Reciprocal Length Research Articles

Enhancing subjective spaciousness for stereo reproduction in car-size acoustical enclosures based on audio signal decorrelation

Audio signal decorrelation has been used for enhancing the spaciousness of auditory source width (ASW) in a stereo reproduction. However, the acoustic environment in car-size acoustical enclosures is quite different from that in a home theater or listening room. Due to the small cabin size and the substantial presence of absorptive surfaces, the reproduced sound field in car-size acoustical enclosures is characterized by the interior mode region up to some hundreds or one thousand hertz and fast decay of pressure at higher frequencies which could affect the perceived performance of audio signal decorrelation. Therefore, the present work evaluates the effect of reflections in an acoustical enclosure model with car-size on the ASW enhanced by decorrelated audio signals, which reproduced by a standard stereo system. The decorrelation algorithm is handled by all-pass filters sets based on a pair of reciprocal maximal length sequence (MLS). Last, a subjective assessment experiment of ASW validates that appropriate decorrelation method can improve perceived spaciousness for sound reproduction in car-size acoustical enclosures.

The length contraction paradox

Reciprocal length contraction and time dilation, as enshrined in the Lorentz transformation, are the bulwark of the special relativity theory. Reciprocal time dilation is typically discussed (in the context of its apparent contradiction) and usually explained away as the result of differing synchronization in inertial reference frames and the relativity of simultaneity. Further, it is generally suggested that time is an abstract concept, and its perceptions may differ with context. However, we suggest that regarding length measurements no such abstraction can be envisaged. In this manuscript, we examine the reciprocal length contraction in detail to assess whether it leads to any contradiction.

Reciprocal restriction fragment length polymorphism (RFLP) analysis reveals mitochondrial heteroplasmy in Caenorhabditis briggsae hybrids.

Although mitochondria are typically inherited maternally, exceptions exist. We previously demonstrated that within-species crosses of Caenorhabditis briggsae result in paternal mitochondrial transmission, and it would be useful to know whether hybrids have only paternal mitochondria (homoplasmy) or paternal and maternal mitochondria (heteroplasmy). We developed a reciprocal restriction fragment length polymorphism analysis to separately detect paternal and maternal mitochondrial DNA. Using new hybrid lines, this approach revealed that some hybrids are heteroplasmous and others have become homoplasmous for the paternal mitotype. These results motivate additional investigation of how paternal mitochondrial transmission is apparently facile in C. briggsae .

Spatial Spreading of the Condensate of Magnetoexcitons in a Quantum Hall Insulator

The spatial spreading of a dense ensemble of spin cyclotron magnetoexcitons in a quantum Hall insulator at the filling factor ν = 2 is visualized using an optical system with a high aperture ratio. It is found that nondiffusive propagation over macroscopic distances is characteristic not only of excitons with a momentum on the order of the reciprocal magnetic length, which form a coherent condensate of magnetoexcitons, but also of excitons with very low momenta. The nondiffusive propagation of magnetoexciton condensates in real space is accompanied by a huge threshold increase in the amplitude of light reflection from excitations. The possible explanations of the observed behavior are discussed.

Topological Approach for Optimizing Railroad Freight Network Restoration after Disruptions

A topology-based method is proposed for optimizing the restoration sequence of damaged components in a disrupted rail freight network. Formulated as a demand-weighted average of reciprocal shortest path lengths, network efficiency is used as an indicator of overall connectivity for origin–destination (OD) pairs having freight demand. With the fixed demand matrix, a given network configuration, and a given disruption scenario, the cumulative loss of network efficiency during the restoration process is computed for each evaluated restoration sequence, using network efficiency values in intermediate network states as well as the duration of each restoration phase (i.e., restoration plus access time). This cumulative loss is treated as a measure of post-disruption network resilience, and is minimized with a simple genetic algorithm (GA) that finds the corresponding optimized restoration sequence, which also determines the optimized restoration schedule. The proposed method is demonstrated in a synthesized numerical case of a small network and a disruption scenario. The GA can find the globally optimal restoration sequence relatively fast, with its effectiveness further verified through exhaustive enumeration for three additional disruption scenarios. Sensitivity analysis results indicate that higher topological centrality and freight throughput of damaged nodes or disruption-induced isolation of some nodes are responsible for higher minimized loss of cumulative efficiency. The optimized restoration sequence tends to prioritize nodes and adjacent links with relatively high freight throughput in normal operation.

