Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Killing K Channels with TEA+

Tetraethylammonium (TEA+) is widely used for reversible blockade of K channels in many preparations. We noticed that intracellular perfusion of voltage-clamped squid giant axons with a solution containing K+ and TEA+ irreversibly decreased the potassium current when there was no K+ outside. Five minutes of perfusion with 20 mM TEA+, followed by removal of TEA+, reduced potassium current to <5% of its initial value. The irreversible disappearance of K channels with TEA+ could be prevented by addition of ≥ 10 mM K+ to the extracellular solution. The rate of disappearance of K channels followed first-order kinetics and was slowed by reducing the concentration of TEA+. Killing is much less evident when an axon is held at −110 mV to tightly close all of the channels. The longer-chain TEA+ derivative decyltriethylammonium (C10+) had irreversible effects similar to TEA+. External K+ also protected K channels against the irreversible action of C10+. It has been reported that removal of all K+ internally and externally (dekalification) can result in the disappearance of K channels, suggesting that binding of K+ within the pore is required to maintain function. Our evidence further suggests that the crucial location for K+ binding is external to the (internal) TEA+ site and that TEA+ prevents refilling of this location by intracellular K+. Thus in the absence of extracellular K+, application of TEA+ (or C10+) has effects resembling dekalification and kills the K channels.

Responses of the phototransduction cascade to dim light.

The biochemistry of visual excitation is kinetically explored by measuring the activity of the cGMP phosphodiesterase (PDE) at light levels that activate only a few tens of rhodopsin molecules per rod. At 23 degrees C and in the presence of ATP, the pulse of PDE activity lasts 4 s (full width at half maximum). Complementing the rod outer segments (ROS) with rhodopsin kinase (RK) and arrestin or its splice variant p44 does not significantly shorten the pulse. But when the ROS are washed, the duration of the signal doubles. Adding either arrestin or p44 back to washed ROS approximately restores the pulse width to its initial value, with p44 being 10 times more efficient than arrestin. This supports the idea that, in vivo, capping of phosphorylated R* is mostly done by p44. When myristoylated (14:0) recoverin is added to unwashed ROS, the pulse duration and amplitude increase by about 50% if the free calcium is 500 nM. This effect increases further if the calcium is raised to 1 microM. Whenever R* deactivation is changed--when RK is exogenously enriched or when ATP is omitted from the buffer--there is no impact on the rising slope of the PDE pulse but only on its amplitude and duration. We explain this effect as due to the unequal competition between transducin and RK for R*. The kinetic model issued from this idea fits the data well, and its prediction that enrichment with transducin should lengthen the PDE pulse is successfully validated.

Overcoming performance and convergence issues of discrete transform based modeling of crosslinking classical and reversible deactivated radical polymerizations

Population balances of polymer species in terms 'of discrete transforms with respect to counts of groups lead to tractable first order partial differential equations when ali rate constants are independent of chain length and loop formation is negligible [l]. Average molecular weights in the absence ofgelation are long known to be readily found through integration of an initial value problem. The extension to size distribution prediction is also feasible, but its performance is often lower to the one provided by methods based upon real chain length domain [2]. Moreover, the absence ofagood starting procedure and a higher numerical sensitivity hás decisively impaired its application to non-linear reversibly deactivated polymerizations, namely NMRP [3].

Rapid solution of finite element equations on locally refined grids by multi-level methods /

"UILU-ENG 80 1712."

An iterative method for solving nonsymmetric linear systems with dynamic estimation of parameters /

Vita.

Numerical studies of the Stone algorithm and comparisons with Alternating Direction Implicit methods /

Thesis (M.S.)--University of Illinois, 1970.

Neck flexor muscle fatigue is side specific in patients with unilateral neck pain

Despite the evidence of greater fatigability of the cervical flexor muscles in neck pain patients, the effect of unilaterality of neck pain on muscle fatigue has not been investigated. This study compared myoelectric manifestations of sternocleidomastoid (SCM) and anterior scalene (AS) muscle fatigue between the painful and non-painful sides in patients with chronic unilateral neck pain. Myoelectric signals were recorded from the sternal head of SCM and the AS muscles bilaterally during sub-maximal isometric cervical flexion contractions at 25% and 50% of the maximum voluntary contraction (MVC). The time course of the mean power frequency, average rectified value and conduction velocity of the electromyographic signals were calculated to quantify myoelectric manifestations of muscle fatigue. Results revealed greater estimates of the initial value and slope of the mean frequency for both the SCM and AS muscles on the side of the patient's neck pain at 25% and 50% of MVC. These results indicate greater myoelectric manifestations of muscle fatigue of the superficial cervical flexor muscles ipsilateral to the side of pain. This suggests a specificity of the effect of pain on muscle function and hence the need for specificity of therapeutic exercise in the management of neck pain patients. (C) 2003 European Federation of Chapters of the International Association for the Study of Pain. Published by Elsevier Ltd. All rights reserved.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

An endurance-strength training regime is effective in reducing myoelectric manifestations of cervical flexor muscle fatigue in females with chronic neck pain

