Nonzero Area Research Articles

Non-reciprocity in optical fiber links: experimental evidence.

Fundamental limits of fiber link are set by non-reciprocal effects that violate the hypothesis of equality between forward and backward path. Non-reciprocal noise arises technically from the set-up asymmetry, and fundamentally by the Sagnac effect when the fiber link encloses a non-zero area. As a pre-requisite for observation of Sagnac effect in fiber links, we present a study on phase noise and frequency stability contributions affecting coherent optical frequency transfer in bi-directional fiber links. Both technical and fundamental limitations of Two-Way optical frequency transfer are discussed. Our model predicts and our experiments substantially verify that the dominant noise mechanism at low Fourier frequencies is the polarization asymmetry induced by the temperature and relative humidity variations impacted on fiber links. The flicker noise floor due to the non-reciprocal noise arising from polarization mode dispersion is evidenced for the first time. We perform a post-processing approach which enables us to remove this polarization noise, improve the long-term stability and remove a frequency bias. We evaluate the uncertainty contributions of all the effects discussed for our 50 km spooled fiber link, dominated by its non-reciprocal noise induced by polarization mode dispersion with uncertainty of 1.9( ± 0.8)( ± 1.2) × 10-20. After correction, the linear drift of the residual phase is as low as 27 yoctosecond/s, leading to an uncertainty of the frequency transfer of 2.6 ( ± 39) × 10-22, confirming its potential for searching for more fundamental effects such as Sagnac effect or transient frequency variation due to dark matter.

Novel Shell Stock–Recruitment Models for Crassostrea virginica as a Function of Regional Shell Effective Surface Area, A Missing Link for Sustainable Management

Stock–recruitment relationships (SRR) are used by many resource managers as a metric to evaluate stock reproductive potential and rebuilding capacity when harvested. This relationship is more evident in traditional finfish stock assessment models where larvae are frequently limited by the abundance of spawning adults, whereas invertebrate resources are much more confounding and often do not express a clear spawning SRR. Oysters in particular appear to be limited more strongly by post-settlement mortality as larvae are regularly demonstrated to be present in high abundance in response to timely shell plants; yet unexpectedly, a brood SRR appears to be present. Because of the unique life history of oysters which provide their own habitat through reef accretion, a posit is that the quantity and quality of such habitat are crucial determinants of recruitment to the stock, and habitat quality acts as a surrogate for brood stock in the stock–recruit relationship. An extensive dataset from Delaware Bay with a 65-y time series was analyzed to assess the relationship between available Crassostrea virginica natural reef materials and subsequent spat (<20 mm) settlement. Live oyster, box (dead and articulated valves), and cultch (disarticulated whole valves and shell fragments) surface areas were calculated for oyster reefs found in each of four regions oriented up-bay to down-bay within the survey area. Surface areas were standardized using RMA regressions which compared available surface area per shell type (live, box, and cultch) and the number of spat recruiting to each shell type. Standardized shell surface areas (i.e., effective surface areas) supported previous accounts that recruitment occurs with higher frequency on live oysters and boxes than cultch, and that excessive cultch availability does not always lead to successively high recruitment. Recruit density was found to not only vary by substrate type but also along a salinity gradient. In high salinity reefs, boxes function as high-quality recruitment substrate and cultch as low-quality substrate, whereas in low-salinity regions cultch is only slightly inferior to live and outcompetes box surfaces as a dominant recruitment substrate. Beverton–Holt and Ricker models were used to express the relationship between total effective surface area and recruitment; these models revealed that medium- and high-salinity regions produced higher recruitment rates than low-salinity reefs. Model steepness also increased at higher salinity, indicating that down-bay reefs responded more rapidly to a change in effective surface area than did up-bay reefs. Steepness was highest at the confluence of the medium-salinity and high-salinity reaches where larval supply provided by the down-bay drift of larvae from up-bay reefs was high, but salinity remained low enough to reduce biofouling and predation compared with the high-salinity region. Unlike the low-salinity region, the relationship between effective surface area and recruitment for the three down-bay regions exhibited compensation; recruitment did not rise linearly with effective surface area. In all four regions, however, recruitment was initiated on a reef at a nonzero effective surface area, an analogy to an Allee effect which existed in each case. By inference, reefs can die before effective surface area disappears.

