Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.

Nonstationary response of structures and its application to earthquake engineering

This thesis presents a simplified state-variable method to solve for the nonstationary response of linear MDOF systems subjected to a modulated stationary excitation in both time and frequency domains. The resulting covariance matrix and evolutionary spectral density matrix of the response may be expressed as a product of a constant system matrix and a time-dependent matrix, the latter can be explicitly evaluated for most envelopes currently prevailing in engineering. The stationary correlation matrix of the response may be found by taking the limit of the covariance response when a unit step envelope is used. The reliability analysis can then be performed based on the first two moments of the response obtained.

The method presented facilitates obtaining explicit solutions for general linear MDOF systems and is flexible enough to be applied to different stochastic models of excitation such as the stationary models, modulated stationary models, filtered stationary models, and filtered modulated stationary models and their stochastic equivalents including the random pulse train model, filtered shot noise, and some ARMA models in earthquake engineering. This approach may also be readily incorporated into finite element codes for random vibration analysis of linear structures.

A set of explicit solutions for the response of simple linear structures subjected to modulated white noise earthquake models with four different envelopes are presented as illustration. In addition, the method has been applied to three selected topics of interest in earthquake engineering, namely, nonstationary analysis of primary-secondary systems with classical or nonclassical dampings, soil layer response and related structural reliability analysis, and the effect of the vertical components on seismic performance of structures. For all the three cases, explicit solutions are obtained, dynamic characteristics of structures are investigated, and some suggestions are given for aseismic design of structures.

Earthquake response of steel braces and braced steel frames

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of "acceleration magnifying" structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

Part I. Influence of membrane morphology on ion-exchange and charge propagation in composite polyelectrolyte electrode coatings. Part II. Dynamic surface tension measurements of polarization relaxation at mercury pool electrodes by the method of Wilhelmy.

Part I. Novel composite polyelectrolyte materials were developed that exhibit desirable charge propagation and ion-retention properties. The morphology of electrode coatings cast from these materials was shown to be more important for its electrochemical behavior than its chemical composition.

Part II. The Wilhelmy plate technique for measuring dynamic surface tension was extended to electrified liquid-liquid interphases. The dynamical response of the aqueous NaF-mercury electrified interphase was examined by concomitant measurement of surface tension, current, and applied electrostatic potential. Observations of the surface tension response to linear sweep voltammetry and to step function perturbations in the applied electrostatic potential (e.g., chronotensiometry) provided strong evidence that relaxation processes proceed for time-periods that are at least an order of magnitude longer than the time periods necessary to establish diffusion equilibrium. The dynamical response of the surface tension is analyzed within the context of non-equilibrium thermodynamics and a kinetic model that requires three simultaneous first order processes.

Structural dynamic eutrophication models

This article discusses problems of modelling the seasonal succession of algal species in lakes and reservoirs, and the adaptive selection of certain groups of algae in response to changes in the inputs and relative concentrations of nutrients and other environmental variables. A new generation of quantitative models is being developed which attempts to translate some important biological properties of species (survival, variation, inheritance, reproductive rates and population growth) into predictions about the survival of the fittest, where ”fitness” is measured or estimated in thermodynamic terms. The concept of ”exergy” and its calculation is explored to examine maximal exergy as a measure of fitness in ecosystems, and its use for calculating changes in species composition by means of structural dynamic models. These models accomodate short-term changes in parameters that affect the adaptive responses (species selection) of algae.

River salinity variations in response to discharge: examples from the western United States during the early 1900s

Major controls on river salinity (total dissolved solids) in the western United States are climate, geology, and human activity. Climate, in general, influences soil-river salinity via salt-balance variations. When climate becomes wetter, river discharge increases and soil-river salinity decreases; when climate becomes drier river discharge decreases and soil-river salinity increases. This study characterizes the river salinity response to discharge using statistical-dynamic methods. An exploratory analysis of river salinity, using early 1900s water quality surveys in the western United States, shows much river salinity variability is in response to storm and annual discharge. Presumably this is because river discharge is largely supported by surface flow.

