Diffuse Counterpart Research Articles

Power Brownian motion: an Ornstein-Uhlenbeck lookout

Abstract The well-known Ornstein-Uhlenbeck process (OUP) is the central go-to Gaussian model for statistical-equilibrium processes. The recently-introduced power Brownian motion (PBM) is a Gaussian model for diffusive motions, regular and anomalous alike. Using the Lamperti transform, this paper establishes PBM as the ‘diffusion counterpart’ of the OUP. Namely, the paper shows that PBM is for diffusive motions what the OUP is for statistical-equilibrium processes. The intimate parallels between the OUP and PBM are explored and illuminated via four main perspectives. 1) Statistical characterizations. 2) Kernel-integration with respect to Gaussian white noise. 3) Spatio-temporal scaling of the Wiener process. 4) Langevin stochastic dynamics driven by Gaussian white noise. To date, the prominent Gaussian models for anomalous diffusion are fractional Brownian motion (FBM), and scaled Brownian Motion (SBM). Due to its intimate OUP parallels, due to the ‘anomalous features’ it displays, due to the fact that it encompasses SBM, and following a detailed comparison to FBM: this paper argues the case for PBM as a central go-to Gaussian model for regular and anomalous diffusion.

Search of extended emission from HESS J1702-420 with eROSITA

is a peculiar TeV complex with a morphology changing from a diffuse source ( at $ 2$ TeV to a point-like one ( at $ 10$ TeV energies. The morphology and spectral properties of could be understood in terms of (diffusive) hadronic or leptonic models in which the observed TeV emission arises correpondingly from proton-proton or IC-radiation of relativistic particles present in the region. In this work, we perform searches of the X-ray counterpart of the source originating from the synchrotron emission of the primary or secondary relativistic electrons produced within leptonic or hadronic models. Such an emission can be extended and remain beyond the detection capabilities of narrow field-of-view instruments such as We utilised the publicly available first-6-months eROSITA dataset (DR1) fully covering the selected analysis region of $>5^ around We discuss biases connected to variable plasma temperature or neutral hydrogen column density in the region and present results based on the background modelling approach. The performed analysis does not allow us to detect the extended X-ray counterpart of of $0.07^ sizes. The derived upper limits are significantly higher than the expected hadronic model flux of the X-ray counterpart. For the leptonic model, the derived limits indicate the magnetic field in the region $B We argue that further advances in the diffuse X-ray counterpart searches could be achieved with either next-generation missions or Msec-long observational campaigns using currently operating instruments.

Nonlinear dynamics and pattern formation in a space–time discrete diffusive intraguild predation model

In this paper, the spatiotemporal dynamics and pattern formation of a space–time discrete intraguild predation model with self-diffusion are investigated. The model is obtained by applying a coupled map lattice (CML) method. First, using linear stability analysis, the existence and stability conditions for fixed points are determined. Second, using the center manifold theorem and the bifurcation theory, the occurrence of flip, Neimark-Sacker, and Turing bifurcations are discussed. It is shown that the patterns obtained are results of Turing, flip, and Neimark-Sacker instabilities. Numerical simulations are performed to verify the theoretical analysis and to reveal complex and rich dynamics of the model, such as times series, maximal Lyapunov exponent, bifurcation diagrams, and phase portraits. Interesting patterns like spiral pattern, polygonal pattern, and the combinations of patterns of spiral waves and stripes are formed. The CML model’s results help to understand how a spatially extended, discrete intraguild predation model forms complex patterns. Notably, the continuous reaction–diffusion counterpart of the model under study is incapable of experiencing Turing instability.

