Mathematical Analysis of Physical Problems

Wallace, Philip R.; Davidon, William C.

doi:10.1119/1.1987154

Cited by 43 publications

(39 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It should not be surprising that expression (44) differs from the mean-square displacement (25) derived from the TPF, because Equation (18) provides different information than the stochastic differential Equation (40). As shown in Section 2.2, the expectation value (25) is equivalent to the mean-square displacement of a particle prior to decay multiplied by the survival probability to time t.…”

Section: Langevin Equation: Update Algorithm and Computer Simulationmentioning

confidence: 99%

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Silverman¹

2017

JMP

View full text Add to dashboard Cite

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

show abstract

Section: Langevin Equation: Update Algorithm and Computer Simulationmentioning

confidence: 99%

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Silverman¹

2017

JMP

View full text Add to dashboard Cite

show abstract

“…It is used also in describing the process of epidermal wound healing [17]. Other applications appear in the theory of superconducting electrodynamics [18] and in the study of excitons [19]. Fisher's equation is a nonlinear equation that obviously generalizes the three-dimensional diffusion model if we rewrite Fisher's equation as…”

Section: Important Partial Differential Equationsmentioning

confidence: 99%

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein‐Gordon equation

Macías‐Díaz

Puri

2005

Numerical Methods Partial

View full text Add to dashboard Cite

In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of the initial-value problem with smooth initial conditions (1)in an open sphere D around the origin, where the internal and external damping coefficients-β and γ, respectively-are constant, and the nonlinear term has the form G ′ (w) = w p , with p > 1 an odd number. The functions φ and ψ are radially symmetric in D, and φ, ψ, rφ and rψ are assumed to be small at infinity. We prove that our scheme is consistent order O(∆t 2 ) + O(∆r 2 ) for G ′ identically equal to zero, and provide a necessary condition for it to be stable order n. Part of our study will be devoted to compare the physical effects of β and γ.

show abstract

“…semiconductors [Wallace 1984], in the investigation of excitons [Rashba and Sturge 1982], and as a model for neutron flux in nuclear reactor kinetics [Kastenberg and Chambré 1968].…”

Section: Total Positivity Conjecturementioning

confidence: 99%

Untitled

2012

Involve

View full text Add to dashboard Cite

Mathematical Analysis of Physical Problems

Cited by 43 publications

References 0 publications

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein‐Gordon equation

Untitled

Contact Info

Product

Resources

About