Numerical solution of moving boundary problems in diffusion processes with attractive and repulsive interactions

Reverberi, Andrea P.; Scalas, Enrico; Vegliò, Francesco

doi:10.1088/0305-4470/35/7/307

Cited by 5 publications

(5 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to find the numerical solution of the model above, we use the finite difference explicit scheme and discretize both the dimensionless space and time variables. We use a version of the standard front‐tracking method 18…”

Section: Numerical Solutionmentioning

confidence: 99%

“…A numerical solution of a particular version of the Stefan problem is presented here, together with its practical application in the optimization of calcimine deliming. The methods used here are similar to the approach adopted in,18 however, the model presented in18 is much simpler (a semi‐infinite domain, simpler boundary conditions, no moving point source, etc.) From the theoretical point of view, the main asset of our contribution lies in the boundary conditions, while most existing models assume either constant (Dirichlet) or no‐flux (Neumann) boundary conditions, we allow the reaction‐diffusion system to exchange mass with the surrounding bath.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical simulation of calcimine deliming in the production of gelatin

2010

View full text Add to dashboard Cite

Calcimine is a valuable by-product originating during the processing of cured hide into leather. It is used as raw material in the production of gelatin and biodegradable sheets. For further usage, it is necessary to remove calcium hydroxide from calcimine by chemical deliming, which is, from the environmental protection point of view, the most important stage of the entire deliming process. In this article, a mathematical description of chemical deliming is proposed, based on the unreacted nucleus approach. Numerical solution of the model is found, concentration fields of the reacting chemicals described, and the evolution of the acido-basic boundary inside calcimine shown. The model is used to justify a simplified way to determine the effective diffusion coefficient of the deliming agent. The model can also be used as a basis for optimization of the deliming process. V

show abstract

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical simulation of calcimine deliming in the production of gelatin

2010

View full text Add to dashboard Cite

show abstract

“…In the limit δt → 0 [implying τ ρ,X → 0, on account of (7)], (10) yields the stochastic differential equation…”

Section: Langevin-itô Equationmentioning

confidence: 99%

“…In this way, it defines a canonical echoic EM environment that is the counterpart of unbounded (anechoic) free space. A characteristic feature of a MT/MSRC is the extreme sensitivity of its interior field to variations in the boundary conditions, at any location, akin to wave chaos displayed by non-integrable cavities (billiards) with or without time-varying closed or partially opened boundaries, e.g., [10][11][12][13][14][15][16][17][18][19][20]. As a result, mode stirring gives rise to a hybrid, i.e., amplitude-plus-frequency-modulated interior field [21,22].…”

Section: Introductionmentioning

confidence: 99%

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes

Arnaut¹

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the field dynamics can be characterized as a generalized diffusion process. The Langevin-Itô and Fokker-Planck equations are derived and their associated statistics and distributions for the complex analytic field, its magnitude and energy density are computed. The energy diffusion parameter is found to be proportional to the square of the ratio of the standard deviation of the source field to the characteristic time constant of the dynamic process, but is independent of the initial energy density, to first order. The energy drift vanishes in the asymptotic limit. The time-energy probability distribution is in general not separable, as a result of nonstationarity. A general solution of the Fokker-Planck equation is obtained in integral form, together with explicit closed-form solutions for several asymptotic cases. The findings extend known results on statistics and distributions of quasi-stationary ideal random fields (pure diffusions), which are retrieved as special cases.PACS numbers: 02.50.Ey, 02.60.Lj, 05.10. Gg, 05.40.Fb, 41.20.Jb, 42.50.Md, 42.65.Sf, 43.55.+p AMS classification scheme numbers: 35C99, 35D99, 37H10, 60G50, 60G60, 78A40 ‡ A summary of selected results in this paper appeared in [1].

show abstract

“…These cavities are often referred to as (mode‐stirred) reverberation chambers (RCs). Also, there is a plethora on related studies of time‐varying media [ Ishimaru , ], moving boundary problems [ Murphy , ; Reverberi et al , ], and other dynamic electromagnetic “open” configurations. However, the effect of time‐dependent perturbations in confined electromagnetic and quantum systems has attracted less attention.…”

Section: Introductionmentioning

confidence: 99%

Transient evolution of eigenmodes in dynamic cavities and time-varying media

Gradoni

Arnaut

2015

Radio Sci.

View full text Add to dashboard Cite

In this paper, we investigate the perturbation of natural eigenmodes of dynamic cavities with boundaries moving at quasi-static speeds relative to the wave velocity. For an arbitrarily shaped source-free cavity, the amplitude of the irrotational mode is modeled as a damped harmonic oscillator with time-varying eigenfrequency, i.e., a parametric oscillator. It is found that the effect of the pure Doppler shift of the resonance frequencies of the eigenmodes is small at nonrelativistic speeds. However, it is known that any spectrum of eigenenergies that is perturbed by a space-and/or time-fluctuating medium can develop frequency shifts of arbitrary magnitude. By using a linear dynamic (time-dependent) shift for the cavity broad resonances, we find that Doppler-like large shifts result in a mere frequency modulation of the total (resultant) field amplitude, while nonuniform red or blue shift can create a hybrid amplitude and frequency modulation. Interestingly, the combined action of red and blue shifts of uniform magnitude can also create a hybrid modulation. If the angle between modal wave vector and stirrer speed is accounted for in the static (time-independent) shift, the resulting red and blue shifts lead to irregular hybrid modulations. This can occur even for regular perturbations in regular cavities. In addition, owing to the stochastic nature of mode-stirred cavities, the effect of random Doppler-like shifts is also investigated, leading to a Fokker-Planck equation whose diffusion coefficient shows quadratic dependence on the mode amplitude. Thus, the analysis of random perturbations offers an effective framework for observed instantaneous Doppler effects in closed electromagnetic environments. The mathematical framework obtained in terms of stochastic differential equations is useful to predict the nonstationary response of dynamic cavities with complicated or unknown boundary geometry.

show abstract

Numerical solution of moving boundary problems in diffusion processes with attractive and repulsive interactions

Cited by 5 publications

References 32 publications

Mathematical simulation of calcimine deliming in the production of gelatin

Mathematical simulation of calcimine deliming in the production of gelatin

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes

Transient evolution of eigenmodes in dynamic cavities and time-varying media

Contact Info

Product

Resources

About