A possible direct exposure of the Earth to the cold dense interstellar medium 2–3 Myr ago

Cold, dense clouds in the interstellar medium of our Galaxy are 4–5 orders of magnitude denser than their diffuse counterparts. Our Solar System has most likely encountered at least one of these dense clouds during its lifetime. However, evidence for such an encounter has not been studied in detail yet. Here we derive the velocity field of the Local Ribbon of Cold Clouds (LRCC) by modelling the 21 cm data from the HI4PI survey, finding that the Solar System may have passed through the LRCC in the constellation Lynx 2–3 million years ago. Using a state-of-the-art simulation of the heliosphere, we show that during the passage, the heliosphere shrinks to a scale of 0.22 au, smaller than the Earth’s orbit around the Sun. This would have put the Earth in direct contact with the dense interstellar medium for a period of time and exposed it to a neutral hydrogen density above 3,000 cm−3. Such a scenario agrees with geological evidence from 60Fe and 244Pu isotopes. The encounter and related increased radiation from Galactic cosmic rays might have had a substantial impact on the Earth’s system and climate.

Unfolding rotational tectonics and topographic evolution from localized verses diffuse plate boundary counterparts

We present a kinematic model developed from geodetic observations, topography analysis and analogue tectonic modelling results, which reveals a striking similarity between the rotational tectonic settings of the Gakkel Ridge-Chersky Range system in the Arctic, and the Central Indian Tectonic Zone within the Indian subcontinent. A crucial aspect of large-scale extensional rift systems is the gradual variation of extension along the rift axis, due to plate rotation about a Euler pole, which may lead to contraction on the opposite side of the Euler pole to form a rotational tectonic system. Our geodetic and topographic analysis, combined with the reanalysis of analogue tectonic modelling results demonstrates such rotational tectonic plate motion in both the Arctic and Indian case. However, the plate boundary between the North American and Eurasian Plates as represented by the Arctic Gakkel Ridge-Chersky Range system is strongly localized, whereas the Central Indian Tectonic Zone that separates the North and South India Plates involves diffuse deformation instead. Furthermore, in both the Arctic and Central Indian we find that the relative Euler rotation pole is located near an indenter-like feature, which possibly controls the present-day rotational tectonics and contrasting topography on opposite sides of the Euler pole.

Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel

We deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable kernels is replacing the usual local diffusion defined by a second order differential operator. Since an appropriate kernel rescaling allows to define a sequence of solutions of the nonlocal diffusion problems converging to their local diffusion counterparts, we also find the corresponding isoperimetric inequalities for the latter, i.e. we prove the classical Talenti's theorem. The novelty of our approach is that we replace the measure geometric tools employed in Talenti's proof, such as the geometric isoperimetric inequality or the coarea formula, by the Riesz's rearrangement inequality. Thus, in addition to providing a proof for the nonlocal diffusion case, our technique also introduces an alternative proof to Talenti's theorem.

