the vector, axial-vector, scalar and pseudo-scalar vertices involving a pair of heavy quarks, QQ̄, were calculated. The results are valid for arbitrary momentum transfer and mass of the heavy quarks. These form factors have a number of applications, including anomalous couplings, the e+e− → QQ̄ cross section, and the forward-backward asymmetry of heavy quarks. Here the QQ̄ threshold cross section ...

This paper describes a steady state model of a multiple effect evaporator system for simulation and control purposes. The model includes overall as well as component mass balance equations, energy balance equations and heat transfer rate equations for area calculations for all the effects. Each effect in the process is represented by a number of variables which are related by the energy and mat...

In this study, three-dimensional simulations are presented for laminar forced convection flow of a radiating gas over a backward-facing step in rectangular duct. The fluid is treated as a gray, absorbing, emitting and scattering medium. The three-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations...

Rarefied gas slip microflow and heat transfer in rectangular microchannels and backward facing steps are numerically investigated. A control-volume based numerical method is used to solve the Navier–Stokes and energy equations with velocity-slip and temperature-jump conditions at the walls. The effects of Knudsen number (Kn ! 0.1), thermal creep, and viscous heating on the velocity and temperat...

We consider a mathematical framework of finite state Markov Decision Processes (MDPs) in which a weighted sum of the classical state-dependent cost and the transfer entropy from the state random process to the control random process is minimized. Physical interpretations of the considered MDPs are provided in the context of networked control systems theory and non-equilibrium thermodynamics. Ba...

In this article, we discuss the automatic inference of sufficient preconditions by abstract interpretation and sketch the construction of an under-approximating backward analysis. We focus on numeric properties of variables and revisit three classic numeric abstract domains: intervals, octagons, and polyhedra, with new under-approximating backward transfer functions, including the support for n...

1 We consider reconstruction of a wave…eld distribution in an input/object plane from data in an output/di¤raction (sensor) plane. A contribution of this paper concerns both a digital modelling for the forward and backward wave…eld propagation. A novel algebraic matrix form of the discrete di¤raction transform (DDT) originated in [1] is proposed for the forward modelling which is aliasing free ...

Transport and mixing processes in dynamical systems are often difficult to study analytically and therefore a variety of numerical methods have been developed. Finite-time Lyapunov exponents (FTLEs) or related stretching indicators are frequently used as a means to estimate transport barriers. Alternatively, eigenvectors, singular vectors, or Oseledets vectors of numerical transfer operators fi...

It is shown that owing to a dominance of np−pair transfer mechanism of backward elastic p 3 He-scattering for incident proton kinetic energies T p > 1 GeV the cross section of this process is defined mainly by the values of the Faddeev component of the wave function of 3 He nucleus, ϕ 23 (q 23 , p 1), at high relative momenta q 23 > 0.6GeV /c of the NN-pair in the 1 S 0 − state and at low spect...

To understand the connection between single-particle optics and the optics of a closely packed surface, controlled laboratory measurements of bidirectional reflectance distribution functions on layers of polymer and glass spheres are carried out. The measurements are compared with predictions from five radiative-transfer models; the Hapke's models, the Lumme-Bowell model, the BRF algorithm of M...