S. L. Sobolev's Applications of Functional Analysis in Mathematical Physics PDF

By S. L. Sobolev

ISBN-10: 0821815571

ISBN-13: 9780821815571

Ebook by way of Sobolev, S. L.

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Extra resources for Applications of Functional Analysis in Mathematical Physics (Translations of Mathematical Monographs, Vol 7)

Sample text

1) one gets dx = --ax + E ( t )z + Asin (Rt) . 19) is exact for white and dichotomous noises, and it is a quite good approximation for other types of colored noise. 4). 20) reduces to A + + [ ( a - D ) 2 R2] 112 cos (Rt + 4). 21) is a monotonic function of D reaching maximum at D = a showing some SR-like behavior [66]. ( (t)Lt = J a2+ (u + R4 ~ + 2 (a2 + 2aX + 2x2 + u2) R2 + (a2 + 2aX - u2)2 x Acos (at + 4). 22) The amplitude of the stationary solution depends on the dynamic parameter a , the amplitude A and the frequency s1 of the periodic force and the strength u2 and the correlation rate X of the noise.

2 The amplitude of a stationary signal as a function of the correlation time for a = A = o2 = 1 and different frequencies of the periodic field. [Reprinted from Ref. 4 Stochastic resonance in a overdamped system with signal-modulated noise In the previous section we considered an overdamped oscillator subject to multiplicative noise and an additive periodic signal. However, one can also consider the case when the signal is multiplied by noise. Such a problem has been considered in [68] for bistable potentials in connection with the periodically modulated noise arising in some optical and astronomical devices.

4 Stochastic resonance in a overdamped system with signal-modulated noise In the previous section we considered an overdamped oscillator subject to multiplicative noise and an additive periodic signal. However, one can also consider the case when the signal is multiplied by noise. Such a problem has been considered in [68] for bistable potentials in connection with the periodically modulated noise arising in some optical and astronomical devices. Recently, a similar problem has been considered for linear systems [69].

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Applications of Functional Analysis in Mathematical Physics (Translations of Mathematical Monographs, Vol 7) by S. L. Sobolev


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