S U M M A R YGreen's functions of the indirect effects of atmospheric loading is formulated taking into account the effect of the atmospheric thickness. This is a modification of the classic paper by Farrell that formulated the indirect effects of ocean loading by approximating the loading mass as a thin layer. Atmospheric loading differs from ocean loading in the ways in which gravitational attraction and pressure act. In the case of ocean loading, because both the gravitational attraction and the pressure can be considered to arise from the mass located at the surface of the Earth, the effects of both are treated together and are included in the load Love numbers defined for the problem. In the case of atmospheric loading, if the atmospheric thickness is taken into account, because the mass is distributed over a large elevation and the pressure is exerted at the surface of the Earth, defining a set of load Love numbers including both effects of gravitational attraction and pressure is no longer possible. In this paper, the indirect effects of gravitational attraction and pressure of atmospheric loading are formulated separately by introducing load Love numbers for each of them respectively. Asymptotic expressions of the various load Love numbers one order of magnitude more accurate than those given be Farrell are obtained by searching for the asymptotic solutions of their governing ordinary-differential equations. These are used to improve the convergence of the Legendre sums in the various Green's functions. We find that the consideration of the atmospheric thickness has a negligible effect when compared with the simple thin-layer approximation.

In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the "charge regulation" behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surfacenonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, L 21 , and its reverse streaming potential effect, L 12 , and show that L 12 ¼ L 21 in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system. All physics is included in the choices of corresponding energy law and kinematic transport of particles. The variational derivations give the coupled force balance equations in a unique and deterministic fashion. We also discuss the situations with different types of boundary conditions. Finally, we show that the Onsager's relation holds for the electrokinetics, near the initial time of a step function applied field.

Intestinal mononuclear phagocytes (MPs) are composed of heterogeneous dendritic cell (DC) and macrophage subsets necessary for the initiation of immune response and control of inflammation. Although MPs in the normal intestine have been extensively studied, the heterogeneity and function of inflammatory MPs remain poorly defined. We performed phenotypical, transcriptional, and functional analyses of inflammatory MPs in infectious Salmonella colitis and identified CX3CR1+ MPs as the most prevalent inflammatory cell type. CX3CR1+ MPs were further divided into three distinct populations, namely, Nos2+CX3CR1lo, Ccr7+CX3CR1int (lymph migratory), and Cxcl13+CX3CR1hi (mucosa resident), all of which were transcriptionally aligned with macrophages and derived from monocytes. In follow-up experiments in vivo, intestinal CX3CR1+ macrophages were superior to conventional DC1 (cDC1) and cDC2 in inducing Salmonella-specific mucosal IgA. We next examined spatial organization of the immune response induced by CX3CR1+ macrophage subsets and identified mucosa-resident Cxcl13+CX3CR1hi macrophages as the antigen-presenting cells responsible for recruitment and activation of CD4+ T and B cells to the sites of Salmonella invasion, followed by tertiary lymphoid structure formation and the local pathogen-specific IgA response. Using mice we developed with a floxed Ccr7 allele, we showed that this local IgA response developed independently of migration of the Ccr7+CX3CR1int population to the mesenteric lymph nodes and contributed to the total mucosal IgA response to infection. The differential activity of intestinal macrophage subsets in promoting mucosal IgA responses should be considered in the development of vaccines to prevent Salmonella infection and in the design of anti-inflammatory therapies aimed at modulating macrophage function in inflammatory bowel disease.

Thromboembolism, one of the leading causes of morbidity and mortality worldwide, is characterized by formation of obstructive intravascular clots (thrombi) and their mechanical breakage (embolization). A novel two-dimensional multi-phase computational model is introduced that describes active interactions between the main components of the clot, including platelets and fibrin, to study the impact of various physiologically relevant blood shear flow conditions on deformation and embolization of a partially obstructive clot with variable permeability. Simulations provide new insights into mechanisms underlying clot stability and embolization that cannot be studied experimentally at this time. In particular, model simulations, calibrated using experimental intravital imaging of an established arteriolar clot, show that flow-induced changes in size, shape and internal structure of the clot are largely determined by two shear-dependent mechanisms: reversible attachment of platelets to the exterior of the clot and removal of large clot pieces. Model simulations predict that blood clots with higher permeability are more prone to embolization with enhanced disintegration under increasing shear rate. In contrast, less permeable clots are more resistant to rupture due to shear rate-dependent clot stiffening originating from enhanced platelet adhesion and aggregation. These results can be used in future to predict risk of thromboembolism based on the data about composition, permeability and deformability of a clot under specific local haemodynamic conditions.

Exogenously applied caveolin-1 scaffolding domain (CAV) has been shown to inhibit inflammatory mediator-induced nitric oxide (NO) production and NO-mediated increases in microvessel permeability. However, the effect of CAV on endothelial basal NO that prevents leukocyte adhesion remains unknown. This study aims to investigate the roles of exogenously applied CAV in endothelial basal NO production, leukocyte adhesion, and adhesion-induced changes in microvessel permeability. Experiments were conducted in individually perfused rat mesenteric venules. Microvessel permeability was determined by measuring hydraulic conductivity (Lp). NO was quantified with fluorescence imaging in DAF-2-loaded vessels. Perfusing venules with CAV inhibited basal NO production without affecting basal Lp. Resuming blood flow in CAV-perfused vessels significantly increased leukocyte adhesion. The firmly adherent leukocytes altered neither basal Lp nor adherens junction integrity. Increases in Lp occurred only upon formyl-Met-Leu-Phe application that induces release of reactive oxygen species from the adherent leukocytes. The application of NO synthase inhibitor showed similar results to CAV, and NO donor abolished CAV-mediated leukocyte adhesion. Immunofluorescence staining showed increases in binding of ICAM-1 to an adhesion-blocking antibody concurrent with a Src-dependent ICAM-1 phosphorylation following CAV perfusion. Pre-perfusing vessels with anti-ICAM-1 blocking antibody or a Src kinase inhibitor attenuated CAV-induced leukocyte adhesion. These results indicate that the application of CAV, in addition to preventing excessive NO-mediated permeability increases, also causes reduction of basal NO and promotes ICAM-1-mediated leukocyte adhesion through Src activation-mediated ICAM-1 phosphorylation. CAV-induced leukocyte adhesion was uncoupled from leukocyte oxidative burst and microvessel barrier function, unless in the presence of a secondary stimulation.

Abstract. Gravitational coupling within an axially symmetric, ellipsoidal Earthgives rise to torques among the mantle, outer core, and inner core. Such torques act along "lines of nodes", i.e., orthogonal to axes of symmetry. In a triaxial Earth model, small deviations from axial symmetry modify the torques in direction as well as magnitude. The perturbative torques depend on three Euler angles specifying the long axis of the inner core relative to that of the mantle shell. Their magnitudes, excluding angular dependences, are •-400 times (i.e., of the order of the inner core boundary flattening) smaller than their biaxial analogs. While triaxiality has a negligible impact on coupling considerations along the line of nodes, it creates gravitational coupling along orthogonal directions that have not been previously investigated. The gravitational coupling torques on the inner core and the mantle that take these triaxial perturbations into account are summarized. To the extent that fluid pressure and electromagnetic effects have not been explicitly modeled here, the present calculations are intended to provide only an order of magnitude estimate of coupling within the Earth along directions not previously examined. It is found that the axial torque on the inner core produces a differential rotation of less than 0.02ø/yr and thus fails by at least one order of magnitude in supplying a mechanism for inner core differential rotation suggested by seismological evidence [Song and Richards, 1996]. This conclusion breaks down only if one is prepared to accept an inner core obliquity surpassing 10 ø .

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