We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\unicode[STIX]{x1D70C}$ and inverse temperature $\unicode[STIX]{x1D6FD}$ differs from the one of the noninteracting system by the correction term $4\unicode[STIX]{x1D70B}\unicode[STIX]{x1D70C}^{2}|\ln \,a^{2}\unicode[STIX]{x1D70C}|^{-1}(2-[1-\unicode[STIX]{x1D6FD}_{\text{c}}/\unicode[STIX]{x1D6FD}]_{+}^{2})$. Here, $a$ is the scattering length of the interaction potential, $[\cdot ]_{+}=\max \{0,\cdot \}$ and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$.

Mild cognitive impairment (MCI) often precedes Alzheimer’s Dementia (AD), and in a high proportion of individuals affected by MCI, there are already neuropathological processes ongoing that become more evident when patients progress to AD. Accordingly, there is a need for reliable biomarkers to distinguish between normal aging and incipient AD. Recent research suggests that, in addition to established biomarkers such as CSF Aß42, total tau and hyperphosphorylated tau, resting state connectivity established by functional magnetic resonance imaging might also be a feasible biomarker for prodromal stages of AD. In order to explore this possibility, we investigated resting state functional connectivity as well as cerebrospinal fluid (CSF) biomarker profiles in patients with MCI (n = 30; age 66.43 ± 7.06 years) and cognitively healthy controls (n = 38; age 66.89 ± 7.12 years). CSF Aß42, total tau and hyperphosphorylated tau concentrations were correlated with measures of cognitive performance (immediate and delayed recall, global cognition, processing speed). Moreover, MCI-related alterations in intrinsic functional connectivity within the default mode network were investigated using functional resting state MRI. As expected, MCI patients showed decreased CSF Aß42 and increased total tau concentrations. These alterations were associated with cognitive performance. However, there were no differences between MCI patients and cognitively healthy controls regarding intrinsic functional connectivity. In conclusion, our results indicate that CSF protein profiles seem to be more closely related to cognitive decline than alterations in resting state activity. Thus, resting state connectivity might not be a reliable biomarker for early stages of AD.

In recent years, the discovery of massive quasars at $z\sim7$ has provided a striking challenge to our understanding of the origin and growth of supermassive black holes in the early Universe. Mounting observational and theoretical evidence indicates the viability of massive seeds, formed by the collapse of supermassive stars, as a progenitor model for such early, massive accreting black holes. Although considerable progress has been made in our theoretical understanding, many questions remain regarding how (and how often) such objects may form, how they live and die, and how next generation observatories may yield new insight into the origin of these primordial titans. This review focusses on our present understanding of this remarkable formation scenario, based on the discussions held at the Monash Prato Centre from November 20 to 24, 2017, during the workshop ‘Titans of the Early Universe: The Origin of the First Supermassive Black Holes’.

Snow can be considered an independent ecosystem that hosts active microbial communities. Snow microbial communities have been extensively investigated in the Arctic and in the Antarctica, but rarely in mid-latitude mountain areas. In this study, we investigated the bacterial communities of snow collected in four glacierized areas (Alps, Eastern Anatolia, Karakoram and Himalaya) by high-throughput DNA sequencing. We also investigated the origin of the air masses that produced the sampled snowfalls by reconstructing back-trajectories. A standardized approach was applied to all the analyses in order to ease comparison among different communities and geographical areas. The bacterial communities hosted from 25 to 211 Operational Taxonomic Units (OTUs), and their structure differed significantly between geographical areas. This suggests that snow bacterial communities may largely derive from ‘local’ air bacteria, maybe by deposition of airborne particulate of local origin that occurs during snowfall. However, some evidences suggest that a contribution of bacteria collected during air mass uplift to snow communities cannot be excluded, particularly when the air mass that originated the snow event is particularly rich in dust.

