Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.

Experimental and Modelling Studies of the Thermodynamics and Kinetics of Phase and Structural Transformations in a Gamma TiAl-based Alloy

This work combines microscopy, synchrotron radiation X-ray diffraction, differential scanning calorimetry and thermodynamic calculations in the characterisation of phase transformation behaviour of a Ti–46Al–1.9Cr–3Nb alloy upon continuous heating at constant rates. It has been found that the Ti–46Al–1.9Cr–3Nb alloy after being forged at 1200 °C without further treatment has a duplex microstructure consisting of fine equiaxed and lamellar ? grains with a small amount of a2 plates and particles and about 1 wt.% B2 phase. Differential scanning calorimetry revealed reproducibly several thermal effects upon heating of the as-forged alloy. These thermal effects are related to the equilibration and homogenisation of the sample, change of phase ratios between a2, ? and B2 phases in particular the increase of B2 in respect to a2 and ?, and the following five phase transformations: a2 + ? + B2 a + ? + B2, a + ? + B2 a + ?, ? + a a, a a + ß, a + ß a + ß + L. The observation of these transformations by differential scanning calorimetry is largely in agreement with literature phase diagrams and thermodynamic calculations, though care is needed to consider the different alloy compositions. Kinetics of the ? + a a phase transformation in the Ti–46Al–1.9Cr–3Nb alloy has been quantitatively derived from the calorimetry data, giving phase compositions at any point during the transformation upon continuous heating.

Statistical modelling of cement slurries for self compacting SIFCON containing silica fume

This paper reports a study carried out to develop a self-compacting fibre reinforced concrete containing a high fibre content with slurry infiltrated fibre concrete (SIFCON). The SIFCON was developed with 10% of steel fibres which are infiltrated by self-compacting cement slurry without any vibration. Traditionally, the infiltration of the slurry into the layer of fibres is carried out under intensive vibration. A two-level fractional factorial design was used to optimise the properties of cement-based slurries with four independent variables, such as dosage of silica fume, dosage of superplasticiser, sand content, and water/cement ratio (W/C). Rheometer, mini-slump test, Lombardi plate cohesion meter, J-fibre penetration test, and induced bleeding were used to assess the behaviour of fresh cement slurries. The compressive strengths at 7 and 28 days were also measured. The statistical models are valid for slurries made with W/C of 0.40 to 0.50, 50 to 100% of sand by mass of cement, 5 to 10% of silica fume by mass of cement, and SP dosage of 0.6 to 1.2% by mass of cement. This model makes it possible to evaluate the effect of individual variables on measured parameters of fresh cement slurries. The proposed models offered useful information to understand trade-offs between mix variables and compare the responses obtained from various test methods in order to optimise self-compacting SIFCON.

Applications of statistical models in proportioning medium strength self-compacting concrete

Self-compacting concrete (SCC) is generally designed with a relatively higher content of finer, which includes cement, and dosage of superplasticizer than the conventional concrete. The design of the current SCC leads to high compressive strength, which is already used in special applications, where the high cost of materials can be tolerated. Using SCC, which eliminates the need for vibration, leads to increased speed of casting and thus reduces labour requirement, energy consumption, construction time, and cost of equipment. In order to obtain and gain maximum benefit from SCC it has to be used for wider applications. The cost of materials will be decreased by reducing the cement content and using a minimum amount of admixtures. This paper reviews statistical models obtained from a factorial design which was carried out to determine the influence of four key parameters on filling ability, passing ability, segregation and compressive strength. These parameters are important for the successful development of medium strength self-compacting concrete (MS-SCC). The parameters considered in the study were the contents of cement and pulverised fuel ash (PFA), water-to-powder ratio (W/P), and dosage of superplasticizer (SP). The responses of the derived statistical models are slump flow, fluidity loss, rheological parameters, Orimet time, V-funnel time, L-box, JRing combined to Orimet, JRing combined to cone, fresh segregation, and compressive strength at 7, 28 and 90 days. The models are valid for mixes made with 0.38 to 0.72 W/P ratio, 60 to 216 kg/m3 of cement content, 183 to 317 kg/m3 of PFA and 0 to 1% of SP, by mass of powder. The utility of such models to optimize concrete mixes to achieve good balance between filling ability, passing ability, segregation, compressive strength, and cost is discussed. Examples highlighting the usefulness of the models are presented using isoresponse surfaces to demonstrate single and coupled effects of mix parameters on slump flow, loss of fluidity, flow resistance, segregation, JRing combined to Orimet, and compressive strength at 7 and 28 days. Cost analysis is carried out to show trade-offs between cost of materials and specified consistency levels and compressive strength at 7 and 28 days that can be used to identify economic mixes. The paper establishes the usefulness of the mathematical models as a tool to facilitate the test protocol required to optimise medium strength SCC.

