The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

Seasonal variations in carbon, nitrogen and phosphorus concentrations and C:N:P stoichiometry in different organs of a Larix principis-rupprechtii Mayr. plantation in the Qinling Mountains, China

Understanding how concentrations of elements and their stoichiometry change with plant growth and age is critical for predicting plant community responses to environmental change. Weusedlong-term field experiments to explore how the leaf, stem and root carbon (C), nitrogen (N) and phosphorous (P) concentrations and their stoichiometry changed with growth and stand age in a L.principis-rupprechtii Mayr. plantation from 2012–2015 in the Qinling Mountains, China. Our results showed that the C, N and P concentrations and stoichiometric ratios in different tissues of larch stands were affected by stand age, organ type andsampling month and displayed multiple correlations with increased stand age in different growing seasons. Generally, leaf C and N concentrations were greatest in the fast-growing season, but leaf P concentrations were greatest in the early growing season. However, no clear seasonal tendencies in the stem and root C, N and P concentrations were observed with growth. In contrast to N and P, few differences were found in organ-specific C concentrations. Leaf N:P was greatest in the fast-growing season, while C:N and C:P were greatest in the late-growing season. No clear variations were observed in stem and root C:N, C:P andN:Pthroughout the entire growing season, but leaf N:P was less than 14, suggesting that the growth of larch stands was limited by N in our study region. Compared to global plant element concentrations and stoichiometry, the leaves of larch stands had higher C, P, C:NandC:PbutlowerNandN:P,andtherootshadgreater PandC:NbutlowerN,C:Pand N:P. Our study provides baseline information for describing the changes in nutritional elements with plant growth, which will facilitates plantation forest management and restoration, and makes avaluable contribution to the global data pool on leaf nutrition and stoichiometry

Second order averaging for the nonlinear Schroedinger equation with strongly anisotropic potential

International audienceWe consider the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein Condensate (BEC) which is highly confi ned in vertical z direction. The highly confi ned potential induces high oscillations in time. If the confi nement in the z direction is a harmonic trap (which is widely used in physical experiments), the very special structure of the spectrum of the confi nement operator will imply that the oscillations are periodic in time. Based on this observation, it can be proved that the GPE can be averaged out with an error of order of epsilon, which is the typical period of the oscillations. In this article, we construct a more accurate averaged model, which approximates the GPE up to errors of order epsilon squared. Then, expansions of this model over the eigenfunctions (modes) of the vertical Hamiltonian Hz are given in convenience of numerical application. Effi cient numerical methods are constructed for solving the GPE with cylindrical symmetry in 3D and the approximation model with radial symmetry in 2D, and numerical results are presented for various kinds of initial data

Regulation of inflammation in Japanese encephalitis

Uncontrolled inflammatory response of the central nervous system is a hallmark of severe Japanese encephalitis (JE). Although inflammation is necessary to mount an efficient immune response against virus infections, exacerbated inflammatory response is often detrimental. In this context, cells of the monocytic lineage appear to be important forces driving JE pathogenesis

Practical diagnosis of cirrhosis in non-alcoholic fatty liver disease using currently available non-invasive fibrosis tests

Unlike for advanced liver fibrosis, the practical rules for the early non-invasive diagnosis of cirrhosis in NAFLD remain not well defined. Here, we report the derivation and validation of a stepwise diagnostic algorithm in 1568 patients with NAFLD and liver biopsy coming from four independent cohorts. The study algorithm, using first the elastography-based tests Agile3+ and Agile4 and then the specialized blood tests FibroMeterV3G and CirrhoMeterV3G, provides stratification in four groups, the last of which is enriched in cirrhosis (71% prevalence in the validation set). A risk prediction chart is also derived to allow estimation of the individual probability of cirrhosis. The predicted risk shows excellent calibration in the validation set, and mean difference with perfect prediction is only −2.9%. These tools improve the personalized non-invasive diagnosis of cirrhosis in NAFLD

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters is an element of and delta measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation

A novel aspect of the structure of the avian thymic medulla.

We provide evidence for the compartmentalization of the avian thymic medulla and identify the avian thymic dendritic cell. The thymic anlage develops from an epithelial cord of the branchial endoderm. Branches of the cord are separated by primary septae of neural crest origin. The dilation of the primary septae produces the keratin-negative area (KNA) of the thymic medulla and fills the gaps of the keratin-positive network (KPN). Morphometric analysis indicates that the KNA takes up about half of the volume of the thymic medulla, which has reticular connective tissue, like peripheral lymphoid organs. The KNA receives blood vessels and in addition to pericytes, the myoid cells of striated muscle structure occupy this area. The myoid cells are of branchial arch or prechordal plate origin providing indirect evidence for the neural crest origin of the KNA. The marginal epithelial cells of the KPN co-express keratin and vimentin intermediate filaments, which indicate their functional peculiarity. The basal lamina of the primary septum is discontinuous on the surface of the KPN providing histological evidence for the loss of the blood-thymus barrier in the medulla. In the center of the KNA, the dendritic cells lie in close association with blood vessels, whereas the B-cells accumulate along the KPN. The organization of the KPN and KNA increases the "surface" of the so-called cortico-medullary border, thereby contributing to the efficacy of central tolerance