First variation of horomorphic forms and some applications

We study various local invariants associated with a singular holomorphic foliation on a complex surface admitting a possibly singular invariant curve. We establish the relation among them and prove/reprove formulas relating the total sum of these invariants to some global invariants of the foliation and the invariant curve

Transient thermal performance prediction method for parabolic trough solar collector under fluctuating solar radiation

As the effect of the global warming is becoming noticeable, the importance for environmental sustainability has been raised. Parabolic trough solar thermal collector system, which is one of the solutions to reduce the carbon dioxide emission, is a mature technology for electricity generation. Malaysia is a tropical country with long daytime, which makes suitable for solar thermal applications with parabolic trough solar thermal collectors. However, the high humidity causes the solar radiation to fluctuate. In order to simulate the solar thermal collectors’ performance at an early design stage of solar thermal power generation systems, fast still accurate transient thermal performance prediction methodis required. Although multiple transient thermal simulation methodologies exist, they are not suited especially at an early design stage where quick but reasonably accurate thermal performance prediction is needed because of their long calculation time. In this paper, a transient thermal prediction method is developed to predict exit temperature of parabolic trough collectors under fluctuating solar radiation. The method is governed by simple summation operations and requires much less calculating time than the existing numerical methods. If the radiation heat loss at the parabolic trough collector tube surface is small, the working fluid temperature rise may be approximated as proportional to the receiving heat flux. The fluctuating solar radiation is considered as a series of heat flux pulses applied for a short period of time. The time dependent solar collector exit temperature is approximated by superimposing the exit temperature rise caused by each heat flux pulse. To demonstrate the capabilities of the proposed methodology, the solar collector exit temperature for one-day operation is predicted. The predicted solar collector exit temperature captures the trend of a finite element analysis result well. Still, the largest temperature difference is 38.8K and accuracy is not satisfactory. Currently, the accuracy of the proposed method is being improved. At the same time, its capabilities are being expanded

Solar-powered adsorption refrigeration cycle optimization

Solar energy is an attractive energy source among various renewable energy resources in Malaysia as relatively high solar radiation is available throughout the year. This solar energy can be utilized for air-conditioning by using solar-powered adsorption refrigeration cycle. Intermittent nature of the solar radiation leads to a challenge for continuous air-conditioning operation. In the present study, a combination of solar-powered adsorption refrigeration system and thermal storage is studied. Activated carbon-ammonia and activated carbon-methanol are the working pairs of the adsorption reaction. Analytical calculation results show that activated carbon-methanol pair indicates higher coefficient of performance (COP) than activated carbon-ammonia pair, while adsorption chiller system with hot water thermal storage has higher COP than the system with ice thermal storage. For the activated carbon-methanol case with hot water thermal storage, the COP is 0.79. Since this COP analysis is based on the ideal case with uniform temperature distribution within the reactor beds, which achieves equilibrium states at the end of the reactions. In more realistic situation, the reaction process will be terminated before reaching to the equilibrium states because of the non-uniform temperature distribution and the time required for the reaction. Transient simulation in which heat transfer and reaction equation are combined will be performed to model actual reactors

Inequalities for characteristic numbers of flags of distributions and foliations

We prove inequalities relating the degrees of holomorphic distributions and of holomorphic foliations forming a flag on $\mathbb{P}^n$. Such inequalities are inspired by the so called Poincar\'e problem for foliations.Comment: Several minor clarifications and correction

Residues of Chern classes

If we have a finite number of sections of a complex vector bundle E over a manifold M, certain Chern classes of E are localized at the singular set S, i.e., the set of points where the sections fail to be linearly independent. When S is compact, the localizations define the residues at each connected component of S by the Alexander duality. If M itself is compact, the sum of the residues is equal to the Poincare dual of the corresponding Chern class. This type of theory is also developed for vector bundles over a possibly singular subvariety in a complex manifold. Explicit formulas for the residues at an isolated singular point are also given, which expresses the residues in terms of Grothendieck residues relative to the subvariety

Localization of Atiyah classes

We construct the Atiyah classes of holomorphic vector bundles using (1,0)-connections and developing a Chern–Weil type theory, allowing us to effectively compare Chern and Atiyah forms. Combining this point of view with the Čech–Dolbeault cohomology, we prove several results about vanishing and localization of Atiyah classes, and give some applications. In particular, we prove a Bott type vanishing theorem for (not necessarily involutive) holomorphic distributions. As an example we also present an explicit computation of the residue of a singular distribution on the normal bundle of an invariant submanifold that arises from the Camacho–Sad type localization