Effect of rf field on spin diffusion

A study was made of the effect of an rf field on spin diffusion. The interaction of spins with the rf field is described quantum mechanically. It is shown that the effect of the rf field on the system of spins can, in some approximation, be interpreted as the effect of a change in the Larmor frequency of the spin and a decrease in the magnitude of the dipole-dipole interaction between spins. These conclusions were obtained on the basis of a unitary transformation which eliminates the explicit form of the spin-photon interaction operator in the Hamiltonian of the system considered. An expression is derived for the spin-diffusion coefficient under saturation. The presence of the rf field results in a decrease in the diffusion coefficient.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–11, September, 1979.     

Self-consistent suppression of plasma diffusion

We consider the self-consistent problem of plasma diffusion in a magnetic field, taking account of a change in the magnetic field. It is shown that an effect arises which leads to a weakening of the diffusion in both cylindrical and toroidal field geometries. Both classical and anomalous fluxes are suppressed. However, the corrections for real plasma parameters in present-day devices are insignificant, and so the fixed magnetic field approximation is justified. M. V. Lomonsov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 70–75, July, 1996.     

Stability of nonlinear diffusion

The nonlinear diffusion equation in bounded geometry with time-independent boundary conditions has a uniquely determined stationary solution. We show that this solution is dynamically stable in the sense of Liapunov. Any initial distribution tends to the stationary one as time goes on. It is shown that the application of the Glansdorff-Prigogine stability criterion requires a more elaborate analysis. We develop a variational procedure which has application in a wide range of nonlinear transport problems.     

Turing instability in reaction-diffusion systems with nonlinear diffusion

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.     

Observation of rf SQUID characteristics in YBCO bulk at 77 K

The online version of the original article can be found at     

Observation of rf SQUID characteristics in YBCO bulk at 77 K

RF SQUID behaviour due to grain boundary weak links in a bulk YBCO is observed at 77 K using modified commercial rf electronics. Porous samples with lowI _c are found to show this characteristic whereas dense samples with higherI _c do not show SQUID behaviour.V-B modulation characteristic is found to be better when the rf pumping frequency is kept slightly higher than the resonance frequency of the tank circuit. Designing of coil for tank circuit with appropriateQ has been found to be very crucial for seeing the SQUID behaviour. Estimation of parameters such as coupling constant, mutual inductance, inductance and radius of the SQUID loop, have been made and their significance is discussed. Flux noise spectrum of the bulk rf SQUID in flux locked mode is also reported.     

双参数奇摄动非线性反应扩散问题

讨论了一类具有双参数的非线性反应扩散方程奇摄动初始边值问题.在适当的假设下,构造了解的渐近展开式并讨论了它的渐近性态.     

Solution spectrum of nonlinear diffusion equations

The stationary version of the nonlinear diffusion equation–c/t +D c = ₁c – ₂c² can be solved with the ansatz c = _p ^{= 1/} A_p(coshkx) ^–p , inducing a band structure with regard to the ratio ₁/₂. The resulting solution manifold can be related to an equilibrium of fluxes of nonequilibrium thermodynamics. The modification of this ansatz yielding the expansion c = skp = 1/ A _pq (coshkx)^–p [(cosht) ^–q–1 sinht + b(cosht)^–q] represents a solution spectrum of the time-dependent nonlinear equation, and the stationary version can be found from the asymptotic behavior of the expansion. The solutions can be associated with reactive processes propagating along molecular chains, and their applicability to biophysical processes such as active transport phenomena and control circuit problems is discussed. There are also applications to cellular kinetics of clonogenic cell assays and spheroids.     

A nonlinear theory of turbulent diffusion

It is shown that the well-known conservation laws for magnetic helicity and passive-scalar fluctuation intensity in the case of negligible molecular diffusion require that the hierarchy of nonlinear equations for the averaged Green function and the hierarchy of Bethe-Salpeter-type equations for fluctuation intensity be treated in a mutually consistent manner. These hierarchies are obtained to the sixth order in turbulent velocity correlators. Asymptotic formulas describing the evolution of scalar fluctuations and magnetic field are presented. A number of new effects are revealed that strongly affect diffusion, but are beyond the scope of the frequently used model of a delta-correlated turbulent field.     

Fractional nonlinear diffusion equation,solutions and anomalous diffusion

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.     

CARS-Background suppression by phase-controlled nonlinear interferometry

We have developed a new technique for efficient suppression of the nonresonant background in coherent anti-Stokes Raman scattering (CARS). The advantage of this technique, which is based upon phase-controlled superposition of an appropriately selected reference signal, is presented in theory and demonstrated experimentally by the example of the S(3) (pure rotational) transition of molecular hydrogen.     

Bosonic amplification of noise-induced suppression of phase diffusion

We study the effect of noise-induced dephasing on collisional phase diffusion in the two-site Bose-Hubbard model. Dephasing of the quasimomentum modes may slow down phase diffusion in the quantum Zeno limit. Remarkably, the degree of suppression is enhanced by a bosonic factor of order N/logN as the particle number N increases.     

Chaos-induced diffusion in nonlinear discrete dynamics

The large-scale motion of one-dimensional discrete systemX _t+1=X _t+f _a(X _t), (t=0, 1,2,...;f _a(X+1)=f _a(X)) is studied. This motion can be asymptotically decoposed into a drift and a diffusion (chaos-induced diffustion). We derive the formulae for the drift velocityv as the average jump number per step and for the diffusion coefficientD in terms of the jump number's time correlation function. It is shown that the coarsegrained probability distribution is asymptotically gaussian. Considering piecewise linear models and the sinusoidal one, we study the onset behavior of diffusion and its gross behavior. It is found thatD is proportional to the length of the region with a non-zero jump number, if the critical dynamics is well-defined. Otherwise we have logarithmic or inverse power corrections to the simple law originating from an intermittency type behavior or from band splitting phenomena. Maps with a smooth maximum (as e.g. the sinusoidal) exhibit several additional types of trajectories: running modes with broken symmetry, localized trajectories, regular periodic or chaotic, non-diffusive or diffusive ones. These dynamical states appear in a nested window structure, which is described.     

Laser-induced generation of surface periodic structures in media with nonlinear diffusion

A model of fast formation of high-contrast periodic structure appearing on a semiconductor surface under action of laser radiation is proposed. The process of growing a surface structure due to the interaction surface plasmon- polaritons excited on nonequilibrium electrons with incident laser radiation are considered in the framework of a medium with nonlinear diffusion of nonequilibrium carriers (defects). A resonance effect of superfast pico- and subpicosecond amplification of the plasmon-polariton structure generated on the surface, the realization of which can result in a high-contrast defect lattice.