Thermalization of Triplet Magneto-Excitons and Spin Transport in a Hall Dielectric

It is found that the thermalization of triplet spin-flip magneto-excitons in a quantum Hall dielectric is an unprecedentedly long process for translation-invariant nonequilibrium electronic systems. It is shown that a magneto-fermionic condensate, a state characterized by the ability to rapidly transfer spin over macroscopic distances, is formed by spin-flip excitons with generalized momenta on the order of the reciprocal magnetic length.

Reconsidering Reciprocal Length Patterns of the Anteromedial and Posterolateral Bundles of the Anterior Cruciate Ligament During In Vivo Gait

Background: Some cadaveric studies have indicated that the anterior cruciate ligament (ACL) consists of anteromedial and posterolateral bundles that display reciprocal function with regard to knee flexion. However, several in vivo imaging studies have suggested that these bundles elongate in parallel with regard to flexion. Furthermore, the most appropriate description of the functional anatomy of the ACL is still debated, with the ACL being described as consisting of 2 or 3 bundles or as a continuum of fibers. Hypothesis: As long as their origination and termination locations are defined within the ACL attachment site footprints, ACL bundles elongate in parallel with knee extension during gait. Study Design: Descriptive laboratory study. Methods: High-speed biplanar radiographs of the right knee joint were obtained during gait in 6 healthy male participants (mean ± SD: body mass index, 25.5 ± 1.2 kg/m2; age, 29.2 ± 3.8 years) with no history of lower extremity injury or surgery. Three-dimensional models of the right femur, tibia, and ACL attachment sites were created from magnetic resonance images. The bone models were registered to the biplanar radiographs, thereby reproducing the in vivo positions of the knee joint. For each knee position, the distances between the centroids of the ACL attachment sites were used to represent ACL length. The lengths of 1000 virtual bundles were measured for each participant by randomly sampling locations on the attachment site surfaces and measuring the distances between each pair of locations. Spearman rho rank correlations were performed between the virtual bundle lengths and ACL length. Results: The virtual bundle lengths were highly correlated with the length of the ACL, defined as the distance between the centroids of the attachment sites (rho = 0.91 ± 0.1, across participants; P < 5 × 10-5). The lengths of the bundles that originated and terminated in the anterior and medial aspects of the ACL were positively correlated (rho = 0.81 ± 0.1; P < 5 × 10-5) with the lengths of the bundles that originated and terminated in the posterior and lateral aspects of the ACL. Conclusion: As long as their origination and termination points are specified within the footprint of the attachment sites, ACL bundles elongate in parallel as the knee is extended. Clinical Relevance: These data elucidate ACL functional anatomy and may help guide ACL reconstruction techniques.

Reliably Estimating the Length of the Effectively Conjugated Segment in Ladder Poly(para-phenylene)s

In 1995 we extrapolated the so-called “effective conjugation length” in (para-phenylene) ladder polymers by relating the optical absorption energy to the reciprocal chain length of ladder-type oligo-(para-phenylene)s, but only based on three short-chain oligomers (a trimer, a pentamer, and a heptamer). The resulting value of 11–12 benzene rings was distinctly lower than the numbers reported for corresponding single-stranded, soluble poly(para-phenylene)s. Here, we report a series of elongated (para-phenylene)-type ladder oligomers that were isolated via repeated recycling size exclusion chromatography steps from an oligomer mixture. Now we are able to extrapolate the length of the “effectively conjugated segment” with much more precision to be 19 ± 2 benzene rings.

