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Cities are playing an increasingly important role in the development and growth of countries. A country's growth and prosperity is largely dependent on the efficient functioning of its cities. The reliance of countries on the ability of their cities to perform crucial central functions, for national growth, continues to rise. South Africa has a long-standing network of cities, towns and localities. These have developed and become hierarchised over the course of history during which population settlements and their distribution have been influenced by colonisation, segregation, industrialisation and globalisation. Since 1911, South Africa has undergone an extended phase of intense urban growth, with areas such as Johannesburg, Cape Town and eThekwini (Durban) agglomerating into dominating economic spaces. There are, however, no universally accepted, distinct criteria that constitute the general characteristics of secondary cities. The common assumption is that secondary cities are those cities that find themselves below the apex of what are considered primary cities. Furthermore, internationally, secondary cities appear to be considered as important catalysts for balanced and dispersed economic growth. In the South African context, the notion of what constitutes secondary cities is to a large extent underdeveloped. The aim of the paper is to appraise interconnected regional networks as a differentiated and novel outlook when determining secondary cities in South Africa. What is evident from the paper is that there are different potential alternatives with which to portray secondary cities.

Gauge symmetry of some models is investigated through Lagrangian formulation in the velocity phase space. It is found that the Lagrangian formulation is a useful instrument to verify whether a given model has gauge symmetry or not. It can derive the complete set of gauge transformation generators of a Lagrangian. The prescription based on Lagrangian formulation has ability to show a direction towards the extension of phase space introducing auxiliary fields to restore the gauge symmetry. It has been found that this prescription works well in the usual phase space as well as extended phase space.

Hydrothermal processes in impact environments on water-rich bodies such as Mars and Earth are relevant to the origins of life. Dawn mapping of dwarf planet (1) Ceres has identified similar deposits within Occator crater. Here we show using Dawn high-resolution stereo imaging and topography that Ceres’ unique composition has resulted in widespread mantling by solidified water- and salt-rich mud-like impact melts with scattered endogenic pits, troughs, and bright mounds indicative of outgassing of volatiles and periglacial-style activity during solidification. These features are distinct from and less extensive than on Mars, indicating that Occator melts may be less gas-rich or volatiles partially inhibited from reaching the surface. Bright salts at Vinalia Faculae form thin surficial precipitates sourced from hydrothermal brine effusion at many individual sites, coalescing in several larger centers, but their ages are statistically indistinguishable from floor materials, allowing for but not requiring migration of brines from deep crustal source(s)., Dawn mission’s second extended phase provided high resolution observations of Occator crater of the dwarf planet Ceres. Here, the authors show stereo imaging and topographic maps of this crater revealing the influence of crustal composition on impact related melt and hydrothermal processes, and compare features to those on Mars, Earth and the Moon.

Before acquiring highest-resolution data of Ceres, questions remained about the emplacement mechanism and source of Occator crater’s bright faculae. Here we report that brine effusion emplaced the faculae in a brine-limited, impact-induced hydrothermal system. Impact-derived fracturing enabled brines to reach the surface. The central faculae, Cerealia and Pasola Facula, postdate the central pit, and were primarily sourced from an impact-induced melt chamber, with some contribution from a deeper, pre-existing brine reservoir. Vinalia Faculae, in the crater floor, were sourced from the laterally extensive deep reservoir only. Vinalia Faculae are comparatively thinner and display greater ballistic emplacement than the central faculae because the deep reservoir brines took a longer path to the surface and contained more gas than the shallower impact-induced melt chamber brines. Impact-derived fractures providing conduits, and mixing of impact-induced melt with deeper endogenic brines, could also allow oceanic material to reach the surfaces of other large icy bodies., The second extended phase of the Dawn mission provided high resolution observations of Occator crater of the dwarf planet Ceres. Here, the authors show that the central faculae were sourced in an impact-induced melt chamber, with a contribution from the deep brine reservoir, while the Vinalia Faculae were sourced by the deep brine reservoir alone.

Strong flare events with an extended phase of gamma ray emission from the catalog by Share et al. have been analyzed in order to explain the characteristics of the impulsive and extended phases of such flares and reveal their connection with activity complexes and coronal holes. It is shown that 74% of such events are closely related to activity complexes. It has been qualitatively demonstrated that the particle acceleration processes during the flare development are associated with the changes in the magnetic topology of the flare region and the evolution of the coronal mass ejection. The possible relation of coronal holes to activity complexes and the role of “exchange” reconnection in these processes are discussed.

