The Carriers of the Interstellar Unidentified Infrared Emission Features: Constraints from the Interstellar C-H Stretching Features at 3.2-3.5 Micrometers

The unidentified infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 micrometer, commonly attributed to polycyclic aromatic hydrocarbon (PAH) molecules, have been recently ascribed to mixed aromatic/aliphatic organic nanoparticles. More recently, an upper limit of <9% on the aliphatic fraction (i.e., the fraction of carbon atoms in aliphatic form) of the UIE carriers based on the observed intensities of the 3.4 and 3.3 micrometer emission features by attributing them to aliphatic and aromatic C-H stretching modes, respectively, and assuming A_34./A_3.3~0.68 derived from a small set of aliphatic and aromatic compounds, where A_3.4 and A_3.3 are respectively the band strengths of the 3.4 micrometer aliphatic and 3.3 micrometer aromatic C-H bonds. To improve the estimate of the aliphatic fraction of the UIE carriers, here we analyze 35 UIE sources which exhibit both the 3.3 and 3.4 micrometer C-H features and determine I_3.4/I_3.3, the ratio of the power emitted from the 3.4 micrometer feature to that from the 3.3 micrometer feature. We derive the median ratio to be ~ 0.12. We employ density functional theory and second-order perturbation theory to compute A_3.4/A_3.3 for a range of methyl-substituted PAHs. The resulting A_3.4/A_3.3 ratio well exceeds 1.4, with an average ratio of ~1.76. By attributing the 3.4 micrometer feature exclusively to aliphatic C-H stretch (i.e., neglecting anharmonicity and superhydrogenation), we derive the fraction of C atoms in aliphatic form to be ~2%. We therefore conclude that the UIE emitters are predominantly aromatic.Comment: 14 pages, 5 figures, 1 table; accepted for publication in The Astrophysical Journa

The Carriers of the "Unidentified" Infrared Emission Features: Clues from Polycyclic Aromatic Hydrocarbons with Aliphatic Sidegroups

The "unidentified" infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 $\mu$m are ubiquitously seen in various astrophysical regions. The UIE features are characteristic of the stretching and bending vibrations of aromatic hydrocarbons. The 3.3 $\mu$m feature resulting from aromatic C--H stretches is often accompanied by a weaker feature at 3.4 $\mu$m often attributed to aliphatic C--H stretches. The ratio of the observed intensity of the 3.3 $\mu$m aromatic C--H feature ($I_{3.3}$) to that of the 3.4 $\mu$m aliphatic C--H feature ($I_{3.4}$) allows one to estimate the aliphatic fraction (i.e. $N_{\rm C,aliph}/N_{\rm C,arom}$, the number of C atoms in aliphatic units to that in aromatic rings) of the UIE carriers, provided the intrinsic oscillator strengths of the 3.3 $\mu$m aromatic C--H stretch ($A_{3.3}$) and the 3.4 $\mu$m aliphatic C--H stretch ($A_{3.4}$) are known. In this article we summarize the computational results on $A_{3.3}$ and $A_{3.4}$ and their implications for the aromaticity and aliphaticity of the UIE carriers. We use density functional theory and second-order perturbation theory to derive $A_{3.3}$ and $A_{3.4}$ from the infrared vibrational spectra of seven PAHs with various aliphatic substituents (e.g., methyl-, dimethyl-, ethyl-, propyl-, butyl-PAHs, and PAHs with unsaturated alkyl-chains). The mean band strengths of the aromatic ($A_{3.3}$) and aliphatic ($A_{3.4}$) C--H stretches are derived and then employed to estimate the aliphatic fraction of the UIE carriers by comparing $A_{3.4}$/$A_{3.3}$ with $I_{3.4}$/$I_{3.3}$. We conclude that the UIE emitters are predominantly aromatic, as revealed by the observationally-derived ratio ~ 0.12 and the computationally-derived ratio ~ 1.76 which suggest an upper limit of $N_{\rm C,aliph}/N_{\rm C,arom}$ ~ 0.02 for the aliphatic fraction of the UIE carriers.Comment: 67 pages, 18 figures, 8 tables; invited article accepted for publication in "New Astronomy Review"; a considerable fraction of this article is concerned with the computational techniques and results, readers who are mainly interested in astrophysics may wish to only read "Introduction", and "Astrophysical Implications

A Semi-parametric Technique for the Quantitative Analysis of Dynamic Contrast-enhanced MR Images Based on Bayesian P-splines

Dynamic Contrast-enhanced Magnetic Resonance Imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the non-linear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome this problems, this paper proposes a semi-parametric penalized spline smoothing approach, with which the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999

Correlated EEMD and effective feature extraction for both periodic and irregular faults diagnosis in rotating machinery

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. Intelligent fault diagnosis of complex machinery is crucial for industries to reduce the maintenance cost and to improve fault prediction performance. Acoustic signal is an ideal source for diagnosis because of its inherent characteristics in terms of being non-directional and insensitive to structural resonances. However, there are also two main drawbacks of acoustic signal, one of which is the low signal to noise ratio (SNR) caused by its high sensitivity and the other one is the low computational efficiency caused by the huge data size. These would decrease the performance of the fault diagnosis system. Therefore, it is significant to develop a proper feature extraction method to improve computational efficiency and performance in both periodic and irregular fault diagnosis. To enhance SNR of the acquired acoustic signal, the correlation coefficient (CC) method is employed to eliminate the redundant intrinsic mode functions (IMF), which comes from the decomposition procedure of pre-processing known as ensemble empirical mode decomposition (EEMD), because the higher the correlated coefficient of an IMF is, the more significant fault signatures it would contain, and the redundant IMF would compromise both the SNR and the computational cost performance. Singular value decomposition (SVD) and sample Entropy (SampEn) are subsequently used to extract the fault feature, by exploiting their sensitivities to irregular and periodic fault signals, respectively. In addition, the proposed feature extraction method using sparse Bayesian based pairwise coupled extreme learning machine (PC-SBELM) outperforms the existing pairwise-coupling probabilistic neural network (PC-PNN) and pairwise-coupling relevance vector machine (PC-RVM) by 1.8%and 2%, respectively, to achieve an accuracy of 93.9%. The experiments conducted on the periodic and irregular faults in the gears and bearings have demonstrated that the proposed hybrid fault diagnosis system is effective

Partition function of the eight-vertex model with domain wall boundary condition

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.Comment: Latex file, 20 pages; V2, references adde

A model for the force stretching double-stranded chain molecules

We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Sequence dependence and excluded volume interaction are taken into account explicitly. Two classes of conformations, hairpin and RNA secondary structure are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structure conformations, a new recursive formula incorporating the secondary structure and end-to-end distribution has been derived. Using the model, we investigate the extension-force curves, contact and population distributions and re-entering phenomena, respectively. we find that the force stretching homogeneous chains of hairpin and secondary structure conformations are very different: the unfolding of hairpins is two-state, while unfolding the latter is one-state. In addition, re-entering transitions only present in hairpin conformations, but are not observed in secondary structure conformations.Comment: 19 pages, 28 figure

Exploring the quantum critical behaviour in a driven Tavis-Cummings circuit

Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly-controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalise the critical spin-field coupling strength, we have observed a four-qubit non-equilibrium quantum phase transition in a dynamical manner, i.e., we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the non-equilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition related science, such as scaling behaviours, parity breaking and long-range quantum correlations.Comment: Main text with 3 figure