A molecular dynamics simulation study of thermal conductivity anisotropy in β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX)

Molecular dynamics (MD) simulations were used to predict the thermal conductivity of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) along directions normal to the (011), (110), and (010) crystal planes. These directions were selected based on the measured morphological importance of the corresponding crystal surfaces. A reverse non-equilibrium MD approach was used wherein a constant heat flux is imposed along a prescribed direction and the resulting steady-state temperature gradient determined. The coefficient of thermal conductivity λ is the quotient of heat flux and temperature gradient (i.e. Fourier’s law). Finite-size effects and sensitivity to imposed heat flux were investigated. The results reveal a modest dependence of the conductivity on crystal orientation, significant finite-size effects, and low sensitivity to imposed flux so long as the Fourier’s law analysis is limited to the spatial interval in the simulation cell for which the temperature gradient is constant. Infinite-length thermal conductivities were estimated by linear regression of λ−1(L) versus reciprocal cell length L−1 for each direction. The predicted values are systematically larger, but within a factor of two, than most published experimental determinations, the latter of which were obtained for pressed-powder or composite samples rather than oriented single crystals.

Finite-size effect of the thermal conductivity in one dimensional chain

Finite-size effect of the thermal conductivity in one dimensional chain is theoretically investigated with a phenomenological model. Boundary temperature dropping and the spectrum-dependent linear temperature profile within the chain are given self-consistently at high temperatures. A general formula of thermal conductivity is presented and a good agreement with the molecular dynamics simulations is obtained. It is found that while decreases with increasing of 1/L monotonically, the well known linear dependence of thermal resistance 1/κ on the reciprocal length 1/L of systems is, however, valid only in two limit cases of and/or .

The interaction between Lateral size effect and grain size when scratching polycrystalline copper using a Berkovich indenter

It has been reported previously that, for single and polycrystalline copper (fcc), the indentation size effect and the grain size effect (GSE) can be combined in a single length-scale-dependent deformation mechanism linked to a characteristic length-scale calculable by a dislocation-slip-distance approach (X. D. Hou and N. M. Jennett, ‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). Recently, we identified a ‘lateral size effect (LSE)’ in scratch hardness measurements in single crystal copper, where the scratch hardness increases when the scratch size is reduced (A. Kareer, X. D. Hou, N. M. Jennett and S. V. Hainsworth ‘The existence of a lateral size effect and the relationship between indentation and scratch hardness’ Philos. Mag. published online 24 March 2016). This paper investigates the effect of grain size on the scratch hardness of polycrystalline copper with average grain sizes between 1.2 and 44.4 μm, when using a Berkovich indenter. Exactly the same samples are used as in the indentation investigation by Hou et al. (‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). It is shown that, not only does the scratch hardness increase with decreasing grain size, but that the GSE and LSE combine in reciprocal length (as found previously for indentation) rather than as a superposition of individual stresses. Applying the same (as indentation) dislocation-slip-distance-based size effect model to scratch hardness yielded a good fit to the experimental data, strongly indicating that it is the slip-distance-like combined length-scale that determines scratch hardness. A comparison of the fit parameters obtained by indentation and scratch on the same samples is made and some distinct differences are identified. The most striking difference is that scratch hardness is over four times more sensitive to grain size than is indentation hardness.

Nonlocal electrostatics in ionic liquids: The key to an understanding of the screening decay length and screened interactions.

