Kinematic interaction

This model, which gives good results for high values of S, can neither be applied to S A nor to compounds with chain structures. More recently, improvements have been achieved by Ishikawa and Oguchi by including into the spin-wave theory kinematic interactions besides dynamic ones270) for CuF2 H20, S = A, / i(exp) = 0.63 and Xi calc. = 0.64. 

In A2FeFj compounds (A = K, Rb, Cs) an important spin reduction has been detected by neutron diffraction202 203 and Mossbauer resonance measurements230-232. The calculations are based only on the spin-wave theory disregardering the kinematic interactions since the spin value is important. Figure 36 describes the variation of the zero-point spin reduction with the anisotropy factor a. a is here (1 - coA/(oE) 2 where mA and a E are the Larmor frequencies corresponding to the anisotropy and exchange fields, respectively. 

Hence, AS has a minimum but is not equal to zero for 3-D magnetic systems and increases when the dimensionality is lowered (J /J - 0). The influence of the anisotropy is more important in low-dimensional compounds, and the more isotropic the system (a - 1), the more is the spin reduced. For small spin values (S = Vi) addition of the kinematic interactions permits to get AS/S = 1 for J /J - 0. 

Let us now consider the case with pr — 0 implying that the particle (and similarly for the antiparticle) either orbits the system M or is so far away from the large system that there is no "gravitational" interaction between m and M. In this situation, we realize, see Eqs. (52) and (53) further below, that the kinematical interaction p/c equals irac(r) for a given value of r or... 

The present model is quite surprising in its simplicity and yet the interpretation is very different compared to classical and quantum mechanical pictures. The ansatz Eq. (2) implies that every fundamental quantum particle will occupy one of two quantum states. When the choice is made the associated antiparticle will be indirectly recognized through the kinematical interaction v and the appearance of the length- and time-scale contractions. We do not, therefore, directly experience mirror- (anti-)particles, unless they are bodily excited. Within the present description, we have proposed a generalized quantum description, which transcends classical features as the contraction of scales mentioned above, including also a dynamical formulation of gravitational interactions. 

The kinematic interaction appears first in terms of fourth order. It can be considered in the theory of nonlinear optical effects in a quite similar fashion as has been done in the article by Toshich (93), who considered nonlinear optical effects of fourth order in the excitonic spectral region. The kinematic interaction of polaritons in organic microcavities will be mentioned in Ch. 10. 

The problem of the kinematic interaction between two paulions is similar to the problem of localized states of an exciton in the presence of a vacancy (98). Indeed, the kinematic interaction governing the relative motion of two Pauli particles is formally analogous to the one-particle potential created by a vacancy, which cannot be occupied by an exciton. In this case the equation determining the localized exciton state energy E is... 

When speaking of kinematic interaction, it should be noted that the problem of its separation in connection with the transition from Pauli operators to Bose operators is far from new. This problem arises, in particular, for the Heisenberg Hamiltonian, which corresponds, for example, to an isotropic ferromagnet with spin a = 1/2 when spin waves whose creation and annihilation operators obey Bose commutation relations are introduced. This problem was dealt with by many people, including Dyson (6), who obtained the low-temperature expansion for the magnetization. However, even before Dyson s paper, Van Kranendonk (7) proposed to take into account of the kinetic interaction by starting from a picture where one spin wave produces an obstacle for the passage of another spin wave, since two flipped spins cannot be located at the same site (for Frenkel excitons this means that two excitons cannot be localized simultaneously on one and the same molecule). 

Kinematic interaction of exciton-polaritons in crystalline organic microcavities... 

The exciton-exciton and polariton-polariton kinematic interactions in a crystalline organic monolayer and in an organic microcavity have been considered in (26). The kinematic interactions in this paper are derived using for Frenkel excitons the transformation from paulions to bosons (see Ch. 3). 

For an organic crystalline monolayer it was found that the exciton-exciton kinematic interaction can be described as scattering, not by hard spheres as in 3D crystals, but as scattering by hard disks. It was shown also that, as in the case of a two-dimensional ultracold trapped atom boson gas, the excitons in a confined monolayer may behave as a dilute degenerate boson gas at low temperature. Then for a microcavity with an organic crystalline monolayer such as a resonant material the polariton-polariton kinematic interaction steming from the polariton excitonic part was derived. 

