Homogeneous potential

We have obtained the expression given in GT, p. 225 for the spectral function of free rotors moving in a homogeneous potential in the interval between strong collisions see also VIG, Eqs. (7.12) and (7.13). So, the subscript F means free. The subscript R in Eq. (74c) is used as an initial letter of restriction. Indeed, as it follows from the comparison of Eq. (77) with Eq. (74a), the second term of the last equation expresses the steric-restriction effect arising for free rotation due to a potential wall. If we set, for example, p = 7t, what corresponds to a complete rotation (without restriction) of a dipole-moment vector p, then we find from Eqs. (74a)-(74c) that LR z) = 0 and L(z) = Lj,(z). This result confirms our statement about restriction. ... 

Common to all these geometries is that for a homogeneous potential distribution... 

Particles of homogeneous potential do not rotate, whatever their shapes ), provided velocity and applied field remain proportional. Therefore, a collection of non-spherlcal particles with a certain orientational distribution will retain this distribution upon electrophoresis. At the same time this makes the "averaging" of v over these orientations, as In 14.3.18), meaningful. 

V-type starch inclusion complex formed using continuous dual feed homogenization potential use as delivery vehicle... 

Another application of scaling is useful for the case of the Dirichlet problem for a homogeneous potential of degree n. In this case, the analog of relation (3.8) is followed by... 

K.D. Sen, J. Katriel, Information entropies for eigendensities of homogeneous potentials, J. Chem. Phys. 125 (2006) 074U71(4p). 

Kramers (44) in 1944 published an elegant paper on the mechanical and optical properties of dilute suspension of bead-rod systems in steady-state, homogeneous, potential flow [see comments just after Eq. (3.1)]. This theory has recently been extended by Bird, Johnson, and Curtiss (5) to include bead-spring systems as well. The latter theory gives for a system of N beads with any kind of connectors ... 

In contrast, the liquid interface can be considered homogeneous which is a precondition for a non-localised adsorption. Any free space at the liquid interface is available for ion adsorption. At the transition from a localised to a non-localised adsorption the exponential term of the Stem-Langmuir equation can be preserved and the pre-exponential multiplier must be changed. This was done by Martynov (1979). The basis of this approach is the notation of a homogeneous potential well along the liquid interface as a whole. 

The homogeneity of a liquid surface leads to identical conditions for the adsorption at any place of the surface which is reflected by the notion of a homogeneous potential well in a layer of thickness A. Its depth is equal to the adsorption energy, its thickness represents the decay of interaction between ions and the interface as the distance increases. Martynov considered this decay and initially introduced the potential well of a complicated configuration. In the framework of this model the adsorption is characterised as the total quantity of the ions within the potential well, i.e. as the product of the well thickness and the ion concentration within it. 

Meanwhile, because of the gauge invariance we caimot observe any constant homogeneous potential since the related strength of the electric field is zero. Does it mean that such a term is not observable at all The answer depends on how we treat different particles and what kind of problem we study. If, e.g., we consider the muon in the same way, but if two effective potentials are not the same (He Ufi), we should be able to observe their difference. The decay of muon and antimuon should have slightly different kinematics and the difference in their lifetime caused by the different phase volume of the decay product, would be proportional to Hg — Ui. To understand that we can have in mind so unrealistically large value of this difference that a muon would decay, but an antimuon would not. 

Other solutions for the singlet configuration-space distribution function are those for the steady-state, homogeneous potential flow of elastic dumbbells with any kind of spring (DPL, Eq. (13.2-14)), and the first few terms in a perturbation solution for steady-state, homogeneous flow of FENE dumbbells (DPL, Eq. (13.2-15)). 

After completion of the ECR treatment a thin polymer modified cementitious coating was applied to avoid further chloride penetration. Half cell potential measurements taken six years after treatment showed a homogeneous potential field at potentials around -50 mV CSE the rebars in the treated area remained fully passive (Elsener and Bohni, 1996a). The same results were found at the Canadian test site (Burlington Skyway) (Roti, 1994). 

No surface treatment was applied after completion of the realkalization. Half cell potential measurements after six months, one year and two years showed a homogeneous potential field with values of around -0.2 V CSE. Thus it seems that the presence of the Na2C03 solution in the pore volume of the concrete can maintain a pH value of >10.5 and the rebars remain passive. Investigations on other buildings after realkalization showed that no leakage of the sodium content in the concrete occurred (except in the outermost 5 mm) over four to six years (Roti, 1994 Odden, 1994). 

Extending the Topological Analysis and Seeking the Real-Space Subsystems in Non-Coulombic Systems with Homogeneous Potential Energy Functions... 

Keywords Quanmm theory of atoms in molecules Topological analysis Non-Coulombic systems Homogeneous potentials Virial theorem... 

A homogeneous potential energy function for a typical A-particle system has the following property V sri,..., srj i) = V ri,.. where is an arbitrary... 

At the mechanical equilibrium [ 1 ], the Hamiltonian of an iV-particle system with a homogeneous potential energy is ... 

The model of N quantum particles confined in a harmonic trap has been widely used to model the Bose-Einstein condensation in trapped dilute gases [57-68], and more recently in trapped Fermi gases [69-73]. A simplified model of the trap may be constmcted assuming a non-interacting system of quanmm particles in an external isotropic harmonic trap, as a homogeneous potential, n = 2, with the following Hamiltonian H = hk = /2m) V - a x +yl +zl), where... 

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