Screened electrostatic interactions in ionic liquids are investigated by means of exact statistical mechanical analysis combined with physical arguments that enhance the transparency and conceptual accessibility of the analysis and results. The constituent ions and immersed particles in the liquid can have arbitrary shapes and any internal charge distributions. The decay of the screened electrostatic potential and the free energy of interaction in ionic liquids can be exponentially damped oscillatory (like in molten simple salts) as well as plain exponential and long-ranged (like in dilute electrolyte solutions). Both behaviors are in agreement with the exact statistical mechanical analysis and reasons for their appearances are investigated. Exact but surprisingly simple expressions for the decay parameter κ of the screened electrostatics are obtained, which replace the classical expression for the Debye-Hückel parameter κDH (the reciprocal Debye length). The expressions are applicable both for cases with plain exponential and oscillatory behaviors. The key importance of nonlocal electrostatics is thereby demonstrated explicitly. Dielectric properties of ionic liquids and other electrolytes are investigated, in particular the static dielectric function ϵ̃(k) and some effective relative permittivities (Ereff and Er∗), which take roles that the dielectric constant εr has for polar liquids consisting of electroneutral molecules. The dielectric constant in the latter case, which is the limit of ϵ̃(k) when the wave number k → 0, can be expressed solely in terms of dipolar features of the molecules. In contrast to this, the effective dielectric permittivities of ionic liquids have contributions also from quadrupolar, octupolar, and higher multipolar features of the constituent ions. The "dielectric constant" of electrolytes does not exist since ϵ̃(k)→∞ when k → 0, a well-known effect of perfect screening. The effective relative permittivities, Ereff, and Er∗ of ionic liquids are obtained from the non-diverging part of ϵ̃(k), but not as a k → 0 limit. Influences of ion associations, especially pairing, are investigated for screened electrostatics and these permittivities. A general, multipolar expansion of ϵ̃(k) is derived and used to analyze dielectric properties of ionic liquids and other electrolytes.

InAs Quantum Dot Lasers With Dry Etched Facet by Br-Ion Beam-Assisted Etching

The etching conditions of the AlGaAs materials in bromine ion beam-assisted etching (Br-IBAE) process have been determined. The etching rates can be varied from several nm/min to $\sim 300$ nm/min through controlling the bromine pressure and the substrate temperature. High-performance InAs quantum dot (QD) lasers have been grown by molecular beam epitaxy system. The broad area QD lasers are fabricated by standard photolithography and metallization processes, while the laser facets are formed by Br-IBAE dry etching process. With the dry-etched facets, the InAs QD lasers have a threshold current density $J_{\mathrm{ th}}$ , and slope efficiency, $\eta _{i}$ of 480 A/cm2 and 34%, respectively. The Br-IBAE dry etched facet reflectivity of 0.28 is obtained from fitting the $J_{\mathrm{ th}}$ versus reciprocal cavity length curves.

Ion strength limit of computed excess functions based on the linearized Poisson-Boltzmann equation.

The linearized Poisson-Boltzmann (L-PB) equation is examined for its κ-range of validity (κ, Debye reciprocal length). This is done for the Debye-Hückel (DH) theory, i.e., using a single ion size, and for the SiS treatment (D. Fraenkel, Mol. Phys. 2010, 108, 1435), which extends the DH theory to the case of ion-size dissimilarity (therefore dubbed DH-SiS). The linearization of the PB equation has been claimed responsible for the DH theory's failure to fit with experiment at > 0.1 m; but DH-SiS fits with data of the mean ionic activity coefficient, γ± (molal), against m, even at m > 1 (κ > 0.33 Å(-1) ). The SiS expressions combine the overall extra-electrostatic potential energy of the smaller ion, as central ion-Ψa>b (κ), with that of the larger ion, as central ion-Ψb>a (κ); a and b are, respectively, the counterion and co-ion distances of closest approach. Ψa>b and Ψb>a are derived from the L-PB equation, which appears to conflict with their being effective up to moderate electrolyte concentrations (≈1 m). However, the L-PB equation can be valid up to κ ≥ 1.3 Å(-1) if one abandons the 1/κ criterion for its effectiveness and, instead, use, as criterion, the mean-field electrostatic interaction potential of the central ion with its ion cloud, at a radial distance dividing the cloud charge into two equal parts. The DH theory's failure is, thus, not because of using the L-PB equation; the lethal approximation is assigning a single size to the positive and negative ions.