P26 Challenging Scenario: Scleroderma/Sjogren overlap with dysautonomia

Introduction/BackgroundScleroderma Overlap conditions are well defined and often behave differently than their limited or diffuse counterparts. The treatment for such patients is usually tailored around the organ system involvement and severity. We present a challenging case of Scleroderma/Sjogren overlap with refractory Raynaud's phenomenon who posed treatment challenges due to severe autonomic dysfunction.Description/Method76-year-old Caucasian lady, non-smoker, who presented in 1990’s with dry eyes, dry mouth and severe Raynaud's phenomenon with recurrent digital ulceration which became infected on multiple occasions. ANA was 1:400 with Extractable nuclear antigen Ro and La positive. Anti DsDNA was negative and C4 was low. Antiphospholipid antibodies and cryoglobulins are negative. She failed calcium channels blockers and phosphodiesterase 5 inhibitors and was intolerant to intravenous (IV) Iloprost which was tried on multiple occasions. IV latanoprost was tried as well. This treatment was complicated when she developed postural hypotension and multiple fall episodes during vasodilator use. This was attributed to autonomic dysfunction secondary to her Sjogren syndrome. She was initiated on Injection Fludrocortisone, however her hypotensive episodes continued. She received monthly intravenous immunoglobulins 20gm (over two days) infusion for a few months for autonomic dysfunction with some response. She eventually developed recurrent diarrhoea and abdominal pain and bloating which was attributed to small bowel overgrowth with rapid bowel transit on a gastric emptying scan. She had a blocked bile duct as well which was unblocked using Endoscopic Retrograde Cholangiopancreatography. Over the next 8 years, she continued struggling with refractory Raynaud’s, having failed IV regional guanethidine blocks and digital sympathectomy. Her postural hypotension decompensated on multiple occasions necessitating plasmapheresis which provided some benefit. In 2020, she was detected to have a PET avid slowly progressing left upper lobe lung lesion. She underwent left video assisted thoracoscopy surgery with upper lobectomy. Histology was suggestive of adenocarcinoma. In 2021, she had another fall episode due to an acute/subacute infarct of left pons. She continues having postural hypotension and requires regular plasmapheresis sessions to manage her symptoms. She is also presently on Bosentan for her raynaud’s phenomenon.Discussion/ResultsThis is a case of overlap of Sjogren syndrome with scleroderma features. Management of Refractory Raynaud’s as part of her scleroderma phenotype was challenging. This case gave us the opportunity to explore all the treatment options available for Raynaud’s phenomenon albeit with poor outcome. She also struggled with autonomic dysfunction leading to postural hypotension and gastrointestinal symptoms which can be seen in upto 50% of patients with Sjogren syndrome. Autonomic failure is often thought to be immune mediated in Sjogren syndrome. This makes way for the use of intravenous immunoglobulin and plasmapheresis to treat these conditions as was done in this case. Increased risk of lung carcinoma with scleroderma is well documented. Autonomic dysfunction can also present as paraneoplastic syndrome with lung carcinoma, however it is more common with small cell lung carcinoma and our patient was diagnosed with Adenocarcinoma. We would have to wait and see if the resection of the tumour has any demonstrable effect on her dysautonomia.Key learning points/ConclusionOverlap connective tissue diseases are often difficult to manage in view of extensive disease heterogeneity. Clinicians need to be aware of challenges in managing Difficult Raynaud’s with Autonomic dysfunction. Treating physicians need to be aware of the high risk of lung malignancy and regular close monitoring is required. This case-based conference gives us the opportunity to discuss further management approaches for her.

Dynamics for nonlocal diffusion problems with a free boundary

In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain global existence, uniqueness and longtime behavior of solution of these two problems. The spreading-vanishing dichotomy is established, and some sufficient conditions for spreading and vanishing are also derived. For scalar models, we prove that accelerated spreading could happen if and only if a threshold condition is violated by kernel function. Then we discuss a classical Lotka-Volterra predator-prey model with nonlocal diffusions and a free boundary which can be seen as nonlocal diffusion counterpart of the model in the work of Wang (2014) [24].

Convergence of solutions of a rescaled evolution nonlocal cross-diffusion problem to its local diffusion counterpart

We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada–Kawasaki–Teramoto nonlocal cross-diffusion problem converges to a solution of the usual problem with local diffusion. In particular, the result may be regarded as a new proof of existence of solutions for the local diffusion problem.

Universality and Intermittency of Pair Dispersion in Turbulence.

Turbulence can disperse a concentrated parcel of pollutants at a rate over nine orders of magnitude higher than its purely diffusive counterpart. One intriguing signature of turbulent dispersion is its superdiffusive scaling. However, the universality of this scaling law is still in question. By leveraging a new laboratory facility, particle pairs with small initial separations can be tracked over four decades of separation in time and five decades of separation in squared displacement, thereby observing the full range of dispersion scaling laws. The results show that the classical Richardson cubic scaling will be reached not for an initial separation asymptotically close to zero but at a critical value, and this value does not appear to depend on the Reynolds number, providing an effective way to study universal dispersion dynamics. Additionally, the results agree well with the prediction based on the multifractal model and may help reconcile different reported scaling laws from laboratory experiments and field studies.

