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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]

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]

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]

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]

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]

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]

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]

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]

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]