A Case Study of the Weather Research and Forecasting Model Applied to the Joint Urban 2003 Tracer Field Experiment. Part 1: Wind and Turbulence

Numerical-weather-prediction models are often used to supply the mean wind and turbulence fields for atmospheric transport and dispersion plume models as they provide dense horizontally- and vertically-resolved geographic coverage in comparison to typically sparse monitoring networks. Here, the Weather Research and Forecasting (WRF) model was run over the month-long period of the Joint Urban 2003 field campaign conducted in Oklahoma City and the simulated fields important to transport and dispersion models were compared to measurements from a number of sodars, tower-based sonic anemometers, and balloon soundings located in the greater metropolitan area. Time histories of computed wind speed, wind direction, turbulent kinetic energy (e), friction velocity ( $$u_*$$ ), and reciprocal Obukhov length (1 / L) were compared to measurements over the 1-month field campaign. Vertical profiles of wind speed, potential temperature ( $$\theta $$ ), and e were compared during short intensive operating periods. The WRF model was typically able to replicate the measured diurnal variation of the wind fields, but with an average absolute wind direction and speed difference of $$35^\circ $$ and $$1.9\hbox { m s}^{-1}$$ , respectively. Using the Mellor-Yamada-Janjic (MYJ) surface-layer scheme, the WRF model was found to generally underpredict surface-layer TKE but overpredict $$u_*$$ that was observed above a suburban region of Oklahoma City. The TKE-threshold method used by the WRF model’s MYJ surface-layer scheme to compute the boundary-layer height (h) consistently overestimated h derived from a $$\theta $$ gradient method whether using observed or modelled $$\theta $$ profiles.

Chain Length Dependence of the Photovoltaic Properties of Monodisperse Donor–Acceptor Oligomers as Model Compounds of Polydisperse Low Band Gap Polymers

Well‐defined conjugated oligomers (Sn) containing from 1 to 8 units of a tricyclic building block involving a dioctyloxybenzothiadiazole unit with two thienyl side rings (S1) are synthesized by a bottom‐up approach. UV–Vis absorption data of solutions show that chain extension produces a narrowing of the HOMO–LUMO gap (ΔE) to values slightly smaller than that of the parent polymer (P1). Plots of ΔE and of the band gap of films (E g) versus the reciprocal chain length show that ΔE and E g converge towards a limit corresponding to an effective conjugation length (ECL) of 7–8 S1 units. UV–Vis absorption and photoluminescence data of solutions and solid films show that chain extension enhances the propensity to inter‐chain aggregation. This conclusion is confirmed by GIXD analyses which reveal that the edge‐on orientation of short‐chain systems evolves toward a face‐on orientation as chain length increases while the π‐stacking distance decreases beyond 7 units. The results obtained on solution‐processed BHJ solar cells show a progressive improvement of power conversion efficiency (PCE) with chain extension; however, the convergence limit of PCE remains inferior to that obtained with the polymer. These results are discussed with regard to the role of mono/polydispersity and chain aggregation.

Wave motion analysis in arch structures via wavelet finite element method

Abstract The application of B-spline wavelet on interval (BSWI) finite element method for wave motion analysis in arch structures is presented in this paper. Instead of traditional polynomial interpolation, scaling functions at certain scales have been adopted to form the shape functions and construct wavelet-based elements. Different from other wavelet numerical methods adding wavelets directly, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The energy functional of the arch is obtained by the generalized shell theory, and the finite element model for wave motion analysis is constructed according to Hamilton's principle and the central difference method in time domain. Taking the practical application into account, damaged arch waveguides are also investigated. Proper analysis of the responses from structure damages allows one to indicate the location very precisely. This paper mainly focuses on the crack in structures. Based on Castigliano's theorem and the Pairs equation, the local flexibility of crack is formulated for BSWI element. Numerical experiments are performed to study the effect of wave propagations in arch waveguides, that is, frequency dispersion and mode spilt in the arch. The responses of the arch with cracks are simulated under the broad-band, narrow-band and chirp excitations. In order to estimate the spatial, time and frequency concentrations of responses, the reciprocal length, time-frequency transform and correlation coefficient are introduced in this investigation.

