Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

Solar transition region in the quiet Sun and active regions

The solar transition region (TR), in which above the photosphere the tempera- ture increases rapidly and the density drops dramatically, is believed to play an important role in coronal heating and solar wind acceleration. Long-lasting up-flows are present in the upper TR and interpreted as signatures of mass supply to large coronal loops in the quiet Sun. Coronal bright points (BPs) are local heating phenomena and we found a different Doppler-shift pattern at TR and coronal temperatures in one BP, which might be related to the twisted loop system. The dominant energy loss in the lower TR is the Ly-alpha emission. It has been found that most Ly-alpha radiance profiles are stronger in the blue peak, an asymmetry opposite to higher order Lyman lines. This asymmetry is stronger when the downflow in the middle TR is stronger, indicating that the TR flows play an important role in the line formation process. The peak separation of Ly-alpha is found to be larger in coronal holes than in the quiet Sun, reflecting the different magnetic structures and radiation fields between the two regions. The Lyman line profiles are found to be not reversed in sunspot plume and umbra regions, while they are obviously reversed in the surrounding plage region. At TR temperatures, the densities of the sunspot plume and umbra are a factor of 10 lower than of the plage, indicating that the sunspot plasma emitting at TR temperatures is higher and possibly more extended above sunspots than above the plage region.Comment: This paper has been withdrawn by the author because it's not a referred pape

A covariant entropy conjecture on cosmological dynamical horizon

We here propose a covariant entropy conjecture on cosmological dynamical horizon. After the formulation of our conjecture, we test its validity in adiabatically expanding universes with open, flat and closed spatial geometry, where our conjecture can also be viewed as a cosmological version of the generalized second law of thermodynamics in some sense.Comment: JHEP style, 9 pages, 1 figure, typos corrected, accepted for publication in JHE

Monte-Carlo approach to calculate the proton stopping in warm dense matter within particle-in-cell simulations

A Monte-Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. The model is based on multiple binary-collisions among electron-electron, electron-ion and ion-ion, taking into account contributions from both free and bound electrons, and allows to calculate particle stopping in much more natural manner. At low temperature limit, when ``all'' electron are bounded at the nucleus, the stopping power converges to the predictions of Bethe-Bloch theory, which shows good consistency with data provided by the NIST. With the rising of temperatures, more and more bound electron are ionized, thus giving rise to an increased stopping power to cold matter, which is consistent with the report of a recently experimental measurement [Phys. Rev. Lett. 114, 215002 (2015)]. When temperature is further increased, with ionizations reaching the maximum, lowered stopping power is observed, which is due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.Comment: 6 pages, 4 figure

Monte-Carlo approach to calculate the ionization of warm dense matter within particle-in-cell simulations

A physical model based on a Monte-Carlo approach is proposed to calculate the ionization dynam- ics of warm dense matters (WDM) within particle-in-cell simulations, and where the impact (col- lision) ionization (CI), electron-ion recombination (RE) and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal re- laxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different composi- tions. The proposed model is implemented into a particle-in-cell (PIC) code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium in the WDM regime, i) the averaged ionization degree increases by including IPD; while ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures, and shows good agreements with that generated from Saha-Boltzmann model or/and FLYCHK code.Comment: 7 pages, 4 figure

The black hole dynamical horizon and generalized second law of thermodynamics

The generalized second law of thermodynamics for a system containing a black hole dynamical horizon is proposed in a covariant way. Its validity is also tested in case of adiabatically collapsing thick light shells.Comment: JHEP style, 8 pages, 2 figures, version to appear in JHEP with typos correcte

Random Time-Scale Invariant Diffusion and Transport Coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that $\overline{\delta^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{\delta^2}$. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in Physics1, 8 (2008

An optimized analytical method for the simultaneous detection of iodoform, iodoacetic acid, and other trihalomethanes and haloacetic acids in drinking water

An optimized method is presented using liquid-liquid extraction and derivatization for the extraction of iodoacetic acid (IAA) and other haloacetic acids (HAA9) and direct extraction of iodoform (IF) and other trihalomethanes (THM4) from drinking water, followed by detection by gas chromatography with electron capture detection (GC-ECD). A Doehlert experimental design was performed to determine the optimum conditions for the five most significant factors in the derivatization step: namely, the volume and concentration of acidic methanol (optimized values  = 15%, 1 mL), the volume and concentration of Na2SO4 solution (129 g/L, 8.5 mL), and the volume of saturated NaHCO3 solution (1 mL). Also, derivatization time and temperature were optimized by a two-variable Doehlert design, resulting in the following optimized parameters: an extraction time of 11 minutes for IF and THM4 and 14 minutes for IAA and HAA9; mass of anhydrous Na2SO4 of 4 g for IF and THM4 and 16 g for IAA and HAA9; derivatization time of 160 min and temperature at 40°C. Under optimal conditions, the optimized procedure achieves excellent linearity (R2 ranges 0.9990–0.9998), low detection limits (0.0008–0.2 µg/L), low quantification limits (0.008–0.4 µg/L), and good recovery (86.6%–106.3%). Intra- and inter-day precision were less than 8.9% and 8.8%, respectively. The method was validated by applying it to the analysis of raw, flocculated, settled, and finished waters collected from a water treatment plant in China