This article provides an overview of the public health approach to suicide in Ireland. The authors provide detail on the current suicide prevention strategy in Ireland, Connecting for Life, which is a whole-of-government, systemic, multicomponent national strategy. As the strategy enters its final extended phase of implementation over the period 2020–2024, the public health elements of Connecting for Life are presented, including the population level and more targeted approaches. The findings of an interim review of the strategy are discussed, in addition to the local and national implementation structures which are in place to assist implementation and monitoring of the strategy.

In lower dimensions, charged AdS black holes in an extended phase space, where the cosmological constant is interpreted as the thermodynamic pressure, are typically absent of liquid/gas phase transitions. We investigate the criticality of lower dimensional charged, dilatonic, asymptotically AdS (CDAdS$_d$) black holes generated from consistent truncations of RNAdS$_{d+2}$ black objects. We demonstrate that CDAdS$_{d}$ black holes in $d, 10 pages, no figures

We introduce leak-in dark matter, a novel out-of-equilibrium origin for the dark matter (DM) in the universe. We provide a comprehensive and unified discussion of a minimal, internally-thermalized, hidden sector populated from an out-of-equilibrium, feeble connection to the hotter standard model (SM) sector. We emphasize that when this out-of-equilibrium interaction is renormalizable, the colder sector undergoes an extended phase of non-adiabatic evolution largely independent of initial conditions, which we dub "leak-in." We discuss the leak-in phase in generality, and establish the general properties of dark matter that freezes out from a radiation bath undergoing such a leak-in phase. As a concrete example, we consider a model where the SM has an out-of-equilibrium B-L vector portal interaction with a minimal hidden sector. We discuss the interplay between leak-in and freezein processes in this theory in detail and demonstrate regions where leak-in yields the full relic abundance. We study observational prospects for B-L vector portal leak-in DM, and find that despite the requisite small coupling to the SM, a variety of experiments can serve as sensitive probes of leak-in dark matter. Additionally, regions allowed by all current constraints yield DM with self-interactions large enough to address small-scale structure anomalies., Comment: 31 pages + appendices, 12 figures

Why did leaders of the Congress movement in South Africa abandon their exclusive reliance on non-violent means in the struggle against apartheid, form an armed unit (Umkhonto we Sizwe), and launch a campaign of spectacular sabotage bombings of symbols of apartheid in 1961? None of the earlier violent struggles from which Congress leaders drew inspiration, and none of the contemporaneous insurgencies against white minority rule elsewhere in southern Africa, involved a similar distinct, preliminary and extended phase of non-lethal symbolic sabotage. Following the 1960 Sharpeville massacre, Congress leaders feared the social and political consequences of increased popular enthusiasm for using violence. Nelson Mandela, Joe Slovo, and the other founders of Umkhonto we Sizwe did not launch their sabotage campaign because they believed it would prompt a change of heart among white South Africans, nor because they believed urban sabotage bombings were a necessary prelude to the launch of rural guerrilla warfare. Rather, the sabotage campaign was a spectacular placeholder, a stopgap intended to advertise the Congress movement's abandonment of exclusive non-violence and thus to discourage opponents of apartheid, both inside and outside South Africa, from supporting rival groups or initiating ‘uncontrolled violent action themselves.

We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in four dimensions, where the equation of state in the extended phase space formalism allows explicit comparison with normal fluid systems. We show that for the two-dimensional parameter manifolds considered here, the scalar curvature is proportional to the thermodynamic volume. This allows us to critically examine the applicability of geometric methods in black hole thermodynamics in extended phase space. We show how several standard features that are expected to hold in normal fluid systems impose severe restrictions on the black hole parameters, leading to the fact that several results in the current literature on the geometry of thermodynamics in extended phase space may be physically invalid. These are true for both charged and rotating AdS black holes. As a by-product of our analysis, we examine a conjecture regarding the equality of the correlation lengths of co-existing phases near criticality, in charged AdS black hole backgrounds, and find reasonable validity., 1 + 11 Pages, Matches published version

