17 results
Search Results
2. Conserved Vectors for a Double Dispersion Equation.
- Author
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Luz Gandarias, Maria and Khalique, Chaudry Masood
- Subjects
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CONSERVATION laws (Physics) , *EQUATIONS , *THEORY of wave motion , *MATHEMATICAL models , *CONSERVATION laws (Mathematics) , *DISPERSION (Chemistry) - Abstract
In this paper we present conservation laws for a (1+1)-dimensional double dispersion equation which was formulated as a mathematical model of the propagation of dispersive waves in a wide variety of circumstances. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
3. A practical treatment for the three-body interactions in the transcorrelated variational Monte Carlo method: Application to atoms from lithium to neon.
- Author
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Umezawa, Naoto, Tsuneyuki, Shinji, Ohno, Takahisa, Shiraishi, Kenji, and Chikyow, Toyohiro
- Subjects
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MONTE Carlo method , *MATHEMATICAL models , *NUMERICAL analysis , *EQUATIONS , *LITHIUM , *NEON - Abstract
We suggest a practical solution to dealing with the three-body interactions in the transcorrelated variational Monte Carlo method (TC-VMC). In the TC-VMC method, which was suggested in our previous paper [N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003)], the Jastrow–Slater-type wave function is efficiently optimized through a self-consistent procedure by minimizing the variance of the local energy. The three-body terms in the transcorrelated self-consistent-field equation, which have been simply ignored in our previous works, are efficiently calculated by the Monte Carlo numerical integration. We found that our treatment for the three-body interactions is successful for atoms from Li to Ne. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
4. Assigning signs to the electronic nonadiabatic coupling terms: The {H2,O} system as a case study.
- Author
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Vibók, Ágnes, Halász, Gábor J., Suhai, Sándor, and Baer, Michael
- Subjects
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ELECTRONICS , *CASE studies , *COUPLING constants , *EQUATIONS , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
This paper is devoted to a specific difficulty related to the electronic nonadiabatic coupling terms (NACT), namely, how to determine correctly their signs. It is well known that correct NACTs, including their signs, are crucial for any numerical treatment of the nuclear Schrödinger equation [see, i.e., A. Kuppermaan and R. Abrol, Adv. Chem. Phys. 124, 283 (2003)]. In most cases the derivation of the correct sign of the nonadiabatic coupling matrix (NACM) is done employing various continuity procedures. However, there are cases where these procedures do not suffice and for these cases we suggest to apply an additional procedure based on a mathematical lemma which asserts that the exponentiated line integral which yields the D matrix is invariant with respect to the initial point of the integration [M. Baer, J. Phys. Chem. A 104, 3181 (2000)]. In the numerical study we apply this lemma to determine the signs of the 3×3 NACM elements for the three excited states of the {H2,O} system (some of these NACTs are presented here for the first time). It turns out that the ab initio treatment yields results from which one can form eight different 3×3 NACMs. However the application of this lemma (which does not require any significant additional numerical effort) reduces this number to two. The final selection is done by an enhanced numerical study which requires more accurate calculations. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
5. Anisotropic fractal media by vector calculus in non-integer dimensional space.
- Author
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Tarasov, Vasily E.
- Subjects
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VECTOR calculus , *FRACTAL dimensions , *ANISOTROPY , *MATHEMATICAL models , *EULER-Bernoulli beam theory , *TIMOSHENKO beam theory , *EQUATIONS - Abstract
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. Economic Communication Model Set.
- Author
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Zvereva, Olga M. and Berg, Dmitry B.
- Subjects
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COMMUNICATION in economics , *MULTIAGENT systems , *MATHEMATICAL models , *ALGORITHMS , *EQUATIONS - Abstract
This paper details findings from the research work targeted at economic communications investigation with agent-based models usage. The agent-based model set was engineered to simulate economic communications. Money in the form of internal and external currencies was introduced into the models to support exchanges in communications. Every model, being based on the general concept, has its own peculiarities in algorithm and input data set since it was engineered to solve the specific problem. Several and different origin data sets were used in experiments: theoretic sets were estimated on the basis of static Leontief's equilibrium equation and the real set was constructed on the basis of statistical data. While simulation experiments, communication process was observed in dynamics, and system macroparameters were estimated. This research approved that combination of an agent-based and mathematical model can cause a synergetic effect. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
7. Control and synchronization of hyperchaotic states in mathematical models of Bènard-Marangoni convective experiments.
- Author
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Mancini, Héctor, Becheikh, Rabei, and Vidal, Gerard
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MATHEMATICAL models , *LYAPUNOV exponents , *DIFFERENTIAL equations , *SYNCHRONIZATION , *EQUATIONS - Abstract
Mathematical models are of great interest for experimentalists since they provide a way for controlling and synchronizing different chaotic states. In previous works, we have used a Takens-Bogdanov (T-B) system under hyperchaotic dynamic conditions (two or more positive Lyapunov exponents) because they adequately reflect the dynamics of the patterns in small aspect ratio pre-turbulent Bènard-Marangoni convection near a codimension-2 point (with resonance between 2:1 modes), in square symmetry (D4). In this paper, we discuss the coupling of two different four dimensional hyperchaotic models derived from the Lorenz equations by using the same method introduced in previous works. As in the former system of used equations, we found that two identical hyperchaotic systems based on either Chen or Lü equation systems evolve into different states in the pattern space, where the synchronization state or the complexity could be controlled by a small external signal, as was shown in T-B equations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
8. Comment on “Analysis of hydroxyl group controlled atomic layer deposition of hafnium oxide from hafnium tetrachloride and water” [J. Appl. Phys. 95, 4777 (2004)].
