Institute of Computational Mathematics and Mathematical Geophysics

Abstract High-energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. To increase the energy of the particles or to reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration 1–5 , in which the electrons in a plasma are excited, leading to strong electric fields (so called ‘wakefields’), is one such promising acceleration technique. Experiments have shown that an intense laser pulse 6–9 or electron bunch 10,11 traversing a plasma can drive electric fields of tens of gigavolts per metre and above—well beyond those achieved in conventional radio-frequency accelerators (about 0.1 gigavolt per metre). However, the low stored energy of laser pulses and electron bunches means that multiple acceleration stages are needed to reach very high particle energies 5,12 . The use of proton bunches is compelling because they have the potential to drive wakefields and to accelerate electrons to high energy in a single acceleration stage 13 . Long, thin proton bunches can be used because they undergo a process called self-modulation 14–16 , a particle–plasma interaction that splits the bunch longitudinally into a series of high-density microbunches, which then act resonantly to create large wakefields. The Advanced Wakefield (AWAKE) experiment at CERN 17–19 uses high-intensity proton bunches—in which each proton has an energy of 400 gigaelectronvolts, resulting in a total bunch energy of 19 kilojoules—to drive a wakefield in a ten-metre-long plasma. Electron bunches are then injected into this wakefield. Here we present measurements of electrons accelerated up to two gigaelectronvolts at the AWAKE experiment, in a demonstration of proton-driven plasma wakefield acceleration. Measurements were conducted under various plasma conditions and the acceleration was found to be consistent and reliable. The potential for this scheme to produce very high-energy electron bunches in a single accelerating stage 20 means that our results are an important step towards the development of future high-energy particle accelerators 21,22 .

Abstract Hydrographic data collected from research cruises, bottom‐anchored moorings, drifting Ice‐Tethered Profilers, and satellite altimetry in the Beaufort Gyre region of the Arctic Ocean document an increase of more than 6,400 km 3 of liquid freshwater content from 2003 to 2018: a 40% growth relative to the climatology of the 1970s. This fresh water accumulation is shown to result from persistent anticyclonic atmospheric wind forcing (1997–2018) accompanied by sea ice melt, a wind‐forced redirection of Mackenzie River discharge from predominantly eastward to westward flow, and a contribution of low salinity waters of Pacific Ocean origin via Bering Strait. Despite significant uncertainties in the different observations, this study has demonstrated the synergistic value of having multiple diverse datasets to obtain a more comprehensive understanding of Beaufort Gyre freshwater content variability. For example, Beaufort Gyre Observational System (BGOS) surveys clearly show the interannual increase in freshwater content, but without satellite or Ice‐Tethered Profiler measurements, it is not possible to resolve the seasonal cycle of freshwater content, which in fact is larger than the year‐to‐year variability, or the more subtle interannual variations.

As a part of the Arctic Ocean Model Intercomparison Project, results from 10 Arctic ocean/ice models are intercompared over the period 1970 through 1999. Models' monthly mean outputs are laterally integrated over two subdomains (Amerasian and Eurasian basins), then examined as functions of depth and time. Differences in such fields as averaged temperature and salinity arise from models' differences in parameterizations and numerical methods and from different domain sizes, with anomalies that develop at lower latitudes carried into the Arctic. A systematic deficiency is seen as AOMIP models tend to produce thermally stratified upper layers rather than the “cold halocline”, suggesting missing physics perhaps related to vertical mixing or to shelf‐basin exchanges. Flow fields pose a challenge for intercomparison. We introduce topostrophy, the vertical component of V × ∇ D where V is monthly mean velocity and ∇ D is the gradient of total depth, characterizing the tendency to follow topographic slopes. Positive topostrophy expresses a tendency for cyclonic “rim currents”. Systematic differences of models' circulations are found to depend strongly upon assumed roles of unresolved eddies.

