Mathematical and Numerical Modeling

(in Romanian )

Time series theory and quantitative finance

An automatic algorithm for monotone trend estimation from a noisy time series was designed and a Monte Carlo method to estimate the errors associated with detrending has been obtained. A new numerical method to estimate the financial volatility from the returns time series was obtained.

• C. Vamos, M. Craciun, Separation of components from a scale mixture of Gaussian white noises, Physical Review E 81 (2010) no. 5, article no. 051125 (impact factor: 2.400).
• C. Vamos, M. Craciun, Serial correlation of detrended time series, Physical Review E 78 (2008) no. 3, article no. 036707 (impact factor: 2.483).
• C. Vamos, Automatic algorithm for monotone trend removal, Physical Review E 75 (2007) no. 3, article no. 036705 (Impact factor: 2.438) (citations in ISI journals).

Mathematical modeling in hydrology

Transport processes in groundwater were modeled as diffusion in random velocity fields in terms of trajectories (Ito equations) and probability distributions (Fokker-Planck equations). The focus was mainly on ergodicity issue and memory effects. The theoretical results were supported by accurate numerical simulations.

• Suciu N., C. Vamos, J. Vanderborght, H. Hardelauf, and H. Vereecken, Numerical investigations on ergodicity of solute transport in heterogeneous aquifers, Water Resources Research 42 (2006) W04409 (impact factor: 2.447) (citations in ISI journals).
• Suciu, N., C. Vamos, H. Vereecken, K. Sabelfeld, and P. Knabner, Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media, Water Resources Research 44 (2008) W08501 (impact factor: 2.447) (citations in ISI journals).
• Suciu, N., C. Vamos, F. A. Radu, H. Vereecken, and P. Knabner, Persistent memory of diffusing particles, Physical Review E 80 (2009) 061134 (Impact Factor: 2.400) (citations in ISI journals).
• Suciu, N., Spatially inhomogeneous transition probabilities as memory effects for diffusion in statistically homogeneous random velocity fields, Physical Review E 81 (2010) 056301 (impact factor: 2.400).

Continuous models of corpuscular systems

The balance equations of continuum fields expressed as space-time coarse-grained averages was derived using the condition that the microscopic particles preserve their identity over a finite time interval within which their motion can be described by piecewise analytical time functions. Applications of this approach were obtained for financial markets, granular flows, natural porous media, lipid bilayers, etc.

• Vamos, C., A. Georgescu, N. Suciu, and I. Turcu, Balance equations for physical systems with corpuscular structure, Physica A 227 (1996) 81-92 (impact factor 1.430) (citations in ISI journals, citations in other journals).
• Vamos, C., N. Suciu, and A. Georgescu, Hydrodynamic equations for one-dimensional systems of inelastic particles, Physical Review E 55 (1997) 6277-6280 (impact factor 2.483) (citations in ISI journals, citations in other journals).
• Vamos, C., N. Suciu and W. Blaj, Derivation of one-dimensional hydrodynamic model for stock price evolution, Physica A 287 (2000) 461-467 (Impact Factor 1.430). (citations in ISI journals)

Numerical modeling of the diffusion with application in technological processes and transport in porous materials

A new algorithm for complex diffusion processes was designed and successfully applied to large scale simulations of transport in groundwater as well as to diffusion in an epidermic structure.

• Vamos, C., N. Suciu, and H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processes, Journal of Computational Physics 186(2) (2003) 527-544 (impact factor 2.372) (citations in ISI journals).
• Suciu N., and C. Vamos, Evaluation of overshooting errors in particle methods for diffusion by biased global random walk, Rev. Anal. Num. Th. Approx. (Rom. Acad.), 35, 119-126, 2006 .
• Suciu, N., C. Vamos, I. Turcu, C.V.L. Pop, and L. I. Ciortea, Global random walk modeling of transport in complex systems, Computing and Visualization in Science 12 (2007) 77-85.

Mathematical modeling of some physico-chemical hydrodynamical phenomena

The viscous flow due to gravitation and gradients of the superficial tension (Marangoni effect) was mathematically modeled. We also introduced a pseudospectral method (collocation type) to solve high order eigenvalue problems in electrohydrodynamics.

• Gheorghiu, C.I., Dragomirescu, I.F., Spectral methods in linear stability. Applications to thermal convection with variable gravity field, Applied Numerical Mathematics 59 (2009) 1290-1302 (impact factor 1.279).
• Gheorghiu C.I., Dragomirescu, I.F., Analytical and numerical solutions to an electrohydrodynamic stability problem, Applied Mathematics and Computation 216 (2010) 3718-3727 (impact factor 1.124).

Numerical modeling of metals and alloys casting

A numerical model for the flow and solidification of the metals and alloys during casting was designed and it was applied to real industrial casting processes.

• V. Soporan, C. Vamos, and C. Pavai, Numerical modeling of the cavities during the alloys solidification, Metalurgia, Vol. III, No. 4, 53-55 (1998).
• V. Soporan, C. Vamos, and C. Pavai, Numerical simulation for technological interpretation of solidification process castings, Metalurgia, Vol. III, No. 4, 56-60 (1998).
• Vasile Soporan, Calin Vamos, Carol Pavai, Numerical Modeling of Solidification (in Romanian), Ed. Dacia, Cluj-Napoca, 2003.

Mathematical modeling in speology

A mathematical model for the propagation of temperature waves, equivalent with an inductive-capacitive electrical circuit, was used to estimate bulk thermal properties of a natural limestone formation from temperature measurements. The results were found to be consistent with cave-microclimate measurements.

• Suciu, N., La determination "in situ" de quelques grandeurs thermiques des calcaires, Trav. Inst Speol. "Emile Racovitza", vol. XX, 179-185, 1981.
• Decu, V., W. Herdlicka, and N. Suciu, Mensuration indirecte de l'eau de condensation de deux grottes des monts de Mehedinti (Carpates Meridionales). Implications ecologiques de la condensation endokarstique, Trav. Inst Speol. "Emile Racovitza", vol. XXI, 43-52, 1982.

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