The research of thermoelastic deformation models with thin elliptic boundary contours plates and accounting uncertainty factors

Consider thin plates with external or internal boundary elliptical contours. It is necessary to take into account the scattering errors of the values of the initial physical, mechanical and geometric parameters based on the use of the heuristic principle of generalization. Known research methods for such systems based on the methodology of accounting for plate deformation under the influence of thermometric factors. Of particular interest is the assessment of the endogenous characteristics of the process using a hybrid technology for accounting for displaying the variability of inputs to these characteristics. Significant relationships of low-variant versions of the model are created for the base component, which is a homogeneous orthorhombic area of nonzero thickness and nonzero area in given coordinates. Axes passing through the middle of the element are defined. Half shafts define an elliptical contour. Stresses in the element are generated by the heat flux, which is symmetric and axial with respect to the coordinate system in the heat flux part.

Computational screening of metal-organic frameworks with open copper sites for hydrogen purification

With the increasing demand for environmental protection worldwide, metal-organic frameworks (MOFs) have been pivotal in the clean energy domain. Due to the high surface areas, large porosities and structural tunability, they are promising for the adsorption separation of H2/CH4 mixtures. High-throughput computational screening was adopted to identify the optimal adsorbents for hydrogen purification from 502 MOFs with open copper sites. Firstly, the adsorption performance of H2/CH4 mixture in 440 MOFs, which exhibit non-zero surface area and over -3.8 Å largest cavity diameter (LCD), was calculated using grand canonical Monte Carlo (GCMC) simulations at 300 K and various pressures. Secondly, we identified the top 9 high-performance MOFs by evaluating the ranking of candidate adsorbent performance according to a combination metric of adsorption performance score (APS, the product of adsorption capacity of CH4 and selectivity of CH4 over H2) and percent regenerability (R%). PCN-39 and MOF-505 exhibit high APS of 101 mol kg−1 and 67.9 mol kg−1, respectively, promising for hydrogen purification. Subsequently, the breakthrough curves of H2/CH4 mixture through the fixed bed packed with some optimal MOFs were predicted to evaluate their effects in practical hydrogen purification. UMODEH08 or UMOBEF04 exhibits the long dimensionless residence time over 30 of CH4 for the H2/CH4 separation. Finally, we also explored the behaviors of the radial distribution functions (RDF) and adsorption equilibrium configurations to further demonstrate how the selected MOFs differentiate CH4 from H2. The investigation on all these observations at molecular level will pave the way for the development of new materials for clean energy applications.

Optical Aharonov—Bohm Effect

A variant of the experiment to observe the optical Aharonov—Bohm effect has been discussed. In the experiment, a unipolar subcycle light pulse has been proposed as a source of the vector potential acting on electrons and having zero electric field strength in the region of a nonzero vector potential. Such a relation between the field and potential appears because the unipolar pulse has a nonzero electric area. An unusual situation where the fact of the passage of the pulse in one of the arms of two-beam interferometer is stored for a very long time after the passage and can be recorded in a two-beam electronic interferometer by a shift of fringes has been discussed. Detailed analysis of the phase shift under the influence of the vector potential created by the inhomogeneous unipolar pulse removes this contradiction and shows the equality of phase incursions in both arms that is unobvious at first glance.

Five-dimensional cohomological localization and squashed q-deformations of two-dimensional Yang-Mills theory

We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five dimensions using cohomological localization techniques and the Atiyah-Singer index theorem. We survey various known results in a unified framework and provide simplified derivations of localization formulas, as well as various extensions including the case of irregular Seifert fibrations. We describe the reductions to four-dimensional gauge theories, and give an extensive description of the dual two-dimensional Yang-Mills theory when the three-dimensional part of the geometry is a squashed three-sphere, including its extension to non-zero area, and a detailed analysis of the resulting matrix model. The squashing parameter b yields a further deformation of the usual q-deformation of two-dimensional Yang-Mills theory, which for rational values b2 = p/s yields a new correspondence with Chern-Simons theory on lens spaces L(p, s).

On stickiness of multiscale randomly rough surfaces

ABSTRACT A new stickiness criterion for solids having random fractal roughness is derived using Persson’s theory with DMT-type adhesion. As expected, we find that stickiness, i.e. the possibility to sustain macroscopic tensile pressures or else non-zero contact area without load, is not affected by the truncation of the PSD spectrum of roughness at short wavelengths and can persist up to roughness amplitude orders of magnitude larger than the range of attractive forces. With typical nanometre values of the latter, the criterion gives justification to the well-known empirical Dalhquist criterion for stickiness that demands adhesives to have elastic modulus lower than about 1 MPa.

Calculating the 'chain splay' of amphiphilic molecules: Towards quantifying the molecular shapes.