Pacific Water (PW) enters the Arctic Ocean through Bering Strait and brings in heat, fresh water, and nutrients from the northern Bering Sea. The circulation of PW in the central Arctic Ocean is only partially understood due to the lack of observations. In this paper, pathways of PW are investigated using simulations with six state-of-the art regional and global Ocean General Circulation Models (OGCMs). In the simulations, PW is tracked by a passive tracer, released in Bering Strait. Simulated PW spreads from the Bering Strait region in three major branches. One of them starts in the Barrow Canyon, bringing PW along the continental slope of Alaska into the Canadian Straits and then into Baffin Bay. The second begins in the vicinity of the Herald Canyon and transports PW along the continental slope of the East Siberian Sea into the Transpolar Drift, and then through Fram Strait and the Greenland Sea. The third branch begins near the Herald Shoal and the central Chukchi shelf and brings PW into the Beaufort Gyre. In the models, the wind, acting via Ekman pumping, drives the seasonal and interannual variability of PW in the Canadian Basin of the Arctic Ocean. The wind affects the simulated PW pathways by changing the vertical shear of the relative vorticity of the ocean flow in the Canada Basin.

Abstract In order to study the effect of the micro‐CT scan resolution and size on the accuracy of upscaled digital rock property estimation of core samples Bentheimer sandstone images with the resolution varying from 0.9 μm to 24 μm are used. We statistically show that the correlation length of the pore‐to‐matrix distribution can be reliably determined for the images with the resolution finer than 9 voxels per correlation length and the representative volume for this property is about 15 3 correlation length. Similar resolution values for the statistically representative volume are also valid for the estimation of the total porosity, specific surface area, mean curvature, and topology of the pore space. Only the total porosity and the number of isolated pores are stably recovered, whereas geometry and the topological measures of the pore space are strongly affected by the resolution change. We also simulate fluid flow in the pore space and estimate permeability and tortuosity of the sample. The results demonstrate that the representative volume for the transport property calculation should be greater than 50 correlation lengths of pore‐to‐matrix distribution. On the other hand, permeability estimation based on the statistical analysis of equivalent realizations shows some weak influence of the resolution on the transport properties. The reason for this might be that the characteristic scale of the particular physical processes may affect the result stronger than the model (image) scale.

The onset of melatonin secretion in the evening is the most reliable and most widely used index of circadian timing in humans. Saliva (or plasma) is usually sampled every 0.5-1 hours under dim-light conditions in the evening 5-6 hours before usual bedtime to assess the dim-light melatonin onset (DLMO). For many years, attempts have been made to find a reliable objective determination of melatonin onset time either by fixed or dynamic threshold approaches. The here-developed hockey-stick algorithm, used as an interactive computer-based approach, fits the evening melatonin profile by a piecewise linear-parabolic function represented as a straight line switching to the branch of a parabola. The switch point is considered to reliably estimate melatonin rise time. We applied the hockey-stick method to 109 half-hourly melatonin profiles to assess the DLMOs and compared these estimates to visual ratings from three experts in the field. The DLMOs of 103 profiles were considered to be clearly quantifiable. The hockey-stick DLMO estimates were on average 4 minutes earlier than the experts' estimates, with a range of -27 to +13 minutes; in 47% of the cases the difference fell within ±5 minutes, in 98% within -20 to +13 minutes. The raters' and hockey-stick estimates showed poor accordance with DLMOs defined by threshold methods. Thus, the hockey-stick algorithm is a reliable objective method to estimate melatonin rise time, which does not depend on a threshold value and is free from errors arising from differences in subjective circadian phase estimates. The method is available as a computerized program that can be easily used in research settings and clinical practice either for salivary or plasma melatonin values.

We give direct experimental evidence for the observation of the full transverse self-modulation of a long, relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a periodic density modulation resulting from radial wakefield effects. We show that the modulation is seeded by a relativistic ionization front created using an intense laser pulse copropagating with the proton bunch. The modulation extends over the length of the proton bunch following the seed point. By varying the plasma density over one order of magnitude, we show that the modulation frequency scales with the expected dependence on the plasma density, i.e., it is equal to the plasma frequency, as expected from theory.

