An investigation of the complete post-buckling behavior of axisymmetric spherical shells

Summary The post-buckling behavior of an elastic spherical shell is studied for large axisymmetric deformations. The complete post-buckling path is given for the experimentally confirmed single dimple solution in a load-deformation diagram, making use of the methods of local bifurcation theory, singular perturbation analysis and numerical analysis. From the specific form of the post-buckling path with its predominating unstable part follows the strong imperfection sensitivity of the shell structure.

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Zusammenfassung Es wird das Nachbeulverhalten einer elastischen Kugelschale für große achsensymmetrische Deformationen untersucht. Der gesamte Nachbeulpfad wird für die experimentell bestätigte single dimple Lösung, die eine starke lokale Eindellung darstellt, angegeben, wobei Methoden der lokalen Verzweigungstheorie, der singulären Störungsrechnung und der numerischen Analysis verwendet wurden. Aus der besonderen Form des Nachbeulpfades mit seinem überwiegend instabilen Teil ist die starke Imperfektionsempfindlichkeit dieser Konstruktion deutlich erkennbar.

     

On the positive solutions of some nonlinear diffusion problems

We consider the nonlinear diffusion equationu _t –a(x, u _{x x} )+b(x, u)=g(x, u) with initial boundary conditions andu(t, 0)=u(t, 1)=0. Here,a, b, andg denote some real functions which are monotonically increasing with respect to the second variable. Then, the corresponding stationary problem has a positive solution if and only if(0, ^*) or(0, ^*]. The endpoint ^* can be estimated by , where ₁ u denotes the first eigenvalue of the stationary problem linearized at the pointu. The minimal positive steady state solutions are stable with respect to the nonlinear parabolic equation.

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Zusammenfassung Wir betrachten die nichtlineare Diffusionsgleichungu _t –a(x, u _x ) _x +b(x, u)=g(x, u) mit Randbedingungen undu (t, 0)=u (t, 1)=0. Dabei sinda, b, undg monoton wachsende Funktionen bzgl. des zweiten Argumentes. Das zugehörige stationäre Problem hat genau dann eine positive Lösung, falls (0, ^*) oder(0, ^*]. Der Endpunkt ^* kann durch abgeschätzt werden, wobei ₁ u den ersten Eigenwert des an der Stelleu linearisierten stationären Problems bezeichnet. Die minimale positive stationäre Lösung ist stabil bzgl. der obigen nichtlinearen parabolischen Gleichung.

     

Selective Voltammetric Detection of Epinephrine in the Presence of Ascorbic Acid at Poly(4-Methoxyphenol)-Modified Electrode1

A gold electrode was modified with electropolymerized films of 4-methoxyphenol by its oxidative polymerization from an alkaline solution by cyclic voltammetry. The modified electrode was then used to determine epinephrine (EP) in the presence of a high concentration of ascorbic acid (AA) by differential pulse voltammetry. The peak positions as well as relative sensitivity EP/AA were affected by the potential window used for the polymerization. For polymerization between 0 and 1.3 V, the peak potentials recorded in a phosphate buffer solution (pH = 7.2) were 516 and 312 mV vs. Ag/AgCl for EP and AA, respectively. In addition the effects of pH and the type of electrolyte on the linearity range and detection limit are investigated. The detection limit for 3s-test is 0.1 M. The high selectivity and sensitivity for epinephrine was found to be due to charge discrimination/analyte accumulation.     

Atomistic Simulation Study of Calcium,Phosphate and Fluoride Ion Association to the Teleopeptide‐Tails of Collagen – Initial Steps to Biomineral Formation

The attachment of single ions to putative adsorption sites in the tails of collagen fibers is investigated by means of molecular dynamics simulations and discussed with respect to the very early steps of apatite/collagen biomineral formation. Our studies clearly demonstrate an increased flexibility of the tails of the triple‐helical collagen protein. Apart from the termini of the backbone, several side chains were also observed to be freely accessible to ion attachment from aqueous solution. The teleopeptide was systematically scanned for suitable adsorption sites for calcium, phosphate and fluoride ions. Association of these ions was then explored from potential of mean force calculations. The resulting energy profiles reveal a variety of favorable protein‐ion bonds and hint at the suitability of the collagen tails to promote apatite aggregation.     

Sm~(3 )在硼酸盐玻璃中的发光及Bi~(3 )对Sm~(3 )的敏化作用

早在六十年代,人们为了寻找较好的激光玻璃,曾对Sm~(3 )离子掺杂的玻璃中的光谱进行过研究。为了探寻新型的激光,发光玻璃,又进一步研究了Sm~(3 )在玻璃中的发光和敏化。我们以寻找一种高亮度,低成本的发光玻璃为目的,研究了基质玻璃组成,敏化离子及其浓度对Sm~(3 )发光性质的影响。 选择B_2O_3-BaO-M_mO_n(M_mO_n=Li_2O,Na_2O,K_2O,MgO,CaO,SrO)玻璃体系,所用原料的纯度皆为分析纯以上,用陶瓷坩埚在1250℃掺杂氧化钐(纯度均大于99％),玻璃的荧光谱和激发光谱,用MPF-4型荧光分光光度计测定。     

Soliton experiments in stimulated Raman scattering

Experimental observations of solitons in stimulated Raman scattering are reported. Soliton formation resulted from the introduction of a phase shift in the incident Stokes beam as predicted by theory. Pulse sharpening and retardation on propagation in the Raman medium have been observed along with amplitude diminution. The first two features were predicted and the third was not. Spontaneous soliton formation has been observed in the absense of any amplitude modulation or apparent phase shift in the optical fields, indicating that additional sets of initial conditions may result in soliton formation.Work performed under the auspices of the U.S. Department of Energy.     

On the tetrad theory of gravity

After reviewing problems which appear in the theory of teleparallelism (tetrad theory) based on a Lagrangian quadratic in the torsion, the possibility of adding higher-order terms is discussed. For a test Lagrangian,O(3)-symmetric vacuum solutions and spatially homogeneous and isotropic solutions are found. The latter contain nonsingular cosmological models.     

A Ramsey-Sperner theorem

Letn≥k≥1 be integers and letf(n, k) be the smallest integer for which the following holds: If ℱ is a family of subsets of ann-setX with |ℱ|<f(n,k) then for everyk-coloring ofX there existA B ∈ ℱ,A∈B, A⊂B such thatB-A is monochromatic. Here it is proven that for a fixedk there exist constantsc _k andd _k such that and ask→∞. The proofs of both the lower and the upper bounds use probabilistic methods.