Non-Abelian isometries of multidimensional universes

A field theory on a(d + n)-dimensional manifold in the presence of ann-dimensional isometry group spanningn-dimensional orbit spaces may be reduced to a field theory on ad-dimensional manifold. The field content of such reduced theories is completely worked out when the isometries may be non-Abelian and the resultant space may have torsion. The equations of motion of the dimensionally reduced theory are obtained directly from the higher-dimensional theory. The reduced theory is given in terms of the metric tensor, a set of scalar fields, and a set of antisymmetric tensor fields.Supported in part by the Department of Energy under Contract DE-AS-2-76ER02978 and in part by the National Science Foundation under Grant NSF Phy 83 134 10.     

Unit radius and the resolution of inverse square law forces

An equation for the solution of inverse square law forces that arise in rectilinear systems from gravitational, electrical, and magnetic fields, produced by complex multibody or multielement sources, is derived from a concept known asunit radius, which is associated with orbital systems, and the use of this equation in computer evaluation of simple models such as disks and spheres shows results that are in good agreement with those predicted by classical methods using a somewhat indirect approach. Additionally, these results show that, within the profile of the model so analyzed, the effective distance between the reference point and the resultant source is equal in all cases to the radius of the model, and that—again within the profile of the model—the magnitude of the resultant source varies directly with the distance of the reference point from the center of the model. Theproximity effect of sources of appreciable dimensions is examined in some detail and there is good evidence to show that as a result of this effect the resultant force when measured at the perimeter of a two-dimensional disk-shaped source is some 23% lower than the value anticipated by classical theory.     

The non-isotropic two-dimensional random walk

Abstract

A formula is obtained for the joint probability density function of the angle and length of the resultant of an N-step non-isotropic random walk in two dimensions for arbitrary step angle and radius probability density and for any fixed number of steps. The problem is attacked by applying the theory of generalized functions concentrated on smooth manifolds. The analysis is presented initially for the case where only the angles are random. The characteristic function is defined for the walk in terms of angular and radial frequencies and the inversion is obtained in terms of a sum of Hankel transforms. The Hankel transform sum is transformed by showing that it can be interpreted in terms of the motions of the two-dimensional Euclidean plane corresponding to the rotations and translations resulting from a sequence of fixed steps. This transformation results in an expression involving integrations over two manifolds defined by delta functions. The properties of the manifolds defined by the delta functions are then considered and this results in some simplification of the formulae. The analysis is then generalized to the case where both the phase and length of each step in the walk are random. Finally, seven examples are presented including the general two-step walk and three walks which lead to generalized K density functions for the resultant.     

Ue(1)-covariant Rξ gauge for the two-Higgs doublet model

A U _e (1)-covariant R _ξ gauge for the two-Higgs doublet model based on BRST (Becchi-Rouet-Stora-Tyutin) symmetry is introduced. This gauge allows one to remove a significant number of nonphysical vertices appearing in conventional linear gauges, which greatly simplifies the loop calculations, since the resultant theory satisfies QED-like Ward identities. The presence of four ghost interactions in these types of gauges and their connection with the BRST symmetry are stressed. The Feynman rules for those new vertices that arise in this gauge, as well as for those couplings already present in the linear R _ξ gauge but that are modified by this gauge-fixing procedure, are presented.     

Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.     

Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading

Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load, which can be expanded in terms of sinusoidal series. For plane stress problems, the stress function is assumed to consist of two parts, one being a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (y), and the other a linear polynomial of x with unknown coefficients depending on y. The governing equations satisfied by these y-dependent functions are derived. The expressions for stresses, resultant forces and displacements are then deduced, with integral constants determinable from the boundary conditions. While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness, the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102, 10432030, and 10725210)     

Overcoming Nonrenormalizability

A suitable counterterm for a Euclidean space lattice version of _n ⁴ theories, n4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support this unconventional choice are presented.     

