Analytical Explanation Research Articles

The mysterious halos in iron gall ink manuscripts: an analytical explanation

Three historical manuscripts, two on parchment (dated 1280 and 1514) and one on paper support (dated 1589–1592), were under study. The three manuscripts were strongly attacked by microorganisms exhibiting dark brownish stains all over the surface except in the adjacent areas to some of the used inks, where a halo around the written text could be observed. In order to understand the origin of these halos, inks and manuscript supports were analyzed using portable energy-dispersive X-ray spectroscopy. Characteristic elements (Fe, Cu, Zn, and Mn) from iron gall inks were identified. Inks surrounded by a halo had in common a high amount of Zn in their composition. Microbiologic assays were performed aseptically on collected samples from the areas of the document with significant contamination and degradation. Samples were inoculated in a selective culture media, and the microorganisms developed were identified according to the macroscopic and microscopic features. For the evaluation of microflora proliferation, scanning electron microscopy was used. Furthermore, in vitro tests were carried out in the presence of zinc sulfate, revealing inhibition capacity for the majority of fungi sampled from these manuscripts.

Dependence of the cosmic microwave background lensing power spectrum on the matter density

The anisotropies in the cosmic microwave background (CMB) provide our best laboratory for testing models of the formation and evolution of large-scale structure. The rich features in the cosmic microwave background anisotropy spectrum, in combination with highly precise observations and theoretical predictions, also allow us to simultaneously constrain a number of cosmological parameters. As observations have progressed, measurements at smaller angular scales have provided increasing leverage. These smaller angular scales provide sensitive measures of the matter density through the effect of gravitational lensing. In this work we provide an analytic explanation of the manner in which the lensing of CMB anisotropies depends on the matter density, finding that the dominant effect comes from the shape of the matter power spectrum set by the decay of small-scale potentials between horizon crossing and matter-radiation equality.

Lateral migration of a viscoelastic drop in a Newtonian fluid in a shear flow near a wall.

Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonian fluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distance from the wall. The drop migration velocity and the deformation scale inversely with the square and the cube of the distance from the wall, respectively. The migration velocity varies non-monotonically with increasing viscoelasticity (increasing Deborah number); initially increasing and then decreasing. An analytical explanation has been given of the effects by computing the migration velocity as arising from an image stresslet field due to the drop. The semi-analytical expression matches well with the simulated migration velocity away from the wall. It contains a viscoelastic stresslet component apart from those arising from interfacial tension and viscosity ratio. The migration dynamics is a result of the competition between the viscous (interfacial tension and viscosity ratio) and the viscoelastic effects. The viscoelastic stresslet contribution towards the migration velocity steadily increases. But the interfacial stresslet-arising purely from the drop shape-first increases and then decreases with rising Deborah number causing the migration velocity to be non-monotonic. The geometric effect of the interfacial stresslet is caused by a corresponding nonmonotonic variation of the drop inclination. High viscosity ratio is briefly considered to show that the drop viscoelasticity could stabilize a drop against breakup, and the increase in migration velocity due to viscoelasticity is larger compared to the viscosity-matched case.

On the existence of vapor-liquid phase transition in dusty plasmas

The phenomenon of phase transition in a dusty-plasma system (DPS) has attracted some attention in the past. Earlier Farouki and Hamaguchi [J. Chem. Phys. 101, 9876 (1994)] have demonstrated the existence of a liquid to solid transition in DPS where the dust particles interact through a Yukawa potential. However, the question of the existence of a vapor-liquid (VL) transition in such a system remains unanswered and relatively unexplored so far. We have investigated this problem by performing extensive molecular dynamics simulations which show that the VL transition does not have a critical curve in the pressure versus volume diagram for a large range of the Yukawa screening parameter κ and the Coulomb coupling parameter Γ. Thus, the VL phase transition is found to be super-critical, meaning that this transition is continuous in the dusty plasma model given by Farouki and Hamaguchi. We provide an approximate analytic explanation of this finding by means of a simple model calculation.

Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks.

Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.

Relation between pairing gaps and transition probabilities in 132,136Te

Nuclear masses were measured very precisely in the region around 132Sn recently. One of the new insights obtained from the measurements is the sudden decrease in the neutron pairing gap as the neutron number N increases across 82. There was an indication of that decrease based on the experimental data of the anomalous first 2+ states of 132,136Te and the numerical results of the quasiparticle random-phase approximation (QRPA). We show a simple analytical explanation of the relation between the anomaly and the neutron pairing gap referring to the most recent experimental gaps and equations of the QRPA.

Identifying all moiety conservation laws in genome-scale metabolic networks.

