Phenomenological approach on wave propagation in dielectric media with two relaxation times

In this paper dielectric phenomena with two relaxation times are discussed. By assuming a sinusoidal form for induction vector D a sinusoidal electric field is generated and it depends on unknown phenomenological coefficients whose expressions together to their numerical values as functions of frequency are obtained. Moreover, electromagnetic wave propagation is analysed obtaining wave vector as function of the aforementioned coefficients. The results are applied to a Vinylidene Chloride-Vinyl Chloride (VDC-VC) to test the applicability of the model.     

Phenomenological equations for multicomponent fluids

Ahydrodynamic equation of motion for each component of a multicomponent fluid is derived on the basis of nonequilibrium thermodynamics. Special care has been directed to the choice of state variables. In some limiting cases, this equation leads to customary phenomenological equations, such as the equation for diffusion and the Navier-Stokes equation. The viscosity is a consequence of nonlocal coupling of forces and fluxes. The reciprocity between the linear coefficients is examined closely.     

Exchange effects in direct reactions

The effect of antisymmetrization in direct reactions is examined by studying the properties of the coupling-normalization kernel function occuring in a resonating-group formulation. From this study, one obtains useful information concerning the general behaviour of direct-reaction processes and some justification for the use of three-body models in phenomenological analyses.     

Phänomenologische Zustandsgrößen,Regressions-Schwankungs-Sätze und Transportkoeffizienten in linearen Onsager-Systemen

Starting from Onsager's assumption that the dynamical equilibrium correlations can be separated into a microscopic and a hydrodynamic part it is shown how to obtain phenomenological state variables in non-equilibrium, regression fluctuation theorems and (in some important cases) microscopic representations of thermal transport coefficients. The results are demonstrated for “pure” heat conduction, but most of them can be easily extended to systems which are described initially by the densities of dynamical constants.     

Phonons and photons in crystals

The simultaneous propagation of phonons and photons in an insulator is discussed from both phenomenological and quantum mechanical points of view. A phenomenological form of the energy of an insulator is first supposed from which is obtained the equation of propagation of modes involving nuclei displacements and an electric field. This equation is then studied, mainly in the vicinity of q=0, in order to show how various limits lead to different types of propagation. The phenomenological equations are then justified from a microscopic point of view. The proof goes in two steps. A linear screened response function of the electrons in a solid is first assumed; one then proves that all the coefficients entering into the phenomenological equations may be obtained from the sole knowledge of this response function and of the charge of the nuclei. The existence of the response function is then justified from a many-body point of view. Finally, the necessary relations between the phenomenological coefficients are proved. Some other possible applications of the microscopic equations are also discussed at the end of the paper.     

Non-newtonian shear viscosity,normal stress coefficients and corresponding states in rheology

A set of mutually consistent material functions, i.e., shear viscosity, primary normal stress, and secondary normal stress coefficients, is presented. They were originally derived by means of a dense-simple-fluid kinetic theory. It is shown that in spite of their origin the material functions can account for the shear rate dependences of rheological material functions for some polymer solutions, if the formulas are treated as phenomenological functions of shear rate. It is also shown that the material functions used are in fact a set of corresponding state rheological equations of state to a good accuracy for the materials examined.     

Macroscopic phenomenological relations for nonlinear processes in kinetic theory

Nonlinear irreversible processes between states which are not local equilibrium states are investigated by methods of the kinetic theory. The phenomenological equations for the second-order fluxes in a multicomponent mixture are derived, and relations between some of the second-order phenomenological coefficients are established. It is shown that new independent forces appear in the second-order equation, namely the gradients of the chemical potentials. Expressions for the entropy, entropy flux, and entropy source are evaluated. These expressions are related to the phenomenological equations and coefficients, e.g., all the second-order contributions of the forces in the equations for the fluxes can be obtained by differentiation of the expression for the second-order entropy source with respect to the coupled forces.     

Fluctuations in nonlinear Markovian systems

We study nonlinear irreversible processes by statistical mechanical methods from a general point of view. Assuming that the macroscopic variables behave approximatively Markovian we derive evolution equations for the mean values as well as for the fluctuations about the mean. The mean values obey nonlinear transport equations and the fluctuations obey linear nonstationary Langevin equations. The equations of motion are completely specified by the entropy and the transport coefficients as functions of the macroscopic state. The theory provides a statistical mechanical basis for some phenomenological approaches put forward recently.     

An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method

The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the ‘cubication’ of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.     

Which is heavier—d oru quark?

For a large class of phenomenological potential models motivated by quantum chromodynamics, we have studied the behaviour of bound state masses as the constituent mass is increased and found that the mass of a quark-antiquark bound state increases when a constituent mass is increased. It appears, for these potentials, thatd quark is heavier thanu quark. An erratum to this article is available at .     

Non-linear constitutive and diffusion equations in the Burnett regime

A phenomenological method is presented to obtain the hydrodynamic equations for a multicomponent, isotropic, non-reactive fluid to any order in the spatial inhomogeneities. Two assumptions are made, the existence of a local equilibrium state and a non-linear dependence of the fluxes on the thermodynamic forces. In particular, the generalized form for the diffusion equation, to fourth order in the gradients, is obtained. Also, we derive the hydrodynamic equations for a binary mixture in a non-linear Burnett regime. The comparison of our results with others given in the literature and, in particular with those recently derived using the time-dependent correlation function formalism, is given. Finally some remarks are made in connection with the question about the existence of the transport coefficients beyond the Navier-Stokes regime.     