We report the first method to calculate a very important molecular level parameter of amphiphilic molecules- the 'chain splay'. The calculations employed a truncated cone geometry, as it is the most probable configuration adopted by various amphiphiles. This approach utilized known parameters including lipid length, cross-sectional area at the head group and molecular volume. This new parameter, i.e. the area at the chain end, perceived to be more sensitive than Israelachvili's famous shape factor or critical packing parameter (CPP). With relevant calculations, we demonstrate the fundamental roles of 'chain splay' to: a) reveal the critical contribution of molecular structure on average molecular shape and consequent self-assemblies, b) track the finest changes in molecular shapes within different bicontinuous cubic phases, c) obtain non-zero areas at the chain ends of amphiphiles that form normal (type 1) phases, d) back-calculate molecular volumes close to theoretical values, and e) find the link between molecular shapes and global curvatures of self-assemblies. This powerful feature advances our abilities towards quantitative estimation of spatial configurations adopted by amphiphilic molecules; moreover, it has a strong impact on predicting biomembrane structuring and nanoscale design of corresponding self-assemblies for a range of emerging applications.

Fast two-step layer-based method for computer generated hologram using sub-sparse 2D fast Fourier transform.

Fast two-step layer-based and sub-sparse two-dimensional Fast Fourier transform (SS-2DFFT) algorithms are proposed to speed up the calculation of computer-generated holograms. In a layer-based method, each layer image may contain large areas in which the pixel values are zero considering the occlusion effect among the different depth layers. By taking advantage of this feature, the two-step layer-based algorithm only calculates the non-zero image areas of each layer. In addition, the SS-2DFFT method implements two one-dimensional fast Fourier transforms (1DFFT) to compute a 2DFFT without calculating the rows or columns in which the image pixels are all zero. Since the size of the active calculation is reduced, the computational speed is considerably improved. Numerical simulations and optical experiments are performed to confirm these methods. The results show that the total computational time can be reduced by 5 times for a three-dimensional (3D) object of a train, 3.4 times for a 3D object of a castle and 10 times for a 3D object of a statue head when compared with a conventional layer-based method if combining the two proposed methods together.

Chromaticity Matrix to Tristimulus Matrix Conversion for RGB Color Spaces&amp;#x2013;Even In the Dark

Two methods to transform primary chromaticities and white point into primary tristimulus values are examined and compared. One method appears in numerous places in the literature; we refer to this as the "familiar" method, and provide a novel interpretation of it. The second is much less well-known and is referred to as the "unfamiliar" method. Necessary and sufficient conditions for computing primary tristimulus values from their chromaticities are identified; in brief, the triangle in the (x, y) chromaticity diagram must have non-zero area. The computational burdens for the methods were compared; the familiar method required slightly more arithmetical operations. Two problems with the familiar method were identified: high potential for rounding error and the inability to contend with a non-luminous primary. The unfamiliar method is less prone to rounding error, and is able to contend with primaries on the alychne. It is recommended that the unfamiliar method be preferred.

Optimal noise functions for location privacy on continuous regions

Users of location-based services (LBSs) are highly vulnerable to privacy risks since they need to disclose, at least partially, their locations to benefit from these services. One possibility to limit these risks is to obfuscate the location of a user by adding random noise drawn from a noise function. In this paper, we require the noise functions to satisfy a generic location privacy notion called $\ell$-privacy, which makes the position of the user in a given region $\mathcal{X}$ relatively indistinguishable from other points in $\mathcal{X}$. We also aim at minimizing the loss in the service utility due to such obfuscation. While existing optimization frameworks regard the region $\mathcal{X}$ restrictively as a finite set of points, we consider the more realistic case in which the region is rather continuous with a non-zero area. In this situation, we demonstrate that circular noise functions are enough to satisfy $\ell$-privacy on $\mathcal{X}$ and equivalently on the entire space without any penalty in the utility. Afterwards, we describe a large parametric space of noise functions that satisfy $\ell$-privacy on $\mathcal{X}$, and show that this space has always an optimal member, regardless of $\ell$ and $\mathcal{X}$. We also investigate the recent notion of $\epsilon$-geo-indistinguishability as an instance of $\ell$-privacy, and prove in this case that with respect to any increasing loss function, the planar Laplace noise function is optimal for any region having a nonzero area.

