On the size dependence of the optical absorption due to small metal particles

The quantum mechanical theory of Kawbata and Kubo is used to calculate the position of the Mie optical absorption peak for small silver particles. The calculated position is close to that obtained with a classical model and does not explain the shift to long wavelength experimentally observed.     

Example of a self-consistent solution for a fermion on domain wall

A self-consistent solution for a fermion coupled to static scalar field in the form of a kink (domain wall) is discussed. In particular, the case when the fermion occupies an excited nonzero frequency level in the presence of the domain-wall field is studied. The effect of the domain-wall profile distortion is calculated analytically.     

Surrogate formulation for diesel and jet fuels using the minimalist functional group (MFG) approach

Surrogate fuels aim to reproduce real fuel combustion characteristics in order to enable predictive simulations and fuel/engine design. In this work, surrogate mixtures were formulated for three diesel fuels (Coryton Euro and Coryton US-2D certification grade and Saudi pump grade) and two jet fuels (POSF 4658 and POSF 4734) using the minimalist functional group (MFG) approach, a method recently developed and tested for gasoline fuels. The diesel and jet fuel surrogates were formulated by matching five important functional groups, while minimizing the surrogate components to two species. Another molecular parameter, called as branching index (BI), which denotes the degree of branching was also used as a matching criterion. The present works aims to test the ability of the MFG surrogate methodology for high molecular weight fuels (e.g., jet and diesel). ¹H Nuclear Magnetic Resonance (NMR) spectroscopy was used to analyze the composition of the groups in diesel fuels, and those in jet fuels were evaluated using the molecular data obtained from published literature. The MFG surrogates were experimentally evaluated in an ignition quality tester (IQT), wherein ignition delay times (IDT) and derived cetane number (DCN) were measured. Physical properties, namely, average molecular weight (AMW) and density, and thermochemical properties, namely, heat of combustion and H/C ratio were also compared. The results show that the MFG surrogates were able to reproduce the combustion properties of the above fuels, and we demonstrate that fewer species in surrogates can be as effective as more complex surrogates. We conclude that the MFG approach can radically simplify the surrogate formulation process, significantly reduce the cost and time associated with the development of chemical kinetic models, and facilitate surrogate testing.     

Scattering of the double sine-Gordon kinks

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity \(v_{{\mathrm {cr}}}\) of the colliding kinks, which separates different regimes of the collision. At \(v_{\mathrm {in}}>v_{\mathrm {cr}}\) we observe kinks reflection, while at \(v_{\mathrm {in}}<v_{\mathrm {cr}}\) their interaction is complicated with capture and escape windows. We obtain the dependence of \(v_{\mathrm {cr}}\) on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon – the escape of two oscillons in the final state. Besides that, at \(v_{\mathrm {in}}<v_{\mathrm {cr}}\) we found the initial kinks’ velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.     

Impact of droplets onto inclined surfaces

Drop impacts onto dry walls and liquid films at low impact angles and low normal Weber numbers are experimentally investigated. Measurements were performed using a high spatial resolution CCD camera and short exposure times, yielding both qualitative and quantitative information about the impact. Whereas a droplet generally deposits on the surface for high impact angles, a rebound can occur at lower angles and for smooth or wetted surfaces. No rebound is observed for rough surfaces. A low viscous liquid (water) will either rebound or deposit on smooth or wetted surfaces. A high viscous liquid (glycerin) may also disjoin into two droplets, depending on the impact angle. A correlation is presented for the size of the secondary droplet. A further correlation quantifies the critical impact angle at which rebounding first occurs in terms of the normal Weber number.     

On the calculation of wall temperatures in the post dryout heat transfer region

A non-equilibrium post dryout heat transfer model for calculating the wall temperature distribution in vertical upflows is presented in this study. The model is based upon the three path heat transfer formulation developed by MIT researchers (Laverty & Rohsenow 1964, Forslund & Rohsenow 1968, Hynek et al. 1969 and Plummer et al. 1974) that involves heat transfer from wall to vapor, from wall to droplets in contact with the wall and from vapor to liquid droplets in the vapor core. Downstream gradients for the bulk vapor temperature, vapor quality, droplet size and vapor velocities are identical to those used by Hynek et al. (1969) and Plummer et al. (1974). Conditions at the dryout location are calculated using a modified version of a technique developed by Hynek et al. (1969).A procedure for determining an average droplet diameter based on a size distribution is introduced. Migration of droplets through the boundary layer and droplet deposition flux are predicted with the model of Gani? & Rohsenow (1979). Heat transfer from the wall to the impinging liquid droplets is calculated with a correlation by Holman & McGinnis (1969). Mechanisms contributing to wall to droplet heat transfer are identified as (a) droplet-wall contact, (b) intensive droplet evaporation inside the boundary layer, and (c) destruction of the boundary layer due to droplet migration to, and rebound from, the hot surface. The significance of the average droplet size and size distribution is demonstrated through its control over the free stream evaporation and droplet deposition rates.Predicted uniform heat flux wall temperature profiles for water, nitrogen and freon 12 are in good agreement with the data of Era et al. (1966), Bennett et al. (1967), Forslund & Rohsenow (1968), Ling et al. (1971), Groeneveld (1972) and Janssen & Kervinen (1975).     

Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

We studied the kink-antikink collision process for the "double sine-Gordon" (DSG) equation in 1+1 dimensions at different values of the potential parameter R>0. For small values of R we discuss the problem of resonance frequencies. We give qualitative explanation of the frequency shift in comparison with the frequency of the discrete level in the potential well of isolated kink. We show that in this region of the parameter R the effective long-range interaction between kink and antikink takes place.     

A note on threshold theorems for epidemics with bunching

This note begins by reviewing the Kermack-McKendrick and Whittle Threshold Theorems for the general epidemic. It then extends these results to the case of the general epidemic with bunching where thexy homogeneous mixing term is replaced byxy/(x+y), 01.Research supported by Office of Naval Research Contract N00014-84-K-0568.