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Analytic model for the description of above-threshold ionization by an intense short laser pulse

We present an analytic model for the description of above-threshold ionization (ATI) of an atom by an intense, linearly polarized short laser pulse. Our treatment is based upon a description of ATI by an infinitely long train of short laser pulses whereupon we take the limit that the time interval between pulses becomes infinite. In the quasiclassical approximation, we provide detailed quantum-mechanical derivations, within the time-dependent effective range (TDER) model, of the closed-form formulas for the differential probability $\mathcal{P}(\mathbf{p})$ of ATI by an intense, short laser pulse that were presented briefly by Frolov et al. [Phys. Rev. Lett. 108, 213002 (2012)] and that were used to describe key features of the high-energy part of ATI spectra for H and He atoms in an intense, few-cycle laser pulse, using a phenomenological generalization of the physically transparent TDER results to the case of real atoms. Moreover, we extend these results here to the case of an electron bound initially in a $p$ state; we also take into account multiple-return electron trajectories. The ATI amplitude in our approach is given by a coherent sum of partial amplitudes describing ionization by neighboring optical cycles near the peak of the intensity envelope of a short laser pulse. These results provide an analytical explanation of key features in short-pulse ATI spectra, such as the left-right asymmetry in the ionized electron angular distribution, the multiplateau structures, and both large-scale and fine-scale oscillation patterns resulting from quantum interferences of electron trajectories. Our results show that the shape of the ATI spectrum in the middle part of the ATI plateau is sensitive to the spatial symmetry of the initial bound state of the active electron. This sensitivity originates from the contributions of multiple-return electron trajectories. Our analytic results are shown to be in good agreement with results of numerical solutions of the time-dependent Schr\odinger equation for He and Ar atoms. Comparison of our results with those of quantitative rescattering theory is also discussed.

Zero‐ and π‐States in a Periodic Array of Deep Photonic Wires

A one‐dimensional periodic rectangular potential, also known as the Kronig‐Penney (KP) potential, transforms the parabolic dispersion of a free particle into a set of bands separated by bandgaps. However, if the potential wells are deep enough, the lowest bands converge into a set of single discrete states, numbered from j = 1 to j = jmax, which can be even or odd, describing the number of extrema. Here, discrete and continuous KP states are experimentally observed within a periodically modulated metal–organic microcavity. Depending on the width of the photonic wires, the thickness of the cavity, and the added metal grating, the parity of the highest localized state jmax can be either even or odd, leading to a complementary parity of the first continuous mode. The apex of this Bloch‐like state in turn either starts at k = 0, or a π‐state at the edges of the Brillouin zone, formed by the periodic metallic wires. An easy analytical explanation and numerical confirmation of zero‐ or π‐phase locking for laser modes in spatially modulated microcavities are provided.

Electrical circuit modeling and analysis of microwave acoustic interaction with biological tissues.

Numerical study of microwave imaging and microwave-induced thermoacoustic imaging utilizes finite difference time domain (FDTD) analysis for simulation of microwave and acoustic interaction with biological tissues, which is time consuming due to complex grid-segmentation and numerous calculations, not straightforward due to no analytical solution and physical explanation, and incompatible with hardware development requiring circuit simulator such as SPICE. In this paper, instead of conventional FDTD numerical simulation, an equivalent electrical circuit model is proposed to model the microwave acoustic interaction with biological tissues for fast simulation and quantitative analysis in both one and two dimensions (2D). The equivalent circuit of ideal point-like tissue for microwave-acoustic interaction is proposed including transmission line, voltage-controlled current source, envelop detector, and resistor-inductor-capacitor (RLC) network, to model the microwave scattering, thermal expansion, and acoustic generation. Based on which, two-port network of the point-like tissue is built and characterized using pseudo S-parameters and transducer gain. Two dimensional circuit network including acoustic scatterer and acoustic channel is also constructed to model the 2D spatial information and acoustic scattering effect in heterogeneous medium. Both FDTD simulation, circuit simulation, and experimental measurement are performed to compare the results in terms of time domain, frequency domain, and pseudo S-parameters characterization. 2D circuit network simulation is also performed under different scenarios including different sizes of tumors and the effect of acoustic scatterer. The proposed circuit model of microwave acoustic interaction with biological tissue could give good agreement with FDTD simulated and experimental measured results. The pseudo S-parameters and characteristic gain could globally evaluate the performance of tumor detection. The 2D circuit network enables the potential to combine the quasi-numerical simulation and circuit simulation in a uniform simulator for codesign and simulation of a microwave acoustic imaging system, bridging bioeffect study and hardware development seamlessly.