Maximum principle preserving finite difference scheme for 1-D nonlocal-to-local diffusion problems

In a recent paper (Du et al., 2018), a quasi-nonlocal coupling method was introduced to seamlessly bridge a nonlocal diffusion model with the classical local diffusion counterpart in a one-dimensional space. The proposed coupling framework removes interfacial inconsistency, preserves the balance of fluxes, and satisfies the maximum principle of diffusion problem. However, the numerical scheme proposed in that paper does not maintain all of these properties on a discrete level. In this paper we resolve this issue by proposing a new finite difference scheme that ensures the balance of fluxes and the discrete maximum principle. We rigorously prove these results and provide the stability and convergence analyses accordingly. In addition, we provide the Courant–Friedrichs–Lewy (CFL) condition for the new scheme and test a series of benchmark examples which confirm the theoretical findings.

Global dynamics and zero-diffusion limit of a parabolic–elliptic–parabolic system for ion transport networks

This paper is concerned with a parabolic–elliptic–parabolic system arising from ion transport networks. It shows that for any properly regular initial data, the corresponding initial–boundary value problem associated with Neumann–Dirichlet boundary conditions possesses a global classical solution in one-dimensional setting, which is uniformly bounded and converges to a trivial steady state, either in infinite time with a time-decay rate or in finite time. Moreover, by taking the zero-diffusion limit of the third equation of the problem, the global weak solution of its partially diffusive counterpart is established and the explicit convergence rate of the solution of the fully diffusive problem toward the solution of the partially diffusive counterpart, as the diffusivity tends to zero, is obtained.

Heavy Elements Unveil the Non-primordial Origin of the Giant H I Ring in Leo

Abstract The origin and fate of the most extended extragalactic neutral cloud known in the local universe, the Leo ring, is still debated 38 yr after its discovery. Its existence is alternatively attributed to leftover primordial gas with some low level of metal pollution versus enriched gas stripped during a galaxy−galaxy encounter. Taking advantage of Multi Unit Spectroscopic Explorer operating at the Very Large Telescope, we performed optical integral field spectroscopy of three H I clumps in the Leo ring where ultraviolet continuum emission has been found. We detected, for the first time, ionized hydrogen in the ring and identify four nebular regions powered by massive stars. These nebulae show several metal lines ([O III], [N II], [S II]) that allowed reliable measures of metallicities, found to be close to or above the solar value (0.8 ≤ Z/Z ⊙ ≤ 1.4). Given the faintness of the diffuse stellar counterparts, less than 3% of the observed heavy elements could have been produced locally in the main body of the ring and not much more than 15% in the H I clump toward M96. This inference, and the chemical homogeneity among the regions, convincingly demonstrates that the gas in the ring is not primordial, but has been pre-enriched in a galaxy disk, then later removed and shaped by tidal forces and it is forming a sparse population of stars.

Fourth order indirect diffusion coupled with shock filter and source for text binarization

In this paper, we present a binarization method for degraded document images with contrast variation or low contrast, which couples a selective shock filter and a time-dependent source to a fourth order indirect diffusion process. The role of the selective shock filter is to enhance the edges as far as possible, while the time-dependent source plays an increasingly predominant role in the process of binarization. The fourth order indirect diffusion not only keeps the merit of noise immunity of the direct diffusion counterpart, but also preferably preserves the low-frequency components to avoid blur and dislocation of weak edges. We develop a novel numerical scheme for solving our model effectively and efficiently, by incorporating finite differencing with the parallel splitting up method in the literature. The proposed algorithm is tested on seven publicly available datasets (Document Image Binarization COmpetition (DIBCO) 2009 to 2014 and 2016). The experimental results indicate that our model is very effective for binarization of document images with contrast variation or low contrast, and has mostly the best effect for document images from the DIBCO datasets, compared with four partial differential equation (PDE) models and four benchmark and recent non-PDE methods.

Molecular characterization of localized pleural mesothelioma.