The evaluation of some integrals that arise in the perturbation theory of liquids

ABSTRACT

The venerable, but still very useful, perturbation theory of liquids of Barker and Henderson involves some integrals that must be obtained numerically. There is no avoiding this for potentials such as the Lennard–Jones potential. However, to obtain the pressure, Barker and Henderson also obtained the necessary density derivatives numerically. This is cumbersome and care must be used to avoid excessive error. In this paper, it is noted that the earlier and less successful perturbation theory of Frisch et al. employed an alternative method, all but forgotten, for the evaluation of similar integrals. Their method still requires numerical integration. However, it allows an investigator to obtain the integrals for the pressure by analytical differentiation. The resultant integrals must still be evaluated numerically, but the extra step and annoyance of numerical differentiation is avoided. It is noted here that this method of using density derivatives can be incorporated into the Barker–Henderson theory.     

Hollow graphene oxide spheres: facile synthesis and formation mechanism

In this work, we introduced a facile approach for preparing hollow graphene oxide spheres (HGOSs). By electrostatic self-assembly polystyrene (PS)/graphene oxide (GO), core/shell microspheres were synthesized. After removal of the sacrificial PS colloidal spheres by toluene solution treatment, HGOSs were prepared successfully. Based on the DLVO theory, van der Waals force and electric double layer repulsion were proposed to quantitatively analyze the self-assembly of the composite structure. The theoretical formulation for the resultant interaction force F versus separation between the surfaces d showed a significant low energy barrier for the aggregation of the GO and PS, which predicted the favorable HGOSs formation.     

Crystallographic orientation dependence of work function: carbon adsorption on Au surfaces

We investigate the work function (WF) variation of different Au crystallographic surface orientations with carbon atom adsorption. Ab initio calculations within density-functional theory are performed on carbon deposited (100), (110), and (111) gold surfaces. The WF behaviour with carbon coverage for the different surface orientations is explained by the resultant electron charge density distributions. The dynamics of carbon adsorption at sub-to-one- monolayer (ML) coverage depends on the landscape of the potential energy surfaces. At higher ML coverage, because of adsorption saturation, the WF will have weak surface orientation dependence. This systematic study has consequential bearing on studies of electric-field noise emanating from polycrystalline gold ion-trap electrodes that have been largely employed in microfabricated electrodes.     

Electronic structure of the diamondlike systems BN1−x Mex (Me = Ti, Cr, Mn, Fe, Ni, Cu)

The local coherent potential method is used within the framework of multiple scattering theory to calculate the electron energy structure of the diamondlike systems BN_1−x Me_x (Me is a 3d transition metal) with the ZnS structure. We used the cluster version of the muffin tin approximation to calculate the crystal potential. The framework of a single approximation is used to compare the electronic energy structure of ternary and binary boron-nitride systems. The width of the hybridized band of the ternary systems BN-Me (Me = Cr, Mn, Fe, Cu) is greater than in the binary system by more than 8 eV and is due to the resultant B-Me interaction. Fiz. Tverd. Tela (St. Petersburg) 39, 1338–1341 (August 1997)     

Polarization interferometer as a proximity sensor

A simple interferometric phasemeter which can be used as a proximity sensor is described. It is based on the measurement of the phase shift between the p- and s- components of a field caused by the processes of attenuation in total internal reflection. The role of the interferometer is to restore the p- and the s- components from the resultant totally reflected field, with minimum amplitude and phase distortions and to let them interfere. The phase shift as a function of the attenuation of the total internal reflection can be determined from the interference signal. The interferometer is of a common path polarization shearing type, consisting of Rochon beamsplitter and a linear polarizer. An experiment for measuring the distance between glass plane surface and a plane attenuater made of Si mono-crystal is described. A good agreement between theory and experiment for separations less than 300 nm is observed. This device can be applied in research and metrology. After further modifications, the optical system could be used for proximity sensing, surface geometry control, variable optical retarders, contamination monitoring, etc.     

Measurements of K-shell ionization cross sections of35Br,37Rb,39Y using low energy protons

K-shell ionization cross section measurements are reported for₃₅Br,₃₇Rb and₃₉Y targets caused by protons over 300–400 keV energy range in 20 keV increment. The K-shell ionization cross sections (σ _k ^l ) at different energies were deduced from the K_α and K_β X-ray production cross sections which were obtained from X-ray yields of the K_α and K_β transitions. The experimental values are compared with the calculated values of ECPSSR theory and empirical reference cross sections. The resultant K-shell ionization cross sections are found to be in reasonable agreement with the ECPSSR theory. The K_α/K_β intensity ratios are also presented and compared with other experimental values and also with the theoretical one-hole values given by Scofield.     