- Author
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Alam, M. A. and Green, M. L.
- Subjects
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MATHEMATICAL models , *DIFFERENTIAL equations , *NUCLEATION , *PHYSICAL & theoretical chemistry , *EQUATIONS , *HYDROXYL group - Abstract
In this comment we address issues raised by Puurunen in a paper comparing our model of atomic layer deposition (ALD) growth to Puurunen’s. The main conclusion is that our models are fundamentally different. In our model, we employ two differential equations, describing the deposition of HfO2 per cycle, and the creation rate of new OH groups per cycle. These two equations enable us to explain all observed ALD growth behaviors related to the concentration of OH nucleation sites. Puurunen’s model is essentially geometry based, and takes into account the concentration of nucleation sites, but contains no equation analogous to our second differential equation describing the evolution of OH groups from cycle to cycle. We then go on to address several specific points that Puurunen raised. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
9. A Lagrangian finite volume method for the simulation of flows with moving boundaries.
- Author
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Ata, Riadh, Soulaïmani, Azzeddine, and Chinesta, Francisco
- Subjects
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LAGRANGE equations , *FINITE volume method , *SIMULATION methods & models , *INTERPOLATION , *KINEMATICS , *MATHEMATICAL models , *EQUATIONS - Abstract
In this paper a Lagrangian formulation of the Natural Element Method (NEM) is proposed to solve shallow water inviscid flows. NEM is a particle-based method which revealed its capabilities in handling large distortion problems. Its main advantage is the interpolant character of its shape function and consequently the easiness of imposing Dirichlet boundary conditions. In this paper we use the NEM method in a collocation form and in a Lagrangian kinematic description. This formulation is found to be a finite volume methodology with flux computation on the Voronoï diagram of the standard triangular or quadrilateral meshes. The Shallow-Water equations are used as the mathematical model. Besides the Lagrangian behavior of the flow which is difficult to capture, these equations have discontinuous solutions. Thus, stabilization issues have been considered. Some inviscid bidimensional flows are used as preliminary benchmark tests. This kind of flows is similar to that of metal casting. Good results were found which promise an interesting future for this method in more complicated applications. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
10. Numerical study of the formation process of ferrofluid droplets.
- Author
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Liu, Jing, Yap, Yit Fatt, and Nguyen, Nam-Trung
- Subjects
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NUMERICAL analysis , *MAGNETIC fluids , *DROPLETS , *MAGNETIC fields , *MATHEMATICAL models , *STRAINS & stresses (Mechanics) , *LIQUID-liquid interfaces , *EQUATIONS - Abstract
This paper numerically investigates the influence of a uniform magnetic field on the droplet formation process at a microfluidic flow focusing configuration. The mathematical model was formulated by considering the balance of forces such as interfacial tension, magnetic force, and viscous stress across the liquid/liquid interface. A linearly magnetizable fluid was assumed. The magnetic force acts as a body force where the magnetic permeability jumps across the interface. The governing equations were solved with finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the particle level set method. The code was validated with the equilibrium steady state of a ferrofluid droplet exposed to a uniform magnetic field. The evolution of the droplet formation in a flow focusing configuration was discussed. The paper mainly analyzes the effects of magnetic Bond number and the susceptibility on the velocity field and the droplet size. The droplet size increased with increasing magnetic strength and susceptibility. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
11. Influence of different boundary conditions on modulating inlet pressure and velocity of regenerator.
- Author
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Zhou, Lihua, Xie, Xiujuan, and Li, Qing
- Subjects
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BOUNDARY value problems , *LOUDSPEAKERS , *SOUND pressure , *THERMOACOUSTICS , *MATHEMATICAL models , *EQUATIONS - Abstract
In present paper, a model driven by double loudspeakers is proposed, which can widely modulate acoustic pressure and oscillating velocity at the inlet boundary of regenerator. For the sake of contrastive analysis, other two models driven by single loudspeaker are built up. Based on linear thermoacoustic theory, the governing equations concerning different boundary conditions in three models are setup and discussed. The modulating ranges of inlet pressure and velocity in three models are compared. It verifies that the model driven by double loudspeakers is preferable than other two models for modulating acoustic pressure and oscillating velocity. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
12. The Analysis of a Mathematical Model Associated to an Economic Growth Process.
- Author
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Bundău, O., Pater, F., and Juratoni, A.