Thermodynamics of $z=4$ Ho\v{r}ava-Lifshitz black holes in 3+1 dimensions is studied in extended phase space. By using the scaling argument we find the Smarr relation and the first law for the black hole solutions of $z=4$ Ho\v{r}ava-Lifshitz gravity. We find that it is necessary to take into account the variation of dimensionful parameters of the theory in the first law. We find that the reverse isoperimetric inequality can be violated for spherical, flat, and hyperbolic horizons and in all such cases we have black holes for which the specific heat at constant pressure and volume are positive. This provides a counterexample to a recent conjecture stating that black holes violating the reverse isoperimetric inequality are thermodynamically unstable. We find for $z=4$ Ho\v{r}ava-Lifshitz black holes with hyperbolic horizons that there are two critical points: one showing Van der Waals behavior, the other reverse Van der Waals behavior., Comment: 27 pages, one-column, 13 figures, v2: matched the published version

The application of generalized continuum mechanics is rapidly increasing in different fields of science and engineering. In the literature, there are several theories extending the classical first-order continuum mechanics formulation to include size-effects [1]. One approach is the strain gradient theory with the intrinsic features of regularizing singular stress fields occurring, e.g., near crack tips. It is crucial to realize that using this theory, the strain energy density is still localized around the crack tip, but does not exhibit any signs of a singularity. Therefore, these models seem to be appropriate choices for studying cracks in mechanical problems. Over the past several years, the phase-field method has gathered considerable popularity in the computational mechanics community, in particular in the field of fracture mechanics [2]. Recently, the authors have shown that integrating the strain gradient theory into the phase-field fracture framework is likely to improve the quality of the final results due to the inherent non-singular nature of this theory [3]. In the present work, we will focus on a general formulation of the first strain gradient theory. To this end, the homogenization approach introduced in Ref. [4] is employed. It is based on a series of systematic finite element simulations using different loading cases to determine the equivalent material coefficients on the macro-scale (i.e., for a strain gradient elastic material) by taking the underlying micro-structure into account.

1.SummaryMemory formation and reinstatement are thought to lock to the hippocampal theta rhythm, predicting that encoding and retrieval processes appear rhythmic themselves. Here, we show that rhythmicity can be observed in behavioral responses from memory tasks, where participants indicate, using button presses, the timing of encoding or retrieval of cue-object associative memories. We found no evidence for rhythmicity in button presses for visual tasks using the same stimuli, or for questions about already retrieved objects. The oscillations for correctly remembered trials center in the slow theta frequency range (1-5 Hz), while responses from later forgotten trials do not lock to the behavioral oscillation. Using intracranial EEG recordings, we show that the memory task induces temporally extended phase consistency in hippocampal local field potentials at slow theta frequencies, but only for correctly remembered trials, providing a mechanistic underpinning for the theta oscillations found in behavioral responses.

Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR fingerprinting. This work uses a new extended phase graph (EPG)‐Bloch model for accurate simulation of transient‐state, gradient‐spoiled MR sequences, and proposes a recurrent neural network (RNN) as a fast surrogate of the EPG‐Bloch model for computing large‐scale MR signals and derivatives. The computational efficiency of the RNN model is demonstrated by comparisons with other existing models, showing one to three orders of acceleration compared with the latest GPU‐accelerated, open‐source EPG package. By using numerical and in vivo brain data, two used cases, namely, MRF dictionary generation and optimal experimental design, are also provided. Results show that the RNN surrogate model can be efficiently used for computing large‐scale dictionaries of transient‐state signals and derivatives within tens of seconds, resulting in several orders of magnitude acceleration with respect to state‐of‐the‐art implementations. The practical application of transient‐state quantitative techniques can therefore be substantially facilitated., This work uses a new extended phase graph (EPG)‐Bloch model for accurately simulating transient‐state, gradient‐spoiled MR sequences, and proposes a recurrent neural network (RNN) model as a fast surrogate. The computational efficiency of the RNN is demonstrated by comparisons with other models, showing one to three orders of acceleration compared with the latest GPU‐accelerated EPG package. Two used cases, namely, MRF dictionary generation and optimal experimental design, are also provided, showing the practical applications facilitated by the RNN model.

Automatic registration of multimodal remote sensing images, which is a critical prerequisite in a range of applications (e.g. image fusion, image mosaic, and image analysis), continues to be a fund...

