Essentially translation invariant pseudodifferential operators on manifolds with cylindrical ends

We study two classes (or calculi) of pseudodifferential operators defined on manifolds with cylindrical ends: the class of pseudodifferential operators that are ``translation invariant at infinity'' and the class of ``essentially translation invariant operators'' that have appeared in the study of layer potential operators on manifolds with straight cylindrical ends. Both classes are close to the $b$-calculus considered by Melrose and Schulze and to the $c$-calculus considered by Melrose and Mazzeo-Melrose. Our calculi, however, are different and, while some of their properties follow from those of the $b$- or $c$-calculi, many of their properties do not. In particular, the ``essentially translation invariant calculus'' is spectrally invariant, a property not enjoyed by the ``translation invariant at infinity'' calculus or the $b$-calculus. For our calculi, we provide easy, intuitive proofs of the usual properties: stability for products and adjoints, mapping and boundedness properties for operators acting between Sobolev spaces, regularity properties, existence of a quantization map and topological properties of our algebras, the Fredholm property. Since our applications will be to the Stokes operator, we systematically work in the setting of Agmon-Douglis-Nirenberg-elliptic operators.Comment: 39 page

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

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

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

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

Worker remittances and the global preconditions of ‘smart development’

With the growing environmental crisis affecting our globe, ideas to weigh economic or social progress by the ‘energy input’ necessary to achieve it are increasingly gaining acceptance. This question is intriguing and is being dealt with by a growing number of studies, focusing on the environmental price of human progress. Even more intriguing, however, is the question of which factors of social organization contribute to a responsible use of the resources of our planet to achieve a given social result (‘smart development’). In this essay, we present the first systematic study on how migration – or rather, more concretely, received worker remittances per GDP – helps the nations of our globe to enjoy social and economic progress at a relatively small environmental price. We look at the effects of migration on the balance sheets of societal accounting, based on the ‘ecological price’ of the combined performance of democracy, economic growth, gender equality, human development, research and development, and social cohesion. Feminism in power, economic freedom, population density, the UNDP education index as well as the receipt of worker remittances all significantly contribute towards a ‘smart overall development’, while high military expenditures and a high world economic openness are a bottleneck for ‘smart overall development’

Long-Term Potentiation in the CA1 Hippocampus Induced by NR2A Subunit-Containing NMDA Glutamate Receptors Is Mediated by Ras-GRF2/Erk Map Kinase Signaling

BACKGROUND: NMDA-type glutamate receptors (NMDARs) are major contributors to long-term potentiation (LTP), a form of synaptic plasticity implicated in the process of learning and memory. These receptors consist of calcium-permeating NR1 and multiple regulatory NR2 subunits. A majority of studies show that both NR2A and NR2B-containing NMDARs can contribute to LTP, but their unique contributions to this form of synaptic plasticity remain poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we show that NR2A and NR2B-containing receptors promote LTP differently in the CA1 hippocampus of 1-month old mice, with the NR2A receptors functioning through Ras-GRF2 and its downstream effector, Erk Map kinase, and NR2B receptors functioning independently of these signaling molecules. CONCLUSIONS/SIGNIFICANCE: This study demonstrates that NR2A-, but not NR2B, containing NMDA receptors induce LTP in pyramidal neurons of the CA1 hippocampus from 1 month old mice through Ras-GRF2 and Erk. This difference add new significance to the observation that the relative levels of these NMDAR subtypes is regulated in neurons, such that NR2A-containing receptors become more prominent late in postnatal development, after sensory experience and synaptic activity