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Full-Text Articles in Physics
Universality Class Of Explosive Percolation In Barabási-Albert Networks, Habib E. Islam, M. K. Hassan
Universality Class Of Explosive Percolation In Barabási-Albert Networks, Habib E. Islam, M. K. Hassan
Physics Faculty Publications
In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point tc = 1 which is the maximum possible value of the relative link density t; Hence we cannot have access to the other phase like percolation in one dimension. However, for m > 1 we find that tc decreases with increasing m and the critical exponents ν, α, β and γ …
Unitary-Quantum-Lattice Algorithm For Two-Dimensional Quantum Turbulence, Bo Zhang, George Vahala, Linda L. Vahala, Min Soe
Unitary-Quantum-Lattice Algorithm For Two-Dimensional Quantum Turbulence, Bo Zhang, George Vahala, Linda L. Vahala, Min Soe
Electrical & Computer Engineering Faculty Publications
Quantum vortex structures and energy cascades are examined for two-dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice algorithm, is employed to simulate the Bose-Einstein condensate governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincare recurrence time. It is demonstrated that such short recurrence times are destroyed by stronger nonlinear interaction. The similar loss of Poincare recurrence is also seen in the 3D GP equation. Various initial conditions are considered in an attempt to discern if 2D QT exhibits inverse …
Poincare Recurrence And Spectral Cascades In Three-Dimensional Quantum Turbulence, George Vahala, Jeffrey Yepez, Linda L. Vahala, Min Soe, Bo Zhang, Sean Ziegeler
Poincare Recurrence And Spectral Cascades In Three-Dimensional Quantum Turbulence, George Vahala, Jeffrey Yepez, Linda L. Vahala, Min Soe, Bo Zhang, Sean Ziegeler
Electrical & Computer Engineering Faculty Publications
The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length2). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length3). The spectral results of J. Yepez et al. …
Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman
Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman
Mathematics & Statistics Faculty Publications
A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQn(x) = zn-1 exp[ -Hn(x)]Π dP(xj), where x = (x1,..., xn) ∈ Rn, where Hn is the Hamiltonian, zn is …