We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gasliquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behaviour. The amplitude of the density modulations is the order parameter in our theory. The theory predicts that the phase transition from the uniform to the modulated fluid phase can be either first order or second order (continuous). The phase diagram exhibits two tricritical points, joined to one another by the line of second order transitions.
The φ 4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the Hierarchical Reference Theory (HRT) in its smooth cut-off formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cut-off implementation of HRT. The correct description of first and second order phase transitions within a microscopic, non-perturbative approach is thus achieved in the smooth cut-off HRT.
Bipartite and global entanglement are analyzed for the ground state of a system of N spin-1 / 2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter ␥, from a separable ͑␥ = ϱ͒ to a maximally entangled state ͑␥ =0͒. From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point ␥ = 0: While at ␥ = 0 the entanglement grows logarithmically with the system size with no upper bound, it saturates for ␥ 0 at a level only depending on ␥.
The temporal evolution of pixel values in Satellite Image Time Series (SITS) is considered criterion for the characterization, discrimination and identification of terrestrial objects and phenomena. Due to the exponential behavior of sequences number with specialization, Sequential Data Mining techniques need to be applied. The spatial aspect of the data was taken into account by the introduction of connectivity measures that characterize the pixels tendency to form objects. The conjunction of corresponding Connectivity Constraints (CC) with the Support Constraint (SC) leads to the extraction of Grouped Frequent Sequential Patterns (GFSP), a concept with proved capability for preliminary description and localization of terrestrial events. This work is focused on efficient SITS extraction of evolutions that fulfil SC and CC. Experiments performed on Bucharest urban interferometric SITS are used to illustrate the potential of the approach to find interesting evolution patterns.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.