Centrifuge modelling-based verification of response spectra design methods for some vulnerable structures

Residential RC framed structures suffered heavily during the 2001 Bhuj earthquake in Gujarat, India. These types of structures also saw severe damage in other earthquakes such as the 1999 Kocaeli earthquake in Turkey and 921 Ji-Ji earthquake in Taiwan. In this paper the seismic response of residential structures was investigated using physical modelling. Idealised soft storey and top heavy, two degrees of freedom (2DOF) portal frame structures were developed and tested on saturated and dry sand models at 25 g using the Schofield Centre 10-m Beam Centrifuge. It was possible to recreate observed field behaviour using these models. As observed in many of the recent earthquakes, soft storey structures were found to be particularly vulnerable to seismic loads. Elastic response spectra methods are often used in the design of simple portal frame structures. The seismic risk of these structures can be significantly increased due to modifications such as removal of a column or addition of heavy water tanks on the roof. The experimental data from the dynamic centrifuge tests on such soft storey or top-heavy models was used to evaluate the predictions obtained from the response spectra. Response spectra were able to predict seismic response during small to moderate intensity earthquakes, but became inaccurate during strong earthquakes and when soil structure interaction effects became important. Re-evaluation of seismic risk of such modified structures is required and time domain analyses suggested by building codes such as IBC, UBC or NEHRP may be more appropriate. © Springer 2006.

Impact response of polyethylene nanocomposites

The quasi-static and dynamic behaviour of Linear Low Density Polyethylene (LLDPE) and two LLDPE nanocomposites were studied. Nanocomposites consisting of LLDPE filled with 1% carbon black and 0.5% nanoclay fillers, by weight, were considered. Under quasi-static tensile loading, an improvement in the energy absorbing capability was achieved by adding 1% carbon black fillers. However, during quasi-static puncture and dynamic impact loading, the advantage provided by the fillers was lost. Thermal softening due to adiabatic heating under high strain rate deformation and difference s in the state of stress are considered as reasons for this reduction. © 2011 Published by Elsevier Ltd.

Dynamic changes in ovarian follicles measured by ultrasonography during gonadotropin stimulation in rhesus monkeys

The objective was to study dynamic changes of ovaries in rhesus macaques stimulated by gonadotropins to identify an indicator for predicting ovarian response to stimulation. Twenty-one cycling monkeys were given 36 IU/d recombinant human follicle-stimulat

Influence of fluid viscosity on the response of buried structures in earthquakes

The use of high viscous pore fluid has been widely established to match the rate of excess pore pressure generation and subsequent dissipation in dynamic centrifuge tests. The appropriate viscosity is linked to the geometric and gravity scaling factors which corresponds to the use of pore fluid of 'N' cSt in a 'N'g centrifuge test. The use of either water (1 cSt) or pore fluid lower than 'N' cSt can influence the behaviour of soil liquefaction in a centrifuge test. In this paper, the floatation of a tunnel following soil liquefaction is investigated using pore fluids with two different viscosities. The results show that the uplift displacement of the tunnel is significantly affected by the pore fluid viscosity. © 2010 Taylor & Francis Group, London.

Dynamic buckling of an inclined strut

The dynamic compressive response of a sandwich plate with a metallic corrugated core is predicted. The back face of the sandwich plate is held fixed whereas the front face is subjected to a uniform velocity, thereby compressing the core. Finite element analysis is performed to investigate the role of material inertia, strain hardening and strain rate hardening upon the dynamic collapse of the corrugated core. Three classes of collapse mode are identified as a function of impact velocity: (i) a three-hinge plastic buckling mode of wavelength equal to the strut length, similar to the quasi-static mode, (ii) a 'buckle-wave' regime involving inertia-mediated plastic buckling of wavelength less than that of the strut length, and (iii) a 'stubbing' regime, with shortening of the struts by local fattening at the front face. The presence of strain hardening reduces the regime of dominance of the stubbing mode. The influence of material strain rate sensitivity is evaluated by introducing strain rate dependent material properties representative of type 304 stainless steel. For this choice of material, strain rate sensitivity has a more minor influence than strain hardening, and consequently the dynamic collapse strength of a corrugated core is almost independent of structural dimension. © 2012 Elsevier Ltd. All rights reserved.

