PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.     

Anomalies of attenuation and phase velocity of surface acoustic waves in YBa2Cu3O7‒δ thin films in the vicinity of Tc

We present measurements of the attenuation and phase velocity of surface acoustic waves in thin YBa₂Cu₃O films as a function of temperature, in magnetic fields up to 3.6 T applied parallel to the c-axis of the films. We have observed anomalies in both, the attenuation and the phase velocity in the vicinity of the superconducting critical temperature which do not depend on the magnetic field. Possible origins of these anomalies, observed, to our knowledge, for the first time in YBa₂Cu₃O thin films, are discussed and compared to bulk acoustic wave experiments. We present a kind of feedback technique for surface acoustic waves which improves the sensitivity of this type of measurement. The actual sensitivity limits are mentioned. Received: 7 August 1997 / Revised: 7 November 1997 / Accepted: 17 November 1997     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients

The convergence of iterative based domain decomposition methods is linked with the absorbing boundary conditions defined on the interface between the sub-domains. For linear elasticity problems, the optimal absorbing boundary conditions are associated with non-local Dirichlet-to-Neumann maps. Most of the methods to approximate these non-local maps are based on a continuous analysis. In this paper, an original algebraic technique based on the computation of local Dirichlet-to-Neumann maps is investigated. Numerical experiments are presented for linear elasticity problems with extreme contrasts in the coefficients.     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Mechanical properties of SBR-networks: I. Determination of crosslink densities by stress-strain-measurements

The tube model is applied for the treatment of stress-strain measurements on SBR networks. It is shown that this theory allows the separation of crosslink and constraint contributions to the stress-strain behavior and, also, a reliable determination of crosslink densities. The consideration of dynamical contributions is discussed and a special numerical method is developed.     

Instantaneous strain recovery elasticity and endothermic heat change in nylon-6 monofilaments and silicone rubbers

The instantaneous elastic moduli for a nylon-6 monofilament were derived on strain recoveries right after creep, stress relaxation, and rapid elongation,E _c ,E _s andE _e , respectively. It was found that during strain recoveryE _s (>E _e ) andE _e increase monotonically with increasing load,m ₁, on the sample. The extrapolated value of E_s atm ₁=0 g is almost equal to Young's modulus, 4.06 GPa. The value ofE _c also increased with increasingm ₁, and atm ₁=600 g (1.93 t cm^–2) reached about 14 GPa. The endothermic heat change right after creep, stress relaxation or rapid elongation,Q, was negligibly small. For comparison,E _s ,E _c andQ were also investigated for silicone rubber. It was found thatE _s (53.8 M Pa at the draw ratioD=1.2) decreased abruptly atD=1.3. In the range ofD=1.4–1.9,E _s was only 22.6 MPa. In the case of stress relaxation,Q increased with increasingD from 4 J mol^–1 (atD=1.2) to 56 J mol^–1 (atD=1.9). FurthermoreE _c (5.58 MPa atm ₁=133.8 g (429.4 kg cm^–2)) increased gradually with increasing m₁ and attained 16.6 MPa atm ₁=548.4 g (1.76 t cm^–2). In the case of creep,Q was in the range of 0–11.5 J mol^–1 and larger when larger loads,m ₂ were removed during the later stages of creep.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayThe author wishes to thank Mr. Keizi Igarashi and Mr. Tetsuya Yasui for helping in the experiments.     

聚乙二醇在高真空条件下的单链弹性

在过去二十年间，高分子的单链弹性已经得到了广泛的研究.然而由于环境和高分子之间往往有着复杂的相互作用，实验中很难得到高分子在严格无扰状态下的单链弹性（即本征弹性）.为此，利用单分子力谱技术研究了高真空条件下聚乙二醇（PEG）的单链弹性.结果表明，由于高真空条件下溶剂分子的干扰被消除，PEG在这一准无扰状态下呈现其本征弹性.在非极性有机溶剂中，由于溶剂分子和PEG之间只有微弱的范德华力作用，PEG表现出和高真空中基本一致的弹性.然而，在不同环境中，力曲线的低力区（F<100 pN）存在着细微的差异.这一现象可归因于不同条件下基底与PEG链之间的吸附力不同.采用的高真空力谱可用于研究其他高分子单链在准无扰状态下的本征弹性.