Nonlinear Magnetoelectric Response of Planar Ferromagnetic-Piezoelectric Structures to Sub-Millisecond Magnetic Pulses

The magnetoelectric response of bi- and symmetric trilayer composite structures to pulsed magnetic fields is experimentally investigated in detail. The structures comprise layers of commercially available piezoelectric (lead zirconate titanate) and magnetostrictive (permendur or nickel) materials. The magnetic-field pulses have the form of a half-wave sine function with duration of 450 μs and amplitudes ranging from 500 Oe to 38 kOe. The time dependence of the resulting voltage is presented and explained by theoretical estimations. Appearance of voltage oscillations with frequencies much larger than the reciprocal pulse length is observed for sufficiently large amplitudes (∼1–10 kOe) of the magnetic-field pulse. The origin of these oscillations is the excitation of bending and planar acoustic oscillations in the structures. Dependencies of the magnetoelectric voltage coefficient on the excitation frequency and the applied magnetic field are calculated by digital signal processing and compared with those obtained by the method of harmonic field modulation. The results are of interest for developing magnetoelectric sensors of pulsed magnetic fields as well as for rapid characterization of magnetoelectric composite structures.

Limits of metastability in amorphous ices: the neutron scattering Debye–Waller factor

Recently, it became clear that relaxation effects in amorphous ices play a very important role that has previously been overlooked. The thermodynamic history of amorphous samples strongly affects their transition behavior. In particular, well-relaxed samples show higher thermal stability, thereby providing a larger window to investigate their glass transitions. We here present neutron scattering experiments using fixed elastic window scans on relaxed forms of amorphous ice, namely expanded high density amorphous ice (eHDA), a variant of low density amorphous ice (LDA-II) and hyperquenched glassy water (HGW). These amorphous ices are expected to be true glassy counterparts of deeply supercooled liquid water, therefore fast precursor dynamics of structural relaxation are expected to appear below the calorimetric glass transition temperature. The Debye-Waller factor shows a very weak sub-T(g) anomaly in some of the samples, which might be the signature of such fast precursor dynamics. However, we cannot find this behavior consistently in all samples at all reciprocal length scales of momentum transfer.

Effect of Solvent Permittivity on the Thermodynamic Behavior of HCl Solutions: Analysis Using the Smaller-Ion Shell Model of Strong Electrolytes

The recently introduced smaller-ion shell (SiS) treatment of strong binary electrolyte solutions [Fraenkel, D. Mol. Phys. 2010, 108, 1435] that extends the Debye-Hückel theory to size-dissimilar ions is very effective for many electrolytes of various families up to moderate ionic concentration. The (molal) mean ionic activity coefficient, γ(±), as a function of the reciprocal screening length, κ, hence ionic strength, I, is given by an analytic mathematical expression that incorporates the three ion-size parameters (ISPs). Experimental γ(±) data are fitted with calculated values derived from ISPs that seem to adequately represent the relevant mean effective ionic sizes. The SiS analysis has been lately shown effective for aqueous HCl, HBr, HI, and HClO(4) at 25 °C, at which the solvent permittivity, ε, is 78.4 [Fraenkel, D. J. Phys. Chem. B 2011, 115, 557]. In this paper, the behavior of HCl in solvents ranging in ε between approximately 10 and 80 is analyzed and discussed. The SiS treatment is found again suitable for computing γ(±) values that agree with experiment. Within the concentration range of the available experimental data, ion pairing is not indicated and, contrary to literature claims, HCl appears fully ionized even at 0.5 m (molal) with ε < 10. ISPs do not seem to be affected by temperature, but co-ion ISPs increase linearly with 1/ε. The chemical nature of the solution has no observable effect on γ(±) and on ISPs. The present analysis supports the view that electrolyte theories in which the solvent is considered at the McMillan-Mayer level can be successful and valuable.