Method Of Higher Derivatives Research Articles

Boundary Value Problem for a Heated Nanofluid Flow in the Presence of Magnetic Field

The aim of this paper is to introduce some new numerical results on the magneto-thermomechanical interaction between heated viscous incompressible magnetic nanofluid and a cold wall in the presence of a spatially varying magnetic field. The governing nonlinear boundary layer equations are converted into coupled nonlinear ordinary differential equations by similarity transformation. The ODE system is solvable numerically for example using higher derivative method. The investigation is focused on the influence of governing parameters corresponding to various physical conditions. Numerical results are exhibited for the dimensionless wall skin friction and for heat transfer coefficients at the wall, along to distributions of the velocity and the temperature.

Anomaly Problem in the N=1 Supersymmetric Electrodynamics as a Consequence of the Inconsistency of the Dimensional Reduction Method

We compare the calculation of the two-loop β-function in the N=1 supersymmetric electrodynamics regularized via higher derivatives and via dimensional reduction. We show that the renormalized effective action is the same for both regularizations. But in the method of higher derivatives, unlike in the dimensional reduction, the β-function defined as the derivative of the renormalized coupling constant with respect to log μ turns out to be purely one-loop. The anomaly problem therefore does not occur in this regularization, because in the method of higher derivatives, the diagrams with counterterm insertions make a nonzero contribution, which is evaluated exactly in all orders of the perturbation theory. When dimensional reduction is used, this contribution is zero. We argue that this result is a consequence of the mathematical inconsistency of the dimensional reduction method and that just this inconsistency leads to the anomaly problem.

One-loop counter-terms in theories regularized by higher covariant derivatives

In an arbitrary field-theory model regularized by the higher covariant derivative method, expressions for one-loop logarithmic divergences are shown to be consistent with the dimensional regularization; the precise form of the regularization terms is irrelevant. Therefore, we explicitly check the self-consistency of the higher derivatives method on the one-loop level. The calculation for the Yang-Mills theory is given.

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

The inclusion of the anharmonicity of molecular vibrations is an important aspect of the goal of making highly accurate theoreticalpredictions of the spectroscopic properties of molecules. Recently developed analytic third derivative methods for selfconsistent-field(SCF) wavefunctions have made it possible to determine the complete cubic and quartic force fields of polyatomic molecules, thus allowing the treatment of anharmonic effects. Here we continue our systematic evaluation of the performance of such theoretical methods by studying several linear molecules which are well characterized experimentally, viz., HCN, DCN, CO 2, N 2O, OCS, C 2H 2, and C 2D 2. A number of anharmonic molecular properties have been determined, including vibration-rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, rotational constants which include zero-point vibrational corrections, and vibrational and rotational l-type doubling constants. These anharmonic molecular constants are not as well converged with respect to basis set enlargement as those which were previously determined for asymmetric top molecules, apparently because all the molecules considered here contain multiple bonds. However, the reported anharmonic constants at the SCF level of theory are still in reasonably good agreement with the corresponding experimental constants. Significant improvements in accuracy are achieved by incorporating electron correlation at the configuration interaction singles and doubles (CISD) level of theory. Standard spectroscopic perturbationtheory methods are used in this study, which are directly and immediately applicable to larger molecular systems than those studied here.

A systematic study of molecular vibrational anharmonicity and vibration—rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules

Recently developed analytic third-derivative methods for self-consistent-field (SCF) wavefunctions have made it possible to theoretically determine a number of anharmonic molecular properties, including vibration—rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, and rotational constants which include zero-point vibrational and centrifugal distortion corrections. Application has been made here to a variety of asymmetric top molecules including H 2O, H 2S, H 2CO, HCO, CH 2( 3B 1), CH 2( 1A 1), CH 2( 1B 1), C 2H 4, and several isotopomers. The formulas employed for the various spectroscopic constants are those derived from standard spectroscopic perturbation theory. For most of these molecules the anharmonic molecular constants which are available from experiments are well reproduced theoretically using a double-zeta plus polarization (DZP) basis set. Particularly good agreement is found for fundamental vibrational frequencies obtained by combining configuration interaction singles and doubles (CISD) harmonic frequencies with SCF anharmonic corrections within the same basis set. This work also provides insight into the applicability of standard spectroscopic perturbation theory to such molecules. Moreover, the methods used here are immediately applicable to molecules significantly larger than those studied here.