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In quantum mechanics, superoscillations, or the more general supershifts, appear as initial conditions of the time-dependent Schrödinger equation. Already in [5], a unified approach was developed, which yields time persistence of the supershift property under certain holomorphicity and growth assumptions on the corresponding Green’s function. While that theory considers the Schrödinger equation on the whole real line $${\mathbb {R}}$$ R , this paper takes the natural next step and considers $$\mathbb {R}\setminus \{0\}$$ R \ { 0 } , while allowing boundary conditions at $$x=0^\pm $$ x = 0 ± . In particular, the singular $$\frac{1}{x^2}$$ 1 x 2 -potential as well as the very important $$\delta $$ δ and $$\delta '$$ δ ′ distributional potentials are covered.

In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some convergence to a plane wave is the standard characterizing feature of a superoscillating function in mathematics and quantum mechanics. Also there exists a certain discrepancy between the representation of superoscillations either as generalized Fourier series, as certain integrals or via special functions. The aim of this work is to close these gaps and give a general definition of superoscillations, covering the well-known examples in the existing literature. Superoscillations will be defined as sequences of holomorphic functions, which admit integral representations with respect to complex Borel measures and converge to a plane wave in the space $\mathcal{A}_1(\mathbb{C})$ of exponentially bounded entire functions.

Radiocarbon, 64 (3), ISSN:0033-8222

A Dy:KPb

Confining clay layers typically protect groundwater aquifers against downward intrusion of contaminants. In the context of groundwater arsenic in Bangladesh, we challenge this notion here by showing that organic carbon drawn from a clay layer into a low-arsenic pre-Holocene (>12 kyr-old) aquifer promotes the reductive dissolution of iron oxides and the release of arsenic. The finding explains a steady rise in arsenic concentrations in a pre-Holocene aquifer below such a clay layer and the repeated failure of a structurally sound community well. Tritium measurements indicate that groundwater from the affected depth interval (40–50 m) was recharged >60 years ago. Deeper (55–65 m) groundwater in the same pre-Holocene aquifer was recharged only 10–50 years ago but is still low in arsenic. Proximity to a confining clay layer that expels organic carbon as an indirect response to groundwater pumping, rather than directly accelerated recharge, caused arsenic contamination of this pre-Holocene aquifer., Generally it is thought that confining clay layers provide protection to low-arsenic groundwaters against intrusion of shallower, high-arsenic groundwater bodies. Here, the authors show that impermeable clay layers can increase arsenic input to underlying groundwater systems due to reduction of iron oxides coupled to carbon oxidation.

In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space $$A_1(\mathbb {C})$$ A 1 ( C ) . Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials.

The main objective of this chapter is to describe the strategy for development of the public transport terminals in the city of Bratislava, Capital of Slovak Republic. In Bratislava, there is a huge development boom from the Danube river bank and on the edge of the Old City, where is risen up a new down town of the city. The territory specified will have around 20 high-rises with different function and there will be more than 22 000 new parking spaces together will app. 2 mil. m2 of new activities. The city position in this issue must consist of systematic regulation of build-out in order to reach contemporary modern conception of forming so called „smart cities“– sustainable living and sustainable mobility. Nowadays, the reality is that, we have saturated flows on the street network around the contact area. In this area a new bus station is built, which will influence an existing public transport network created by city bus and trolleybus network. For changing the modal split toward better using the public transport (PT), there is a complex of technical studies to realize around the centre a new tramway lines connecting the operated tramway network in Bratislava. The article deals with the suburb terminal in city of Bratislava, which is a central BUS station directly in this new city centre (just realized and put in operation to the end of 2021) and a smart solution of tramway links around this centre. The other main issue is about the methods of the traffic surveys and results of traffic model, which will be used not only for the prognosis scenarios of dynamic traffic flows but also for changing the modal split for the public transport to reflect the new tram routes. The results of technical studies and possible discussion on put inside this area a modern nonconventional elevated automatic public transport system is an open deal. The appraisal of saturated traffic flows, new traffic form investment and the bus station together with a huge city PT lines create a methodology of traffic modelling for improving the operation of the territory with designing the new tramway lines as a form of sustainable mobility. Some tools for decision making and steps for realization will be shown. The main issue is to change the modal split for PT. There are identifying opportunities to improve the attractiveness of public transport, together with suburban bus service (SBS), thus providing for its precedence over individual car traffic in the city of Bratislava (Fig. 1) and its agglomeration in the Bratislava region. The solution is shown how is possible to be a part of the integrated public transport services possibility to operate regular all days’ mobility problems in the city and not only to cover the rush hours. Behind is an overview of 5 years work of traffic engineers and planners to keep clear systematic approach and solutions with developers and municipality administration.