Abstract Accelerating since the early 1990s, the Greenland Ice Sheet mass loss exerts a significant impact on thermohaline processes in the sub‐Arctic seas. Surplus freshwater discharge from Greenland since the 1990s, comparable in volume to the amount of freshwater present during the Great Salinity Anomaly events, could spread and accumulate in the sub‐Arctic seas, influencing convective processes there. However, hydrographic observations in the Labrador Sea and the Nordic Seas, where the Greenland freshening signal might be expected to propagate, do not show a persistent freshening in the upper ocean during last two decades. This raises the question of where the surplus Greenland freshwater has propagated. In order to investigate the fate, pathways, and propagation rate of Greenland meltwater in the sub‐Arctic seas, several numerical experiments using a passive tracer to track the spreading of Greenland freshwater have been conducted as a part of the Forum for Arctic Ocean Modeling and Observational Synthesis effort. The models show that Greenland freshwater propagates and accumulates in the sub‐Arctic seas, although the models disagree on the amount of tracer propagation into the convective regions. Results highlight the differences in simulated physical mechanisms at play in different models and underscore the continued importance of intercomparison studies. It is estimated that surplus Greenland freshwater flux should have caused a salinity decrease by 0.06–0.08 in the sub‐Arctic seas in contradiction with the recently observed salinification (by 0.15–0.2) in the region. It is surmised that the increasing salinity of Atlantic Water has obscured the freshening signal.

We measure the effects of transverse wakefields driven by a relativistic proton bunch in plasma with densities of 2.1×10^{14} and 7.7×10^{14} electrons/cm^{3}. We show that these wakefields periodically defocus the proton bunch itself, consistently with the development of the seeded self-modulation process. We show that the defocusing increases both along the bunch and along the plasma by using time resolved and time-integrated measurements of the proton bunch transverse distribution. We evaluate the transverse wakefield amplitudes and show that they exceed their seed value (<15 MV/m) and reach over 300 MV/m. All these results confirm the development of the seeded self-modulation process, a necessary condition for external injection of low energy and acceleration of electrons to multi-GeV energy levels.

In the present article, different types of semantics for the logic N4, the paraconsistent variant of Nelson's constructive logic with strong negation, will be considered. N4 will be characterized in terms of so-called Fidel-structures. It will be stated that Fidel-structures are equivalent to twist-structures. Further, the N4-lattices, generalization of N-lattices, will be defined and it will be proved that they can be represented as twist-structures. It will be proved that N4-lattices form a variety νN4 and there is a natural dual isomorphism between the lattice of subvarieties of νN4 and the lattice of N4-extensions.

ABSTRACT In this paper, we present new seismic and heat‐flow data that show the base of the hydrate stability zone (BHSZ) in Lake Baikal to be locally characterized by abnormal variations in depth, with distinct regions of deeper‐than‐normal and regions of shallower‐than‐normal BHSZ. These variations are related to strong lateral variations in heat flow, and occur in close association with important rift‐basin faults. Areas of shallow BHSZ are also characterized by the presence of several methane seeps and mud volcanoes at the lake floor. We infer that the seeps are the surface expression of escape pathways for overpressured fluids generated by the dissociation of pre‐existing hydrates, in response to a thermal pulse caused by an upward flow of hydrothermal fluids towards the BHSZ. It thus seems that present‐day hydrate dissociation in Lake Baikal is modulated by the tectonic activity in the rift rather than by – climatically controlled – changes in lake level or water temperature.

