On the relationship between eulerian and lagrangian turbulent diffusivities

In homogeneous turbulence the eulerian and lagrangian diffusivities of a scalar field are equal. A procedure is described for relating them in inhomogeneous turbulence.     

Derivation of the probability distribution of velocities of a detector-recorded brownian particle

The probability distribution of velocities in the given space region (detector) is found for particles of a passive admixture in a stream of external gas. Since direct calculation of the above probability density involves significant difficulties, the solution is based on the classical problem of the probability distribution of coordinates and velocity of a Brownian particle at a fixed time. Analyzing dependence of the solution on the parameters of the initial problem, we obtain conditions under which the assumptions on the character of particle motion hold true. State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 10, pp. 1301–1313, October 1998.     

On the brownian motion of a frequencymodulated oscillator

The Langevin equations for a harmonically bound particle, where the force constant is a given function of time, is solved. The mean and mean-square properties of the solution are determined. The analysis is then specialized to the case of a force constant periodic in time. It is shown that the mean fluctuations remain bounded in time precisely when the mean motion is stable (remains bounded).This work was supported in part by NSF Grant CHE77-14553.     

On the theory of brownian motion. VIII. A Brownian particle in a dilute gas with inelastic collisions

The Fokker-Planck equation for a heavy particle in a dilute gas of light particles is derived from a Boltzmann equation. Inelastic collisions between the heavy and light particles are considered, and explicit quadratures for the frictional coefficients are given in terms of the scattering kernels. It is shown that the general formulation reduces properly to known results in the cases of pure elastic and pure diffuse scattering, respectively.     

Photon time-interval statistics of laser light scattered by brownian particles

Measurements are reported and some theoretical expressions are given for half-open photon time-interval statistics of laser light scattered by particles in brownian motion. Expressions in terms of cumulants are shown not to be valid in general.     

On the lagrangian turbulence in continua

Lagrangian turbulence in continua is introduced as a failure of euclidian metric of a material (frozen) system of coordinates. Criteria of such a turbulence for fluids and solids are derived.     

An effective lagrangian for multiphoton processes and a non-linear Born-Infeld lagrangian

An effective lagrangian for multiphoton processes (of Euler-Heisenberg type) is computed for an electromagnetic field interacting with massive scalar, fermion and vector particles. It is found that if the charges g_I, masses m_I and numbers N_I of massive particles satisfy the “supersymmetric” conditions, N_Sm_S⁴+3N_Vm_V⁴?2N_Fm_F⁴=0 and g_I²/m_I⁴ is I-independent, where I=S, F, V stands for scalars, fermions and vectors respectively, then not only quartic divergences (poles at n=0 in dimensional regularization) proportional to constant terms cancel out but also maximally helicity changing interaction terms vanish in the effective lagrangian. A possibility to relate a non-linear Born-Infeld lagrangian to the effective lagrangian is examined.     

Local observables and particle statistics I

We consider the family of those states which become asymptotically indistinguishable from the vacuum for observations in far away regions of space. The pure states of this family may be subdivided into superselection sectors labelled by generalized charge quantum numbers. The principle of locality implies that within this family one may define a natural product composition (leading for instance from single particle states ton-particle states). Intrinsically associated with then-fold product of states of one sector there is a unitary representation ofP ⁽ⁿ⁾, the permutation group ofn elements, analogous in its role to that arising in wave mechanics from the permutations of the arguments of ann-particle wave function. We show that each sector possesses a statistics parameter which determines the nature of the representation ofP ⁽ⁿ⁾ for alln and whose possible values are 0, ±d ^–1 (d a positive integer). A sector with 0 has a unique charge conjugate (antiparticle states); if =d ^–1 the states of the sector obey para-Bose statistics of orderd, if =–d ^–1 they obey para-Fermi statistics of orderd. Some conditions which restrict to ± 1 (ordinary Bose or Fermi statistics) are given.     

Local observables and particle statistics II

Starting from the principles of local relativistic Quantum Theory without long range forces, we study the structure of the set of superselection sectors (charge quantum numbers) and its implications for the particle aspects of the theory. Without assuming the commutation properties (or even the existence) of unobservable fields connecting different sectors (charge-carrying fields), one has a particle-antiparticle symmetry, an intrinsic notion of statistics for identical particles, and a spin-statistics theorem. Particles in pseudoreal sectors cannot be their own antiparticles (a variant of Carruthers' theorem). We also show how scattering states and transition probabilities are obtained in this frame.Partly supported by CNR.     

On the theory of turbulence: A non eulerian renormalized expansion

A non Eulerian framework for a renormalized theory of isotropic homogeneous steady state turbulence at high Reynold's numbers is developed. By construction it is invariant under random Galilei transformations. A direct interaction factorization is free of infrared singularities and yields Kolmogorov scaling for the static as well as for the dynamic correlation and response functions.     

Lifetime statistics for a Bloch particle in ac and dc fields

We study the statistics of the Wigner delay time and resonance width for a Bloch particle in ac and dc fields in the regime of quantum chaos. It is shown that after appropriate rescaling the distributions of these quantities have a universal character predicted by the random matrix theory of chaotic scattering.     

Spontaneous radiation of a brownian nanoparticle

It is shown that a charged Brownian nanoparticle (or an electron) similar to a two-level atom can generate spontaneous and induced radiation upon switching on an external field. The diffusion mechanism of charging nanoparticles is examined. The radiation process is a macroscopic quantum phenomenon, which can be used in synthetic biology, medicine, and other fields of science and engineering.     

On the relationship between Twistors and Clifford algebras

Basis p-forms of a complexified Minkowski spacetime can be used to realize a Clifford algebra isomorphic to the Dirac algebra of matrices. Twistor space is then constructed as a spin space of this abstract algebra through a Witt decomposition of the Minkowski space. We derive explicit formulas relating the basis p-forms to index one twistors. Using an isomorphism between the Clifford algebra and a space of index two twistors, we expand a suitably defined antisymmetric index two twistor basis on p-forms of ranks zero, one, and four. Together with the inverse formulas they provide a complete passage between twistors and p-forms.     

On a quantum statistics of quasiparticles

An example of quasiparticles whose statistics is neither Bose nor Fermi is presented. Experiments which permit the determination of the statistics are proposed. The collision integral for quasiparticles of arbitrary statistics is presented.     

Study of the relationship between particle sizes of polymer powders and their radiative properties

The reflectance of a surface considered as smooth relative to the wavelength mainly consists of a specular component while for a rough surface, the reflectance is composed of both specular and diffuse (or volume) components, their relative importance depending on the nature of the reflecting material. The present samples consist of polypropylene powders and the influence of particle size on total and diffuse reflectance is discussed over two wavelength ranges: 0.25–2.5 and 2.5–15.5 μm. The results of this study indicate firstly, that in the first wavelength range, the areas of the absorbance peaks increase while they decrease for the other wavelength range with particle size and secondly, that the reflectance values calculated for the wavelength range 0.25–2.5 μm, with respect to a blackbody at 5800 K, vary with particle size.     

Spatial structure of a particle collision region and its relationship with the angular distribution of a detectable particle

Within the framework of the SO(2.1) algebra formalism, a relationship is obtained between the differential cross section over the transverse particle momentum and the differential distribution over the spatial parameter b describing coordinates of the production region of this particle. The relationship obtained between the cross sections over q _⊥ and b is exact and is not related with a definite model; therefore, the spatial target structure can be analyzed on the basis of experimental data on the angular distributions of the detectable particle. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 33–37, June, 2008.