An efficient model for the dynamic behaviour of a single pile in viscoelastic soil

This paper presents a novel, three-dimensional, single-pile model, formulated in the wavenumber domain and adapted to account for boundary conditions using the superposition of loading cases. The pile is modelled as a column in axial vibration, and a Euler-Bernoulli beam in lateral vibration. The surrounding soil is treated as a viscoelastic continuum. The response of the pile is presented in terms of the stiffness and damping coefficients, and also the magnitude and phase of the pile-head frequency-response function. Comparison with existing models shows that excellent agreement is observed between this model, a boundary-element formulation, and an elastic-continuum-type formulation. This three-dimensional model has an accuracy equivalent to a 3D boundary-element model, and a runtime similar to a 2D plane-strain analytical model. Analysis of the response of the single pile illustrates a difference in axial and lateral vibration behaviour; the displacement along the pile is relatively invariant under axial loads, but in lateral vibration the pile exhibits localised deformations. This implies that a plane-strain assumption is valid for axial loadings and only at higher frequencies for lateral loadings. © 2013 Elsevier Ltd.

The soft impact response of composite laminate beams

The quasi-static and dynamic responses of laminated beams of equal areal mass, made from monolithic CFRP and Ultra high molecular weight Polyethylene (UHMWPE), have been measured. The end-clamped beams were impacted at mid-span by metal foam projectiles to simulate localised blast loading. The effect of clamping geometry on the response was investigated by comparing the response of beams bolted into the supports with the response of beams whose ends were wrapped around the supports. The effect of laminate shear strength upon the static and dynamic responses was investigated by testing two grades of each of the CFRP and UHMWPE beams: (i) CFRP beams with a cured matrix and uncured matrix, and (ii) UHMWPE laminates with matrices of two different shear strengths. Quasi-static stretch-bend tests indicated that the load carrying capacity of the UHWMPE beams exceeds that of the CFRP beams, increases with diminishing shear strength of matrix, and increases when the ends are wrapped rather than through-bolted. The dynamic deformation mode of the beams is qualitatively different from that observed in the quasi-static stretch-bend tests. In the dynamic case, travelling hinges emanate from the impact location and propagate towards the supports; the beams finally fail by tensile fibre fracture at the supports. The UHMWPE beams outperform the CFRP beams in terms of a lower mid-span deflection for a given impulse, and a higher failure impulse. Also, the maximum attainable impulse increases with decreasing shear strength for both the UHMWPE and CFRP beams. The ranking of the beams for load carrying capacity in the quasi-static stretch-bend tests is identical to that for failure impulse in the impact tests. Thus, the static tests can be used to gauge the relative dynamic performances of the beams. © 2013 Elsevier Ltd. All rights reserved.

Factors affecting seismic response of submarine slopes

The response of submerged slopes on the continental shelf to seismic or storm loading has become an important element in the risk assessment for offshore structures and "local" tsunami hazards worldwide. The geological profile of these slopes typically includes normally consolidated to lightly overconsolidated soft cohesive soils with layer thickness ranging from a few meters to hundreds of meters. The factor of safety obtained from pseudo-static analyses is not always a useful measure for evaluating the slope response, since values less than one do not necessarily imply slope failure with large movements of the soil mass. This paper addresses the relative importance of different factors affecting the response of submerged slopes during seismic loading. The analyses use a dynamic finite element code which includes a constitutive law describing the anisotropic stress-strain-strength behavior of normally consolidated to lightly overconsolidated clays. The model also incorporates anisotropic hardening to describe the effect of different shear strain and stress histories as well as bounding surface principles to provide realistic descriptions of the accumulation of the plastic strains and excess pore pressure during successive loading cycles. The paper presents results from parametric site response analyses on slope geometry and layering, soil material parameters, and input ground motion characteristics. The predicted maximum shear strains, permanent deformations, displacement time histories and maximum excess pore pressure development provide insight of slope performance during a seismic event. © 2006 Author(s). This work is licensed under a Creative Commons License.

Efficient numerical models for investigating the statistics of random dynamic systems

The study of random dynamic systems usually requires the definition of an ensemble of structures and the solution of the eigenproblem for each member of the ensemble. If the process is carried out using a conventional numerical approach, the computational cost becomes prohibitive for complex systems. In this work, an alternative numerical method is proposed. The results for the response statistics are compared with values obtained from a detailed stochastic FE analysis of plates. The proposed method seems to capture the statistical behaviour of the response with a reduced computational cost.