Maximum IR-drop in On-Chip Power Distribution Networks of Wire-Bonded Integrated Circuits

A compact IR-drop model for on-chip power distribution networks in wire-bonded ICs is presented. Chip dimensions, metal coverage and piecewise distribution of the IC consumption are taken into account to obtain closed form expressions for the maximum IR-drop as well as its place. Comparison with simulations shows an error as small as 2% in most the cases.Postprint (published version

Mathematical modelling of fibre coating

Tecnical document resulting from the 158th European Study Group with Industry (ESGI)In this report we formulate and analyse a mathematical model describing the evo- lution of a thin liquid film coating a wire via an extrusion process. We consider the Navier-Stokes equations for a 2D incompressible Newtonian fluid coupled to the standard equation relating the fluid surface tension with the curvature. Taking the lubrication theory approximation and assuming steady state, the problem is reduced to a single third-order differential equation for the thin film height. An approximate analytical solu- tion for the final film height is derived and compared with a numerical solution obtained by means of a shooting scheme. Good agreement between the two solutions is obtained, resulting in a relative error of around 5%. The approximate solution reveals that the key control parameters for the process are the initial film height, the fluid surface tension and viscosity, the wire velocity and the angle of exit at the extruder.Preprin

A mathematical model for the energy stored in green roofs

A simple mathematical model to estimate the energy stored in a green roof is developed. Analytical solutions are derived corresponding to extensive (shallow) and intensive (deep) substrates. Results are presented for the surface temperature and energy stored in both green roofs and concrete during a typical day. Within the restrictions of the model assumptions the analytical solution demonstrates that both energy and surface temperature vary linearly with fractional leaf coverage, albedo and irradiance, while the effect of evaporation rate and convective heat transfer is non-linear. It is shown that a typical green roof is significantly cooler and stores less energy than a concrete one even when the concrete has a high albedo coating. Evaporation of even a few millimetres per day from the soil layer can reduce the stored energy by a factor of more than three when compared to an equivalent thickness concrete roof.Peer ReviewedPostprint (published version

Maximum IR-drop in On-Chip Power Distribution Networks of Wire-Bonded Integrated Circuits

A compact IR-drop model for on-chip power distribution networks in wire-bonded ICs is presented. Chip dimensions, metal coverage and piecewise distribution of the IC consumption are taken into account to obtain closed form expressions for the maximum IR-drop as well as its place. Comparison with simulations shows an error as small as 2% in most the cases

Maximum IR-drop in On-Chip Power Distribution Networks of Wire-Bonded Integrated Circuits

A compact IR-drop model for on-chip power distribution networks in wire-bonded ICs is presented. Chip dimensions, metal coverage and piecewise distribution of the IC consumption are taken into account to obtain closed form expressions for the maximum IR-drop as well as its place. Comparison with simulations shows an error as small as 2% in most the cases

On the asymptotic wavenumber of spiral waves in lambda - omega systems

In this paper we consider spiral wave solutions of a general class of $\lambda -\omega$ systems with a small twist parameter q and we prove that the asymptotic wavenumber of the spirals is a ${{\mathcal{C}}^{\infty}}$ -flat function of the perturbation parameter q.Peer ReviewedPostprint (author's final draft

On the asymptotic wavenumber of spiral waves in lambda - omega systems

In this paper we consider spiral wave solutions of a general class of $\lambda -\omega$ systems with a small twist parameter q and we prove that the asymptotic wavenumber of the spirals is a ${{\mathcal{C}}^{\infty}}$ -flat function of the perturbation parameter q.Peer Reviewe

Applications of Industrial Mathematics

Peer ReviewedPostprint (published version