ABSTRACT Numerical simulations of wave propagation produce different errors and the most well known is numerical dispersion, which is only valid for homogeneous media. However, there is a lack of error studies for heterogeneous media or even for the canonical case of media that have two constant velocity layers. The error associated with media that have two layers is called an interface error, and it typically converges to zero with a lower order of convergence compared to the theoretical convergence rate of the finite-difference schemes (FDS) for homogeneous media. We evaluated a detailed numerical study of the interface error for three staggered-grid FDS that are commonly used in the simulation of seismic-wave propagation. We determined that a standard staggered-grid scheme (SSGS) (also known as the Virieux scheme), a rotated staggered-grid scheme (RSGS), and a Lebedev scheme (LS) preserve the second order of convergence at horizontal/vertical solid-solid interfaces when the medium parameters have been properly modified, such as by harmonic averaging of finely layered media for the stiffness tensor and arithmetic mean for the density. However, for a fluid-solid interface aligned with the grid line, a second-order convergence can only be achieved by an SSGS. In addition, the presence of a fluid-solid interface reduces the order of convergence for the LS and the RSGS to a first order of convergence. The presence of inclined interfaces makes high-order (second and more) convergence impossible.

We performed a set of numerical experiments in order to better simulate the circulation of Atlantic Water in the Arctic Ocean by employing a coupled ice‐ocean Arctic regional model. We found that the inflow of Atlantic Water via Fram Strait is weak in the case of high viscosity and diffusivity coefficients (1 · 10 8 cm 2 /s and 1 · 10 7 cm 2 /s) and creates an anticyclonic circulation in the Eurasian basin. This flow increases significantly when both coefficients are scaled down (to 1 · 10 7 cm 2 /s and 0.5 · 10 6 cm 2 /s) but the current path is then unstable, and it becomes mostly anticyclonic after about a decade of integration. A further reduction of these coefficients leads to growing instabilities due to insufficient grid resolution. Short‐term integration of the model with doubled space resolution shows better agreement with observations, but long‐term calculation is still restricted by simulation time. Alternatively, a lower resolution version of this model benefits from parameterizations of subscale processes. Incorporation of the Neptune parameterization of eddy‐topography interaction into the model intensifies the current steered by subsurface topography and results in cyclonic circulation of the Atlantic Water in every subbasin and in the whole Arctic region. In the absence of salinity restoring there was strong salinity drift at the surface, resulting in a salinity increase in the central Arctic by 3 units from 1960 to 2005. The Arctic freshwater content is driven basically by year‐to‐year variations of convective mixing involving more saline water from lower layers. After cooling and increasing in salinity through brine rejection, the surface water becomes denser, leading to even stronger convective mixing. One‐dimensional model tests showed how model performance could be improved by implementing a lower vertical diffusion coefficient and higher vertical resolution.

Depending on the reaction conditions and the nature of substituents at the triple bond, anionic cyclizations of hydrazides of o-acetylenyl benzoic acids can be selectively directed along three alternative paths, each of which provides efficient access to a different class of nitrogen heterocycles. The competition between 5-exo and 6-endo cyclizations of the "internal" nitrogen nucleophile is controlled by the nature of alkyne substituents under the kinetic control conditions. In the presence of KOH, the initially formed 5-exo products undergo a new rearrangement that involves a ring-opening followed by recyclization to the formal 6-exo-products and rendered irreversible by a prototropic isomerization. DFT computations provide insight into the nature of factors controlling relative rates of 5-exo, 6-endo, and 6-exo cyclization paths, ascertain the feasibility of direct 6-exo closure and relative stability for the anionic precursor for this process, provide, for the first time, the benchmark data for several classes of anionic nitrogen cyclizations, and dissect stereoelectronic effects controlling relative stability of cyclic anionic intermediates and influencing reaction stereoselectivity. We show that the stability gain due transformation of a weak pi-bond into a stronger sigma-bond (the usual driving force for the cyclizations of alkynes) is offset in this case by the transformation of a stable nitrogen anion into an inherently less stable carbanionic center. As a result, the cyclizations are much more sensitive to external conditions and substituents than similar cyclizations of neutral species. However, the exothermicity of such anionic cyclizations is increased dramatically upon prototropic isomerization of the initially formed carbanions into the more stable N-anions. Such tautomerizations are likely to play the key role in driving such cyclizations to completion but may also prevent future applications of such processes as the first step in domino cyclization processes.

Abstract AWAKE is a proton-driven plasma wakefield acceleration experiment. We show that the experimental setup briefly described here is ready for systematic study of the seeded self-modulation of the 400 GeV proton bunch in the 10 m long rubidium plasma with density adjustable from 1 to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>10</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> </mml:math> cm −3 . We show that the short laser pulse used for ionization of the rubidium vapor propagates all the way along the column, suggesting full ionization of the vapor. We show that ionization occurs along the proton bunch, at the laser time and that the plasma that follows affects the proton bunch.

Circulant graphs have been extensively investigated over the past 30 years because of their broad application to different fields of theory and practice. Two known surveys on circulant networks including a survey on undirected circulants have been published: by Bermond et al. [Distributed loop computer networks: A survey, J. Parallel Distributed Comput.24 (1995) 2–10] and by Hwang [A survey on multi-loop networks, Theoret. Comput. Sci.299 (2003) 107–121]. The present paper includes the results which have not been presented there, in particular the works of Russian researchers, and also a lot of new results obtained in the area of research of circulant networks. We focus on the survey connected with study of structural and communicative properties of circulant networks.

For the first time, a high-resolution regional model is developed for the slope and shelf circulation within the Great Australian Bight and for the Gulfs region of South Australia. The results indicate the extent, nature, and dynamical interaction of a variety of circulation features that are most likely to be important for the region. In particular, the positive wind stress curl south of Australia leads to an equatorward Sverdrup transport in the deep ocean, westward Flinders Current along the slope, and upwelling of the (600 m) deep permanent thermocline. The wind stress curl also leads to a seaward topographic Sverdrup transport within the wide sloping shelf of the bight and results in an anticyclonic gyre that is intensified off the Eyre Peninsula and reduced in magnitude by the joint effect of baroclinicity and topographic relief. In the western half of the bight, the seaward surface Ekman and topographic transports are shown to converge with the onshore component of the Flinders Current leading to a ridge in sea level, eastward current over the shelf break, and downwelling to 100 m or so. The shelfbreak circulation is similar farther east but is driven by the anticyclonic gyre within the bight and a trough in sea level along the shelf slope: the latter results from the geostrophic adjustment to density anomalies that arise from wintertime downwelling and the Flinders Current. Limited hydrographic, satellite, and current meter data support the existence of an eastward shelfbreak current. Off the Gulfs and Robe regions, the wind-forced coastal currents are to the northwest and both the model and observations indicate that upwelling occurs to depths of up to 150 m.

In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive nonconforming finite element method. In each step of the algorithm, the iterative solution of the discrete system is controlled by an adaptive stopping criterion, and the local refinement is based on either a simple edge residual or a volume term, depending on an adaptive marking strategy. We prove that this marking strategy guarantees a strict reduction of the error, augmented by the volume term and an additional oscillation term, and quasi-optimal complexity of the generated sequence of meshes.

Abstract The coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.

This paper uses Covasim, an agent-based model (ABM) of COVID-19, to evaluate and scenarios of epidemic spread in New York State (USA) and the UK. Epidemiological parameters such as contagiousness (virus transmission rate), initial number of infected people, and probability of being tested depend on the region's demographic and geographical features, the containment measures introduced; they are calibrated to data about COVID-19 spread in the region of interest. At the first stage of our study, epidemiological data (numbers of people tested, diagnoses, critical cases, hospitalizations, and deaths) for each of the mentioned regions were analyzed. The data were characterized in terms of seasonality, stationarity, and dependency spaces, and were extrapolated using machine learning techniques to specify unknown epidemiological parameters of the model. At the second stage, the Optuna optimizer based on the tree Parzen estimation method for objective function minimization was applied to determine the model's unknown parameters. The model was validated with the historical data of 2020. The modeled results of COVID-19 spread in New York State and the UK have demonstrated that if the level of testing and containment measures is preserved, the number of positive cases in New York State remain the same during March of 2021, while in the UK it will reduce.