Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

Performance of a CW pumped Nd:YVO4 amplifier with kHz pulses

Until recently, simple and reliable high repetition-rate laser sources with nanosecond pulses much shorter than from conventional A-O Q-switch lasers were not available. However over the past 2 years we have developed such lasers based on proprietary fast E-O switching technology, which allows designs delivering 1 ns pulses and subnanosecond jitter for good synchronisation. The technology provides pulses with multi-kW peak power and repetition-rates to >100 kHz.Most recently, the performance of these short pulse lasers has been developed further by implementing oscillator/amplifier (master oscillator and power amplifier, MOPA) technology which increases the output to >1 W average power. Here we report on a simple model that has been used to predict the performance of the CW pumped Nd:YVO₄ amplifier used in the MOPA laser. The model is based on the well-known expressions for the saturated gain applying to laser pulses, but more usually applied to pulse-excited amplifiers. The model is shown to allow a good interpretation of the amplifier behaviour for kHz pulses and to be a useful tool for predicting the performance of the MOPA laser.     

Entropy estimate for high-dimensional monotonic functions

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L^p norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a d-dimensional monotone density.     

An algorithm for computing Jordan chains and inverting analytic matrix functions

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n × n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)⁻¹b(λ) may be obtained from the previous terms by solving an (n + d) × (n+d) linear system, where d is the order of the zero of det A(λ) at λ = 0. The matrix representing this linear system contains A(0) as a principal submatrix, which can be useful if A(0) is sparse. The last several iterations can be eliminated if left Jordan chains are computed in addition to right Jordan chains. The performance of the algorithm in floating point and exact (rational) arithmetic is reported for several test cases. The method is shown to be forward stable in floating point arithmetic.     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

Glass transitions in hydrogen-bonded polymer complexes

Mutual precipitates of poly (N, N-dimethyl acrylamide) and poly (4-hydroxystyrene) were collected from dioxane, methanol, or acetone. The glass transition (T_g) temperatures of the precipitates are higher than the weight-average values. Clear films cast from dimethylformamide solutions have lower T_g values. Complexation also occurred between poly (ethyl oxazoline) and poly (4-hydroxystyrene) in dioxane and between poly (vinyl pyrrolidone) and poly (4-hydroxystyrene) in methanol. Again, the glass transition temperatures of the precipitates are higher than the values for the blend films. The ΔC_p values associated with the glass transitions of the complexes are smaller than those of the blends having the same compositions. Negative excess heat capacities of mixing have been observed for several precipitates.     

Random orderings of the integers and card shuffling

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.     

A 24-GHz Patch Array with a Power Amplifier/Low-Noise Amplifier MMIC

This paper presents an active patch array designed at 24 GHz. It can be used as a front-end component for a phased array. A series resonant array structure is chosen which is compact and easy excite. With 5 elements, the array proved a 12-dB antenna gain. A power amplifier and a low noise amplifier are designed on a single GaAs chip (PALNA). Bias switch is used in the PALNA, which greatly reduces the switch loss in a transceiver and increases the efficiency. 20-dB small signal gain is achieved in both power amplifier and low noise amplifier. The active patch array is built by the combination of the patch array and PALNA. The measured active gain of this antenna is 35-dB for the PA mode and 31-dB for the LNA mode. This active patch array can obtain an EIRP of 34 dBm with a total radiated power of 22dBm and a maximum PAE of 32%. To check the noise performance, we applied sources at both normal temperature and 77K (liquid nitrogen) and extracted the noise figure (3.5 dB) of the active antenna by the Y factor method. The results proved that the active antenna is working efficiently as both a transmitting and receiving antenna.     

Geometry optimization in Cartesian coordinates: Constrained optimization

An efficient algorithm for constrained geometry optimization in Cartesian coordinates is presented. It incorporates mode-following techniques within both the classical method of Lagrange multipliers and the penalty function method. Both constrained minima and transition states can be located and, unlike the standard Z-matrix using internal coordinates, the desired constraints do not have to be satisfied in the initial structure. The algorithm is as efficient as a Z-matrix optimization while presenting several additional advantages.