Localized pleural mesothelioma is a rare solitary circumscribed pleural tumor that is microscopically similar to diffuse malignant pleural mesothelioma. However, the molecular characteristics and nosologic relationship with its diffuse counterpart remain unknown. In a consecutive cohort of 1110 patients with pleural mesotheliomas diagnosedin 2005-2018, we identified six (0.5%) patients diagnosed with localized pleural mesotheliomas. We gathered clinical history, evaluated the histopathology, and in select cases performed karyotypic analysis and targeted next-generation sequencing. The cohort included three women and three men (median age 63; range 28-76), often presenting incidentally during radiologic evaluation for unrelated conditions. Neoadjuvant chemotherapy was administered in two patients. All tumors (median size 5.0 cm; range 2.7-13.5 cm) demonstrated gross circumscription (with microscopic invasion into lung, soft tissue, and/or rib in four cases), mesothelioma histology (four biphasic and two epithelioid types), and mesothelial immunophenotype. Of four patients with at least 6-month follow-up, three were alive (up to 8.9 years). Genomic characterization identified several subgroups: (1) BAP1 mutations with deletions of CDKN2A and NF2 in two tumors; (2) TRAF7 mutations in two tumors, including one harboring trisomies of chromosomes 3, 5, 7, and X; and (3) genomic near-haploidization, characterized by extensive loss of heterozygosity sparing chromosomes 5 and 7. Localized pleural mesotheliomas appear genetically heterogeneous and include BAP1-mutated, TRAF7-mutated, and near-haploid subgroups. While the BAP1-mutated subgroup is similar to diffuse malignant pleural mesotheliomas, the TRAF7-mutated subgroup overlaps genetically with adenomatoid tumors and well-differentiated papillary mesotheliomas, in which recurrent TRAF7 mutations have been described. Genomic near-haploidization, identified recently in a subset of diffuse malignant pleural mesotheliomas, suggests a novel mechanism in the pathogenesis of both localized pleural mesothelioma and diffuse malignant pleural mesothelioma. Our findings describe distinctive genetic features of localized pleural mesothelioma, with both similarities to and differences from diffuse malignant pleural mesothelioma.

The daylight climate of Athens: Variations and tendencies in the period 1992–2017, the brightening era

Though numerous daylight studies have been conducted worldwide, works for the daylight climate and/or the daylight variations/trends are rare. This gap is treated here. Therefore, the innovative trend analysis and the month–hour diagrams are applied to the illuminance time series at Athens over the period of 1992–2017 under all-/clear-sky conditions. For all skies, the global illuminance shows a broad maximum at summer noon, while the diffuse counterpart is in spring. Under clear skies, the global illuminance maximum becomes broader, covering spring/summer. However, the diffuse illuminance maximum splits into minor ones in April and June. The innovative trend analysis method finds that the identified trends are + 2.83%/decade (−1.89%/decade) for the global (diffuse) illuminance, under all skies. In clear skies, the above values are modified to +2.66%/decade (−2.00%/decade). These results confirm a recovery in the Athens daylight levels as in the solar radiation ones found by many researchers. Another outcome of the study concerns the observed decline in diffuse illuminance levels in the examined period, which may be attributed to a decline in cloudiness and an increase of sunshine over the area. Also, the variation of the global and diffuse illuminance efficacies on a month–hour basis is examined using the month–hour diagram method.

Oxygen transport in polymer electrolyte membrane fuel cells based on measured electrode pore structure and mass transport properties

Oxygen transport to the reaction sites through electrode structure is crucial to the operation and performance of polymer electrolyte membrane fuel cells. In this study, a 3-D steady-state simulation is developed to investigate the oxygen transport phenomena utilizing the measured ex-situ transport properties and the actual dimensions of the cell components as input parameters, and the simulation is validated with the in-situ experimental data on the current-voltage relation. The pore structure is measured by the method of Standard Porosimetry based on capillary equilibrium. The indicators for the ability of mass convection and diffusion in the electrodes, permeability and effective diffusibility, are measured based on the Darcy’s and Fick’s laws, respectively. The simulation results demonstrate that the average through-plane convective oxygen flux is about 20% of its diffusive counterpart under small current densities (0.10 A·cm−2), while it is reduced to only 5–14% under high current densities (1.22 A·cm−2). The local oxygen transport also varies significantly with the locations inside the cathode electrode under various average current densities. The results suggest that if measures can be taken to enhance the convection in the porous electrode under high current densities, the transport of oxygen to the reaction sites can be considerably improved.

