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

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

Nonlinear dynamic analysis of masonry buildings and definition of seismic damage states

A large part of the building stock in seismic-prone areas worldwide are masonry structures that have been designed without seismic design considerations. Proper seismic assessment of such structures is quite a challenge, particularly so if their response well into the inelastic range, up to local or global failure, has to be predicted, as typically required in fragility analysis. A critical issue in this respect is the absence of rigid diaphragm action (due to the presence of relatively flexible floors), which renders particularly cumbersome the application of popular and convenient nonlinear analysis methods like the static pushover analysis. These issues are addressed in this paper that focusses on a masonry building representative of Southern European practice, which is analysed in both its pristine condition and after applying retrofitting schemes typical of those implemented in pre-earthquake strengthening programmes. Nonlinear behaviour is evaluated using dynamic response-history analysis, which is found to be more effective and even easier to apply in this type of building wherein critical modes are of a local nature, due to the absence of diaphragm action. Fragility curves are then derived for both the initial and the strengthened building, exploring alternative definitions of seismic damage states, including some proposals originating from recent international research programmes

Problems associated with direct displacement-based design of concrete bridges with single-column piers, and some suggested improvements

Currently available displacement-based design (DBD) procedures for bridges are critically evaluated with a view to identifying extensions and/or modifications of the procedure, for it to be applicable to final design of a fairly broad class of bridges. An improved direct DBD procedure is presented, including a suite of comprehensive design criteria and proper consideration of the degree of fixity of the pier top. The design of an overpass bridge (originally designed to a current European Code), applying the improved ‘direct’ displacement-based design (DDBD) procedure is presented and both ‘conventional’ and displacement-based designs are assessed using non-linear response-history analysis (NLRHA); comparisons are made in terms of both economy and seismic performance of the different designs. It is seen that DDBD provided a more rational base shear distribution among piers and abutments when compared to the force-based design procedure and adequately captured the displacement pattern, closely matching the results of the more rigorous NLRHA

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

The effect of interferon beta-1b treatment on MRI measures of cerebral atrophy in secondary progressive multiple sclerosis.

The recently completed European trial of interferon beta-1b (IFN beta -1b) in patients with secondary progressive multiple sclerosis (SP multiple sclerosis) has given an opportunity to assess the impact of treatment on cerebral atrophy using serial MRI. Unenhanced T-1-weighted brain imaging was acquired in a subgroup of 95 patients from five of the European centres; imaging was performed at 6-month intervals from month 0 to month 36. A blinded observer measured cerebral volume on four contiguous 5 mm cerebral hemisphere slices at each time point, using an algorithm with a high level of reproducibility and automation. There was a significant and progressive reduction in cerebral volume in both placebo and treated groups, with a mean reduction of 3.9 and 2.9%, respectively, by month 36 (P = 0.34 between groups). Exploratory subgroup analyses indicated that patients without gadolinium (Gd) enhancement at the baseline had a greater reduction of cerebral volume in the placebo group (mean reduction at month 36: placebo 5.1%, IFN beta -1b 1.8%, P < 0.05) whereas those with Gd-enhancing lesions showed a trend to greater reduction of cerebral volume if the patient was on IFN<beta>-1b (placebo 2.6%, IFN beta -1b, 3.7%; P > 0.05). These results are consistent with ongoing tissue loss in both arms of this study of secondary progressive multiple sclerosis. This finding is concordant with previous observations that disease progression, although delayed, is not halted by IFN beta. The different pattern seen in patients with and without baseline gadolinium enhancement suggests that part of the cerebral volume reduction observed in IFN beta -treated patients may be due to the anti-inflammatory/antioedematous effect of the drug. Longer periods of observation and larger groups of patients may be needed to detect the effects of treatment on cerebral atrophy in this population of patients with advanced disease

No evidence of disease activity status in patients treated with early vs. delayed subcutaneous interferon β-1a.

