Methods for calculating Available Transfer Capability (ATC) of the transmission systems may be grouped under Static and Dynamic methods. This paper presents a fast dynamic method for ATC calculations, which considers both Transient Stability Limits and Voltage Stability Limits as terminating criteria. A variation of Energy Function Method is used to determine the transient stability limit and t...

We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schrödinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this...

Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many other areas of physics such as nuclear and particle physics. The universal properties include a geometric spectrum of three-body bound states ...

The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp + pd configurations ...

We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates periodically in time. Coupling between the cavities leads to synchronization of the oscillations and classical correlations between the cavities. In the quantum lim...

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions referred to as limit-state functions of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces referred to as limit-state surfaces in the high-dimension...

We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit, that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our...

Path entanglement is a key resource for quantum metrology. Using path-entangled states, the standard quantum limit can be beaten, and the Heisenberg limit can be achieved. However, the preparation and detection of such states scales unfavourably with the number of photons. Here we introduce sequential path entanglement, in which photons are distributed across distinct time bins with arbitrary s...