Purpose Multi-echo spin-echo (MSE) transverse relaxometry mapping using multi-component models is used to study disease activity in neuromuscular disease by assessing the T-2 of the myocytic component (T-2water). Current extended phase graph algorithms are not optimized for fat fractions above 50% and the effects of inaccuracies in the T-2fat calibration remain unexplored. Hence, we aimed to improve the performance of extended phase graph fitting methods over a large range of fat fractions, by including the slice-selection flip angle profile, a through-plane chemical-shift displacement correction, and optimized calibration of T-2fat.Methods Simulation experiments were used to study the influence of the slice flip-angle profile with chemical-shift and T-2fat estimations. Next, in vivo data from four neuromuscular disease cohorts were studied for different T-2fat calibration methods and T-2water estimations.Results Excluding slice flip-angle profiles or chemical-shift displacement resulted in a bias in T-2water up to 10 ms. Furthermore, a wrongly calibrated T-2fat caused a bias of up to 4 ms in T-2water. For the in vivo data, one-component calibration led to a lower T-2fat compared with a two-component method, and T-2water decreased with increasing fat fractions.Conclusion In vivo data showed a decline in T-2water for increasing fat fractions, which has important implications for clinical studies, especially in multicenter settings. We recommend using an extended phase graph-based model for fitting T-2water from MSE sequences with two-component T-2fat calibration. Moreover, we recommend including the slice flip-angle profile in the model with correction for through-plane chemical-shift displacements.

Purpose To investigate magnetic resonance neurography (MRN) of the lumbosacral plexus (LSP) with cerebrospinal fluid (CSF) suppression by using submillimeter resolution for three-dimensional (3D) turbo spin echo (TSE) imaging. Materials and methods Using extended phase graph (EPG) analysis, the signal response of CSF was simulated considering dephasing from coherent motion for frequency-encoding voxel sizes ranging from 0.3 to 1.3 mm and for CSF velocities ranging from 0 to 4 cm/s. In-vivo MRN included 3D TSE data with frequency encoding parallel to the feet/head axis from 15 healthy adults (mean age: 28.5 ± 3.8 years, 5 females; acquisition voxel size: 2 × 2 × 2 mm3) and 16 pediatric patients (mean age: 6.7 ± 4.1 years, 7 females; acquisition voxel size: 0.7 × 0.7 × 1.4 mm3) acquired at 3 Tesla. Five of the adults were scanned repetitively with changing acquisition voxel sizes (1 × 2 × 2 mm3, 0.7 × 2× 2 mm3, and 0.5 × 2 × 2 mm3). Measurements of the bilateral ganglion of the L5 nerve root, averaged between sides, as well as the CSF in the thecal sac were obtained for all included subjects and compared between adults and pediatric patients and between voxel sizes, using a CSF-to-nerve signal ratio (CSFNR). Results According to simulations, the CSF signal is reduced along the echo train for moving spins. Specifically, it can be reduced by over 90% compared to the maximum simulated signal for flow velocities above 2 cm/s, and could be most effectively suppressed by considering a frequency-encoding voxel size of 0.8 mm or less. For in-vivo measurements, mean CSFNR was 1.52 ± 0.22 for adults and 0.10 ± 0.03 for pediatric patients (p Conclusions Applying frequency-encoding voxel sizes in submillimeter range for 3D TSE imaging with frequency encoding parallel to the feet/head axis may considerably improve MRN of LSP pathology in adults in the future because of favorable CSF suppression.

The Journal of Chemical Physics, 152 (8), ISSN:0021-9606, ISSN:1089-7690

Circular carrier squeezing interferometry (CCSI) is proposed and applied to suppress phase shift error in simultaneous phase-shifting point-diffraction interferometer (SPSPDI). By introducing a defocus, four phase-shifting point-diffraction interferograms with circular carrier are acquired, and then converted into linear carrier interferograms by a coordinate transform. Rearranging the transformed interferograms into a spatial-temporal fringe (STF), so the error lobe will be separated from the phase lobe in the Fourier spectrum of the STF, and filtering the phase lobe to calculate the extended phase, when combined with the corresponding inverse coordinate transform, exactly retrieves the initial phase. Both simulations and experiments validate the ability of CCSI to suppress the ripple error generated by the phase shift error. Compared with carrier squeezing interferometry (CSI), CCSI is effective on some occasions in which a linear carrier is difficult to introduce, and with the added benefit of eliminating retrace error.

The Extended Phase Opposition Disposition PWM (EPODPWM) technique has been applied in the two-level inverters successfully, but it is impossible to apply directly the EPODPWM technique to multilevel inverters. This paper proposes two kinds of EPODPWM techniques suitable for a cascaded multilevel inverter, analyzes the control strategy with the EPODPWM and obtains the design of its parameters. The simulation results show the proposed EPODPWM methods can get high magnitudes of the output fundamental frequency component, low total harmonic distortion and simpler digital implementation.

