One-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady, isothermal, isochoric, spatially homogeneous, closed reactive systems are calculated. The technique is based on global analysis of the composition space of the reactive system. The identification of all the system’s finite and infinite critical points plays a major role in calculating the system’s slo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

Homogeneous nucleation of a new phase near an Ising-like critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order parameter associated with the critical point. The total magnetisation of the nucleus scales as the response function and so it diverges. Vapour-liquid critic...

Nucleic Acid Testing (NAT) promises rapid, sensitive and specific diagnosis of infectious, inherited and genetic disease. The next generation of diagnostic devices will interrogate the genetic determinants of such conditions at the point-of-care, affording clinicians prompt reliable diagnosis from which to guide more effective treatment. The complex biochemical nature of clinical samples, the l...

Phase diagrams of some globular proteins have a fluid-fluid transition as well as a fluid-crystal transition. Homogeneous nucleation of the crystal from the fluid phase near the critical point of the fluid-fluid transition is examined. As the fluid-fluid critical point is approached, the number of molecules in the critical nucleus, the nucleus at the top of the free energy barrier to nucleation...

The paper first discusses the real fluids circulating in the earth’s crust, and justifies the need to examine the natural convection in a porous medium of a simple pure fluid with properties resembling those near the thermodynamic critical point. The literature on natural convection in a homogenous porous medium between isothermal horizontal plates, the lower one hotter, is then reviewed. Resul...

– Results are presented of studies on dielectric permittivity (ε) for the isothermal pressure (P ) path of approaching the near-critical consolute point in 1-nitropropane–hexadecane solution. The pretransitional anomaly is well portrayed by the relation isomorphic to that applied in temperature (T ) studies under atmospheric pressure. However, the ε(P ) anomaly is much larger, with almost negli...

Abstract: The equation of state associated with N = 4 supersymmetric Yang–Mills in four dimensions, for SU(N) in the large N limit, is investigated using the AdS/CFT correspondence. An asymptotically AdS black-hole on the gravity side provides a thermal background for the Yang–Mills theory on the boundary in which the cosmological constant is equivalent to a volume. The thermodynamic variable c...