Different critical points of chiral and deconfinement phase transitions in (2+1)-dimensional fermion-gauge interacting model

Based on the truncated Dyson-Schwinger equations for fermion and massive boson propagators in QED$_3$, the fermion chiral condensate and the mass singularities of the fermion propagator via the Schwinger function are investigated. It is shown that the critical point of chiral phase transition is apparently different from that of deconfinement phase transition and in Nambu phase the fermion is confined only for small gauge boson mass.Comment: 5 Pages and 3 figure

New Method for Numerically Solving the Chemical Potential Dependence of the Dressed Quark Propagator

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the inverse dressed quark propagator at finite chemical potential is analytic in the neighborhood of $\mu=0$, a new method for obtaining the dressed quark propagator at finite chemical potential $\mu$ from the one at zero chemical potential is developed. Using this method the dressed quark propagator at finite chemical potential can be obtained directly from the one at zero chemical potential without the necessity of numerically solving the corresponding coupled integral equations by iteration methods. A comparison with previous results is given.Comment: Revtex, 14 pages, 5 figure

General formula for the four-quark condensate and vacuum factorization assumption

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):|{\tilde 0}>$. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for $<{\tilde 0}|:{\bar q}(0)\gamma_\mu q(0){\bar q}(0)\gamma_\mu q(0):| {\tilde 0}>$ holds only when the dressed vertex is taken to be the bare one. This property also holds for all other type of four-quark condensate.Comment: Revtex4, 11 pages, no figure

Expanding the Toolkit for Metabolic Engineering

The essence of metabolic engineering is the modification of microbes for the overproduction of useful compounds. These cellular factories are increasingly recognized as an environmentally-friendly and cost-effective way to convert inexpensive and renewable feedstocks into products, compared to traditional chemical synthesis from petrochemicals. The products span the spectrum of specialty, fine or bulk chemicals, with uses such as pharmaceuticals, nutraceuticals, flavors and fragrances, agrochemicals, biofuels and building blocks for other compounds. However, the process of metabolic engineering can be long and expensive, primarily due to technological hurdles, our incomplete understanding of biology, as well as redundancies and limitations built into the natural program of living cells. Combinatorial or directed evolution approaches can enable us to make progress even without a full understanding of the cell, and can also lead to the discovery of new knowledge. This thesis is focused on addressing the technological bottlenecks in the directed evolution cycle, specifically de novo DNA assembly to generate strain libraries and small molecule product screens and selections