Layer potential theory for the anisotropic Stokes system with variable L∞ symmetrically elliptic tensor coefficient

© 2021 The Authors. The aim of this paper is to develop a layer potential theory in L2-based weighted Sobolev spaces on Lipschitz bounded and exterior domains of Rn , n ≥ 3, for the anisotropic Stokes system with L∞ viscosity tensor coefficient satisfying an ellip- ticity condition for symmetric matrices with zero matrix trace. To do this, we explore equivalent mixed variational formulations and prove the well-posedness of some transmission problems for the anisotropic Stokes system in Lipschitz domains of Rn, with the given data in L2-based weighted Sobolev spaces. These results are used to define the volume (Newtonian) and layer potentials and to obtain their properties. Then, we analyze the well-posedness of the exterior Dirichlet and Neumann problems for the anisotropic Stokes system with L∞ symmetrically elliptic tensor coefficient by representing their solutions in terms of the obtained volume and layer potentials.EPSRC grant EP/M013545/1: "Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs"; Babeş-Bolyai University research grant AGC35124/31.10.2018; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC 2075-390740016

Dirichlet and transmission problems for anisotropic stokes and Navier-Stokes systems with L∞ tensor coefficient under relaxed ellipticity condition

EPSRC, UK; Babes Bolyai University research grant; DFG, German Research Foundatio

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

Hydrodynamic coupling and rotational mobilities near planar elastic membranes

We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied frequencies.Comment: 14 pages, 7 figures. Revised manuscript resubmitted to J. Chem. Phy

Perivascular adipose tissue and coronary vascular disease

Coronary perivascular adipose tissue is a naturally occurring adipose tissue depot that normally surrounds the major coronary arteries on the surface of the heart. Although originally thought to promote vascular health and integrity, there is a growing body of evidence to support that coronary perivascular adipose tissue displays a distinct phenotype relative to other adipose depots and is capable of producing local factors with the potential to augment coronary vascular tone, inflammation, and the initiation and progression of coronary artery disease. The purpose of the present review is to outline previous findings about the cardiovascular effects of coronary perivascular adipose tissue and the potential mechanisms by which adipose-derived factors may influence coronary vascular function and the progression of atherogenesis

Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds

M. Kohr acknowledges the support of the Grant PN-II-ID-PCE-2011-3-0994 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI. The research has been also partially supported by the Grant EP/M013545/1: “Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs” from the EPSRC, UK

Actin/alpha-actinin-dependent transport of AMPA receptors in dendritic spines: role of the PDZ-LIM protein RIL

The efficacy of excitatory transmission in the brain depends to a large extent on synaptic AMPA receptors, hence the importance of understanding the delivery and recycling of the receptors at the synaptic sites. Here we report a novel regulation of the AMPA receptor transport by a PDZ (postsynaptic density-95/Drosophila disc large tumor suppressor zona occludens 1) and LIM (Lin11/rat Isl-1/Mec3) domain-containing protein, RIL (reversion-induced LIM protein). We show that RIL binds to the AMPA glutamate receptor subunit GluR-A C-terminal peptide via its LIM domain and to alpha-actinin via its PDZ domain. RIL is enriched in the postsynaptic density fraction isolated from rat forebrain, strongly localizes to dendritic spines in cultured neurons, and coprecipitates, together with alpha-actinin, in a protein complex isolated by immunoprecipitation of AMPA receptors from forebrain synaptosomes. Functionally, in heterologous cells, RIL links AMPA receptors to the alpha-actinin/actin cytoskeleton, an effect that appears to apply selectively to the endosomal surface-internalized population of the receptors. In cultured neurons, an overexpression of recombinant RIL increases the accumulation of AMPA receptors in dendritic spines, both at the total level, as assessed by immunodetection of endogenous GluR-A-containing receptors, and at the synaptic surface, as assessed by recording of miniature EPSCs. Our results thus indicate that RIL directs the transport of GluR-A-containing AMPA receptors to and/or within dendritic spines, in an alpha-actinin/actin-dependent manner, and that such trafficking function promotes the synaptic accumulation of the receptors

Contribution of Cystine-Glutamate Antiporters to the Psychotomimetic Effects of Phencyclidine

Altered glutamate signaling contributes to a myriad of neural disorders, including schizophrenia. While synaptic levels are intensely studied, nonvesicular release mechanisms, including cystine–glutamate exchange, maintain high steady-state glutamate levels in the extrasynaptic space. The existence of extrasynaptic receptors, including metabotropic group II glutamate receptors (mGluR), pose nonvesicular release mechanisms as unrecognized targets capable of contributing to pathological glutamate signaling. We tested the hypothesis that activation of cystine–glutamate antiporters using the cysteine prodrug N-acetylcysteine would blunt psychotomimetic effects in the rodent phencyclidine (PCP) model of schizophrenia. First, we demonstrate that PCP elevates extracellular glutamate in the prefrontal cortex, an effect that is blocked by N-acetylcysteine pretreatment. To determine the relevance of the above finding, we assessed social interaction and found that N-acetylcysteine reverses social withdrawal produced by repeated PCP. In a separate paradigm, acute PCP resulted in working memory deficits assessed using a discrete trial t-maze task, and this effect was also reversed by N-acetylcysteine pretreatment. The capacity of N-acetylcysteine to restore working memory was blocked by infusion of the cystine–glutamate antiporter inhibitor (S)-4-carboxyphenylglycine into the prefrontal cortex or systemic administration of the group II mGluR antagonist LY341495 indicating that the effects of N-acetylcysteine requires cystine–glutamate exchange and group II mGluR activation. Finally, protein levels from postmortem tissue obtained from schizophrenic patients revealed significant changes in the level of xCT, the active subunit for cystine–glutamate exchange, in the dorsolateral prefrontal cortex. These data advance cystine–glutamate antiporters as novel targets capable of reversing the psychotomimetic effects of PCP

Splenic peliosis with spontaneous splenic rupture: report of two cases

BACKGROUND: Peliosis is a rare condition characterised by multiple cyst-like, blood-filled cavities within the parenchyma of solid organs. Most commonly affecting the liver, isolated splenic peliosis is an even more unique phenomenon. Patients with the condition are often asymptomatic. However, this potentially lethal condition can present with spontaneous organ rupture. We present two such cases, discuss their management and review what is currently known in the existing literature. CASE PRESENTATION: A previously well twenty-six year old woman presented with abdominal pain following a trivial episode of coughing. A diagnosis of spontaneous splenic rupture was made following clinical and radiological examination. She underwent emergency splenectomy and made a full, uneventful recovery. Histopathological examination confirmed splenic peliosis. The second case describes an eighty six year old lady who sustained a trivial fall and developed pain in her left side. A CT confirmed splenic rupture. She became haemodynamically unstable during her admission and underwent emergency splenectomy. Histopathological examination revealed splenic peliosis. She went on to make an uneventful recovery. CONCLUSION: Splenic peliosis is very rare. It has a number of associations including immunosuppression, drug therapy and infection. Although patients are often asymptomatic, life-threatening spontaneous organ rupture may occur. If the diagnosis of peliosis is confirmed, additional investigations should be considered to detect its presence in other organs. Furthermore, the presence of the condition may be relevant if further medical or surgical intervention is planned