On the mechanical characterization of compact bone structure using the homogenization theory

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677–687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has a non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization.

The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.     

Spontaneous calcium transients regulate neuronal plasticity in developing neurons

Calcium ions play critical roles in neuronal differentiation. We have recorded transient, repeated elevations of calcium in embryonic Xenopus spinal neurons over periods of 1 h in vitro and in vivo, confocally imaging fluo 3-loaded cells at 5 s intervals. Calcium spikes and calcium waves are found both in neurons in culture and in the intact spinal cord. Spikes rise rapidly to approximately 400% of baseline fluorescence and have a double exponential decay, whereas waves rise slowly to approximately 200% of baseline fluorescence and decay slowly as well. Imaging of fura 2-loaded neurons indicates that intracellular calcium increases from 50 to 500 nM during spikes. Both spikes and waves are abolished by removal of extracellular calcium. Developmentally, the incidence and frequency of spikes decrease, whereas the incidence and frequency of waves are constant. Spikes are generated by spontaneous calcium-dependent action potentials and also utilize intracellular calcium stores. Waves are produced by a mechanism that does not involve classic voltage-dependent calcium channels. Spikes are required for expression of the transmitter GABA and for potassium channel modulation. Waves in growth cones are likely to regulate neurite extension. The results demonstrate the roles of a novel signaling system in regulating neuronal plasticity, that operates on a time scale 10⁴ times slower than that of action potentials. © 1995 John Wiley & Sons, Inc.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

A cross-diffusion model of forest boundary dynamics

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction — diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction — cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.     

Bifurcation analysis of periodic SEIR and SIR epidemic models

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.     

天然林内红松种群年龄更替数学模型及研究

本文给出天然林内红松种群年令更替数学模型（1）。通过对（1）进行定性分析,得到主要结论是：系统（1）在第一象限内存在唯一稳定周期解的充要条件是bk-bc-2d＞0其生态意义是天然林内红松幼树与母树随时间变化会产生一个有规律、互为消涨的变化特征。     

Effects of Ultrasonic Seed Treatment on Rice Performances under the Seawater Irrigation

Irrigation with desalinated seawater is an effective way to use ocean resources and save freshwater resources. However, seawater irrigation would cause yield loss of rice. In order to explore the effects of ultrasonic seed treatment on rice performances under seawater irrigation, the present study was conducted with three irrigation treatments (fresh water (SW0), ten times diluted seawater (SW1%, 0.34% salinity), and five times diluted seawater (SW2%, 0.68% salinity)) and two seed treatments (ultrasonic treated seeds (UT) and untreated seeds (CK)). Compared with SW0 + CK treatment, SW1 + CK and SW2 + CK treatments significantly decreased grain yield by 56.19% and 66.69%, spikelets per panicle by 30.11% and 55.80%, seed-setting rate by 23.05% and 18.87%, and 1000-grain weight by 4.55% and 14.50%, respectively. Seawater irrigation also significantly increased malonaldehyde (MDA) and proline contents and the activities of superoxide dismutase (SOD) and peroxidase (POD). Ultrasonic seed treatment significantly increased the grain number per panicle, seed-setting rate, and grain yield of rice under seawater irrigation. Compared with CK, UT treatment substantially reduced MDA content, SOD activity, and POD activity in SW1 and SW2 conditions. Furthermore, UT treatment significantly increased proline content and down-regulated proline dehydrogenase activity under seawater irrigation. We deduced that ultrasonic seed treatment enhanced the salinity tolerance of rice by inducing the proline accmulation. Our findings indicated that ultrasonic seed treatment could an effective strategy to promote rice productivity under seawater irrigation.     

一类三维非线性系统空间周期解的存在性及唯一性

本文研究了一类描述天然林内红松林种群变化的三维非线性教学模型     

一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

Theoretical Study of the TiO2 and MgO Surface Acidity and the Adsorption of Acids and Bases

We present ab-initio periodic Hartree–Fock calculations (crystal program) of small molecules on TiO₂ and MgO. The adsorption of the molecules may be molecular or dissociative. This depends on their acid and basic properties in the gas phase. For the molecular adsorption, the molecules are adsorbed as bases on Ti(+IV) sites, the adsorption energies correlate with the proton affinities. The dissociations on the surface correlate with the gas phase cleavages: thus, the dissociation of MeOH leads to a preferential basic cleavage (the fragment HO– is adsorbed on a Ti⁺⁴ ion and the fragment Me⁺ is adsorbed on a O²– ion of the oxide). The opposite result is obtained with MeSH. Another important factor is the adsorbate–adsorbate interaction: favorable cases are a sequence of H-bonds for the hydroxyl groups resulting from the water dissociation and the mode of adsorption for the ammonium ions. Lateral interactions also force the adsorbed CO₂ molecules to bend over the surface so that their mutual orientation resembles the geometry of the CO₂ dimer. With respect to water adsorption, MgO appears to be a basic oxide. As experimentally observed, NH₃ adsorbs preferentially on TiO₂ and CO₂ on MgO. However, this difference of reactivity should not be expressed in terms of acid vs. basic behaviour but in terms of hard and soft acidity. The MgO surface is a 'soft' acidic surface that reacts preferentially with the soft base, CO₂.