Dynamic Multivariate Statistical Process Control using Subspace Identification

This paper points out a serious flaw in dynamic multivariate statistical process control (MSPC). The principal component analysis of a linear time series model that is employed to capture auto- and cross-correlation in recorded data may produce a considerable number of variables to be analysed. To give a dynamic representation of the data (based on variable correlation) and circumvent the production of a large time-series structure, a linear state space model is used here instead. The paper demonstrates that incorporating a state space model, the number of variables to be analysed dynamically can be considerably reduced, compared to conventional dynamic MSPC techniques.

Statistical Monitoring of Dynamic Multivariate Processes: Part I: Modeling Auto- and Cross-Correlation

The work in this paper is of particular significance since it considers the problem of modelling cross- and auto-correlation in statistical process monitoring. The presence of both types of correlation can lead to fault insensitivity or false alarms, although in published literature to date, only autocorrelation has been broadly considered. The proposed method, which uses a Kalman innovation model, effectively removes both correlations. The paper (and Part 2 [2]) has emerged from work supported by EPSRC grant GR/S84354/01 and is of direct relevance to problems in several application areas including chemical, electrical, and mechanical process monitoring.

Statistical Monitoring of Dynamic Multivariate Processes: Part II: Identifying Fault Magnitude and Signature

This paper builds on work presented in the first paper, Part 1 [1] and is of equal significance. The paper proposes a novel compensation method to preserve the integrity of step-fault signatures prevalent in various processes that can be masked during the removal of both auto- and cross correlation. Using industrial data, the paper demonstrates the benefit of the proposed method, which is applicable to chemical, electrical, and mechanical process monitoring. This paper, (and Part 1 [1]), has led to further work supported by EPSRC grant GR/S84354/01 involving kernel PCA methods.

Non-ideal behaviour of a room temperature ionic liquid in an alkoxyethanol or poly ethers at T = (298.15 to 318.15) K

Non-ideal behaviour of 1-butyl-3-methylimidazolium hexafluorophosphate [bmim][PF6] in ethylene glycol monomethyl ether; CH3OCH2CH2OH (EGMME), ethylene glycol dimethyl ether; CH3OCH2CH2OCH3 (EGDME) and diethylene glycol dimethyl ether; CH3(OCH2CH2)2OCH3 (DEGDME) have been investigated over the whole composition range at T = (298.15 to 318.15) K. To gain insight into the mixing behaviour, results of density measurements were used to estimate excess molar volumes, image, apparent molar volumes, Vphi,i, partial molar volumes, image, excess partial molar volumes, image, and their limiting values at infinite dilution, image, image, and image, respectively. Volumetric results have been analyzed in the light of Prigogine–Flory–Patterson (PFP) statistical mechanical theory. Measurements of refractive indices n were also performed for all the binary mixtures over whole composition range at T = 298.15 K. Deviations in refractive indices ?phin and the deviation of molar refraction ?xR have been calculated from experimental data. Refractive indices results have been correlated with volumetric results and have been interpreted in terms of molecular interactions. Excess properties are fitted to the Redlich–Kister polynomial equation to obtain the binary coefficients and the standard errors.