Uncertainty propagation in the derivation of phenomenological rate coefficients from theory: A case study of n-propyl radical oxidation

Global uncertainty and sensitivity analysis is used to study the propagation of uncertainties in fundamental theoretical parameters through to uncertainties in the predicted temperature and pressure dependent phenomenological rate coefficients. Predictions are obtained from ab initio transition state theory based master equation calculations. The fundamental parameters for these rate predictions include barrier heights, well depths, vibrational frequencies, collision frequency, and energy transfer parameters. A random sampling high-dimensional model representation (HDMR) approach is used to perform the global sensitivity analysis. This approach determines the predicted distributions of the phenomenological rate coefficients based on a quasi-random sample of the fundamental parameters within their uncertainty range. Sensitivity analysis then identifies the main parameters which contribute to variance in the predicted distributions. Here the approach is applied to a study of the oxidation of the propyl radical, employing the parameters derived in our recent theoretical study. We find rates at 3σ variances that typically differ from the most frequent values by factors of 4–6, with the uncertainties decreasing with increasing temperature. For the well skipping reactions there are more parameters that contribute significantly to the variance, the second-order sensitivities are greater, and the uncertainties increased with increasing pressure. For the other reactions, the uncertainties tend to decrease with increasing pressure.     

A possible alternative to Preisach's model of static hysteresis

Summary A phenomenological model which represents a possible alternative to the well-known Preisach's model of magnetic hysteresis is here presented. The main feature of the proposed model, which differentiates it from Preisach's one, is that the individual elementary ?particles? are not themselves hysteretic; it is the mechanism by which the state of these particles is modified that introduces hysteretic behaviour. The model appears to be computationally less cumbersome than Preisach's one, while having the same application range. The authors of this paper have agreed to not receive the proofs for correction.     

Superconducting state evolution with applied magnetic flux in mesoscopic rings

The magnetic flux dependence of the vortex state for small mesoscopic superconducting rings surrounded by a medium is investigated by the phenomenological Ginzburg-Landau theory. The influences of the ring size and the surface superconductivity on the free energy and total supercurrent are studied. For narrow rings, the persistent current evolves towards a periodic behaviour with magnetic flux. The complete paramagnetic or diamagnetic state, corresponding to positive or negative current flowing in the whole ring, can occur. A remarkable intermittent superconducting behaviour for the ground-state transition is found when the strength of surface-suppressed superconductivity is enlarged or the ring size is decreased. Consequently, a pure superconducting state with positive total current can be obtained.     

The 1-(1.9 MeV β-)2+ transition in the decay of148Pm

The non-unique first-forbidden 1^?(1.9 MeVβ ^?)2⁺ transition in the decay of¹⁴⁸Pm is studied. The nuclear matrix elements are evaluated using for the ground state of the odd-odd¹⁴⁸Pm a phenomenological wave function derived in a previous work in the framework of the two-quasiparticle model and assuming that the first excited 2⁺ state in¹⁴⁸Sm can be described as the first quadrupole phonon state. This model provides nuclear matrix elements which are capable of describing experimental data like the spectrum shape factor, the longitudinal polarization of the electrons and a particular set ofβ-γ directional correlation coefficients, but it fails to interpret the large logft value of this transition. In addition, the validity of theξ-approximation is discussed.     

Molecular derivation of the hydrodynamic equations for a binary fluid

In this paper, the hydrodynamic equations and the associated transport coefficients are derived for a simple binary fluid from molecular considerations. This is a generalization of the methods of Felderhof and Oppenheim and of Selwyn to multicomponent systems. A linear response formalism is used to describe the relaxation of the binary system from an initial nonequilibrium state. Explicit molecular expressions are given for the transport coefficients in terms of time correlation functions of generalized current densities. These densities have the useful property of not containing a conserved part. The correlation functions are then related to a set of phenomenological coefficients in the theory of nonequilibrium thermodynamics. This explicit identification enables one to relate the correlation functions to experimentally measured transport coefficients.Supported by the National Science Foundation.     

Phase shift calculation for low-energy electron scattering from mercury

Summary The relativistic formalism is used to study the scattering of electrons from mercury at low energy. A method of numerical integration is applied to calculate phase shifts by including a local exchange approximation and phenomenological polarization potential. The phase shifts are found to exhibit a resonant behaviour which is in conformity with the results of some earlier calculations. In contrast to the previous methods, this approach has a general validity over the entire energy range and is free from divergences. The author of this paper has agreed to not receive proofs for correction.     

Magnetic properties of MnAs nanocrystals embedded in GaAs

A phenomenological model for explaining the magnetic properties of MnAs nanocrystals embedded in GaAs is proposed. It is shown that experimental data of DC magnetization as a function of temperature, obtained according to zero-field-cooled and field-cooled protocols, can be understood assuming a transition of the system from a low temperature state in which very slow dynamics is observed (frozen state) to a high-temperature state in which dynamics is fast (quasi superparamagnetic state).