EIGENVALUE COLLISION FOR PT-SYMMETRIC WAVEGUIDE

We consider a model of a planar PT-symmetric waveguide and study the phenomenon of the eigenvalue collision under perturbation of the boundary conditions. This phenomenon was discovered numerically in previous works. The main result of this work is an analytic explanation of this phenomenon.

Pattern formation in three species food web model in spatiotemporal domain with Beddington–DeAngelis functional response

A mathematical model is proposed to study a three species food web model of preypredator system in spatiotemporal domain. In this model, we have included three state variables, namely, one prey and two first order predators population with Beddington-DeAngelis predation functional response. We have obtained the local stability conditions for interior equilibrium and the existence of Hopf-bifurcation with respect to the mutual interference of predator as bifurcation parameter for the temporal system. We mainly focus on spatiotemporal system and provided an analytical and numerical explanation for understanding the diffusion driven instability condition. The different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained. Furthermore, the higher-order stability analysis of the spatiotemporal domain is explored.

Complexity and indeterminism of evidence-based public health: an analytical framework

Improving the evidence in public health is an important goal for the health promotion community. With better evidence, health professionals can make better decisions to achieve effectiveness in their interventions. The relative failure of such evidence in public health is well-known, and it is due to several factors. Briefly, from an epistemological point of view, it is not easy to develop evidence-based public health because public health interventions are highly complex and indeterminate. This paper proposes an analytical explanation of the complexity and indeterminacy of public health interventions in terms of 12 points. Public health interventions are considered as a causal chain constituted by three elements (intervention, risk factor, and disease) and two levels of evaluation (risk factor and disease). Public health interventions thus differ from clinical interventions, which comprise two causal elements and one level of evaluation. From the two levels of evaluation, we suggest a classification of evidence into four typologies: evidence of both relations; evidence of the second (disease) but not of the first (risk factor) relation; evidence of the first but not of the second relation; and no evidence of either relation. In addition, a grading of indeterminacy of public health interventions is introduced. This theoretical point of view could be useful for public health professionals to better define and classify the public health interventions before acting.

A Practical Analysis of Performance Optimization in OSTBC Based Nonlinear MIMO-OFDM Systems

This paper presents a practical performance analysis of an orthogonal space-time block code (OSTBC) based multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the presence of nonlinear power amplifiers (PAs). The equivalent single-input single-output (SISO) scalar model is introduced and this then is used to construct a model for the nonlinear MIMO-OFDM system. Based on an unique inter-modulation product (IMP) analysis, it is shown how the receiver signal-to-noise ratio (SNR) may be derived to a polynomial based function of the system operating point. It is also shown that expressions for the asymptotical behavior of this SNR, when the linear and highly nonlinear PA operations are applied, may also be derived. Based on these derivations, it is further shown that the optimal system operating point, which corresponds to the maximum receiver SNR and SEP lower bound, can be identified and be derived to a polynomial based expression. Additionally, a general expression for the different integral expressions of SEP for the phase shift keying (PSK) and quadrature amplitude modulation (QAM) signals is found. By means of these analytical results, it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear MIMO-OFDM systems.

Analysis and experimental demonstration of novel 8PolSK-QPSK modulation at 5 bits/symbol for passive mitigation of nonlinear impairments

We propose a new modulation format providing 5 bits of information per recovered symbol while maintaining constant the total optical power. The proposed format applies a simple power constrain to the DP-8QAM format. This modulation format provides a passive way to mitigate nonlinear impairments due to Kerr effects occurring during propagation, and most specifically in the first 40 km. This report presents, to the authors' knowledge, a new transmission format using solely phase and polarization as modulation methods. The performance of this format, named 8PolSK-QPSK, is experimentally compared with that of the DP-8QAM format as both require equal transmitter complexity and implementation penalty, at the expense of a 20% increase in signaling baud rate. The greater nonlinear tolerance of this format is experimentally demonstrated. Moreover, thorough analysis of the Manakov-PDM propagation equation applied to both formats provides analytic explanation of the 8PolSK-QPSK's improved performance. The constant power property of the symbol set of the proposed format mitigates self- and cross-phase modulation (SPM, XPM) nonlinear effects and is experimentally validated over a long-haul transmission system in a WDM scenario. A total throughput of 7 × 129 Gbps is maintained for the transmission format comparison. Simulation of the same transmission system allows separate analysis of the strength of SPM, XPM and Cross-Polarization Modulation (XPolM) nonlinear effects and demonstrate reduced nonlinear impairments for the proposed format in the first span. We show an experimental reduction of the required OSNR for a BER threshold of 1.4 × 10(-2) of 0.5 dB for 8PolSK-QPSK compared to DP-8QAM in back-to-back. After 1920 km of SMF fiber, we demonstrate a required OSNR (ROSNR) diminution for increasing launch power, allowing a ROSNR relief of 0.95 dB at optimal launch power of -1 dBm for the proposed format. Using the same threshold, we show an increased reach by more than 34%, or 975 km, at optimal launch power. We also demonstrate that the relative reach increase for 8PolSK-QPSK compared to DP-8QAM monotonically increases with increasing BER threshold and that the BER growth with distance, after the first span, is equal for both formats.

