Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u _t = m ₀ u + Q(x)u + u _xx + d|u|² u ?|u|⁴ u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u ₀ with stationary localized structures which accumulate at the Maxwell point m ₀ = ?3d ²/16. When spatial forcing is included its wavelength is imprinted on u ₀ creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.     

Structure and properties of polystyrene-polyethylene interpenetrating polymer network (ipn)-like systems

A series of samples of polystyrene (PS) –polyethylene (PE) interpenetrating polymer network (IPN)–like system was prepared by synthesis in situ. The measurement of uniaxial compression modulus of the IPN samples was used for the determination of mean molar mass of the polymer chain between two junction points of the polymer network – M̌_C. The electron microscopic records gave an evidence about two phase structure of the IPN samples. Generally, the crystalline part of PE network in all IPN investigated samples is relatively low. The influence of the concentration of crosslinking agent on mechanical behaviour of the IPN samples was studied.     

AN IMPROVED ARC-LENGTH METHOD AND APPLICATION IN THE POST-BUCKLING ANALYSIS FOR COMPOSITE STRUCTURES

Based on the conventional arc- length method, an improved arc- length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc- length . An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and sheik structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

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Raman spectroscopy in high polymer research and production

The mechanism of RAMAN scattering depends on molecular polarizability changes and therefore this method is especially useful for the study of non-polar bonds. This is shown by reviewing some analytical applications. Knowledge on polymer structure was especially promoted by studies of the lowest-frequency bending modes, of correlation splittings in case of crystallinity, and by measurements on depolarization of the laser light. RAMAN spectroscopy has possibilities for in-situ and multi-method measurements. Newer developments serving the polymer sciences are surface enhanced RAMAN scattering and the RAMAN spectroscopy of electroconducting polymers.     

Recognition hysteresis of the acetylcholine receptor of torpedo Californica

The nicotinic acetylcholine receptor (nAcChR) of the electric organ of Torpedo californica fish exhibits a pronounced hysteresis loop in the high affinity binding of the neurotransmitter acetylcholine (AcCh). When increasing amounts of AcCh are added (pulse mode) an extremely long-lived, metastable conformer distribution is obtained (lower hysteresis branch) between low affinity AcCh binding states (R_l) and high (R_h) and very high (R_vh) affinity states. Dialysis conditions always lead to the equilibrium binding curve (upper hysteresis branch; K̄_A = 5 × 10⁻⁹M, 4°C; one A bound to the R-monomer of M_r ≈ 290 000). Cyclic, pulse mode addition and dilution of AcCh results in scanning loops within the main hysteresis. The kinetic analysis of the changes in free and bound AcCh during the open-system conditions of dialysis, that releases the metastability, shows that the AcCh (A) binding proceeds along an induced-fit pathway according to A+R_h ⇋ AR_n ⇋ AR_vh. The rate constant of the step AR_h → AR_vh is k₂ = 6 × 10⁻³s⁻¹ and that of the reverse step is k₋₂ = 3 × 10⁻⁴s⁻¹. Direct binding of A to free R_vh can be excluded. Therefore, the state R_vh does not preexist, it is induced and only stable, as AR_vh, by bound AcCh. The metastability can be described in terms of long-lived AR_vh ·R₁ hybrid dimers. Physiologically, the metastable hybrid may be viewed as a saving device: the functionally important, channel-active R₁ conformer is, at low AcCh-concentrations [A] < 1μM, prevented to convert to the desensitized states R_h and AR_vh. Furtheron, AcCh enhances the phosphorylation of phosphatidyl inositol and the auto-phosphorylation of the receptor. If the AcCh binding hysteresis causes a phosphorylation hysteresis the desensitized nAcChR may serve as a memory molecule of the transsynaptic information signalling of the neurotransmission.