Kinematics of Origami Structures With Smooth Folds

Origami provides both inspiration and potential solutions to the fabrication, assembly, and functionality of various structures and devices. Kinematic modeling of origami-based objects is essential to their analysis and design. Models for rigid origami, in which all planar faces of the sheet are rigid and folds are limited to straight creases having only zeroth-order geometric continuity, are available in the literature. Many of these models include constraints on the fold angles to ensure that any initially closed strip of faces is not torn during folding. However, these previous models are not intended for structures with non-negligible fold thickness or with maximum curvature at the folds restricted by material or structural limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate idealizations of structural response, and a new approach is needed. In this work, a novel model analogous to those for rigid origami with creased folds is presented for sheets having realistic folds of nonzero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of smooth folds and constraints on their associated shape variables are presented. A numerical implementation of the model allowing for kinematic simulation of sheets having arbitrary fold patterns is also described. Simulation results are provided showing the capability of the model to capture realistic kinematic response of origami sheets with diverse fold patterns.

Modeling and analysis of origami structures with smooth folds

Origami has the potential to impact numerous areas of design and manufacturing. Modeling and analysis of origami structures allow for the understanding of their behavior and the development of computational tools for their design. Most available origami models are limited to the idealization of folds as creases of zeroth-order geometric continuity, which is not proper for origami structures having non-negligible fold thickness or with maximum curvature at the folds restricted by material limitations. Structural analysis of origami sheets having creased folds requires further idealizations of the fold mechanical response such as the representation of the folds as torsional springs. In view of this, a novel model analogous to that for rigid origami is presented in this work for origami structures having folds of non-zero surface area that exhibit higher-order geometric continuity (termed smooth folds). This origami model allows for a proper structural analysis of origami sheets using plate or shell representations for the folds. The shape formulation of the smooth folds and the kinematic constraints on their associated shape variables are presented. Modeling of origami structures with smooth folds exhibiting elastic behavior is performed by determining the configuration of the structure that minimizes its total potential energy subject to the derived kinematic constraints. The presented results show that the structural response determined using the proposed model is in good agreement with both experiments and higher-fidelity finite element analyses.

Geometric Design and Construction of Structurally Stabilized Accordion Shelters

Accordion patterns are widely used for deployable shelters, due to their simple construction, elegant deployment mechanism, and folded plate form with an inherent structural efficiency. This paper proposes two new accordion-type shelters that use modified geometries to improve on the structural stability and stiffness of the typical accordion form. The first shelter is termed a distributed frame accordion shelter and is generated by separating fully folded accordion frames between spacer plates aligned with the transverse direction. A transverse stiffness and increased flexural rigidity can therefore be achieved while maintaining a nonzero floor area. The second shelter is termed a diamond wall accordion shelter and is generated by inserting secondary wall elements that increase wall sectional depth and counteract the coupled rotational-transverse displacements at accordion roof–wall junctions. For both shelter types, a geometric parameterization and a full-scale prototype are presented. Good correlation is seen between the designed and constructed surfaces. A numerical investigation also shows that the new forms have substantially increased flexural rigidities compared to the typical accordion form.

Application of Multi-Attribute Crossplots to Tight Gas in X Area, Western China

The gas-bearing reservoir in X area is mainly the tight sandstone reservoir characterized by low porosity and permeability, frequently lateral variation and poor connectivity of single sand. The previous research results reveal that the general seismic attributes analysis cannot meet the requirement of fluid identification. This is because the relationship between seismic attributes and their implication is uncertain and ambiguous, which decreases the precision of both reservoir prediction and fluid identification. To overcome the problem, multi-attribute crossplot technology is proposed from the mathematical statistical point of view rather than the correspondence between the seismic attributes and their geological implication. In this method, the wells which have the same statistical law are classified firstly, and then all the interest wells are retained while the wells beyond the statistical law are eliminated, and the seismic attributes sensitive to the same types of eliminated wells are optimized and used to generate crossplots. The nonzero area of their crossplots results just predicts the potential distribution. The discontinuity of subsurface geological conditions results in the non-continuous shape and the seismic bin lead to the mosaic form. The optimization of sensitive attributes relative to the same types of wells is independent from each other, and thus the order of attributes in crossplots does not affect the final prediction results. This method is based on the statistical theory and suitable for the areas such as the study area abundant of lots of well data. Application to X area proves the effectiveness of this method and predicts plane distribution about different types of gas production. Due to the effect of faults and other geological factors, the partition prediction results using multi-attribute crossplots reach 95% of coincidence which is obviously and far higher than the results of the whole area. The final prediction results show that the potential areas with medium and high gas production are mainly concentrated in the northern part of the study area, where lots of development research will be strengthened.