In previous sections we have considered collective properties of Frenkel excitons in three-dimensional molecular crystals only. In one- and two-dimensional molecular crystals the kinematic interaction appearing in the transition from Pauli to Bose operators can be, generally speaking, quite large, so that the description of Frenkel excitons in terms of Bose excitations can be very rough. Below we consider this problem in more detail. 

First we must keep in mind that if we are not interested in collective properties of excitons and, in particular, we not consider exciton-exciton scattering, then in a good approximation we can take into account only those crystal states where the number of excitons is 0 or 1. It is evident that in these states, independent of the crystal dimension, the kinematic interaction identically vanishes so that the Frenkel exciton can be considered both as a boson as well as a fermion (i.e. it can be described by Bose or Fermi operators) and both descriptions will give identical results. 

Quite another situation occurs when we consider collective properties of excitons. In this case, as shown above, the kinematic interaction can play an important role. However, the mutual scattering of elementary excitations, which causes this interaction, is quite different in three-, two- and one-dimensional crystals. In three-dimensional crystals at not very large concentration of excitations this scattering at least does not change the statistics. 

If we take into account not only the nearest, but also the farther neighbors, the additional so-called kinematic interaction between Fermi quasiparticles appears. For molecular chains the contribution of such additional resonance intermolecular interactions to one exciton energy is relatively small (36) even if a transition from the ground to an excited state is dipole allowed. However, its influence on the statistics of elementary excitations in these molecular structures has never... 

The RR spectral motif is altered once again when the cubanelike [Fe4S4 (Cys)4] chromophores are considered, as illustrated in Fig. 22. The dominant band is the breathing mode of the cube at around 336 cm", and other modes of the cube range up to 400 cm" and down to 240 cm". The terminal modes are found at approximately 360 (72 ) and 390 (Aj ) cm". It is interesting that the terminal mode symmetry order is inverted from that found in [Fe(Cys)4]" complexes (Fig. 19), reflecting the kinematic interactions with the cube modes. 

EFFECT OF THE KINEMATIC INTERACTION OF SPIN-PHONON EXCITATIONS IN A PARAMAGENT. 

EFFECT OF THE KINEMATIC INTERACTION OF SPIN-PHONON EXCITATIONS IN A PARAMAGNET. //ENGLISH TRANSLATION OF FIZ. TVERDOGO TELA 10IV 359-66,1968.//... 

Under what conditions (i.e. soil stiffness and geometry, intensity and frequency of shaking) kinematic interactions may govern the pile design. Conversely, under which conditions could these effects be neglected... 

Importance of kinematic interaction in design and construction cost. 

Computed bending moments for the two input motion (PGA = 0.027g and PGA = 0.069g) are presented in Figs. 26.9b and 26.10b respectively. A significant amount of kinematic interaction is observed close to the layer interface (z = 440 mm), where high values of strain amplitude are detected. 

Significant kinematic interactions were observed in the tests... 

Cairo R, Dente G (2007) Kinematic interaction analysis of piles in layered soils. In 14th European conference on soil mechanics and geotechnical engineering, ISSMGE-ERTC 12 Workshop Geotechnical Aspects of EC8, Madrid (Spain), Patron Editore, Bologna, cd-rom, paper n. 13... 

Saitoh M (2005) Fixed-head pile bending by kinematic interaction and criteria for its minimization at optimal pile radius. J Geotech Geoenviron Eng 131(10) 1243-1251 Sica S, Mylonakis G, Simonelli AL (2007) Kinematic bending of piles analysis vs code provisions. In Proceedings of the 4th international conference on earthquake geotechnical engineering, Thessaloniki... 

Kinematic interaction - the stiffening effect of the building s foundation on the soil around it and its effect on the soil vibrations. 

Pseudo-static soil-structure interaction models account for the kinematic interaction between the soil and the underground structure neglecting inertial interaction. They are often used for practical design purposes when the structure is not too complex (NCHRP 611, Anderson et al. (2008)). 

The mechanisms governing soil-structure interaction can be divided into two distinct interactions inertial and kinematic interaction. 

---