Some model reduction techniques for multiple time scale dynamical systems make use of the identification of low-dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensi...

High efficiency and fast dynamic response are two main control objectives for dual active bridge (DAB) DC-DC converters. Traditional extended phase shift (EPS) control can significantly enhance the conversion efficiency of DAB DC-DC converters by reducing current stress; however, it cannot fulfill fast dynamic response requirements. In this paper, a novel hybrid control scheme consisting of EPS control and direct power control (DPC), named as EPS-DPC, is proposed. EPS-DPC control has salient features in both efficiency and dynamic performance. In order to verify the outstanding performance of the proposed EPS-DPC scheme, an experimental comparison was carried out on a scale-down DAB DC-DC converter among several control strategies, including single phase shift control with traditional voltage-loop (SPS-TVL), EPS control with traditional voltage-loop (EPS-VTL), and EPS-DPC. Experimental results have been high consistent with theoretical analysis, and verified these advantages of the proposed EPS-DPC scheme.

We consider chiral Schwinger model with Faddeevian anomaly, and carry out the quantization of both the gauge-invariant and non-invariant version of this model has been. Theoretical spectra of this model have been determined both in the Lagrangian and Hamiltonian formulation and a necessary correlation between these two are made. BRST quantization using BFV formalism has been executed which shows spontaneous appearance of Wess–Zumino term during the process of quantization. The gauge invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition.

In this paper, we study an extended phase space thermodynamics of a nonlinearly charged AdS black hole. We examine both the local and global stabilities, and possible phase transition of the black hole solutions. Finally, we compute quasi-normal modes via scalar perturbations and compare the obtained results with those of RN-AdS black hole., Comment: 17 pages with 15 captioned figures. Published in EPJC

We discuss the P−V criticality and phase transition in the extended phase space of anti-de Sitter(AdS) black holes in four-dimensional Rastall theory and recover the Van der Waals (VdW) analogy of small/large black hole (SBH/LBH) phase transition when the parameters ωs and ψ satisfy some certain conditions. Later, we further explore the quasinormal modes (QNMs) of massless scalar perturbations to probe the SBH/LBH phase transition. It is found that it can be detected near the critical point, where the slopes of the QNM frequencies change drastically in small and large black holes.

In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) spacetimes from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space that naturally incorporates the structure of a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and equations of state of Schwarzschild black holes are mapped to that of Reissner-Nordstr\"{o}m black holes in AdS, with charge as the deformation parameter. In addition, the equations of state of general black holes in AdS are shown to emerge from the high-temperature ideal gas limit equations via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up, and the corresponding characteristic curves of contact vector fields are explicitly obtained to model thermodynamic processes of black holes. Extension to thermodynamic cycles in this framework is also discussed., Comment: 32 pages, 1 figure

PURPOSE: Slice-selective, gradient-crushed, transient-state sequences such as those used in magnetic resonance fingerprinting (MRF) relaxometry are sensitive to slice profile effects. While balanced steady-state free precession MRF profile effects have been studied, less attention has been given to gradient-crushed MRF forms. Extensions of the extended phase graph (EPG) formalism are proposed, called slice-selective EPG (ssEPG), that model slice profile effects. THEORY AND METHODS: The hard-pulse approximation to slice-selective excitation in the spatial domain is reformulated in k-space. Excitation is modeled by standard EPG shift and transition operators. This ssEPG modeling is validated against Bloch simulations and phantom slice profile measurements. ssEPG relaxometry accuracy and variability are compared with other EPG methods in phantoms and human leg in vivo. The role of ΔB(0) interactions with slice profile and gradient crushers are investigated. RESULTS: Simulations and slice profile measurements show that ssEPG can model highly dynamic slice profile effects of gradient-crushed sequences. The MRF ssEPG T(2) estimates over 0 < T(2) < 100 ms improve accuracy by > 10 ms at some values, relative to other modeling approaches. Small deviations in B(0) can produce substantial bias in T(2) estimations from a range of MRF sequence types, and these effects can be modeled and understood by ssEPG. CONCLUSION: Transient-state, gradient-crushed sequences such as those used in MRF are sensitive to slice profile effects, and these effects depend on RF pulse choice, gradient crusher strength, and ΔB(0). It was found ssEPG was the most accurate EPG-based means to model these effects.