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its explicit form. With this efficient general technique, we are able to treat various potentials.

Dr. rer.nat. Clemens Schlosser, a physicist by training, well known to the German and international scientific community for his contributions to the monitoring of environmental radioactivity and especially the radionuclide component of the International Monitoring System, passed away on August 2, 2021 after a long and brave battle with ALS. Even during the last years, during which his illness compromised his strength, he devoted all the time possible to his life's work that was so close to his heart.

COVID-19 has revealed that science needs to learn how to better deal with the irreducible uncertainty that comes with global systemic risks as well as with the social responsibility of science towards the public good. Further developing the epistemological principles of new theories and experimental practices, alternative investigative pathways and communication, and diverse voices can be an important contribution of history and philosophy of science and of science studies to ongoing transformations of the scientific enterprise.

The main goal of this note is to study the time evolution of superoscillations under the 1D-Schrodinger equation with attractive or repulsive Dirac $$\delta $$ -potential located at the origin of the real line. Such potentials are of particular interest since they simulate short range interactions and the corresponding quantum system is an explicitly solvable model. Moreover, we give the large time asymptotics of this solution, which turns out to be different for the repulsive and the attractive model. The method that we use to study the time evolution of superoscillations is based on the continuity of the time evolution operator acting in a space of exponentially bounded entire functions.

Groundwater supports agriculture and provides domestic water for over 250 million people in the Bengal Basin. Our analysis of stable water isotope ratios in rain, surface, and groundwater shows that the proportion of groundwater recharge originating from stagnant surface water bodies has increased by about 50% over the last seventy years while the relative contribution from direct infiltration of rain has decreased. This regional shift in the source of groundwater shows how the simultaneous expansion of irrigated rice, excavated ponds and groundwater pumping has changed the hydrologic system by cycling evaporated standing water through the subsurface. Analysis of water isotope data also reveals that most recharge from standing water enters during the latter part of the dry season (February-April), while most rainwater recharge occurs in the early months of the monsoon (June-August) before aquifers fill to capacity and reject additional recharge of rainwater.

Across South Asia, millions of villagers have reduced their exposure to high-arsenic (As) groundwater by switching to low-As wells. Isotopic tracers and flow modeling are used in this study to understand the groundwater flow system of a semi-confined aquifer of Pleistocene (>10 kyr) age in Bangladesh that is generally low in As but has been perturbed by massive pumping at a distance of about 25 km for the municipal water supply of Dhaka. A 10- to 15-m-thick clay aquitard caps much of the intermediate aquifer (>40- to 90-m depth) in the 3-km(2) study area, with some interruptions by younger channel sand deposits indicative of river scouring. Hydraulic heads in the intermediate aquifer below the clay-capped areas are 1–2 m lower than in the high-As shallow aquifer above the clay layer. In contrast, similar heads in the shallow and intermediate aquifer are observed where the clay layer is missing. The head distribution suggests a pattern of downward flow through interruptions in the aquitard and lateral advection from the sandy areas to the confined portion of the aquifer. The interpreted flow system is consistent with (3)H-(3)He ages, stable isotope data, and groundwater flow modeling. Lateral flow could explain an association of elevated As with high methane concentrations within layers of gray sand below certain clay-capped portions of the Pleistocene aquifer. An influx of dissolved organic carbon from the clay layer itself leading to a reduction of initially orange sands has also likely contributed to the rise of As.

Climate science provides strong evidence of the necessity of limiting global warming to 1.5 °C, in line with the Paris Climate Agreement. The IPCC 1.5 °C special report (SR1.5) presents 414 emissions scenarios modelled for the report, of which around 50 are classified as ‘1.5 °C scenarios’, with no or low temperature overshoot. These emission scenarios differ in their reliance on individual mitigation levers, including reduction of global energy demand, decarbonisation of energy production, development of land-management systems, and the pace and scale of deploying carbon dioxide removal (CDR) technologies. The reliance of 1.5 °C scenarios on these levers needs to be critically assessed in light of the potentials of the relevant technologies and roll-out plans. We use a set of five parameters to bundle and characterise the mitigation levers employed in the SR1.5 1.5 °C scenarios. For each of these levers, we draw on the literature to define ‘medium’ and ‘high’ upper bounds that delineate between their ‘reasonable’, ‘challenging’ and ‘speculative’ use by mid century. We do not find any 1.5 °C scenarios that stay within all medium upper bounds on the five mitigation levers. Scenarios most frequently ‘over use’ CDR with geological storage as a mitigation lever, whilst reductions of energy demand and carbon intensity of energy production are ‘over used’ less frequently. If we allow mitigation levers to be employed up to our high upper bounds, we are left with 22 of the SR1.5 1.5 °C scenarios with no or low overshoot. The scenarios that fulfil these criteria are characterised by greater coverage of the available mitigation levers than those scenarios that exceed at least one of the high upper bounds. When excluding the two scenarios that exceed the SR1.5 carbon budget for limiting global warming to 1.5 °C, this subset of 1.5 °C scenarios shows a range of 15–22 Gt CO2 (16–22 Gt CO2 interquartile range) for emissions in 2030. For the year of reaching net zero CO2 emissions the range is 2039–2061 (2049–2057 interquartile range).

