Dimers on two-dimensional lattices

We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43

Submillimeter satellite radiometer first semiannual engineering progress report

Development of 560 GHz fourth harmonic mixer and 140 GHz third harmonic generator for use in radiomete

Submillimeter satellite radiometer Final engineering report

All solid-state superheterodyne Dicke radiometer for submillimeter wavelength

A restatement of the normal form theorem for area metrics

An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area metrics. This result is similar to the Jordan normal form theorem for (1,1)-tensors, and the result shows that any area metric belongs to one of 23 metaclasses with explicit coordinate expressions for each metaclass. In this paper we restate and prove this result for skewon-free (2,2)-tensors and show that in general, each metaclasses has three different coordinate representations, and each of metaclasses I, II, ..., VI, VII need only one coordinate representation.Comment: Updated proof of Proposition A.2 (Claim 5). Fixed typo in Theorem 6 (Metaclass XXIII

Cataclysmic Variables and a New Class of Faint UV Stars in the Globular Cluster NGC 6397

We present evidence that the globular cluster NGC 6397 contains two distinct classes of centrally-concentrated UV-bright stars. Color-magnitude diagrams constructed from U, B, V, and I data obtained with the HST/WFPC2 reveal seven UV-bright stars fainter than the main-sequence turnoff, three of which had previously been identified as cataclysmic variables (CVs). Lightcurves of these stars show the characteristic ``flicker'' of CVs, as well as longer-term variability. A fourth star is identified as a CV candidate on the basis of its variability and UV excess. Three additional UV-bright stars show no photometric variability and have broad-band colors characteristic of B stars. These non-flickering UV stars are too faint to be extended horizontal branch stars. We suggest that they could be low-mass helium white dwarfs, formed when the evolution of a red giant is interrupted, due either to Roche-lobe overflow onto a binary companion, or to envelope ejection following a common-envelope phase in a tidal-capture binary. Alternatively, they could be very-low-mass core-He-burning stars. Both the CVs and the new class of faint UV stars are strongly concentrated toward the cluster center, to the extent that mass segregation from 2-body relaxation alone may be unable to explain their distribution.Comment: 11 pages plus 3 eps figures; LaTeX using aaspp4.sty; to appear in The Astrophysical Journal Letter

Temperature Effects on Threshold Counterion Concentration to Induce Aggregation of fd Virus

We seek to determine the mechanism of like-charge attraction by measuring the temperature dependence of critical divalent counterion concentration ($\rm{C_{c}}$) for the aggregation of fd viruses. We find that an increase in temperature causes $\rm{C_c}$ to decrease, primarily due to a decrease in the dielectric constant ($\epsilon$) of the solvent. At a constant $\epsilon$, $\rm{C_c}$ is found to increase as the temperature increases. The effects of $T$ and $\epsilon$ on $\rm {C_{c}}$ can be combined to that of one parameter: Bjerrum length ($l_{B}$). $\rm{C_{c}}$ decreases exponentially as $l_{B}$ increases, suggesting that entropic effect of counterions plays an important role at the onset of bundle formation.Comment: 12 pages, 3 figure

Boolean Models of Bistable Biological Systems

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch

The arctic curve of the domain-wall six-vertex model

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of $q$-enumerated (with $0<q\leq 4$) large alternating sign matrices. In particular, as $q\to 0$ the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction

Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras

We determine the structure of the partition algebra $P_n(Q)$ (a generalized Temperley-Lieb algebra) for specific values of Q \in \C, focusing on the quotient which gives rise to the partition function of $n$ site $Q$-state Potts models (in the continuous $Q$ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is non-semi-simple iff $Q$ is a non-negative integer less than $n$. We determine the dimension of the key irreducible representation in every specialization.Comment: 4 page

Radiative Reactions and Coherence Modeling in the High Altitude Electromagnetic Pulse

A high altitude nuclear electromagnetic pulse (EMP) with a peak field intensity of 5 x 10^4 V/m carries momentum that results in a retarding force on the average Compton electron (radiating coherently to produce the waveform) with magnitude near that of the geomagnetic force responsible for the coherent radiation. The retarding force results from a self field effect. The Compton electron interaction with the self generated magnetic field due to the other electrons accounts for the momentum density in the propagating wave; interaction with the self generated electric field accounts for the energy flux density in the propagating wave. Coherent addition of radiation is also quantitatively modeled.Comment: 23 pages, 0 figure