Biomedical subjects
Publications and source records attributed to M Gitterman.
The output signal of a undamped linear oscillator with a random frequency subject to a periodic force shows nonmonotonic dependence on the strength and the rate of color noise (stochastic resonance). The effect is absent for white noise.
Exact solutions are obtained for the thermal decay of a metastable state for two different forms of the potential and for uniform and localized boundary conditions by using the Laplace transform method. The exact inverse Laplace transforms are found for a symmetric case, and the results are compared with other calculations and with the Kramers rate.
An exact solution is obtained for a particle moving in a piecewise square nonsymmetric potential of fluctuating height. It turns out that the population of a metastable state increases in the presence of fluctuations similar to a previously found effect due to an external periodic field.
It is shown that for systems with a periodic potential, the flux is very sensitive to the strength of additive or/and multiplicative noise. Multiplicative noise becomes important when its strength is of the order of the barrier height, and it provides a means of additional control of the flux (voltage-current characteristics for a Josephson junction). In addition to a numerical analysis, the cases of weak and strong additive noise have also been considered analytically.
An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.
When the random force acting on a particle diffusing in an interval [0,L] and subjected to a constant external force is a Gaussian white noise, the "Brownian" mean-squared displacement is described by the seminal relation =2Dt(gamma) with gamma=1. However, for more complicated random forces the diffusion may be slower (gamma<1, "subdiffusion") or faster (gamma>1, "superdiffusion") than the "normal" diffusion. For both these cases we calculated the mean free passage time (MFPT)-the time needed to reach one of the traps at boundaries. The simple formulas for the different diffusive regimes are compared quantitatively for the simplest case of the absence of an external field and for an initial position in the middle of the interval. It turns out that the MFPT's for anomalous diffusion can be both larger or smaller than that for normal diffusion depending on the values of the length of the interval and the diffusion coefficient. Moreover, the MFPT can show nonmonotonic changes with the degree of departure from normal diffusion.
The mean free passage time for one-dimensional diffusion on a line segment under the influence of a deterministic telegraph signal proves to be a nonmonotonic function of the signal rate ("stochastic resonance") if symmetry breaking takes place. The symmetry breaking may be expressed either in nonsymmetric boundary conditions (one end absorbing and the other reflecting) or in a nonsymmetric telegraph signal. The latter case is considered in detail. It turns out that the larger the asymmetry of a telegraph signal, the wider the range of parameters for which a stochastic resonance occurs.
Exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise. Stochastic resonance is absent for Gaussian white noise. However, when the multiplicative noise has the form of an asymmetric dichotomous noise, the signal-to-noise ratio (SNR) becomes a nonmonotonic function of the correlation time and the asymmetry of noise. Moreover, the SNR turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise.
We consider the influence of small periodic oscillations of barriers on the stationary motion of a particle through a piecewise washboard potential. Up to the second order in the amplitude of oscillation the corrections to the flux can be both positive and negative and, for equal widths of the well and barrier, they do not depend on the frequency of the oscillations.
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We present a new generalized compartmental model for calcium kinetics as measured by tracer concentration in blood plasma. The parameter measuring incorporation of calcium in bone discriminates between different levels of physical development in female teenagers and between teenagers and adults.
Most theoretical analyses of tracer kinetics in capillaries contain an implicit assumption that the tissues to which they are connected have homogeneous material properties. The microscopic description of the exchange of tracer molecules and tissues is then modeled in terms of first-order kinetics. We consider a class of more general models allowing us to assess the robustness of simplifying assumptions made above. It is shown that when amorphous properties are important the kinetics of the system may differ considerably from those predicted by standard theories.