The dilemma between tunable range of a lens power and an aperture size in gradient-index (GRIN) type of liquid crystal (LC) lenses is well known due to the limitation of birefringence of LC martials and the nature of soft matters. In order to overcome the dilemma of the power law, a multi-layered LC lens was previously proposed by us. However, the aperture size of GRIN LC lenses is still difficult to exceed 10 mm. In this paper, we proposed an electrically tunable GRIN LC lens via nematic liquid crystals with a method of spatially extended phase distribution. A GRIN LC lens with an aperture size of 20 mm is achieved. The proposed GRIN LC lens consists of two LC elements modulating wavefronts at different regions of the lens aperture extending to 20 mm. The lens power of the GRIN LC lens is continuously tunable, while the LC lens can function as a positive lens, a negative lens, and a bifocal lens. The proposed GRIN LC lens not only overcomes the dilemma of the power law but also provides a more practical approach that could benefit the ophthalmic applications and augmented reality systems.

Effects of graviton mass on the Joule-Thomson expansion process of neutral AdS black holes in four dimensional spacetime is studied within the extended phase space. For m=0, there are no inversion curves and the whole P−T plane with M>0 is the cooling region. While for m≠0, the properties of the Joule-Thomson expansion are found to be controlled by a combined parameter k+c2m2. When k+c2m2>0, we analytically obtain the inversion curves T˜(P˜) where the Joule-Thomson coefficients are zero. They separate the P−T plane into the heating region (left side) and cooling region (right side). The position of the heating region and cooling region in P−T plane are in contrast to those of the van der Waals system. The inversion curve contains two branches, one with positive slope and the other with negative slope. This feature is found for the first time in the black hole system and is similar with that of the van der Waals system. When k+c2m2=0, the inversion curve is a straight line, above which is the cooling region and below which is a region with M<0. When k+c2m2<0, there are no inversion curves and the whole P−T plane with M>0 is the cooling region.

In this paper, a switching strategy is proposed for the extended phase shift (EPS) controlled dual active bridge (DAB) converter which using the hybrid switch (HyS) configured by paralleling SiC MOSFET and Si IGBT, considering the special soft switching characteristic of DAB. For most of the existing literature, the common switching strategy of HyS is to switch on the SiC MOSFET before Si IGBT and switch off the SiC MOSFET after Si IGBT. However, if only using this switching strategy, the SiC MOSFET may be damaged by long-time operating at the over rated current condition. The proposed switching strategy for the HyS is that the SiC MOSFET is only conducted for a short while during the process of switching Si IGBT on or off. The proposed switching strategy can shorten the conduction time of SiC MOSFET, decrease the losses of HyS and extend the safe operation area of HyS. Simulation results on a 30 kW HyS DAB converter verify the availability of the proposed switching strategy.

In this work, we attempt to study the thermodynamic behavior of static Van der Waals (VdW) black hole with an anti-de Sitter (AdS) background in the extended phase space. Treating the negative cosmological constant as thermodynamic pressure, we obtain the expressions for enthalpy, Gibb’s free energy and Helmholtz free energy. We study the stability and Joule–Thomson expansion for the black hole. Next, we construct a heat engine by considering the VdW black hole as the working substance. We investigate the maximum efficiency of the black hole heat engine for the Carnot cycle. We also discuss the work done and the efficiency of a new heat engine. Finally, we study the efficiency of the black hole heat engine for the Rankine cycle.

The model of varying mass function, including periastron effect, in terms of Delaunay variables will be expanded. The Hamiltonian of the problem is developed in the extended phase space by introducing a new canonical pair of variable ( $$q_4, Q_4$$ ). The first “ $$q_4 $$ ” is defined as explicit function of time and the initial mass of the system. The conjugate momenta “ $$Q_4$$ ” is assigned as the momenta raises from the varying mass. The short-period analytical solution through a second-order canonical transformation using “Hori’s” method developed by “Kamel” is obtained. The variation equations for the orbital elements are obtained too. The results of the effect of the varying mass and the periastron effect in the case $$n = 2$$ are analyzed.

