.Comment: 21 pages, 16 figure
Spanning Trees in Random Satisfiability Problems
Working with tree graphs is always easier than with loopy ones and spanning
trees are the closest tree-like structures to a given graph. We find a
correspondence between the solutions of random K-satisfiability problem and
those of spanning trees in the associated factor graph. We introduce a modified
survey propagation algorithm which returns null edges of the factor graph and
helps us to find satisfiable spanning trees. This allows us to study
organization of satisfiable spanning trees in the space spanned by spanning
trees.Comment: 12 pages, 5 figures, published versio
A Modal Series Representation of Genesio Chaotic System
In this paper an analytic approach is devised to represent, and study the
behavior of, nonlinear dynamic chaotic Genesio system using general nonlinear
modal representation. In this approach, the original nonlinear ordinary
differential equations (ODEs) of model transforms to a sequence of linear time-
invariant ODEs. By solving the proposed linear ODEs sequence, the exact
solution of the original nonlinear problem is determined in terms of uniformly
convergent series. Also an efficient algorithm with low computational
complexity and high accuracy is presented to find the approximate solution.
Simulation results indicate the effectiveness of the proposed method.Comment: International Journal of Instrumentation and Control Systems (IJICS)
Vol.2, No.3, July 201
Intermittent exploration on a scale-free network
We study an intermittent random walk on a random network of scale-free degree
distribution. The walk is a combination of simple random walks of duration
and random long-range jumps. While the time the walker needs to cover all
the nodes increases with , the corresponding time for the edges displays a
non monotonic behavior with a minimum for some nontrivial value of . This
is a heterogeneity-induced effect that is not observed in homogeneous
small-world networks. The optimal increases with the degree of
assortativity in the network. Depending on the nature of degree correlations
and the elapsed time the walker finds an over/under-estimate of the degree
distribution exponent.Comment: 12 pages, 3 figures, 1 table, published versio
Basal complex: a smart wing component for automatic shape morphing
Insect wings are adaptive structures that automatically respond to flight forces, surpassing even cutting-edge engineering shape-morphing systems. A widely accepted but not yet explicitly tested hypothesis is that a 3D component in the wing’s proximal region, known as basal complex, determines the quality of wing shape changes in flight. Through our study, we validate this hypothesis, demonstrating that the basal complex plays a crucial role in both the quality and quantity of wing deformations. Systematic variations of geometric parameters of the basal complex in a set of numerical models suggest that the wings have undergone adaptations to reach maximum camber under loading. Inspired by the design of the basal complex, we develop a shape-morphing mechanism that can facilitate the shape change of morphing blades for wind turbines. This research enhances our understanding of insect wing biomechanics and provides insights for the development of simplified engineering shape-morphing systems
Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
We study the entropy landscape of solutions for the bicoloring problem in
random graphs, a representative difficult constraint satisfaction problem. Our
goal is to classify which type of clusters of solutions are addressed by
different algorithms. In the first part of the study we use the cavity method
to obtain the number of clusters with a given internal entropy and determine
the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT
transitions. In the second part of the paper we analyze different algorithms
and locate their behavior in the entropy landscape of the problem. For instance
we show that a smoothed version of a decimation strategy based on Belief
Propagation is able to find solutions belonging to sub-dominant clusters even
beyond the so called rigidity transition where the thermodynamically relevant
clusters become frozen. These non-equilibrium solutions belong to the most
probable unfrozen clusters.Comment: 38 pages, 10 figure
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