Calibration of planetary brightness temperature spectra at near-millimeter and submillimeter wavelengths with a Fourier-transform spectrometer

A medium-resolution Fourier-transform spectrometer for ground-based observation of astronomical sources at near-millimeter and submillimeter wavelengths is described. The steps involved in measuring and calibrating astronomical spectra are elaborated. The spectrometer is well suited to planetary spectroscopy, and initial measurements of the intrinsic brightness temperature spectra of Uranus and Neptune at wavelengths of 1.0 to 1.5 mm are presented

Principles of vortex light generation from electronically excited nanoscale arrays

It has recently been shown possible to directly generate an optical vortex (a beam of light endowed with orbital angular momentum) by spontaneous emission from a molecular exciton array. This contrasts with most established methods, which typically rely on the modification of a conventional beam by an appropriate optical element (for example, a q-plate) to impose the requisite helical twist of a vortex. The new procedure is achieved by nanofabricating a chiral arrangement of chromophores into a ring of specifically configured symmetry, supporting a doubly degenerate (conjugated) exciton with the appropriate azimuthal phase progression. It emerges that the symmetry elements present in the phase structure of the optical field, produced by emission from these degenerate excitons on a array, exhibits precisely the sought character of an optical vortex. The highest order of exciton symmetry, including the corresponding splitting of the electronic states, dictates the maximum magnitude of the topological charge. Work is now progressing on computer simulations aiming to reveal the detailed pattern of polarization behaviour in the emitted light, in which the vector character of the beam progresses around the phase singularity along the beam propagation axis. Significantly, this analysis points to the emission of radiation with polarization varying over the beam profile

Analysis techniques for complex-field radiation pattern measurements

Complex field measurements are increasingly becoming the standard for state-of-the-art astronomical instrumentation. Complex field measurements have been used to characterize a suite of ground, airborne, and space-based heterodyne receiver missions [1], [2], [3], [4], [5], [6], and a description of how to acquire coherent field maps for direct detector arrays was demonstrated in Davis et. al. 2017. This technique has the ability to determine both amplitude and phase radiation patterns from individual pixels on an array. Phase information helps to better characterize the optical performance of the array (as compared to total power radiation patterns) by constraining the fit in an additional plane [4]. Here we discuss the mathematical framework used in an analysis pipeline developed to process complex field radiation pattern measurements. This routine determines and compensates misalignments of the instrument and scanning system. We begin with an overview of Gaussian beam formalism and how it relates to complex field pattern measurements. Next we discuss a scan strategy using an offset in z along the optical axis that allows first-order optical standing waves between the scanned source and optical system to be removed in post-processing. Also discussed is a method by which the co- and cross-polarization fields can be extracted individually for each pixel by rotating the two orthogonal measurement planes until the signal is the co-polarization map is maximized (and the signal in the cross-polarization field is minimized). We detail a minimization function that can fit measurement data to an arbitrary beam shape model. We conclude by discussing the angular plane wave spectral (APWS) method for beam propagation, including the near-field to far-field transformation

Reexamination of Hagen-Poiseuille flow: shape-dependence of the hydraulic resistance in microchannels

We consider pressure-driven, steady state Poiseuille flow in straight channels with various cross-sectional shapes: elliptic, rectangular, triangular, and harmonic-perturbed circles. A given shape is characterized by its perimeter P and area A which are combined into the dimensionless compactness number C = P^2/A, while the hydraulic resistance is characterized by the well-known dimensionless geometrical correction factor alpha. We find that alpha depends linearly on C, which points out C as a single dimensionless measure characterizing flow properties as well as the strength and effectiveness of surface-related phenomena central to lab-on-a-chip applications. This measure also provides a simple way to evaluate the hydraulic resistance for the various shapes.Comment: 4 pages including 3 figures. Revised title, as publishe

Form factors of descendant operators: Free field construction and reflection relations

The free field representation for form factors in the sinh-Gordon model and the sine-Gordon model in the breather sector is modified to describe the form factors of descendant operators, which are obtained from the exponential ones, \e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra associated to the field $\phi(x)$. As a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector. Another check is related to the so called reflection relations, which identify in the breather sector the descendants of the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi} for generic values of $\alpha$. We prove the operators defined by the obtained families of form factors to satisfy such reflection relations. A generalization of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor corrections; v4,v5: misprints corrected; v6: minor mistake correcte

An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

Making Mastery Work: A Close-Up View of Competency Education

As schools move towards a 21st century model of preparing students for college and a career, it is becoming unnecessary to maintain a system based on time spent in the classroom, according to the report's authors. Rather, learning happens at different times in a variety of settings, and progress should be demonstrated by mastery of content, not merely grade promotion. In the proficiency-based systems examined in "Making Mastery Work", students advance at their own pace as part of a cycle of continuous learning and achievement. This mix of freedom and responsibility is positively impacting both the teaching and the learning at the ten schools studied by Nora Priest, Antonia Rudenstine and Ephraim Weisstein, the report's authors. Issues examined through the collected experiences of the participating schools include: the creation of a transparent mastery and assessment system, time flexibility, curriculum and instruction, leadership for competency education development, and the role of data and information technology in a competency-based education model

A statistical model with a standard Gamma distribution

We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $\lambda$. We focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard Gamma distribution. The model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity $\lambda$. Alternatively, from the nature of the equilibrium distribution, we show that the model can also be interpreted as a perfect gas at an effective temperature $T(\lambda)$, where particles exchange energy in a space with an effective dimension $D(\lambda)$.Comment: 5 pages, including 4 figures. Uses REVTeX styl

First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy

We analyze in detail the fermionic self-energy \Sigma(\omega, T) in a Fermi liquid (FL) at finite temperature T and frequency \omega. We consider both canonical FLs -- systems in spatial dimension D >2, where the leading term in the fermionic self-energy is analytic [the retarded Im\Sigma^R(\omega,T) = C(\omega^2 +\pi^2 T^2)], and non-canonical FLs in 1<D <2, where the leading term in Im\Sigma^R(\omega,T) scales as T^D or \omega^D. We relate the \omega^2 + \pi^2 T^2 form to a special property of the self-energy -"the first-Matsubara-frequency rule", which stipulates that \Sigma^R(i\pi T,T) in a canonical FL contains an O(T) but no T^2 term. We show that in any D >1 the next term after O(T) in \Sigma^R(i\pi T,T) is of order T^D (T^3\ln T in D=3). This T^D term comes from only forward- and backward scattering, and is expressed in terms of fully renormalized amplitudes for these processes. The overall prefactor of the T^D term vanishes in the "local approximation", when the interaction can be approximated by its value for the initial and final fermionic states right on the Fermi surface. The local approximation is justified near a Pomeranchuk instability, even if the vertex corrections are non-negligible. We show that the strength of the first-Matsubara-frequency rule is amplified in the local approximation, where it states that not only the T^D term vanishes but also that \Sigma^R(i\pi T,T) does not contain any terms beyond O(T). This rule imposes two constraints on the scaling form of the self-energy: upon replacing \omega by i\pi T, Im\Sigma^R(\omega,T) must vanish and Re\Sigma^R (\omega, T) must reduce to O(T). These two constraints should be taken into consideration in extracting scaling forms of \Sigma^R(\omega,T) from experimental and numerical data.Comment: 22 pages, 3 figure