This essay addresses the issue of gravitational phase transitions in the early universe. We suggest that a second order phase transition observed in the Causal Dynamical Triangulations approach to quantum gravity may have a cosmological relevance. The phase transition interpolates between a non-geometric crumpled phase of gravity, and an extended phase with classical properties. Transitions of this kind have been postulated earlier in the context of geometrogenesis in Quantum Graphity. We show that critical behavior may also be associated with a signature change event in Loop Quantum Cosmology. In both cases, classical spacetime originates at the critical point associated with a second order phase transition., Essay written for the Gravity Research Foundation 2014 Awards for Essays on Gravitation

The thermodynamics and overcharging problem in RN-AdS black holes with a cloud of strings and quintessence are investigated by the absorption of scalar particles and fermions in extended phase space. The cosmological constant is treated as the pressure of the black hole. The parameters related to quintessence and the cloud of strings are treated as thermodynamic variables. We find that the first law of thermodynamics is satisfied and the second law of thermodynamics is indefinite. Furthermore, we find that near-extremal and extremal black holes cannot be overcharged.

We investigate the relations between the black hole shadow and charged AdS black hole critical behaviour in the extended phase space. Using the thermo-shadow formalism built-in [1], we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN-AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from the observational point of view., Comment: 16 pages, 1 Tikz and 6 pdf figures, accepted in IJMPA

The effect of particle overtaking on transport in a narrow channel is studied using a 1d model of a driven tracer in a quiescent bath. In contrast with the well-studied non-driven case, where the tracer's long-time dynamics changes from sub-diffusive to diffusive whenever overtaking is allowed, the driven tracer is shown to exhibit a phase transition at a finite overtaking rate. The transition separates a phase in which the stationary bath density profile, as seen in the tracer's frame, is extended, as in the non-overtaking case, to a phase with a localized bath density profile. In the extended phase the tracer velocity vanishes in the thermodynamic limit while it remains finite in the localized phase. The phase diagram of the model, as well as the tracer velocity and the bath density profile in both phases, are studied, demonstrating their distinct features., 9 pages and 6 figures

PURPOSE To compare magnetization transfer (MT) and CEST effects between 1.5T and 3T in phantom and in vivo experiments. METHODS A pulsed saturation scheme using block-shaped pulses separated by gaps was used to overcome the single RF amplifier duty cycle limitations of a clinical 1.5T scanner. Modeling was performed by incorporating the extended phase graph formalism into a Bloch-McConnell simulation. Two saturation pulse types (with long and short pulses) were used. Estimated parameters for MT (the semi-solid pool fraction, M0B ; the semi-solid transverse relaxation time, T2B ) and CEST (asymmetry; areas) were compared between 1.5T and 3T in phantoms and in the healthy brain. RESULTS Improved fits were shown after inclusion of extended phase graphs. Semi-solid pool fractions in phantom (for agar with ammonium chloride) were higher for short compared to long pulses at 3T (by 19% over all concentrations) and higher at 1.5T compared to 3T (by 5%) using short pulses. In the in vivo experiments, differentiation of white and gray matter was seen in the brain at both field strengths with improved white-gray matter contrast at 3T. In white matter, the mean semi-solid fractions were 18 ± 2% at 3T and 15 ± 2% at 1.5T. The CEST asymmetry in white matter was negative (-4.9 ± 0.4%) at 3T and zero (0.0 ± 0.3%) at 1.5T. CONCLUSIONS The pulsed saturation method with short pulses, using the extended phase graph formalism in the Bloch McConnell simulations, led to improved model fits to the data, when compared to those without extended phase graphs.

As charged fermions drop into the BTZ black holes, we check the laws of thermodynamics and weak cosmic censorship conjecture in the normal phase space and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics as well as the weak cosmic censorship are valid. While in the extended phase space, though the first law and weakcosmic censorship conjecture are still valid, the second law is dependent on the variation of the renormalization energy $dK$. In addition, in the extended phase space, the configurations of the extremal and near-extremal black holes will not be changed for they are stable while in the normal phase space, the extremal and near-extremal black holes will evolve into non-extremal black holes., Comment: Chin. Phys. C 43 (2019) no.10, 105104