Objective: The purpose of this study was to investigate whether an endurance-strength training program is effective in reducing myoelectric manifestations of sternocleidomastoid (SCM) and anterior scalene (AS) muscle fatigue which have been found to be greater in people with chronic neck pain. Methods: Fifty-eight female patients with chronic non-severe neck pain were randomized into one of two 6-week exercise intervention groups: an endurance-strength training regime for the cervical flexor muscles or a referent exercise intervention involving low load retraining of the cranio-cervical flexor muscles. The primary outcomes were a change in maximum voluntary contraction (MVC) force and change of the initial value and rate of change of the mean frequency, average rectified value and conduction velocity detected from the SCM and AS muscles during sub-maximal isometric cervical flexion contractions at 50, 25 and 10% MVC. Results: At the 7th week follow-up assessment, the endurance-strength training group revealed a significant increase in MVC force and a reduction in the estimates of the initial value and rate of change of the mean frequency for both the SCM and AS muscles (P < 0.05). Both exercise groups reported a reduced average intensity of neck pain and reduced neck disability index score (P < 0.05). Conclusions: An endurance-strength exercise regime for the cervical flexor muscles is effective in reducing myoelectric manifestations of superficial cervical flexor muscle fatigue as well as increasing cervical flexion strength in a group of patients with chronic non-severe neck pain. Significance: Provision of load to challenge the neck flexor muscles is required to reduce the fatigability of the SCM and AS muscles in people with neck pain. Improvements in cervical muscle strength and reduced fatigability may be responsible for the reported efficacy with this type of exercise program. (c) 2006 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All fights reserved.

Dynamic simulation of chemical plant

A CSSL- type modular FORTRAN package, called ACES, has been developed to assist in the simulation of the dynamic behaviour of chemical plant. ACES can be harnessed, for instance, to simulate the transients in startups or after a throughput change. ACES has benefited from two existing simulators. The structure was adapted from ICL SLAM and most plant models originate in DYFLO. The latter employs sequential modularisation which is not always applicable to chemical engineering problems. A novel device of twice- round execution enables ACES to achieve general simultaneous modularisation. During the FIRST ROUND, STATE-VARIABLES are retrieved from the integrator and local calculations performed. During the SECOND ROUND, fresh derivatives are estimated and stored for simultaneous integration. ACES further includes a version of DIFSUB, a variable-step integrator capable of handling stiff differential systems. ACES is highly formalised . It does not use pseudo steady- state approximations and excludes inconsistent and arbitrary features of DYFLO. Built- in debug traps make ACES robust. ACES shows generality, flexibility, versatility and portability, and is very convenient to use. It undertakes substantial housekeeping behind the scenes and thus minimises the detailed involvement of the user. ACES provides a working set of defaults for simulation to proceed as far as possible. Built- in interfaces allow for reactions and user supplied algorithms to be incorporated . New plant models can be easily appended. Boundary- value problems and optimisation may be tackled using the RERUN feature. ACES is file oriented; a STATE can be saved in a readable form and reactivated later. Thus piecewise simulation is possible. ACES has been illustrated and verified to a large extent using some literature-based examples. Actual plant tests are desirable however to complete the verification of the library. Interaction and graphics are recommended for future work.

Block co-polymerization by transformation reactions

The aim of this study was to use the transformation of anionic to metathesis polymerization to produce block co-polymers of styrene-b-pentenylene using WC16 /PStLi and WC16/PStLi/ AlEtC12 catalyst systems. Analysis of the products using SEC and 1H and 13C NMR spectroscopy enabled mechanisms for metathesis initiation reactions to be proposed. The initial work involved preparation of the constituent homo-polymers. Solutions of polystyryllithium in cyclohexane were prepared and diluted so that the [PStLi]o<2x10-3M. The dilution produced initial rapid decay of the active species, followed by slower spontaneous decay within a period of days. This was investigated using UV / visible spectrophotometry and the wavelength of maximum absorbance of the PStLi was found to change with the decay from an initial value of 328mn. to λmax of approximately 340nm. after 4-7 days. SEC analysis of solutions of polystyrene, using RI and UV / visible (set at 254nm.) detectors; showed the UV:RI peak area was constant for a range of polystyrene samples of different moleculor weight. Samples of polypentenylene were prepared and analysed using SEC. Unexpectedly the solutions showed an absorbance at 254nm. which had to be considered when this technique was used subsequently to analyse polymer samples to determine their styrene/ pentenylene co-polymer composition. Cyclohexane was found to be a poor solvent for these ring-opening metathesis polymerizations of cyclopentene. Attempts to produce styrene-b-pentenylene block co-polymers, using a range of co-catalyst systems, were generally unsuccessful as the products were shown to be mainly homopolymers. The character of the polymers did suggest that several catalytic species are present in these systems and mechanisms have been suggested for the formation of initiating carbenes. Evidence of some low molecular weight product with co-polymer character has been obtained. Further investigation indicated that this is most likely to be ABA block copolymer, which led to a mechanism being proposed for the termination of the polymerization.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant

We study the Cauchy problem for the Laplace equation in a quadrant (quarter-plane) containing a bounded inclusion. Given the values of the solution and its derivative on the edges of the quadrant the solution is reconstructed on the boundary of the inclusion. This is achieved using an alternating iterative method where at each iteration step mixed boundary value problems are being solved. A numerical method is also proposed and investigated for the direct mixed problems reducing these to integral equations over the inclusion. Numerical examples verify the efficiency of the proposed scheme.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.