A new surface classification algorithm for monitoring snow and ice masses based on data from the moderate-resolution imaging spectroradiometer (MODIS) is presented. The algorithm is applied to the Greenland ice sheet for the period 2000–05 and exploits the spectral variability of ice and snow reflectance to determine the surface classes dry snow, wet snow and glacier ice. The result is a monthly glacier surface type (GST) product on a 1 km resolution grid. The GST product is based on a grouped criteria technique with spectral thresholds and normalized indices for the classification on a pixel-by-pixel basis. The GST shows the changing surface classes, revealing the impact of climate variations on the Greenland ice sheet over time. The area of wet snow and glacier ice is combined into the glacier melt area (GMA) product. The GMA is analyzed in relation to the different surface classes in the GST product. The results are validated with data from weather stations and similar types of satellite-derived products. The validation shows that the automated algorithm successfully distinguishes between the different surface types, implying that the product is a promising indicator of climate change impact on the Greenland ice sheet.

Liligo glacier, in the central eastern Karakoram, Pakistan, is a small, south-to-north-flowing glacier situated in a transverse valley on the left (south) side of Baltoro glacier. New processing of satellite imagery enables a better quantification of terminus oscillations over the past 30 years. From the beginning of the 1970s to the beginning of the 21st century, Liligo glacier advanced about 2 km (60ma–1). The progress was characterized by a significant evolution of terminus morphology, similar to that observed on the same glacier during the advance event near the beginning of the 20th century, and to those of many other Karakoram glaciers. This suggests indications of a surge-type mechanism. Field observations performed in 2004 indicated there was probably no confluence at that time between Liligo and Baltoro glaciers and that a quiescent phase had started in the early years of the 21st century.

We study the impact of the enforcement of financial regulation by the United Kingdom’s regulatory authorities on the market price of penalized firms. Existing studies rely on analyses of multiple events that may distort the measurement of reputational losses. In the United Kingdom, the entire enforcement process involves only one public announcement and is accompanied by complete information on legal penalties. We find that reputational losses are nearly nine times the size of fines and are associated with misconduct harming customers or investors but not third parties.

Animals played an important role in the formation of psychoanalysis as a theoretical and therapeutic enterprise. They are at the core of texts such as Freud's famous case histories of Little Hans, the Rat Man, or the Wolf Man. The infantile anxiety triggered by animals provided the essential link between the psychology of individual neuroses and the ambivalent status of the “totem” animal in so-called primitive societies in Freud's attempt to construct an anthropological basis for the Oedipus complex in Totem and Taboo. In the following, we attempt to track the status of animals as objects of indirect observation as they appear in Freud's classical texts, and in later revisionist accounts such as Otto Rank's Trauma of Birth and Imre Hermann's work on the clinging instinct. In the 1920s and 1930s, the Freudian conception of patients' animal phobias is substantially revised within Hermann's original psychoanalytic theory of instincts which draws heavily upon ethological observations of primates. Although such a reformulation remains grounded in the idea of “archaic” animal models for human development, it allows to a certain extent to empiricize the speculative elements of Freud's later instinct theory (notably the death instinct) and to come to a more embodied account of psychoanalytic practice.

After almost three decades of intensive fundamental research and development activities intermetallic titanium aluminides based on the -TiAl phase have found applications in automotive and aircraft engine industries. The advantages of this class of innovative high-temperature materials are their low density as well as their good strength and creep properties up to 750°C. A drawback, however, is their limited ductility at room temperature, which is reflected by a low plastic strain at fracture. This behavior can be attributed to a limited dislocation movement along with microstructural inhomogeneity. Advanced TiAl alloys, such as β-solidifying TNM™ alloys, are complex multi-phase materials which can be processed by ingot or powder metallurgy as well as precision casting methods. Each production process leads to specific microstructures which can be altered and optimized by thermo-mechanical processing and/or subsequent heat-treatments. The background of these heat-treatments is at least twofold, i.e. concurrent increase of ductility at room temperature and creep strength at elevated temperature. In order to achieve this goal the knowledge of the occurring solidification processes and phase transformation sequences is essential. Therefore, thermodynamic calculations were conducted to predict phase fraction diagrams of engineering TiAl alloys. After experimental verification, these phase diagrams provided the base for the development of heat treatments to adjust balanced mechanical properties. To determine the influence of deformation and kinetic aspects, sophisticated ex- and in-situ methods have been employed to investigate the evolution of the microstructure during thermo-mechanical processing and subsequent multi-step heat-treatments. For example, in-situ high-energy X-ray diffraction was conducted to study dynamic recovery and recrystallization processes during hot-deformation tests. Summarizing all results a consistent picture regarding microstructure formation and its impact on mechanical properties in TNM alloys can be given.