In this paper, we attempt to study the Joule-Thomson expansion for the regular black hole in an anti-de Sitter background, and obtain the inversion temperature and curve for the Bardeen-AdS black hole in the extended phase space. We investigate the isenthalpic and inversion curves for the Bardeen-AdS black hole in the T-P plane to find the intersection points between them are exactly the inversion points discriminating the heating process from the cooling one. And, the inversion curve for the regular(Bardeen)-AdS black hole is not closed and there is only a lower inversion curve in contrast with that of the Van der Walls fluid. Most importantly, we find the ratio between the minimum inversion and critical temperature for the regular(Bardeen)-AdS black hole is 0.536622, which is always larger than all the already-known ratios for the singular black hole. This larger ratio for the Bardeen-AdS black hole in contrast with the singular black hole may stem from the fact that there is a repulsive de Sitter core near the origin of the regular black hole., 17 pages, 6 figures; Added discussion in section 4

In this paper, we present the analytic solution for Anti-de Sitter-Nonlinear electrodynamics (AdS-NED) black hole in four dimensions. We study tunneling of vector particles from the AdS-NED black hole to find Hawking temperature as well as its thermodynamical properties in usual and extended phase space. Then we explore the properties of pressure–volume criticality by analyzing the phase diagram and its free energy. Finally, we investigate the Joule–Thomson coefficient, in which the inversion curve of warming and cooling are studied, and the ratio between the inverse temperature and critical temperature are computed in the black hole solution.

We study the extended phase space thermodynamics of black holes in massive gravity. Particularly, we examine the critical behaviour of this black hole using the extended phase space formalism. Extended phase space in a sense that in which the cosmological constant should be treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. In this phase space, we derive the black hole equation of state, the critical pressure, the critical volume and the critical temperature at the critical point. We also derive the critical ratio of this black hole. Moreover, we derive the black hole reduced equation of state in terms of the reduced pressure, the reduced volume and the reduced temperature. Furthermore, we examine the Ehrenfest equations of black holes in massive gravity in the extended phase space at the critical point. We show that the Ehrenfest equations are satisfied of this black hole and the black hole encounters a second order phase transition at the critical point in the said phase space. This is re-examined by evaluating the Pregogine-Defay ratio~($\varPi$). We determine the value of this ratio is $\varPi=1$. The outcome of this study is completely analogous to the nature of liquid-gas phase transition at the critical point. This investigation also further gives us the profound understanding between the black hole of massive gravity with the liquid-gas system., Accepted for publication in Modern Physics Letters A (MPLA)

This paper presents the application of the Extended Phase Space Topology (EPST) method in model-based diagnostics of nonlinear systems. A detailed nonlinear mathematical model of a servo electro-hydraulic system has been used to demonstrate the procedure. Two faults have been considered associated with the servo valve including the increased friction between spool and sleeve and the degradation of the permanent magnet of the valve armature. The faults have been simulated in the system by the variation of the corresponding parameters in the model and the effect of these faults on the output flow response has been investigated. A regression-based artificial neural network has been developed and trained using the EPST extracted features to estimate the original values of the faulty parameters and to identify the severity of the faults in the system.

In this paper we study the thermodynamics of Einstein-Gauss-Bonnet (EGB)-AdS black holes minimally coupled to a cloud of strings in an extended phase space where the cosmological constant is treated as pressure of the black holes and its conjugate variable is the thermodynamical volume of the black holes. To investigate the analogy between EGB black holes surrounded by a cloud of strings and liquid-gas system we derive the analytical solutions of the critical points and probe the effects of a cloud of strings on $P-V$ criticality. There is obtained resemblance between "small black hole/large black hole" (SBH/LBH) phase transition and the liquid-gas phase transition. We see that impact of a cloud of strings can bring Van der Waals-like behavior, in absence of the Gauss-Bonnet (GB) counterpart. In the other words, in the EGB black hole with $\alpha \to 0$ and when it is surrounded by a cloud of strings the Hawking-Page phase transition would be disappeared and SBH/LBH phase transition recovers. Also there is not happened Joule-Thomson effect., Comment: 18 pages, 4 figure

In extended phase space, a static black hole in massive gravity is studied as a holographic heat engine. In the massive gravity theory considered, the graviton gain a mass due to Lorentz symmetry breaking. Exact efficiency formula is obtained for a rectangle engine cycle for the black hole considered. The efficiency is computed by varying two parameters in the theory, the scalar charge Q and $\lambda$. The efficiency is compared with the Carnot efficiency for the heat engine. It is observed that when Q and $\lambda$ are increased that the efficiency for the rectangle cycle increases. When compared to the Schwarzschild AdS black hole, the efficiency for the rectangle cycle is larger for the Massive gravity black hole., Comment: Accepted to be published in Modern Physics letters A