A nano-structured PbSe polycrystalline material prepared by ion beam implantation: Properties and comparison with the diffusion counterpart

Manipulating the stoichiometric distribution along depth direction is a promising technique to modulate the optical and optoelectronic properties of the mid-infrared sensitive lead chalcogenides at room temperature. Here, we demonstrate an optoelectronic sensitization method based on O+ beam implantation at 50 kV for polycrystalline PbSe, which can manipulate the depth profile and hence the structural properties to modulate the optical and the optoelectronic performances. Unlike the diffused material presented in previous works, the resulting material is nano-polycrystalline with average grain sizes of 17.1–29.3 nm. The optoelectronic characterizations indicate that the optoelectronic properties can indeed be modulated by the implantation dose. The responsivity up to 2.09 A/W at 4 μm has been obtained at room temperature from the sample with implantation dose of 1 × 1018 cm−2. Comparing with the diffusion counterpart, the ion prepared PbSe nanomaterial exhibits completely different structural, compositional, optical, and electrical properties. The high responsivity of this material is attributed to the high optical absorption and carrier mobility induced by O+ beam. However, the high dark current has been also observed in this material, mainly due to its low inherent potential barrier height between crystallites.

The solar radiation climate of Athens: Variations and tendencies in the period 1992–2017, the brightening era

Solar radiation at the surface of the Earth undergoes short- and long-term variations mostly influenced by changes in atmospheric composition and cloud cover. These two factors characterise the solar radiation climate at a place. This study deals with the solar radiation climate over Athens focusing on the variations and trends of the global and diffuse horizontal irradiances recorded at the Actinometric Station of the National Observatory of Athens. The analysis shows that the global radiation over Athens in the period 1992–2017 presents a maximum in July and in May, June around noon under all and clear skies. For the diffuse component, this occurs in spring and in May (noontime) under all- and clear-sky conditions. The global radiation trends are positive (+0.41%/decade and +2.36%/decade for all and clear skies, respectively), while its diffuse counterpart shows negative trends (−6.93%/decade and −9.27%/decade for similar sky conditions, respectively) in the period 1992–2017. These findings confirm the recovery in the solar radiation levels over Athens in the recent 25 years.

A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control

Various forms of numerical shock instabilities are known to plague many contact and shear preserving approximate Riemann solvers, including the popular Harten-Lax-van Leer with Contact (HLLC) scheme, during high speed flow simulations governed by the Euler system of equations. In this paper we propose a simple and inexpensive novel strategy to prevent the HLLC scheme from developing such spurious solutions without compromising on its linear wave resolution ability. The cure is primarily based on a reinterpretation of the HLLC scheme as a combination of its well-known diffusive counterpart, the HLL scheme, and an antidiffusive term responsible for its accuracy on linear wavefields. In our study, a linear analysis of this alternate form indicates that shock instability in the HLLC scheme could be triggered due to the unwanted activation of the antidiffusive term appearing in its mass and interface-normal momentum flux component discretizations on interfaces that are not aligned with the shock front. This inadvertent activation results in weakening of the favourable dissipation provided by its inherent HLL scheme and causes unphysical mass flux variations along the shock front. To mitigate this, we propose a modified HLLC scheme that employs a simple differentiable pressure-ratio based multidimensional shock sensor to achieve smooth control of these critical antidiffusive terms near shocks. Using a linear perturbation analysis and a matrix based stability analysis, we establish that the resulting scheme, called HLLC-ADC (Anti-Diffusion Control), is shock stable over a wide range of freestream Mach numbers. Results from standard numerical test cases demonstrate that the HLLC-ADC scheme is indeed free from the most common manifestations of shock instability including the Carbuncle phenomenon without significant loss of accuracy on shear dominated viscous flows.