Humanity currently extracts almost 70 billion tons of materials per year. During the last century global materials extraction and use have increased by one order of magnitude. Growth accelerated in the last decade, when materials extraction grew with the global economy at an annual rate of 3.6%. For sustainable development it is of key importance to understand the spatial and temporal dynamics of global material use and the underlying drivers. This paper explores changes in global material use during the last century from a systemic perspective based on the concept of socio-economic metabolism.

In recent years socio-economic (or, more narrowly termed industrial) metabolism became a prominent concept in sustainability science as many global sustainability problems are directly associated with humanities growing demand for raw materials and their transformation into wastes and emissions after processing and use. Material Flow Analysis (MFA) is one of the approaches available to study social metabolism. It provides data and headline indicators for resource use in national economies and is widely used in science and by policy makers.

This paper presents results from a global material flow analysis and explores long term the development of global material extraction and use. It shows that in particular the period after WWII was characterized by a rapid expansion of resource use, driven by both population and economic growth. Within this period a shift from the dominance of renewable biomass towards mineral and fossil materials, which now account for 70% of all used materials, was observed. Overall, material use increased at a slower pace than the global economy, but faster than world population. As a consequence, material intensity (i.e. the amount of materials required per unit of GDP) declined throughout the 20th century, while materials use per capita doubled. The use of materials is by no means equally distributed around the globe. Per capita material use varies by a factor of 20 across countries. At the turn of the millennium, 15% of the global population living in industrialized countries were using half of all mineral and fossil resources; in contrast, the least developed countries, inhabiting 11% of global population, appropriated only 1% of these strategically important materials. In recent years, however, the emerging economies gained significance as drivers for physical growth. So far there is no evidence that growth of global materials use is slowing down. The paper discusses the implications of the results from the material flow analysis for sustainable development.

The development of suitable hot-forming processes, e.g. forging, is an important step towards the serial production of TiAl parts. Several microstructure parameters change during hot-forming. However, the underlying mechanisms can normally only be inferred from post process metallographic studies.

We used a deformation dilatometer modified for working in the HZG synchrotron beamlines at DESY for hot-deformation experiments. This setup enables the in situ monitoring of the interaction and evolution of microstructure parameters during processing. We observed the evolution of phase fractions, grain size and crystallographic texture during deformation while simultaneously recording the process parameters, like temperature, force and length change.

Here we present the hot compressive deformation behaviour of a Ti-43Al-4Nb-1Mo-0.1B (in at.%) alloy. Several specimens were deformed at three temperatures each with two compression rates. During the experiments the Debye-Scherrer diffraction rings were continuously recorded.

A robust processing route at low cost is an essential requirement for high-temperature materials used in automotive engines. Because of their excellent high-temperature properties, their low density, high elastic modulus as well as high specific strength, intermetallic γ-TiAl based alloys are potential candidates for application in advanced automotive turbochargers. So-called 3rd generation alloys, such as TNM™ alloys with a nominal composition of Ti-43.5Al-4Nb-1Mo-0.1B (in at%), are multi-phase alloys consisting of γ-TiAl, α2-Ti3Al and a low volume fraction of βo-TiAl phase. In this paper a novel hot-processing route, which is a combination of a one-shot hot-forging step and a controlled cooling treatment, leads to mechanical properties required for turbocharger turbine wheels. The observed strength can be attributed to the small lamellar spacing within the α2/γ colonies of the nearly lamellar microstructure. In order to analyze the microstructure and the prevailing phase fractions microscopic examinations and X-ray diffraction measurements were conducted. The mechanical properties were determined by hardness measurements as well as tensile and creep tests. The evolution of the microstructure during the hot-forming process is described and its relation to the obtained mechanical properties.