Chemical vapor deposition reactor

An improved chemical vapor deposition reactor is characterized by a vapor deposition chamber configured to substantially eliminate non-uniformities in films deposited on substrates by control of gas flow and removing gas phase reaction materials from the chamber. Uniformity in the thickness of films is produced by having reactive gases injected through multiple jets which are placed at uniformally distributed locations. Gas phase reaction materials are removed through an exhaust chimney which is positioned above the centrally located, heated pad or platform on which substrates are placed. A baffle is situated above the heated platform below the mouth of the chimney to prevent downdraft dispersion and scattering of gas phase reactant materials

Induced junction solar cell and method of fabrication

An induced junction solar cell is fabricated on a p-type silicon substrate by first diffusing a grid of criss-crossed current collecting n+ stripes and thermally growing a thin SiO2 film, and then, using silicon-rich chemical vapor deposition (CVD), producing a layer of SiO2 having inherent defects, such as silicon interstices, which function as deep traps for spontaneous positive charges. Ion implantation increases the stable positive charge distribution for a greater inversion layer in the p-type silicon near the surface. After etching through the oxide to parallel collecting stripes, a pattern of metal is produced consisting of a set of contact stripes over the exposed collecting stripes and a diamond shaped pattern which functions as a current collection bus. Then the reverse side is metallized

Optimum reentry trajectories of a lifting vehicle

Research results are presented of an investigation of the optimum maneuvers of advanced shuttle type spacecraft during reentry. The equations are formulated by means of modified Chapman variables resulting in a general set of equations for flight analysis which are exact for reentry and for flight in a vacuum. Four planar flight typical optimum manuevers are investigated. For three-dimensional flight the optimum trajectory for maximum cross range is discussed in detail. Techniques for calculating reentry footprints are presented

Yang-Mills, Complex Structures and Chern's Last Theorem

Recently Shiing-Shen Chern suggested that the six dimensional sphere $\mathbb{S}^6$ has no complex structure. Here we explore the relations between his arguments and Yang-Mills theories. In particular, we propose that Chern's approach is widely applicable to investigate connections between the geometry of manifolds and the structure of gauge theories. We also discuss several examples of manifolds, both with and without a complex structure.Comment: Chern's proof remains incomplete, and we have edited some statements in our article accordingl

Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics

Improved chemical vapor-deposition reactor

Formation of large particles on substrate is eliminated by actively exhausting reacted gases. Effluent gas backflow is prevented by pumping in curtain of nitrogen above fresh reactive gases from several directions

Extension of the Poincar\'e Group and Non-Abelian Tensor Gauge Fields

In the recently proposed generalization of the Yang-Mills theory the group of gauge transformation gets essentially enlarged. This enlargement involves an elegant mixture of the internal and space-time symmetries. The resulting group is an extension of the Poincar\'e group with infinitely many generators which carry internal and space-time indices. This is similar to the super-symmetric extension of the Poincar\'e group, where instead of an anti-commuting spinor variable one should introduce a new vector variable. The construction of irreducible representations of the extended Poincar\'e algebra identifies a vector variable with the derivative of the Pauli-Lubanski vector over its length. As a result of this identification the generators of the gauge group have nonzero components only in the plane transversal to the momentum and are projecting out non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite space-like components.Comment: 21 page

On number fields with nontrivial subfields

What is the probability for a number field of composite degree $d$ to have a nontrivial subfield? As the reader might expect the answer heavily depends on the interpretation of probability. We show that if the fields are enumerated by the smallest height of their generators the probability is zero, at least if $d>6$. This is in contrast to what one expects when the fields are enumerated by the discriminant. The main result of this article is an estimate for the number of algebraic numbers of degree $d=e n$ and bounded height which generate a field that contains an unspecified subfield of degree $e$. If $n>\max\{e^2+e,10\}$ we get the correct asymptotics as the height tends to infinity

Calabi-Yau 3-folds from 2-folds

We consider type IIA string theory on a Calabi-Yau 2-fold with D6-branes wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the supergravity solution for any given wrapped brane configuration in terms of SU(2) structures. We reduce the problem of finding a supergravity solution for the wrapped branes to finding a harmonic function on R$\times$CY$_2$. We then lift this solution to 11-dimensions as a product of R$^{(4.1)}$ and a Calabi-Yau 3-fold. We show how the metric on the 3-fold is determined in terms of the wrapped brane solution. We write down the distinguished (3,0) form and the K{\"a}hler form of the 3-fold in terms of structures defined on the base 2-d complex manifold. We discuss the topology of the 3-fold in terms of the D6-branes and the underlying 2-fold. We show that in addition to the non-trivial cycles inherited from the underlying 2-fold there are $N-1$ new 2-cycles. We construct closed (1,1) forms corresponding to these new cycles. We also display some explicit examples. One of our examples is that of D6-branes wrapping the 2-cycle in an A$_1$ ALE space, the resulting 3-fold has $h^{(1,1)}=N$, where $N$ is the number of D6-branes.Comment: 30 page

Seismic Safety Analysis of Earth Dam — Case History Studies

The method of seismic safety analysis for earth dam was examined by using actual performances of earth dams during the Chi-Chi Earthquake. Results of analysis under design earthquakes were also collected and compared with the performance records of earth dams. From the results of these studies, it appears that the Seed-Lee-Idriss approach can provide reasonable predictions on the dynamic responses and post-earthquake performance of well-compacted earth dam