“If I Could Make It, You Too Can Make It!” Personal Pronouns in Political Discourse: A CDA of President Jonathan’s Presidential Declaration Speech

This paper attempts to use Critical Discourse Analysis to unravel the complex webs of political associations and identities that go into political speeches of Nigerian presidents using one as a model. Nigeria has always been plagued by leadership problems and a lack of critical appreciation of crises of interests that abound in our political sphere. This article aims to offer a linguistic evaluation of a given political discourse in Nigeria in the mode of close engagement with the constructions and context of the discourse. It shows how personal pronouns are used by President Jonathan in his presidential declaration of interest speech to construct various identities and to transpose sentiments and sympathies in order to probably promote a political agenda. The use of Fairclough’s (1989) three-tier analytical framework, i.e., description, interpretation and explanation helps to reconstruct the import and real ideological thrust of the speech. The description level shows the linguistic associations, the interpretation level, the pragmatic and intertexual, while the explanation level shows how the socio-cultural practices in the Nigerian society are drawn upon to reflect in these two in a dialectical cycle. In essence, this study, in a systematic way, shows in general how ideologies in the status quo are (or can be) sustained and reproduced by discursively supplanting the consciousness of the people. The pronouns used in the speech end up creating identities that foster the president’s political interest and sustain the state of affairs while at the same time mystifying the real class and power struggle at the political center.

Predicting the bifurcation structure of localized snaking patterns

We expand upon a general framework for studying the bifurcation diagrams of localized spatially oscillatory structures. Building on work by Beck et al., the present work provides rigorous analytical results on the effects of perturbations to systems exhibiting snaking behavior. Starting with a reversible variational system possessing an additional Z2 symmetry, we elucidate the distinct effects of breaking symmetry and breaking variational structure, and characterize the resulting changes in both the bifurcation diagram and the solutions themselves. We show how to predict the branch reorganization and drift speeds induced by any particular given perturbative term, and illustrate our results via numerical continuation. We further demonstrate the utility of our methods in understanding the effects of particular perturbations breaking reversibility. Our approach yields an analytical explanation for previous numerical results on the effects of perturbations in the one-dimensional cubic–quintic Swift–Hohenberg model and allows us to make predictions on the effects of perturbations in more general settings, including planar systems. While our numerical results involve the Swift–Hohenberg model system, we emphasize the general applicability of the analytical results.

A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.

Demystifying Analytical Approaches for Urine Drug Testing to Evaluate Medication Adherence in Chronic Pain Management

ABSTRACTThis comprehensive review of analytical methods used for urine drug testing for the support of pain management describes the methods, their strengths and limitations, and types of analyses used in clinical laboratories today. Specific applications to analysis of opioid levels are addressed. Qualitative versus quantitative testing, immunoassays, chromatographic methods, and spectrometry are discussed. The importance of proper urine sample collection and processing is addressed. Analytical explanations for unexpected results are described. This article describes the scientific basis for urine drug testing providing information which will allow clinicians to differentiate between valid and questionable claims for urine drug testing to monitor medication adherence among chronic pain patients.

Theoretical investigation of the capture effect in intensity-modulation direct-detection microwave photonic links

We introduce the capture effect concept in microwave photonic links (MWPLs) for the first time to our knowledge. The capture effect or the small-signal suppression is the change in the amplitude ratio of the two signals between input and output of the intensity-modulation direct-detection (IMDD) MWPLs. An analytical explanation of the performance of external IMDD MWPLs due to the effects of nonlinearity combined with sum of several input sinusoidal signals is given. We have investigated the suppression of a weaker signal in these links. General analytic expression for the small-signal suppression is derived using a nonlinear analytical approach. We show that the small-signal suppression is quite dependent on the input back-off, the power ratio of input signals, and on the number of input sinusoidal signals. The theoretical maximum possible signal suppression was found to be 6 dB. This analytical asymptotic value is verified by numerical results. We show the influence of the capture effect of the nonlinear MWPL on the optoelectronic oscillator operation that is verified by experimental data in the literature that has already been published.