Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

Oxidation kinetics of thin copper films and wetting behaviour of copper and Organic Solderability Preservatives (OSP) with lead-free solder

The oxide formation on thin copper films deposited on Si wafer was studied by XPS, SEM and Sequential Electrochemical Reduction Analysis SERA. The surfaces were oxidized in air with a reflow oven as used in electronic assembly at temperatures of 100 °C, 155 °C, 200 °C, 230 °C and 260 °C. The SERA analyses detected only the formation of Cu₂O but the XPS analysis done for the calibration of the SERA equipment proved also the presence of a CuO layer smaller than 2 nm above the Cu₂O oxide. The oxide growth follows a power-law dependence on time within this temperature range and an activation energy of 33.1 kJ/mol was obtained. The wettability of these surfaces was also determined by measuring the contact angle between solder and copper substrate after the soldering process. A correlation between oxide thickness and wetting angle was established. It was found that the wetting is acceptable only when the oxide thickness is smaller than 16 nm. An activation energy of 27 kJ/mol was acquired for the spreading of lead free solder on oxidized copper surfaces.From wetting tests on copper surfaces protected by Organic Solderability Preservatives (OSP), it was possible to calculate the activation energy for the thermal decomposition of these protective layers.     

Fierz–Pauli equation for massive gravitons from Induced Matter theory of gravity

Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on a 4D curved spacetime which has the form of a Fierz–Pauli one. In our model the mass of gravitons mg$m_g$ is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz–Pauli one.     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Big rational surfaces

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of \mathbbP²{\mathbb{P}^2} at distinct points lying on a (possibly reducible) cubic.     

pH-Dependent Excited-State Properties of N,N-di(2-phosphonoethyl)-1,4,5,8-naphthalenediimide

Abstract— The effect of the protonation state of a novel aqueous soluble N,N'-di(2-phosphonoethyl)-l,4,5,8-naphthalene-diimide (DPN) on its spectroscopic properties is studied. In aqueous solution DPN depicts linear Lambert-Beer plots up to the solubility limits at pH 1.0, 7.1 and 10.1, in accordance with its solubilization as a monomer. A small increase in the extinction coefficients with pH is observed. Conversely a strong decrease in the fluorescence emission yields are observed with the increase in pH. These results are shown to originate from the distinct efficiencies of the intersystem crossing of DPN as a function of the net charge on the phosphono moieties. Accordingly, from the decrease in fluorescence emission, titration curves were obtained resulting in two pKa of –1.5 and 6.7 in agreement with the potentiometric analysis. In parallel monitoring the amount of heat deposited in the system shows an inverse pattern, that is, increase in the thermal tensing time-resolved signal with pH. Laser flash photolysis and thermal Iensing data in the absence and presence of oxygen show the interplay of an intersystem crossing process with the protonation state of the dye. The changes in protonation from neutral to two- and four-fold charged species are accompanied by an enhancing effect on the naphthalenediimide ring toward spin inversion (triplet formation) and consequently in different fluorescence yields