Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 75 page

Constraints on fluid flow processes in the Hellenic Accretionary Complex (eastern Mediterranean Sea) from numerical modeling

The dynamics of accretionary convergent margins are severely influenced by intense deformation and fluid expulsion. To quantify the fluid pressure and fluid flow velocities in the Hellenic subduction system, we set up 2-D hydrogeological numerical models following two seismic reflection lines across the Mediterranean Ridge. These profiles bracket the along-strike variation in wedge geometry: moderate compression and a >4 km thick underthrust sequence in the west versus enhanced compression and <1 km of downgoing sediment in the center. Input parameters were obtained from preexisting geophysical data, drill cores, and new geotechnical laboratory experiments. A permeability-porosity relationship was determined by a sensitivity analysis, indicating that porosity and intrinsic permeability are small. This hampers the expulsion of fluids and leads to the build up of fluid overpressure in the deeper portion of the wedge and in the underthrust sediment. The loci of maximum fluid pressure are mainly controlled by the compactional fluid source, which generally decreases toward the backstop. However, pore pressure is still high at the decollement level at distances <100 km from the deformation front, either by the incorporation of low permeability evaporites or additional compaction of the wedge sediments in the two profiles. In the west, however, formation of a wide accretionary complex is facilitated by high pore pressure zones. When compared to other large accretionary complexes such as Nankai or Barbados, our results not only show broad similarities but also that near-lithostatic pore pressures may be easier to maintain in the Hellenic Arc because of accentuated collision, some underthrust evaporates, and a thicker underthrust sequence

DAS field dataset to compare technologies and deployment scenarios – Antarctica Dataset

This report describes a Distributed Acoustic Sensing (DAS) dataset acquired by the British Antarctic Survey (BAS) and the University of Oxford in Antarctic during 2020. The field dataset contributes to the Deliverable D1.1 of the DigiMon project (DAS field dataset to compare technologies and deployment scenarios), which is associated with tasks 1.2 and 1.3 of the project

Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 86 page

Some sharp inequalities for integral operators with homogeneous kernel

One goal of this paper is to show that a big number of inequalities for functions in L-p(R+), p >= 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp

On the existence of solutions to the relativistic Euler equations in 2 spacetime dimensions with a vacuum boundary

We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in 2 spacetime dimensions with an equation of state of the form $p=K\rho^2$ that have a fluid vacuum boundary. Near the fluid vacuum boundary, the sound speed for these solutions are monotonically decreasing, approaching zero where the density vanishes. Moreover, the fluid acceleration is finite and bounded away from zero as the fluid vacuum boundary is approached. The existence results of this article also generalize in a straightforward manner to equations of state of the form $p=K\rho^\frac{\gamma+1}{\gamma}$ with $\gamma > 0$.Comment: A major revision of the second half of the pape

White matter hyperintensities are an independent predictor of cognitive decline 3 years following first-ever stroke-results from the PROSCIS-B study

Background: White matter hyperintensities (WMH) are the result of cerebral small vessel disease and may increase the risk of cognitive impairment (CI), recurrent stroke, and depression. We aimed to explore the association between selected cerebrovascular risk factors (CVRF) and WMH load as well as the effect of increased WMH burden on recurrent vascular events, CI, and depression in first-ever ischemic stroke patients.Methods: 431 from the PROSpective Cohort with Incident Stroke (PROSCIS) were included; Age-Related White Matter Changes (ARWMC) score was used to assess WMH burden on FLAIR. The presence of CVRF (defined via blood pressure, body-mass-index, and serological markers of kidney dysfunction, diabetes mellitus, and hyperlipoproteinemia) was categorized into normal, borderline, and pathological profiles based on commonly used clinical definitions. The primary outcomes included recurrent vascular events (combined endpoint of recurrent stroke, myocardial infarction and/or death), CI 3 years post-stroke, and depression 1-year post-stroke.Results: There was no clear association between CVRF profiles and WMH burden. High WMH lesion load (ARWMC score ≥ 10) was found to be associated with CI (adjusted OR 1.05 [95% CI 1.00-1.11]; p Conclusion: Higher WMH burden was associated with a significant decline in cognition 3 years post-stroke in this cohort of first-ever stroke patients

The Devastating 2022 M6.2 Afghanistan Earthquake: Challenges, Processes, and Implications

On June 21st, a Mw6.2 earthquake struck the Afghan-Pakistan-border-region, situated within the India-Asia collision. Thousand thirty-nine deaths were reported, making the earthquake the deadliest of 2022. We investigate the event\u27s rupture processes by combining seismological and geodetic observations, aiming to understand what made it that fatal. Our Interferometric Synthetic Aperture Radar-constrained slip-model and regional moment-tensor inversion, confirmed through field observations, reveal a sinistral rupture with maximum slip of 1.8 m at 5 km depth on a N20°E striking, sub-vertical fault. We suggest that not only external factors (event-time, building stock) but fault-specific factors made the event excessively destructive. Surface rupture was favored by the rock foliation, coinciding with the fault strike. The distribution of Peak-Ground-Velocity was governed by the sub-vertical fault. Maximum slip was large compared to other events globally and might have resulted in peak-frequencies coinciding with resonance-frequencies of the local buildings and demonstrates the devastating impact of moderate-size earthquakes

On the gravitational potential of modified Newtonian dynamics

Producción CientíficaThe mathematical structure of the Poisson equation of Modified Newtonian Dynamics (MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev space whose Orlicz function is related to Milgrom’s μ-function, where there exists existence and uniqueness of weak solutions. Since these do not have in principle much regularity, a further study is performed where the gravitational field is not too large, where MOND is most relevant. In that case the field turns out to be H¨older continuous. Quasilinear MOND is also analyzed