A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations

In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c*>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation

Dimensional analysis of the earthquake-induced pounding between inelastic structures

In this paper the seismic response of inelastic structures with unilateral contact is revisited with dimensional analysis. All physically realizable contact types are captured via a non-smooth complementarity approach. The implementation of formal dimensional analysis leads to a condensed presentation of the response and unveils remarkable order even though two different types of non-linearity coexist in the response: the boundary non-linearity of unilateral contact and the inelastic behaviour of the structure itself. It is shown that regardless the intensity and frequency content of the excitation, all response spectra become self-similar when expressed in the appropriate dimensionless terms. The proposed approach hinges upon the notion of the energetic length scale of an excitation which measures the persistence of ground shaking to impose deformation demands. Using the concept of persistency which is defined for excitations with or without distinct pulses, the response is scaled via meaningful novel intensity measures: the dimensionless gap and the dimensionless yield displacement. The study confirms that contact may have a different effect on the response displacements of inelastic structures depending on the spectral region. In adjacent inelastic structures, such as colliding buildings or interacting bridge segments, contact is likely to alter drastically the excitation frequencies’ at which the system is most vulnerable. Finally, it is shown that the proposed approach yields maximum response displacements which correlate very well with the persistency of real earthquakes for a bridge system with considerably complex behaviour

Dimensional analysis of yielding and pounding structures for records without distinct pulses

The seismic response of two fundamental mechanical configurations of earthquake engineering, the elastic–plastic system and the pounding oscillator, is revisited with the aid of dimensional analysis. Starting from the previous work of the authors which focused on pulse-type excitations, the paper offers an alternative, yet physically motivated, way to present the response of yielding and pounding structures under excitations with arbitrary time history. It is shown, that when the appropriate time and length scales are adopted, dimensional analysis can be implemented and remarkable order emerges in the response. Regardless of the acceleration level and frequency content of the excitation, all response spectra become self-similar and when expressed in dimensionless terms, resulting from dimensional analysis, follow a single master curve. The study proposes such scales together with the associated selection criteria among the available in literature strong ground motion parameters and shows that the proposed approach reduces drastically the scatter in the response

A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term

In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated

Bovine Dermal Matrix as Coverage of Facial Nerve Grafts

Introduction. Soft tissue defects over functional structures represent a challenge for the reconstructive surgeon. Often complex, reconstructive procedures are required. Occasionally, elderly or sick patients do not qualify for these extensive procedures. Case. We present the case of a 91-year-old lady with large hemifacial defect with exposed bone and nerves after tumor resection. We first performed radical resection including the fascia of the temporalis muscle and the frontal branch of the facial nerve. Due to the moribund elderly patient with a potentially high perioperative risk, we decided against flap reconstruction but to use bovine collagen/elastin matrix and split thickness skin graft. Results. No postoperative complications occurred and STSG and matrix healed uneventfully. Discussion. In selected cases, where complex reconstruction is not appropriate, this procedure can be a safe, easy, and fast alternative for covering soft tissue defects even on wound grounds containing nerve grafts

Seismic retrofitting and health monitoring of school buildings of Cyprus

The vulnerability of existing buildings to seismic forces and their retrofitting is an international problem. The majority of structures in seismic-prone areas worldwide are structures that have been designed either without the consideration of seismic forces, or with previous codes of practice specifying lower levels of seismic forces. In Cyprus, after the three earthquakes that occurred in 1995, 1996, and 1999, the Cyprus State, acting in a pioneering way internationally, has decided the seismic retrofitting of all school buildings, taking into account the sensitivity of the society towards these structures, which house the future generation of the society. In this paper the overall assessment methodology is presented, along with details of the over 10 year ongoing retrofitting program of the school buildings of Cyprus, with emphasis on the description of the program and the development of a wireless monitoring system. In addition, mathematical models of selected school buildings are presented and comparison is made with in-situ measurement

Background to the Monolithicity Factors for the Assessment of Jacketed Reinforced Concrete Columns

The paper presents the background to the expressions adopted in the new Eurocode 8—3 for jacketed reinforced concrete columns. These are based on the commonly adopted concept of monolithicity factors (ratios of resistance of the jacketed section to that of an identical monolithic one). These factors are derived here in two ways: (i) by fitting experimental results for jacketed columns and (ii) by an extended parametric study of substandard reinforced concrete (R/C) members that were retrofitted by adding R/C jackets, analysed using a model developed by the authors that takes into account slip at the interface. Apart from the cross-section geometry and the thickness of the jacket, parameters of the investigation were the material properties of the core cross-section and the jacket, as well as the percentage of longitudinal reinforcement of the jacket and the percentage of dowels placed to connect the existing member to the jacket. It was found that the parameter that had the most visible effect on these factors was the normalised axial load (ν). The finally adopted factors are either simple functions of ν or constant values

Vulnerability assessment and feasibility analysis of seismic strengthening of school buildings

The majority of structures in seismic-prone areas worldwide are structures that have been designed either without seismic design considerations, or using codes of practice that are seriously inadequate in the light of current seismic design principles. In Cyprus, after a series of earthquakes that occurred between 1995 and 1999, it was decided to carry out an unprecedented internationally seismic retrofitting of all school buildings, taking into account the sensitivity of the society towards these structures. In this paper representative school buildings are analysed in both their pristine condition and after applying retrofitting schemes typical of those implemented in the aforementioned large-scale strengthening programme. Non-linear analysis is conducted on calibrated analytical models of the selected buildings and fragility curves are derived for typical reinforced concrete and unreinforced masonry structures. These curves are then used to carry out a feasibility study, including both benefit-cost and life-cycle analysis, and evaluate the effectiveness of the strengthening programme

Bridge-specific fragility analysis: when is it really necessary?

In seismic assessment of bridges the research focus has recently shifted on the derivation of bridge-specific fragility curves that account for the effect of different geometry, structural system, component and soil properties, on the seismic behaviour. In this context, a new, component-based methodology for the derivation of bridge-specific fragility curves has been recently proposed by the authors, with a view to overcoming the inherent difficulties in assessing all bridges of a road network and the drawbacks of existing methodologies, which use the same group of fragility curves for bridges within the same typological class. The main objective of this paper is to critically assess the necessity of bridge-specific fragility analysis, starting from the effect of structure-specific parameters on component capacity (limit state thresholds), seismic demand, and fragility curves. The aforementioned methodology is used to derive fragility curves for all bridges within an actual road network, with a view to investigating the consistency of adopting generic fragility curves for bridges that fall within the same class and quantifying the degree of over- or under-estimation of the probability of damage when generic bridge classes are considered. Moreover, fragility curves for all representative bridges of the analysed concrete bridge classes are presented to illustrate the differentiation in bridge fragility for varying structural systems, bridge geometry, total bridge length and maximum pier height. Based on the above, the relevance of bridge-specific fragility analysis is assessed, and pertinent conclusions are drawn