Abstract Background Clinically isolated syndrome (CIS) is defined as a monophasic clinical episode highly suggestive of multiple sclerosis (MS). Regardless, studies have shown that treatment at this early stage of MS can delay a second event and prolong the transition to clinically diagnosed MS. The objective of this post-hoc analysis was to determine the effect of early CIS treatment with once weekly (qw) or three times weekly (tiw) subcutaneous interferon (scIFN) β-1a vs. delayed treatment (DT) on the composite endpoint of no evidence of disease activity (NEDA)-3. Methods In REFLEX, patients with CIS were randomized to double-blind scIFN β-1a 44 µg tiw, qw, or placebo for 24 months. Upon clinically-definite MS, patients switched to open-label scIFN β-1a tiw. Patients who completed REFLEX entered an extension (REFLEXION). Patients initially randomized to placebo switched to tiw (DT); scIFN β-1a patients continued their initial qw/tiw regimen for up to 60-months post-randomization. This post-hoc analysis was conducted in the integrated intent-to-treat REFLEX plus REFLEXION population (tiw, n = =171; qw, n = =175; DT, n = =171). All p values are nominal. CIS was defined using the McDonald 2010 criteria. Results Patients receiving early treatment (ET) with scIFN β-1a tiw and qw were more likely to achieve NEDA-3 than DT at year 2 (tiw vs. DT: OR 4.26, 95% CI 2.02–8.98, p = =0.0001; qw vs. DT: OR 2.99, 95% CI 1.39–6.43, p = =0.005). Compared with DT, ET with scIFN β-1a tiw was more likely to achieve NEDA-3 at year 3 (OR 3.73, 95% CI 1.63–8.55, p = =0.002) and year 5 (OR 12.96, 95% CI 1.66–101.04, p = =0.015). Between ET regimens, the odds of achieving NEDA-3 were not significantly improved by scIFN β-1a 44 µg tiw at year 2 (OR 1.42, 95% CI 0.81–2.50, p = =0.22) but were at year 3 (OR 2.26, 95% CI 1.11–4.60, p = =0.024) and year 5 (OR 3.22, 95% CI 1.01–10.22, p = =0.048), indicating that the beneficial effects of more frequent scIFN β-1a dosing become more apparent over time in patients with CIS. In the subgroup of patients with Gd+ lesions at baseline the odds for achieving NEDA-3 were higher for ET up to year 2 compared with DT (tiw: OR 10.21, 95% CI 1.23–84.82, p = =0.03; qw: OR 8.97, 95% CI 1.08–74.28, p = =0.04). In patients without Gd+ lesions at baseline, those receiving ET were more likely to achieve NEDA-3 at year 2 (OR 3.56, 95% CI 1.56–8.10, p = =0.003), year 3 (OR 2.54, 95% CI 1.05–6.18, p = =0.04) and year 5 (OR 9.63, 95% CI 1.19–77.79, p = =0.034) than patients who received DT. Conclusions ET with scIFN β-1a tiw was associated with a higher likelihood of achieving NEDA-3 not only at 2 but also at 3 and 5 years

The effect of preloading on the strength of jacketed R/C columns

The influence of core preloading on the strength of jacketed reinforced concrete (R/C) columns is analytically investigated. A recently proposed method for arbitrary composite section analysis in biaxial bending and axial load is extended to include preloading actions. A parametric evaluation of the preloading effect using quantitative indices is performed, considering the variability of several parameters such as section geometry, amount of reinforcement, and various axial and moment preloading levels. Results are presented in the form of 3D failure surfaces and moment-curvature curves. Specific cases where the preloading effect is more pronounced are finally highlighted

Flexural behaviour of reinforced concrete jacketed columns under reversed cyclic loading

The objective of the present study is the development of an analytical model for predicting the response under reversed cyclic loading of structural members with ‘old-type’ detailing, strengthened with reinforced concrete (RC) jacketing. The analytical model introduces one additional degree of freedom between the existing member (core of the retrofitted member) and its outer RC shell, thus allowing slip to take place at the interface between the existing member and the jacket. Shear resistance mechanisms, such as aggregate interlock, friction, and dowel action, are mobilized to resist slip. Existing constitutive models are further improved to describe the mechanisms that resist sliding under cyclic shear reversals and implemented for the first time in an analytical model for deriving the response of RC jacketed members. A calculation algorithm is developed to estimate the flexural response under cyclic loading taking into account slip at the interfaces. The sensitivity of the proposed analytical model to the shear transfer mechanisms degradation rules, as well as to the crack spacing estimation, was evaluated. The validity of the proposed analytical model is assessed against experimental results