Incomplete Delta Functions

By applying projection operators to state vectors of coordinates, we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call incomplete delta functions. We show that this class of functions satisfy identities similar to those satisfied by the Dirac delta function. The incomplete delta functions may be employed advantageously in projected subspaces and in the link between functions defined on the whole space and the projected subspace. We apply a similar procedure to finite-dimensional vector spaces for which we define incomplete Kronecker deltas. Dispersion relations for the momenta are obtained and sums over poles are defined and obtained with the aid of differences of incomplete delta functions.     

Delta electroproduction in nuclei

We compute delta electroproduction in nuclei using a relativistic nuclear model. Iron is predicted to have the largest per nucleon cross section and narrowest width, but the variation in A is no larger than an 18% effect. Predictions are made for the SLAC NPAS NE5 experiment and a recently completed Bates laboratory experiment.     

Delta doping in silicon

Two-dimensional doping sheets (“δ-doping”) are integral parts of many novel semiconductor device concepts. Their practical realization in silicon (Si), however, was long delayed by the difficulty to introduce dopants into Si in a well-controlled way during epitaxial growth. Recent advances in the understanding of epitaxial growth and the incorporation of dopants in Si have overcome these difficulties and opened a new field in Si materials and device research. In this article, we review the growth, processing, and characterization of epitaxially grown 5-doped Si. Furthermore, we discuss the electronic subband states of such structures. Finally, we give an overview of device concepts that use 5-doping and analyze their properties.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Delta excitation in antiproton-deuteron annihilation

TheΔ-excitation in $\bar pd$ annihilation at rest was studied. The annihilation amplitude from the statistical model and theπN amplitude from the resonance model were adopted in our calculations. We analyze the invariant mass of theπ ⁺p andπ ^?p systems selecting the protons with momenta above 400 MeV/c and with respect to the different final reaction channels. Our model reproduces reasonably the experimental data.     

Dirac Delta Function of Matrix Argument

International Journal of Theoretical Physics - Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information...     

Neutron Star Matter Including Delta Isobars

In this paper a new phase structure of neutron star matter including nucleons and delta isobars is presented.Particle fractions populated and pion condensations in neutron star matter are investigated in this model. The existence of the pion condensations can postpone the appearance of delta isobars. We found that both the pion condensation and reduce of the ratio of delta isobar to nucleons couplings can soften the corresponding equation of state. The maximum masses and their corresponding radii of neutron stars are calculated, and the obtained values are in observational region.     

Neutron Star Matter Including Delta Isobars

In this paper a new phase structure of neutron star matter including nucleons and delta isobars is presented. Particle fractions populated and pion condensations in neutron star matter are investigated in this model. The existence of the pion condensations can postpone the appearance of delta isobars. We found that both the pion condensation and reduce of the ratio of delta isobar to nucleons couplings can soften the corresponding equation of state. The maximum masses and their corresponding radii of neutron stars are calculated, and the obtained values are in observational region.     

Fast Soliton Scattering by Delta Impurities

We study the Gross-Pitaevskii equation with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L ² norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.     

Controlled Vortex Breakdown on Modified Delta Wings

This paper studies the effect of perturbation to the breakdown of the leading-edge vortices over delta wings. The passive perturbation in the normal direction is achieved by installing the hemisphere-like bulges on the delta wing along the projection of the vortices. The key purpose of this perturbation is to delay or suppress vortex breakdown over delta wings according to the self-induction mechanism theory. The design of bulge-like surface for delta wings offers a minimization of initial vorticity gradient and an elimination of linearly mutual induction within the vortex core. Three delta wings with swept angles of 60°, 65dg and 70° have been used. Dye flow visualization and force measurement in different water tunnels are performed at the water speed of U=0.10, 0.15, 0.20 and 0.25 m/s. In flow visualization, the results show contributions of bulges as perturbation to leading-edge vortices. The best outcome of perturbing the vortex core occurs in the case of the 65° delta wing. The breakdown positions on the 65° delta wing are delayed in almost the entire range of angles of attack, and that, the results are presented here.     

一种气体低温吸附模型与计算

研究化学氧碘激光器中工作气体氧的低温吸附.考察气体流过沸石多孔床的压力与速度的关系,建立吸附剂吸收的物质量与气流中物质量关系的吸附平衡方程.由吸附物量较少的特点,得出在确定的压力梯度下速度近似为常数.吸附平衡方程与吸附速率方程,构成低温吸附模型方程,其中,亨利等温线方程作为辅助关系.对模型方程做数值求解,得到气流中单态氧浓度及吸收的单态氧浓度随时间变化的规律,及浓度分布的长时间渐近特征.     

Limiting Case of 1D Delta Anyon Model

In order to analyze a limiting case of the 1D delta anyon model, the coupling strength of the δ interaction c is modified to become a function of the anyonic parameter κ. A pedagogic derivation of the solution for this modified model using the method of anyon-boson mapping plus Bethe ansatz is presented. The limiting case as κ → π and simultaneously c → 0, which was previously neglected, is analyzed. Some unexpected properties of this limiting case are discovered. The BAEs are compared with previous results.