Irradiance-moments characterization of off-axis Gaussian beam combinations by means of the Wigner distribution function

The irradiance-moments characterization of off-axis Gaussian beam combinations is presented in use of the Wigner distribution function (WDF). Analytical expressions for the propagation through an optical paraxial ABCD system, beam propagation factor (M² factor), beam width, far field divergence angle and kurtosis parameter of the resultant beam are derived and illustrated with specific numerical examples. It is reexamined that a flat-topped irradiance profile of the resultant beam can be achieved at a certain plane by appropriately choosing beamlet parameters. As compared with previous work, our results show the advantage of using the WDF and irradiance-moments methods.     

Antisite defects and Mg doping in LiFePO<Subscript>4</Subscript>: a first-principles investigation

Atomic and electronic structures of LiFePO₄ with the antisite defect and Mg doping at Li and Fe sites have been investigated using first-principles density-functional theory with the on-site Coulomb interaction taken into account. It is demonstrated that the most favorable antisite defect type is the exchange defect, in which Li and Fe ions exchange positions. The resultant longer Fe–O bond and narrower band gap drop a hint that the electronic and ionic transport properties may be improved. For the case of Mg doping, Mg is preferentially doped at the Fe site instead of the Li site to form a new LiFe_1−y Mg _y PO₄ solid solution, leading to a higher ionic conductivity. Moreover, the dependence of the electrochemical properties on the concentration of Mg dopant has also been discussed.     

Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.     

Experimental observations of redistributed energy in wave interference

Attempts to explain the redistribution of energy in interference has been done from time to time, under two of the most accepted theories, wave and quantum; however its mechanism still lacks clear interpretation. In this study, a new experiment has been designed and conducted to observe the redistributed energy in wave interference. Experimental observations on the redistributed energy that occurs in two interfering coherent waves are presented. Re-distributed energy at a certain region, (single bright fringe) in space due to interference of two waves was isolated at a plane and measured at a distant plane away from the isolated plane. The measured energy distribution of the isolated interference pattern was compared with the resultant calculated from the two individual interfering components based on wave theory. The calculated resultant due to the two individual components does not tally with the experimental observed pattern. Hence, the outcome of this experiment is in disagreement with the expected predictions as per the wave theory.     

Wavelet-modified fringe-adjusted joint transform correlator

In this paper, we implement a wavelet-modified fringe-adjusted joint transform correlator (JTC) for real-time target recognition applications. In real-time situation the input scene is captured using a charge-coupled device (CCD) camera. The obtained joint power spectrum is multiplied by a pre-synthesized fringe-adjusted filter and the resultant function is processed with an appropriately scaled wavelet filter. Three performance measure parameters: correlation peak intensity, peak-to-sidelobe ratio, and signal-to-clutter ratio have been calculated for fringe-adjusted joint transform correlator (FJTC) and wavelet-modified fringe-adjusted joint transform correlator (WFJTC). The WFJTC has been found to yield better results in comparison to conventional FJTC. To suppress the undesired strong dc, the resultant function is differentiated. Differential processing wavelet-modified fringe-adjusted joint power spectrum removes the zero-order spectra and hence improves the detection efficiency. To focus the correlation terms in different planes in order to capture one of the desired autocorrelation peaks and discard the strong dc and another autocorrelation peak, chirp-encoding technique has also been applied. Targets with Gaussian and speckle noise have also been used to check the correlation outputs. Computer simulation and experimental results are presented.     

Conditions for applicability of the Newtonian approximation of the theory of relativity and the correspondence principle

The assertion of correspondence between the theory of relativity and Newtonian mechanics, and the resultant condition of applicability of the latter, has only mathematical meaning. Analysis of the basic principles of both theories is used to show their physical incompatibility while the conditions for the applicability of the Newtonian approximation of the theory of relativity are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–48, July, 1991.