In this paper we study the time dependent Schrodinger equation with all possible self-adjoint singular interactions located at the origin, which include the δ and δ ′ -potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability and oscillatory properties of the solution of the Schrodinger equation subject to a generalized point interaction when the initial datum is a superoscillatory function.

Non-technical summaryWe summarize some of the past year's most important findings within climate change-related research. New research has improved our understanding of Earth's sensitivity to carbon dioxide, finds that permafrost thaw could release more carbon emissions than expected and that the uptake of carbon in tropical ecosystems is weakening. Adverse impacts on human society include increasing water shortages and impacts on mental health. Options for solutions emerge from rethinking economic models, rights-based litigation, strengthened governance systems and a new social contract. The disruption caused by COVID-19 could be seized as an opportunity for positive change, directing economic stimulus towards sustainable investments.Technical summaryA synthesis is made of ten fields within climate science where there have been significant advances since mid-2019, through an expert elicitation process with broad disciplinary scope. Findings include: (1) a better understanding of equilibrium climate sensitivity; (2) abrupt thaw as an accelerator of carbon release from permafrost; (3) changes to global and regional land carbon sinks; (4) impacts of climate change on water crises, including equity perspectives; (5) adverse effects on mental health from climate change; (6) immediate effects on climate of the COVID-19 pandemic and requirements for recovery packages to deliver on the Paris Agreement; (7) suggested long-term changes to governance and a social contract to address climate change, learning from the current pandemic, (8) updated positive cost–benefit ratio and new perspectives on the potential for green growth in the short- and long-term perspective; (9) urban electrification as a strategy to move towards low-carbon energy systems and (10) rights-based litigation as an increasingly important method to address climate change, with recent clarifications on the legal standing and representation of future generations.Social media summaryStronger permafrost thaw, COVID-19 effects and growing mental health impacts among highlights of latest climate science.

A Dy:KPb2Cl5 laser oscillating at 4.4 m under diode laser pumping at 1.7 m is demonstrated for the first time. Maximum output pulse energy of 0.3 mJ was achieved at 5.2 mJ of absorbed pump energy.

A Dy:KPb2Cl5 (KPC) laser oscillating at approximately 4.4 µm under diode laser pumping at 1.7 µm is demonstrated for the first time. A maximum output pulse energy of 1.1 mJ was achieved at 10 mJ of absorbed pump energy. Tunable laser oscillation in the 4.2–4.5 µm spectral range was recorded with this crystal. Limitations of Dy:KPC for laser oscillation due to its challenging thermo-optical properties are discussed. This crystal is a further addition to the range of low-phonon-energy materials doped with Dy ions that can be applied for laser oscillation in the mid-infrared spectral range under direct diode laser pumping.