Short note on the bending models for a membrane in capsule mechanics: Comparison between continuum and discrete models

With regard to the out-of-plane bending energy of an elastic surface membrane, capsule deformation was compared between Helfrich's isotropic continuum model and discrete models using a triangulated surface. The in-plane deformation of the membrane was modeled by the neo-Hookean or Skalak law. Two mechanical problems were numerically simulated. One was the deformation of a spherical capsule under simple shear flow and the other was the equilibrium shape of a capsule with a nonzero excess surface area, assuming the shape mechanics of a normal red blood cell. The numerical simulations demonstrated that a discrete model based on locally averaged mean curvature satisfactorily reproduces the mechanical behavior determined by Helfrich's isotropic continuum model, whereas a discrete model without the averaging exhibited different deformation behavior. Differences in the mechanical behavior between bending models may cause differences in estimated bending rigidity values of up to one order of magnitude.

More on black holes and quantum information

On reading Steve Giddings’s article, I felt the need to share some information about the original work of Karl Schwarzschild.11. K. Schwarzschild, Sitzungsber. K. Preuss. Akad. Wiss., Jan.–June 1916, 189, http://www.biodiversitylibrary.org/item/93032#page/31/mode/1up.His solution contained no coordinate singularity; it had only the singularity at the origin. That was neither a mistake nor an oversight on Schwarzschild’s part. By choosing a nontrivial scaling factor for the angular part of the metric, he had carefully avoided producing the coordinate singularity. As a side effect, such a choice results in a nonzero surface area for a sphere of zero radius. However, that result should not be a problem since one is not dealing with flat space anyway.REFERENCESSection:ChooseTop of pageREFERENCES <<1. K. Schwarzschild, Sitzungsber. K. Preuss. Akad. Wiss., Jan.–June 1916, 189, http://www.biodiversitylibrary.org/item/93032#page/31/mode/1up. Google Scholar© 2013 American Institute of Physics.

Adhesion of a Cylindrical Shell in the Presence of DLVO Surface Potential

A theoretical model is built for a micrometer size cylindrical shell adhering to a rigid surface in the presence of an electrolyte. In the presence of surface electrostatic double layers and van der Waals attraction according to the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, the shell deforms and settles in either the primary (1min) or secondary (2min) energy minimum depending on whether it has sufficient energy to overcome the repulsive energy barrier. The adhesion-detachment mechanics are constructed and solved computationally, yielding the relations between applied load, deformed profile, and mechanical stress distribution in the shell. The critical compressive load needed for transition from 2min to 1min is found for several repulsive barrier heights. At a critical pull-off tensile force, shell in the 1min detaches spontaneously at a nonzero contact area, but the one in the 2min detaches smoothly with the contact shrinking to a line contact. The model is relevant to bacterial adhesion in environmental engineering and microelectromechanical systems for microfluidics applications.

Automated drusen segmentation and quantification in SD-OCT images

Spectral domain optical coherence tomography (SD-OCT) is a useful tool for the visualization of drusen, a retinal abnormality seen in patients with age-related macular degeneration (AMD); however, objective assessment of drusen is thwarted by the lack of a method to robustly quantify these lesions on serial OCT images. Here, we describe an automatic drusen segmentation method for SD-OCT retinal images, which leverages a priori knowledge of normal retinal morphology and anatomical features. The highly reflective and locally connected pixels located below the retinal nerve fiber layer (RNFL) are used to generate a segmentation of the retinal pigment epithelium (RPE) layer. The observed and expected contours of the RPE layer are obtained by interpolating and fitting the shape of the segmented RPE layer, respectively. The areas located between the interpolated and fitted RPE shapes (which have nonzero area when drusen occurs) are marked as drusen. To enhance drusen quantification, we also developed a novel method of retinal projection to generate an en face retinal image based on the RPE extraction, which improves the quality of drusen visualization over the current approach to producing retinal projections from SD-OCT images based on a summed-voxel projection (SVP), and it provides a means of obtaining quantitative features of drusen in the en face projection. Visualization of the segmented drusen is refined through several post-processing steps, drusen detection to eliminate false positive detections on consecutive slices, drusen refinement on a projection view of drusen, and drusen smoothing. Experimental evaluation results demonstrate that our method is effective for drusen segmentation. In a preliminary analysis of the potential clinical utility of our methods, quantitative drusen measurements, such as area and volume, can be correlated with the drusen progression in non-exudative AMD, suggesting that our approach may produce useful quantitative imaging biomarkers to follow this disease and predict patient outcome.

4d partition function on S1 × S3 and 2d Yang–Mills with nonzero area

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.