Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Two-directional active damper

Damper system to be used in studies of payload isolation technology is suitable as a laboratory apparatus. It provides easily adjustable damping and acts as multichannel shaker system

Radio Frequency Response of the Strongly Interacting Fermi Gases at Finite Temperatures

The radio frequency spectrum of the fermions in the unitary limit at finite temperatures is characterized by the sum rule relations. We consider a simple picture where the atoms are removed by radio frequency excitations from the strongly interacting states into a state of negligible interaction. We calculate the moments of the response function in the range of temperature $0.08 \epsilon_F < T < 0.8 \epsilon_F$ using auxiliary field Monte Carlo technique (AFMC) in which continuum auxiliary fields with a density dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap - pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at T=0, the effective mass has to be $m^* \sim 1.43 m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.Comment: 2 figure

Comets: Cosmic connections with carbonaceous meteorites, interstellar molecules and the origin of life

The ions, radicals, and molecules observed in comets may be derived intact or by partial decomposition from parent compounds of the sort found either in the interstellar medium or in carbonaceous meteorites. The early loss of highly reducing primitive atmosphere and its replacement by a secondary atmosphere dominated by H2O, CO2, and N2, as depicted in current models of the earth's evolution, pose a dilemma for the origin of life: the synthesis of organic compounds necessary for life from components of the secondary atmosphere appears to be difficult, and plausible mechanisms have not been evaluated. Both comets and carbonaceous meteorites are implicated as sources for the earth's atmophilic and organogenic elements. A mass balance argument involving the estimated ratios of hydrogen to carbon in carbonaceous meteorites, comets, and the crust and upper mantle suggests that comets supplied the earth with a large fraction of its volatiles. The probability that comets contributed significantly to the earth's volatile inventory suggests a chemical evolutionary link between comets, prebiotic organic synthesis, and the origin of life

Origin of life

The pathways of organic chemical synthesis, the chemical evolution on the early Earth leading to life was constrained by the development of the planet by accretion and core formation. The accretion and differentiation into the core-mantle-crust-atmosphere system strongly influenced the temperature and composition of the atmosphere, surface, and interior; but large gaps persist in our understanding of these processes. The time-span over which Earth acquired its volatiles, the composition of these volatiles, and the conditions under which outgassing of volatiles occurred to form the atmosphere, are unknown. Uncertainties in existing models for Earth accretion and early planetary development allows a wide range of possible prebiotic atmospheric compositions at the time and temperature when liquid water appeared and thermally-labile organic compounds could survive. These compositions range from strongly reducing atmospheres to mildly reducing ones

The carbon chemistry of meteorites: Relationships to comets

The carbonaceous meteorites exhibiting alteration by liquid water bear a strong relationship to comets. Not only is their elemental composition closer to solar in relative abundances than other meteorites, they are water rich; and they contain isotopic compositions among refractory and volatile elements indicative of presolar components. Some of these isotopic anomalies occur in organic compounds and carbonaceous grains signifying the presence of discrete and identifiable carbon components derived from interstellar and circumstellar matter. Insofar as comets and meteorites are ultimately formed from interstellar gas and dust, and comets have been subjected to considerably less aqueous and thermal evolution than carbonaceous meteorites, the interstellar imprint should be much stronger and better preserved in comets

Utilization of information theory in digital data guidance systems Quarterly progress report no. 1, 1 Sep. - 30 Nov. 1965

Information theory in improving digital data guidance syste