A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6]

Experimental and numerical investigations of the optical and thermal aspects of a PCM-glazed unit

This paper reports on the thermal and optical characterisation of PCM (phase change material) RT27 using the T-history method and spectrophotometry principles, respectively, and the experimental and numerical performance evaluation of a PCM-glazed unit. Various relationships describing the variations in the extinction, scattering and absorption coefficients within the phase change region were developed, and were validated in a numerical CFD model. The results show that: (i) during rapid phase changes, the transmittance spectra from the PCM are unstable, while under stable conditions visible transmittance values of 90% and 40% are obtained for the liquid and phases, respectively; (ii) the radiation scattering effects are dominant in the solid phase of the PCM, while radiation absorption dominates in the liquid phase; (iii) the optical/radiation performance of PCM can be successfully modelled using the liquid fraction term as the main variable; (iv) the addition of PCM improves the thermal mass of the unit during phase change, but risks of overheating may be a significant factor after the PCM has melted; (v) although the day-lighting aspects of PCM-glazed units are favourable, the change in appearance as the PCM changes phase may be a limiting factor in PCM-glazed units

A Domain Decomposition method based on iterative Operator Splitting method.

In this article a new approach is proposed for constructing domain decomposition methods based on iterative operator splitting methods. We study the convergence properties of such a method. The main feature of the method is the decoupling the space and time dimension. We confirm with two numerical applications the effectiveness of the proposed iterative operator splitting method in comparison with classical Schwarz waveform relaxation method as a standard method for domain decomposition. We provide improved results and convergence rates. The efficiency of considering the whole domain in the case of the iterative operator splitting method allows more accurate results

Comparison of thermistor linearization techniques for accurate temperature measurement in phase change materials

Alternate energy technologies are developing rapidly in the recent years. A significant part of this trend is the development of different phase change materials (PCMs). Proper utilization of PCMs requires accurate thermal characterization. There are several methodologies used in this field. This paper stresses the importance of accurate temperature measurements during the implementation of T-history method. Since the temperature sensor size is also important thermistors have been selected as the sensing modality. Two thermistor linearization techniques, one based on Wheatstone bridge and the other based on simple serial-parallel resistor connection, are compared in terms of achievable temperature accuracy through consideration of both, nonlinearity and self-heating errors. Proper calibration was performed before T-history measurement of RT21 (RUBITHERM® GmbH) PCM. Measurement results suggest that the utilization of serial-parallel resistor connection gives better accuracy (less than ±0.1°C) in comparison with the Wheatstone bridge based configuration (up to ±1.5°C)

On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for $$u_t = u \Delta u + u \int_\Omega |\nabla u|^2$$ in bounded domains \Om\sub\R^n which arises in game theory. We prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for publication in "Optimization Letters"

A bifurcation-type theorem for the positive solutions of a nonlinear Neumann problem with concave and convex terms

We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a “concave” and of a “convex” terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation