Diagnosis of a unit-wide disturbance caused by saturation in a manipulated variable

It is well known that faulty control valves with friction in the moving parts lead to limit cycle oscillations which can propagate to other parts of the plant. However, a control loop with healthy valve can also undergo oscillatory behavior. The root cause of a unit-wide oscillation in a distillation column was traced to a pressure control loop in a case study at Mitsui Chemicals. The diagnosis was made by means of a new technique of pattern matching of the time-resolved frequency spectrum using a wavelet analysis tool. The method identified key characteristics shared by measurements at various places in the column and quantified the similarities. Non-linearity was detected in the time trend of the pressure measurement, a result which initially suggested the root cause was a faulty actuator or sensor. Further analysis showed, however, that the source of non-linearlity was periodic saturation of the manipulated variable caused by slack tuning. The problem was remidied by changing the controller tuning settings and the unit-wide disturbance then went away

Computing in String Field Theory Using the Moyal Star Product

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as a closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.Comment: 77 pages, LaTeX. v3: corrections of signs or factors (for a list of corrections see beginning of source file

Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors

Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields. For s-wave pairing, triangular, square, hexagonal states are favored depending on the temperature, while square states are favored at low temperatures for d-wave pairing. In these states, orderparameters have two-dimensional structures such as square and triangular lattices.Comment: 11 pages (LaTeX, revtex.sty), 3 figures; added reference

Effect of humidity on transonic flow

An experimental investigation of the effects of humidity-induced condensation on shock/boundary-layer interaction has been conducted in a transonic wind-tunnel test. The test geometry considered was a wall-mounted bump model inserted in the test section of the wind tunnel. The formation of a λ-shape condensation shock wave was shown from schlieren visualization and resulted in a forward movement of the shock wave, reduced shock wave strength, and reduced separation. Empirical correlations of the shock wave strength and humidity/dew point temperature were established. For humidity levels below 0.15 or a dew point temperature of 268 K, the effect of humidity was negligible. The unsteady pressure measurements showed that if a condensation shock wave formed and interacted with a main shock wave, the flow becomes unsteady with periodic flow oscillations occurring at 720 Hz

Bayesian photon counting with electron-multiplying charge coupled devices (EMCCDs)

The EMCCD is a CCD type that delivers fast readout and negligible detector noise, making it an ideal detector for high frame rate applications. Because of the very low detector noise, this detector can potentially count single photons. Considering that an EMCCD has a limited dynamical range and negligible detector noise, one would typically apply an EMCCD in such a way that multiple images of the same object are available, for instance, in so called lucky imaging. The problem of counting photons can then conveniently be viewed as statistical inference of flux or photon rates, based on a stack of images. A simple probabilistic model for the output of an EMCCD is developed. Based on this model and the prior knowledge that photons are Poisson distributed, we derive two methods for estimating the most probable flux per pixel, one based on thresholding, and another based on full Bayesian inference. We find that it is indeed possible to derive such expressions, and tests of these methods show that estimating fluxes with only shot noise is possible, up to fluxes of about one photon per pixel per readout.Comment: Fixed a few typos compared to the published versio

Fluctuation-Driven First-Order Transition in Pauli-limited d-wave Superconductors

We study the phase transition between the normal and non-uniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state in quasi two-dimensional d-wave superconductors at finite temperature. We obtain an appropriate Ginzburg-Landau theory for this transition, in which the fluctuation spectrum of the order parameter has a set of minima at non-zero momenta. The momentum shell renormalization group procedure combined with dimensional expansion is then applied to analyze the phase structure of the theory. We find that all fixed points have more than one relevant directions, indicating the transition is of the fluctuation-driven first order type for this universality class.Comment: 5 page