809 research outputs found
What makes slow samples slow in the Sherrington-Kirkpatrick model
Using results of a Monte Carlo simulation of the Sherrington-Kirkpatrick
model, we try to characterize the slow disorder samples, namely we analyze
visually the correlation between the relaxation time for a given disorder
sample with several observables of the system for the same disorder sample.
For temperatures below but not too low, fast samples (small relaxation
times) are clearly correlated with a small value of the largest eigenvalue of
the coupling matrix, a large value of the site averaged local field probability
distribution at the origin, or a small value of the squared overlap is more robust) . There is a strong correlation between the values of
the relaxation time for two distinct values of the temperature, but this
correlation decreases as the system size is increased. This may indicate the
onset of temperature chaos
Interconnection of port-Hamiltonian systems and composition of Dirac structures
Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results in another port-Hamiltonian system with Dirac structure defined by the composition of the Dirac structures of the subsystems. In this paper the composition of Dirac structures is being studied, both in power variables and in wave variables (scattering) representation. This latter case is shown to correspond to the Redheffer star product of unitary mappings. An equational representation of the composed Dirac structure is derived. Furthermore, the regularity of the composition is being studied. Necessary and sufficient conditions are given for the achievability of a Dirac structure arising from the standard feedback interconnection of a plant port-Hamiltonian system and a controller port-Hamiltonian system, and an explicit description of the class of achievable Casimir functions is derived
- …