From realistic to simple models of fluids. III. Primitive models of carbon dioxide,hydrogen sulphide and acetone,and their properties

Recently developed methodology to construct primitive models of associating fluids as direct descendants of complex realistic intermolecular potential functions [L. Vl?ek, I. Nezbeda. Molec. Phys., 102, 485 (2004).] is extended to polar fluids and applied to three substances of practical importance: quadrupolar carbon dioxide, and dipolar hydrogen sulphide and acetone. It is shown that the structural properties (in terms of the site–site correlation functions) of the primitive models of polar fluids reproduce very well those of their parent realistic models but, nonetheless, they perform worse than in the case of associating fluids. A number of thermodynamic properties of the developed models obtained by computer simulations is also reported (for their later use in theoretical investigation) and discussed.     

Time domain numerical model for linear and nonlinear grating assisted co-directional coupler

A time domain algorithm for the dynamic analysis of linear and nonlinear devices based on coupled modes propagating with different group velocities is presented for the first time. As a test case, the numerical algorithm is applied to the analysis of a linear grating assisted co-directional coupler, in order to investigate quantitatively its limitations. As an application example, we show the simulation results on the switching dynamics of a current injection controlled grating assisted co-directional coupler sampled Bragg reflectors laser.     

Poly(amidoamine) dendrimers peripherally modified with 1,8-naphthalimides. Photodegradation and photostabilization on polyamide matrix

Some novel fluorescent poly(amidoamine) dendrimers supported by a polyamide-6 matrix have been prepared and studied for the first time. The colour characteristics of the novel materials have been determined and found to be dependent on the nature of 1,8-naphthalimides bonded to their periphery amino groups. The materials have been treated with protons and cuprum cations. The resulting into changes in the colour characteristics and photostability of the dendrimers has been investigated. It has been shown that these ions inhibit the photodegradation of dendrimers molecules studied.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

Shortest expected delay routing for Erlang servers

The queueing problem with Poisson arrivals and two identical parallel Erlang servers is analyzed for the case of shortest expected delay routing. This problem may be represented as a random walk on the integer grid in the first quadrant of the plane. An important aspect of the random walk is that it is possible to make large jumps in the direction of the boundaries. This feature gives rise to complicated boundary behavior. Generating function approaches to analyze this type of random walk seem to be extremely complicated and have not been successful yet. The approach presented in this paper directly solves the equilibrium equations. It is shown that the equilibrium distribution of the random walk can be written as an infinite linear combination of products. This linear combination is constructed in a compensation procedure. The starting solutions for this procedure are found by solving the shortest expected delay problem with instantaneous jockeying. The results can be used for an efficient computation of performance criteria, such as the waiting time distribution and the moments of the waiting time and the queue lengths.     

Minimal surfaces with prescribed topological type on a Schwarzian chain inMc3

Similar to the investigations of unstable polygonal minimal surfaces by Courant [1] we introduce here a variational principle for the free boundary problem with prescribed topological type which produces minimal surfaces in Riemannian manifolds with constant curvature. For special boundary configurations the surfaces have no branch points. The approach can be applied to numerical algorithms since it is constructive.     

Abels Unmöglichkeitsbeweis im Spiegel der modernen Galoistheorie

Ohne Zusammenfassung Eingegangen am 14.07.1997 / Angenommen am 02.10.1997     

Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.