Data from GEOTRACES cruises GN01 (HLY1502) and GN04 (PS94) have been archived at the Biological & Chemical Oceanography Data Management Office (BCO-DMO; https://www.bco-dmo.org/deployment/638807) and PANGAEA (https://www.pangaea.de/?q=PS94&f.campaign%5B%5D=PS94) websites, respectively. The inorganic carbon data are available at the NOAA Ocean Carbon Data System (OCADS ; doi :10.3334/CDIAC/OTG.CLIVAR_ARC01_33HQ20150809). In addition to these national data archives, the data used in this paper is available as a supplementary downloadable excel file; International audience; A major surface circulation feature of the Arctic Ocean is the Transpolar Drift (TPD), a current that transports river‐influenced shelf water from the Laptev and East Siberian Seas toward the center of the basin and Fram Strait. In 2015, the international GEOTRACES program included a high‐resolution pan‐Arctic survey of carbon, nutrients, and a suite of trace elements and isotopes (TEIs). The cruises bisected the TPD at two locations in the central basin, which were defined by maxima in meteoric water and dissolved organic carbon concentrations that spanned 600 km horizontally and ~25‐50 m vertically. Dissolved TEIs such as Fe, Co, Ni, Cu, Hg, Nd, and Th, which are generally particle‐reactive but can be complexed by organic matter, were observed at concentrations much higher than expected for the open ocean setting. Other trace element concentrations such as Al, V, Ga, and Pb were lower than expected due to scavenging over the productive East Siberian and Laptev shelf seas. Using a combination of radionuclide tracers and ice drift modeling, the transport rate for the core of the TPD was estimated at 0.9 ± 0.4 Sv (106 m3 s‐1). This rate was used to derive the mass flux for TEIs that were enriched in the TPD, revealing the importance of lateral transport in supplying materials beneath the ice to the central Arctic Ocean and potentially to the North Atlantic Ocean via Fram Strait. Continued intensification of the Arctic hydrologic cycle and permafrost degradation will likely lead to an increase in the flux of TEIs into the Arctic Ocean.

In this perspective on the future of the Arctic, we explore actions taken to mitigate warming and adapt to change since the Paris agreement on the temperature threshold that should not be exceeded in order to avoid dangerous interference with the climate system. Although 5 years may seem too short a time for implementation of major interventions, it actually is a considerable time span given the urgency at which we must act if we want to avoid crossing the 1.5 to

The contribution deals with issues of road administration in municipalities in terms of the requirements for engineering renovations of urban communications networks. The goal is to declare an end to the degradation of the quality and service of local roads in cities. The reason is the lack of funding. The engineering analysis should demonstrate the need to make an informed request for reconstruction of local roads in our towns and cities. The aim of this paper is to describe the processes that are related to specific engineering work but are closely linked to the performance of the preparation on both sides, i.e., the administration versus the design. Why do we passively observe the gradual destruction of the quality of our local roads in the cities? Before our eyes the road constructions of roadways crumble, on the other hand, the level of their transport service on them only presents us with traffic jams. How can you know the status of the background of our streets and their pavements in an urbanized area? A couple of technical studies oriented towards the advance of public transport, especially for Bratislava, the capital of Slovakia which were based on traffic modelling together with engineering designs were published (Borš et.al, 2017; Pomichal et.al, 2017; Koštial et.al, 2017; Schlosser and Schlosser, 2016; Schlosser and Orthová, 2016; Schlosser et.al, 2016; Schlosser et.al, 2017; Schlosser et.al, 2017). Some answers to the complexities of this issue are set out in this article.

Tectonic landforms reveal that the West Antarctic Ice Sheet (WAIS) lies atop a major volcanic rift system. However, identifying subglacial volcanism is challenging. Here we show geochemical evidence of a volcanic heat source upstream of the fast-melting Pine Island Ice Shelf, documented by seawater helium isotope ratios at the front of the Ice Shelf cavity. The localization of mantle helium to glacial meltwater reveals that volcanic heat induces melt beneath the grounded glacier and feeds the subglacial hydrological network crossing the grounding line. The observed transport of mantle helium out of the Ice Shelf cavity indicates that volcanic heat is supplied to the grounded glacier at a rate of ~ 2500 ± 1700 MW, which is ca. half as large as the active Grimsvötn volcano on Iceland. Our finding of a substantial volcanic heat source beneath a major WAIS glacier highlights the need to understand subglacial volcanism, its hydrologic interaction with the marine margins, and its potential role in the future stability of the WAIS., The West Antarctic Ice Sheet sits atop an extensional rift system with volcano-like features, yet we do not know if any of these volcanoes are active, because identifying subglacial volcanism remains a challenge. Here, the authors find evidence in helium isotopes that a large volcanic heat source is emanating from beneath the fast-melting Pine Island Ice Glacier.

