Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Prediction of the equilibrium structures and photomagnetic properties of the Prussian blue analogue RbMn[Fe(CN)6] by density functional theory

A periodic density functional theory method using the B3LYP hybrid exchange-correlation potential is applied to the Prussian blue analogue RbMn[Fe(CN)6] to evaluate the suitability of the method for studying, and predicting, the photomagnetic behavior of Prussian blue analogues and related materials. The method allows correct description of the equilibrium structures of the different electronic configurations with regard to the cell parameters and bond distances. In agreement with the experimental data, the calculations have shown that the low-temperature phase (LT; Fe(2+)(t(6)2g, S = 0)-CN-Mn(3+)(t(3)2g e(1)g, S = 2)) is the stable phase at low temperature instead of the high-temperature phase (HT; Fe(3+)(t(5)2g, S = 1/2)-CN-Mn(2+)(t(3)2g e(2)g, S = 5/2)). Additionally, the method gives an estimation for the enthalpy difference (HT LT) with a value of 143 J mol(-1) K(-1). The comparison of our calculations with experimental data from the literature and from our calorimetric and X-ray photoelectron spectroscopy measurements on the Rb0.97Mn[Fe(CN)6]0.98 x 1.03 H2O compound is analyzed, and in general, a satisfactory agreement is obtained. The method also predicts the metastable nature of the electronic configuration of the high-temperature phase, a necessary condition to photoinduce that phase at low temperatures. It gives a photoactivation energy of 2.36 eV, which is in agreement with photoinduced demagnetization produced by a green laser.

Properties of seawater bitterns with regard to liquid-desiccant cooling

This study concerns the properties of the concentrated bittern solutions occurring as by-product from solar salt works, in relation to their potential use as liquid desiccants in cooling systems. Solutions of compositions similar to those of bitterns have been made up in the laboratory, as have concentrated mixtures of MgCl2–MgSO4–H2O. Measurements of vapour pressure have been carried out using an isoteniscope and are reported together with measurements of density and viscosity. Several theoretical models representing these properties are reviewed and compared against the experimental results; the average agreement between theory and experiment is within 5% for vapour pressure and better for the preferred models of the other two properties. Based on these findings, an expression is provided for the equilibrium relative humidity of bitterns as a function of concentration relative to raw seawater. The vapour pressures of bittern solutions are found to be similar to those of solutions containing only magnesium chloride but having the same mass fraction of total salts. Therefore magnesium chloride solution is a reasonable model for bitterns for the purpose of developing the proposed cooling system.

Using overlay test to evaluate fracture properties of field-aged asphalt concrete

Field material testing provides firsthand information on pavement conditions which are most helpful in evaluating performance and identifying preventive maintenance or overlay strategies. High variability of field asphalt concrete due to construction raises the demand for accuracy of the test. Accordingly, the objective of this study is to propose a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the overlay test (OT). The OT is selected because of its efficiency and feasibility for asphalt field cores with diverse dimensions. The fracture properties refer to the Paris’ law parameters based on the pseudo J-integral (A and n) because of the sound physical significance of the pseudo J-integral with respect to characterizing the cracking process. In order to determine A and n, a two-step OT protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. To ensure the accuracy of determined undamaged and fracture properties, a new analysis method is then developed for data processing, which combines the finite element simulations and mechanical analysis of viscoelastic force equilibrium and evolution of pseudo displacement work in the OT specimen. Finally, theoretical equations are derived to calculate A and n directly from the OT test data. The accuracy of the determined fracture properties is verified. The proposed methodology is applied to a total of 27 asphalt field cores obtained from a field project in Texas, including the control Hot Mix Asphalt (HMA) and two types of warm mix asphalt (WMA). The results demonstrate a high linear correlation between n and −log A for all the tested field cores. Investigations of the effect of field aging on the fracture properties confirm that n is a good indicator to quantify the cracking resistance of asphalt concrete. It is also indicated that summer climatic condition clearly accelerates the rate of aging. The impact of the WMA technologies on fracture properties of asphalt concrete is visualized by comparing the n-values. It shows that the Evotherm WMA technology slightly improves the cracking resistance, while the foaming WMA technology provides the comparable fracture properties with the HMA. After 15 months aging in the field, the cracking resistance does not exhibit significant difference between HMA and WMAs, which is confirmed by the observations of field distresses.

Improved methodology to evaluate fracture properties of warm-mix asphalt using overlay test

This study developed a reliable and repeatable methodology to evaluate the fracture properties of asphalt mixtures with an overlay test (OT). In the proposed methodology, first, a two-step OT protocol was used to characterize the undamaged and damaged behaviors of asphalt mixtures. Second, a new methodology combining the mechanical analysis of viscoelastic force equilibrium in the OT specimen and finite element simulations was used to determine the undamaged properties and crack growth function of asphalt mixtures. Third, a modified Paris's law replacing the stress intensity factor by the pseudo J-integral was employed to characterize the fracture behavior of asphalt mixtures. Theoretical equations were derived to calculate the parameters A and n (defined as the fracture properties) in the modified Paris's law. The study used a detailed example to calculate A and n from the OT data. The proposed methodology was successfully applied to evaluate the impact of warm-mix asphalt (WMA) technologies on fracture properties. The results of the tested specimens showed that Evotherm WMA technology slightly improved the cracking resistance of asphalt mixtures, while foaming WMA technology provided comparable fracture properties. In addition, the study found that A decreased with the increase in n in general. A linear relationship between 2log(A) and n was established.

Physicochemical properties of hydrogels for use in ophthalmology

This chapter deals with the physicochemical aspects of structure-property relationships in synthetic hydrogels, with particular reference to their application in optometry and ophthalmology. It demonstrates the ways in which the amount of water contained in the hydrogel network can be manipulated by changes in copolymer composition and illustrates the advantages and limitations imposed by use of water as a means of influencing surface, transport and mechanical properties of the gel. The chapter then illustrates how this basic understanding has formed a platform for the development of synthetic interpenetrating networks and macroporous materials, and of hybrids of natural and synthetic hydrogels. The behaviour of these more complex systems is not so centrally dominated by the equilibrium water content as is the case with homogeneous synthetic hydrogels, thus providing advantageous ways of extending the properties and applications of these interesting materials.