Characteristics of homogeneous charge compression ignition (HCCI) combustion and emissions of n-heptane

This paper reports the outcome from a systematic investigation carried out on HCCI (Homogeneous Charge Compression Ignition) combustion of a diesel type fuel. The n heptane was chosen in this study to study the premixed diesel HCCI combustion characteristics with port fuel injection. Measurements were carried out in a single-cylinder, 4-stroke and variable compression ratio engine. Premixed n-heptane/air/EGR mixture was introduced into the cylinder by a port fuel injector and an external EGR system. The operating regions with regard to Air/Fuel ratio and EGR rate were established for different compression ratios and intake temperatures. The effects of compression ratios, intake temperatures, Air/Fuel ratios and EGR rates on knock limit, auto-ignition timing, combustion rate, IMEP, and engine-out emissions, such as NOx, CO, and unburned HC, were analysed. The results have shown HCCI combustion of n-heptane could be implemented without intake charge heating with a typical diesel engine compression ratio. The attainable HCCI operating region was mainly limited by the knock limit, misfir, and low IMEP respectively. Higher intake temperature or compression ratio could extend the misfire limit of the HCCI operation at low load but they would reduce the maximum IMEP limit at higher load conditions. Compared with conventional diesel combustion, HCCI combustion lead to extremely low NOx emissions ( less than 5 ppm) and smoke free exhaust. But HCCI diesel combustion was found to produce higher HC and CO emissions. An increase in intake temperature or compression ratio helped to reduce HC and CO emissions.

Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]

The Relativistic Levinson Theorem in Two Dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_{j}$ of the bound states and the sum of the phase shifts $\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$: $$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$ $$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\ (n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~ j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right.$$ \noindent The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email: [email protected], [email protected]

Evolution of the proton sd states in neutron-rich Ca isotopes

We analyze the evolution with increasing isospin asymmetry of the proton single-particle states 2s1/2 and 1d3/2 in Ca isotopes, using non-relativistic and relativistic mean field approaches. Both models give similar trends and it is shown that this evolution is sensitive to the neutron shell structure, the two states becoming more or less close depending on the neutron orbitals which are filled. In the regions where the states get closer some parametrizations predict an inversion between them. This inversion occurs near $^{48}$Ca as well as very far from stability where the two states systematically cross each other if the drip line predicted in the model is located far enough. We study in detail the modification of the two single-particle energies by using the equivalent potential in the Schroedinger-like Skyrme-Hartree-Fock equations. The role played by central, kinetic and spin-orbit contributions is discussed. We finally show that the effect of a tensor component in the effective interaction considerably favors the inversion of the two proton states in $^{48}$Ca.Comment: 7 figure

Isovector Giant Dipole Resonance of Stable Nuclei in a Consistent Relativistic Random Phase Approximation

A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $\beta$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also reproduce the isovector giant dipole resonance of nuclei along the $\beta$-stability line.Comment: 4 pages, 1 Postscript figure, to be submitted to Chin.Phys.Let

The Complete KLT-Map Between Gravity and Gauge Theories

We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.Comment: 41 pages, 16 figures, published version, typos corrected, references adde

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

A systematic phenomenological study of the cos⁡2ϕ\cos 2 \phi asymmetry in unpolarized semi--inclusive DIS

We study the $\cos 2 \phi$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the non perturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from some information about the Boer--Mulders function $h_1^{\perp}$, which represents a transverse--polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where is dominated by the kinematical higher--twist contribution, and turns to be of order of few percent. We show that a larger asymmetry in $\pi^-$ production, compared to $\pi^+$ production, would represent a signature of the Boer--Mulders effect.Comment: 14 pages, 12 figure