We present tritium (3H) and helium isotope (δ3He) data from the South China Sea (SCS), to estimate apparent oxygen utilization rates (AOURs). The observed δ3He values are close to the theoretical solubility equilibrium value of -1.7% in the upper mixed layer, followed by an increase with depth down to ~1500 m. Below 1500 m depth, δ3He is homogenously distributed with a value of 20.9% ± 1.0%. The distribution of δ3He reveals that a significant fraction of 3He throughout the water column over the entire SCS basin is allochthonous, derived from mantle sources originated from the Pacific Ocean. By using the salinity-normalized “potential” alkalinity (NPA) as a conservative mixing tracer, 3He produced by tritium decay (tritiogenic) was separated from mantle 3He, and the apparent 3H–3He ages of the SCS water masses were subsequently calculated to be 11 ± 5 years at 100 m depth and 50 ± 4 years at 1000 m. Together with the observed dissolved oxygen concentrations, we estimated the mean AOURs and obtained values of 4.15 ± 0.27 μmol kg−1·yr−1 for the depth range of 100–500 m, and 0.81 ± 0.23 μmol kg−1·yr−1 for that between 800 and 1000 m depth. The depth-integrated AOURs between 100 and 1000 m depth, yield a spatially and temporally averaged export flux of organic carbon of 1.96 ± 0.16 mol-C·m−2·yr−1, comparable with previous estimates based on either 238U/234Th disequilibrium or nutrient and oxygen mass balance calculations in the SCS.

Dual-domain transport is an alternative conceptual and mathematical paradigm to advection-dispersion for describing the movement of dissolved constituents in groundwater. Here we test the use of a dual-domain algorithm combined with advective pathline tracking to help reconcile environmental tracer concentrations measured in springs within the Shenandoah Valley, USA. The approach also allows for the estimation of the three dual-domain parameters: mobile porosity, immobile porosity, and a domain exchange rate constant. Concentrations of CFC-113, SF6, 3H, and 3He were measured at 28 springs emanating from carbonate rocks. The different tracers give three different mean composite piston-flow ages for all the springs that vary from 5 to 18 years. Here we compare four algorithms that interpret the tracer concentrations in terms of groundwater age: piston flow, old-fraction mixing, advective-flow path modeling, and dual-domain modeling. Whereas the second two algorithms made slight improvements over piston flow at reconciling the disparate piston-flow age estimates, the dual-domain algorithm gave a very marked improvement. Optimal values for the three transport parameters were also obtained, although the immobile porosity value was not well constrained. Parameter correlation and sensitivities were calculated to help quantify the uncertainty. Although some correlation exists between the three parameters being estimated, a watershed simulation of a pollutant breakthrough to a local stream illustrates that the estimated transport parameters can still substantially help to constrain and predict the nature and timing of solute transport. The combined use of multiple environmental tracers with this dual-domain approach could be applicable in a wide variety of fractured-rock settings.

The spatial heterogeneity of dissolved arsenic (As) concentrations in shallow groundwater of the Bengal Basin has been attributed to transport of As (and reactive carbon) from external sources or to the release of As from within grey sand formations. We explore the latter scenario in this detailed hydrological and geochemical study along a 300 m transect of a shallow aquifer extending from a groundwater recharge area within a sandy channel bar to its discharge into a nearby stream. Within the 10–20 m depth range, groundwater ages along the transect determined by the 3H–3He method increase from

Hydrothermal vents along the ocean's tectonic ridge systems inject superheated water and large amounts of dissolved metals that impact the deep ocean circulation and the oceanic cycling of trace metals. The hydrothermal fluid contains dissolved mantle helium that is enriched in 3He relative to the atmosphere, providing an isotopic tracer of the ocean's deep circulation and a marker of hydrothermal sources. This work investigates the potential for the 3He/4He isotope ratio to constrain the ocean's mantle 3He source and to provide constraints on the ocean's deep circulation. We use an ensemble of 11 data-assimilated steady-state ocean circulation models and a mantle helium source based on geographically varying sea-floor spreading rates. The global source distribution is partitioned into 6 regions, and the vertical profile and source amplitude of each region are varied independently to determine the optimal 3He source distribution that minimizes the mismatch between modeled and observed δ3He. In this way, we are able to fit the observed δ3He distribution to within a relative error of ∼15%, with a global 3He source that ranges from 640 to 850 mol yr−1, depending on circulation. The fit captures the vertical and interbasin gradients of the δ3He distribution very well and reproduces its jet-sheared saddle point in the deep equatorial Pacific. This demonstrates that the data-assimilated models have much greater fidelity to the deep ocean circulation than other coarse-resolution ocean models. Nonetheless, the modelled δ3He distributions still display some systematic biases, especially in the deep North Pacific where δ3He is overpredicted by our models, and in the southeastern tropical Pacific, where observed westward-spreading δ3He plumes are not well captured. Sources inferred by the data-assimilated transport with and without isopycnally aligned eddy diffusivity differ widely in the Southern Ocean, in spite of the ability to match the observed distributions of CFCs and radiocarbon for either eddy parameterization.