- Subjects
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MATHEMATICAL models , *POPULATION , *EQUATIONS , *MANIFOLDS (Mathematics) , *ECONOMIC development - Abstract
In this paper we consider a version of the Ramsey growth model in infinite and continuous time with logistic population growth, introduced by [2]. In this model, the consumer chooses at any moment in time the level of consumption so as to maximize the global utility given by exponential function. This economical growth model of Ramsey leads to an optimal control problem. We show that the optimal solution of our control problem is the solution of a four differential equation system. We prove that this system has a unique nontrivial steady state equilibrium which is a saddle point with a two dimensional stable manifold. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
13. A New Solution of the Rendering Equation with Stratified Monte Carlo Approach.
- Author
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Penzov, Anton A., Dimov, Ivan T., and Koylazov, Vladimir N.
- Subjects
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MONTE Carlo method , *EQUATIONS , *MATHEMATICS , *ALGEBRA , *MATHEMATICAL models - Abstract
This paper is turned to the advanced Monte Carlo methods for realistic image creation. It offers a new stratified approach for solving the rendering equation. We consider the numerical solution of the rendering equation by separation of integration domain. The hemispherical integration domain is symmetrically separated into 16 parts. First 8 sub-domains are equal size of orthogonal spherical triangles. They are symmetric each to other and grouped with a common vertex around the normal vector to the surface. The hemispherical integration domain is completed with more 8 sub-domains of equal size spherical quadrangles, also symmetric each to other. All sub-domains have fixed vertices and computable parameters. The bijections of unit square into an orthogonal spherical triangle and into a spherical quadrangle are derived and used to generate sampling points. Then, the symmetric sampling scheme is applied to generate the sampling points distributed over the hemispherical integration domain. The necessary transformations are made and the stratified Monte Carlo estimator is presented. The rate of convergence is obtained and one can see that the algorithm is of super-convergent type. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
14. Unsteady LES of a Backward Facing Step Flow.
- Author
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Lungu, Adrian
- Subjects
- *
MATHEMATICAL models , *TURBULENCE , *VISCOUS flow , *EQUATIONS , *FINITE volume method - Abstract
The paper proposes a numerical technique based on the finite volume method for solving the three-dimensional unsteady viscous over a backward facing step. The mathematical model is based on the momentum and continuity equations written for the uncompressible viscous flow. Closure to the turbulence is considered by employing the LES model. The convergence of the unsteady solution is realized through an iterative process within the limits of an error imposed apriori. The engineering application spectrum is represented by the several practical flow cases over sudden expanded domains. The study emphasizes the 3D vortical character of the flow that was observed during the experiments. The theoretical relevance of the work consists in the originality of the numerical method employed to solve the aforementioned equations. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
15. Thermodynamic and transport properties of two-temperature SF6 plasmas.
- Author
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Wang, WeiZong, Rong, MingZhe, Wu, Yi, Spencer, Joseph W., Yan, Joseph D., and Mei, DanHua
- Subjects
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THERMODYNAMIC equilibrium , *TEMPERATURE , *PLASMA gases , *MATHEMATICAL models , *EQUATIONS , *THERMAL conductivity , *VISCOSITY - Abstract
This paper deals with thermodynamic and transport properties of SF6 plasmas in a two-temperature model for both thermal equilibrium and non-equilibrium conditions. The species composition and thermodynamic properties are numerically determined using the two-temperature Saha equation and Guldberg-Waage equation according to deviation of van de Sanden et al. Transport properties including diffusion coefficient, viscosity, thermal conductivity, and electrical conductivity are calculated with most recent collision interaction potentials by adopting Devoto's electron and heavy particle decoupling approach but expanded to the third-order approximation (second-order for viscosity) in the frame of Chapman-Enskog method. The results are computed for various values of pressures from 0.1 atm to 10 atm and ratios of the electron temperature to the heavy particle temperature from 1 to 20 with electron temperature range from 300 to 40 000 K. In the local thermodynamic equilibrium regime, results are compared with available results of previously published studies. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
16. Higher-order continuum approximation for rarefied gases.
- Author
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Spiegel, Edward A. and Jean-Luc Thiffeault, Edward A.
- Subjects
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KINETIC theory of gases , *EQUATIONS , *FLUID dynamics , *STATISTICAL mechanics , *MATHEMATICS , *MATHEMATICAL models - Abstract
The Hilbert–Chapman–Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman–Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman–Enskog approach. The new equations contain higher order terms that are discarded in the Chapman–Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or Bhatnagar–Gross–Krook model of kinetic theory. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2003
- Full Text
- View/download PDF
17. Reduction of lattice equations to the Painlevé equations: PIV and PV.
- Author
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Nakazono, Nobutaka
- Subjects
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EQUATIONS , *PAINLEVE equations , *DIFFERENTIAL equations , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
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